A theoretical study of the spectrophysics and photochemistryof formaldehydeCitation for published version (APA):Kemper, M. J. H. (1980). A theoretical study of the spectrophysics and photochemistry of formaldehyde.Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR153278

DOI:10.6100/IR153278

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A THEORETICAL STUDY OF THE SPECTROPHYSICS AND

PHOTOCHEMISTRY OF FORMALDEHYDE

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL EINDHOVEN, OP GEZAG VAN DE RECTOR MAGNIFICUS, PROF. IR. J. ERKELE~S, VOOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VAN DEKANEN IN HET OPENBAAR TE VERDEDIGEN OP

VRIJDAG 21 NOVEMBER 1980 TE 16.00 UUR

DOOR

MARTIN JOZEF HUBERT KEMPER

GEBOREN TE HEERLEN

DRUK WIBRO HELMOND

DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR

DE PROMOTOREN

PROF. DR. H.M. BUCK

EN

PROF. DR. R.P.H. RETTSCHNICK

CONTENTS

I. Introduction

II. Coupled potential surfaces and unimolecular photochemistry.

II.1. The calculation of coupling elements II.2. Ab-initia calculation on the photo-

chemistry of formaldehyde. The search for a hydroxycarbene intermediate. J. Amer. Chem. Soc. 1978,100,7841

II!. A theoretica! study on the reactivity and spectra of H2co and HCOH. A dimeric model for formaldehyde photochemistry.

IV.

v.

J. Amer. Chem. Soc. submitted

The calculation of radiative transitions.

IV.1. Ab-initio Cl calculation of single vibronic level fluorescence emission spectra and absolute radiative life­times of H2co (1A

2).

J. Chem. Phys. 1979,70,2854 IV.2. A comparitive study of theoretica!

methods for calculating forbidden transitions. Chem. Phys. submitted

Some future developments.

Summary Samenvatting Levensloop

Dankwoord

7

12

13

17

23

72

73

78

94

98 100

102 103

I. INTRODUCT ION

In principle, quantum mechanics can predict all physical and chemical phenomena, which occur after the excitation of a molecule to a higher electronic state (e.g. s0 + hv----111-81). What is needed for such a description is shown in Scheme I. Using an ab-initio or semi-empirica! computer program, the Schrödinger equation for the electrons in a fixed nuclear frame iS solved. This gives wave functions and eigenvalues (energies) for the ground and excited states. If one repeats the calcula­tion for a large set of geometries, potential energy surfaces are obtained. The minima and saddle points on a specific sur­face represent (meta)stable structures and reaction paths, respectively, on the surface; in other words, they describe the thermal chemistry. From the potential surfaces force con­stants can be calculated; these constants can be transformed into infra-red and Raman frequencies. The surfaces can also be used to calculate in a numerical way the anharmonic vibration functions. From the electron wave functions of ground and excited state, electronic transition moments and non-Born­Oppenheimer (BO) couplings are calculated. Together with the vibration functions this gives the total transition moment (a measure for the probability of a radiative transition), and the total coupling between the ground and excited state. With these total couplings one describes radiationless transitions (e.g. s 1 1"1.1V-t>-~). The total transition moments can be used for the calculation of the vibrational structure of UV-absorption and -emission spectra. Also, radiative lifetimes can be calcu­lated. Another important phenomenon in photochemistry is energy transfer according to the Förster/Dexter mechanism. The total transition moments are needed for this purpose also.

7

The practical elaboration of this seemingly simple Scheme is far from being trivial and straightforward. The prediction of stable molecular structures is the only subject in the Scheme, which can be done routinely; quantum mechanica! cal­culations being what they are however, even this is only true for not too extraordinary molecules. The calculation of coupling elements between potential energy surfaces has only recently become possible. A quantitative theory of radiationless tran­sitions was deve1oped by van Dijk et al 1 -q. In addition to this, UV-absorption spectra and i.r. frequencies were calcu­lated3. These studies 1 -~ concentrated on the formaldehyde

molecule because of several reasons. Formaldehyde gives, after exci tation to the s1 state, all the phenomena related to Scheme I: it has well-resolved absorption and fluorescence emission spectra; a radiationless transition depopulates the excited s1 state, and there are dissociation as well as addi­tion products. Moreover, from a theoretical point of view, this four-atom molecule is regarded as a suitable compromise between very computable, but photochemically "uninteresting;, two-atom molecules, and systems which have interesting reactions, but are much too large for reliable calculation.

This thesis consists of a number of published and submitted papers on the related aspects of Scheme I; again, forma,ldehyde is the model compound. Chapter II concerns the calculation of non-BO couplings for several unimolecular reaction coordinates, and mentions, for the first time, the possibility of dimeric interactions. Such a dimeric model for formaldehyde photo­chemistry is developed in Chapter III, together with the cal­culation of i.r. and Raman spectra. Chapter IV concerns the calculation of radiative transitions. All papers carry their own abstract, introduction, and conclusions, to which the reader is referred for more information. A survey of the main c9nclusions and some possible future developments are given in Chapter V.

8

Schrödinger equation for

electrons

electron wave functions eigenvalues

electronic non 00 trans. moment coupling

vibration potential

1

..... Ï"-- fllllctions surf aces

total trans. iroment

1

UV-absorption total couplings stable structures & emission energy "radiationless i.r. and reaction paths rad. lifetime transfer transitions" Raman "thermal chemistry"

IV v II III II, III, V

Sèheme I. Some aspects, needed for the description of ohotophysical and photochemical ~ behaviour. The Roman numerals indicate the Chapters which are related to these

aspects.

A large number of methods used in this thesis are nowadays standard ones. Notably ab-initio calculations 5 with the GAUSSIAN programs 6 ' 7 and ST0-3G 8 , 4-31G 9 , and 6-31G* 10 basis sets are well described and documented 11 in the literature. Concerning these methods the reader is referred to the cited literature. The calculation of coupling elements however, is much less widely known. Therefore, Section II.1 contains a brief description of such a calculation, in order to facili­tate the understanding of the work presented in Section II.2.

The papers in this thesis all carry more than one author's name; this is completely deserved, because these papers could not have been written in the present form without the work and knowledge of these colleagues. Of course, the full respon­sibility for the form and contents of these papers is carried by the author of this thesis.

10

REFERENCES

(1) van Dijk,J.M.F. Thesis, Eindhoven lhliversity of Technology 1977 (2) van Dijk,J.M.F.; Kemper,M.J.H.; Kerp,J.H.M.; Buck,H.M.; Visser,G.J.

Olem. Phys. Letters 1978,54,353 (3) van Dijk,J.M.F.; Kemper,M.J.H.; Kerp,J.H.M.; Buck,H.M.

J. Chem. Phys. 1978,69,2453 (4) van Dijk,J.M.F.; Kemper,M.J.H.; Kerp,J.H.M.; Buck,H.M.

J. Chem. Phys. 1978,69,2462 (5) Any standard text on quantlllll chemistry, e.g.:

McWeeny ,R.; Sutcliffe ,B.1. "Methods of M::>lecular Quantum Mechanics", Academie Press, wndon 1969

(6) Hehre,W.J. et al Q:PE 1973,11,236 (7) Pople,J.A. et al Q:PE 1978, 11,368 (8) Hehre,W.J.; Stewart,R.F.; Pople,J.A. J. Chem. Phys. 1969,51,2657 (9) Ditchfield,R.; Hehre,W.J.; Pople,J.A. J. Chem. Phys. 1971,54,724

(10) (a) Hariharan, P.C.; Lathan,W .A.; Pople,J .A. Chem. Phys. Letters 1972,14,385; (b) Hariharan,P.C.; Pople, J.A. Chem. Phys. Letters 1972, 16,217; (c) Hariharan, P.C.; Pople,J.A. Theor. Chim. Acta 1973,28,213

(11) Lathan,W.A.; Curtiss,L.A.; Hehre,W.J.; Lisle,J.B.; Pople,J.A. Progr. Phys. Org. Chem. 1974, 11, 175

t1

12

II. COUPLED POTENTIAL SURFACES AND

UNIMOLECULAR PHOTOCHEMISTRY

II.1 THE CALCULATION OF COUPLING ELEMENTS.

The Born-Oppenheimer approximation, which leads to separate

wave functions for electrons and nuclei, has been extremely

successful in molecular spectroscopy. Unfortunately, this

success has given rise to the uneradicable misunderstanding

that these electron and vibrational functions, and also the

potential energy surf aces which are produced by standard

quantum chemica! methods, really exist in nature 1• Actually

however, Born-Oppenheimer functions are merely the mathematica!

results of the human incapability to solve in a direct way the

complete Schrödinger equation for a molecule. (The same can be said for atomie orbi tals, molecular orbi tals, .etc.). This misunderstanding resulted in the fact, that it was not before

1968 that Jortner and co-wo.rkers 2 - 5 showed that precisely these

non-BO couplings "cause" radiationless transitions. We will now briefly describe this theory, together with van Dijk's 6

calculational method.

The interaction between a molecule and an electromagnetic

field prepares the molecule into an excited state I~>. Due to

the linewidth of the exciting light, this excited state is a

linear combination of exact eigenfunctions: I~> ~ cm l~m>.

These exact eigenfunctions can be expanded in a complete set

of zero-order states {lun>}

The set {lun>} can be defined in many ways 6 ' 7 • In the

adiabatic Born-Oppenheimer (ABO) formalism , which we will

use throughout this section, the functions lun> are eigen­

functions of

Ho H - TN

( 1)

13

H is the total Hamiltonian which describes electrons and nuclei; TN is the kinetic energy operator for the nuclei. Returning to equation (1), iu0> carries oscillator strength

to the ground state; in the formaldehyde case it is interpre­ted as the vibronic level in 1A2 (S 1) of which the decay is

described. The states lun> (n~O) are the vibronic levels, s0x. of the ground state. The fact that a linear combination of exact eigenfunctions is prepared gives rise to a time-dependent (sharply decreasing) oscillator strength. This is because of

the interfering phase factors: exp (-iEmt), where Em is the ei~envalue of the exact eigenfunction ~m· Mathematically, the decay of I~> is described by the time-evolution:

To quantify this theory, the coefficients am have to be

calculated. They are obtained by diagonalizing the inter­

action matrix of zero-order st~tes 2 • In other words, we have

to calculate the coupling elements vn = <u0 1TN1un>. Because of the ABO formalism we have 8 :

q, and x are electron and vibrational wave functions 1 , respec­tive ly; q, depends explicitely on the set of electron coordinates q and parametrically on the set of nuclear coordinates Q. The subscripts n and m merely identify the functions. Using TN P2/2M, where M is the complete set of nuclear masses, we obtain for the coupling of a single vibronic level (4' 1x1i) in

s 1 with a high vibrational level (4'oXoj) in s0 :

where we neglected 6 the term with P2 • The subscripts q and Q

14

denote the integration variable. If P is expressed in mass­weighted normal coordinates, we get:

!: k

<~11 au/aQk l~o> --~~~~~~~q a/aQk

EO E1

The summation is over the normal coordinates. U represents all potential energy terms: electron-electron repulsion, nuclear­nuclear repulsion, and electron-nuclear attraction. The first

term contributes nothing because it does not depend on Qk; the second term gives zero because of the orthogonality of ~O and ~ 1 . This leaves

(3)

The summations e and n are over all electrons and nuclei,

respectively. Zn is the nuclear charge; ren is the electron­nucleus distance:

j 1 x, y, z.

n e sj' and qj' are the cartesian coordinates of nucleus n and electron e, respectively. Because we differentiate in equation (3) to normal coordinates, we have to use the trans­formation

where the D's are elements of the transformation Jacobian between normal and cartesian coordinates. Now, equation (3) is easily 6 transformed into:

15

Here, we have something that is computable: ~ (qj, - sj 1 )/r;n is the j'-th component of the electric field operator for nucleus n. These integrals can be calculated routinely by several quantum chemical programs. c10 (Q) is now a linear combination of these integrals. Finally, the c10 function is integrated between the appropriate vibration functions (eq (2)).

REFERENCES AND NOfES

(1) This misunderstanding is so widespread, that even at many places in this thesis such an incorrect impression is created.

(2) Bixon,M.; Jortner,J. J. Chem. Phys. 1968,48,715 (3) Jortner ,J.; Berry ,R. S. J. Chem. Phys. 1968 ,48,2757 (4) Bixon,M.; Jortner,J. J. Chem. Phys. 1969,50,3284 (5) Bi:xon,M.; Jortner,J. J. Chem. Phys. 1969,50,4061 (6) van Dijk,J.M.F. Thesis, Eindhoven University of Technology 1977 (7) van Dijk,J.M.F.; Kemper,M.J.H.; Buck,H.M. Chem. Phys. Letters

1976,44'190 (8) Born,M.; Huang,K. "Dynamical Theory of Crystal Lattices", Clarendon

Press, Oxford 1954, Appendix VIII;

t6

II. 2

Kemper, VOJI Dijk, Buck / Photoehemistry of Formaldehyde 7841

Ab Initio Calculation oh the Photochemistry of Formaldehyde. The Search for a Hydroxycarbene Intermediate

M. J. H. K-per, * J. M. F. vu Dijll.l and H.M. Back

Contributi()ll /rom the Departmelll of Organic Chemistry, Eindhoven Unlversity of Ted1nalogy. Eindhoven. The Netherlands. Received April 28, 1978 •

Alonnct: Ab initio ca!culations on the H,CO-HCOH rearrangement have been performed. The electronic ooupling hetween the 8 1 and So surfacos, which can induce intesnal conversion. is calculated for this rearrangement and for the reaction coordi· nates leading direclly to radical and molecvlar products. The coupling is caleulated with true adiabatic Born-Oppenheimer functioml, i.e .• the wave functions and coupling integrals are explicilly calculated as functions of the nuclear geometry. The coupling for the hydro<ycarbene rearrangement tums out to be the largest one. This indicalés that the hydro<ycarhene can serve as an intermediate state in the formaldehyde photochemistry. We also report calculations on the bimolecular H,CO· HCOH reaf!•angemenl; lhis interaction givcs rise toa decrease of the energy harrier involved.

............... During the last decade there has been a growing interest

in the pbotochemiatry of the formaldehyde molecule. The ex· perimental wor1c2-s clearly shows the increasing power of the techniques available today. One of the most striking experi· men tal results was obtained by Houst on and Moore. 5 They found, under C<lllisionless ronditions, a time lag of at least 4 /IS between the decay of the fonnaldehyde S1 state and the appearance of the CO photoproduct. They rould not even ex· clude that, under collisionless ronditions, no photodissociation occurs at all. In view of this point it is interesting to no te that Y eimg and Moore4 found that the total ra te at which rollisions remove moleeules from single vibronic levels of H2CO is as much as ten timea the hard sphere rollision rate, thus indi<:ating sornc long-range interaction between the excited molecule and its nc:ighbors. The ronclusion from their work is that some intermediate is involved in the photodissociation of forma!· dehyde, out of which the molecular and radical products are formed:

h• H~O (So).....,. H2CO (S1l - X - products

of the obtained values for the HCOH sta tea, but very recently a large-scale Cl calculation by Lucchese and Schaefer12

showed that the results of Popte and Altmann are qualitatively correct and that the hydroxycarbene possibility is quite fea· sible. We also performed, as a continliation of oor study of the decay of the H2CO (S1) state, ab initio SCF and SCF-CI calculations on the formaldehyde-hydroxycarbene rear­rangement. The emphasis in this study, however. does not lie on calculating reliable values for the varioos HCOH states. Just as important as the knowledge of the energiea of the local minima on the potential energy surface is the answer to the queation how the molecule can reach these local minima. The m<JSt attractive candidate for the intermediate X is the HCOH (So-lrans) state, which lies. according to oor results, about 20 kcal/mol below H~O (81). To reach this state, the H~O (S1) molecule has to leave somewhere the S1 potential energy surface. Although the roupling in the equilibrium state is too small to induce internal ronversion, as stated above, this sit· uation can, in principle, change further away on the reaction coordinate. So in section Il we calculate the electronic roupling elements between the S1 and So surfaces as functions of three reaction coordinates: leading to hydroxycarbene, direct radical dissociation. and direct molecul!tr dissociation, respectively. As we will sec in section II, the energy barrier between the So* state and the HCOH local minimum wilt be too high for a single molecule to reach this minimum. Thai is why we de­scribe in section 111 calculations of an interaction between a pair of formaldehyde molecules in order to investigate the possibility oflowering thisenergy harrier. The way the mole­cules interact in the model described in section 111 is inspired by the H2CO-HCOH reaction pathway; in sectfon IV we wil! briefly discuss other kinds of interactions.

One: of the main tasks of formaldehyde photochemistry is now to unravel the nature of this intennediate state X. For this state several possibilities exist: in tbc first place. intemal ron-mo.i to an isoenergctic vibrational state, So*, of the electronic ground state. This So• state should then, onder collisionless ronditions, have a lifetime of at least 4 ,.s, after which disso­ciation to the pbotoproducts takes place. Recently we showed, however, by mcans of an allCIU"ate ab initiocalculation,0--• that the roupling in the equilibrium state is too small to induce in· temal conversion. The second candidate is intersystem crossing to T1•. Apart from theexperimental findingsofTang etal.,9

which sbowed that the triplet state plays a negligible mecha· nislic ro1e in the pbotochcmistry of the 224' (Si) level, it is not ll. 'I1le Unimolecular Reammgemat HiCQ-HCOH clear at all, from a theoretica! point of view, bow the T 1 state, A. Calculatioul Method. The calculational method is de· which lies only 3000 cm-1 below Si. can give a level density scribed in detail elsewhere;7 we will here only repeat the main for this fout-atomie molecule that is high enough to give an features. For the calculation of the electronic wave functions exponential decay. There exists. however, a third possibility of formaldehyde at the different points of the reaction roor-for the intermediate state: the hydroxycarbene HCOH. The dinates we used Clementi's IBMOL s program Il with a ron-fll'SI question that arises conceming this candidate involves the tracted Gaussian basis set given by Dunning: 14 for carbon and energies of the different HCOH ronfigurations (So·trans, oxygen a (9s5p) [4s3p) set; for hydrogen a (4s) [2s) set. Fur-So-<;is, and T1·gauche) relative to the prepared H~O (S1) ther, we used Goscinski's transition operator method15 in order state. Calculations by Pople's group10 and Altmann et al.1 1 to describe the So and S1 surfaces with the same accuracy. For plai:e !hem below the H:tCQ (Si) state. These calculations were the ronfiguration interaction we included 175 configu.rations performed without ronfigu.ration interaction, leading among selected by the point system of Morokuma and Konishi. •6 The othen to a H~O So-T 1 energy gap much lower than the ex· electronic wave functions obtained are true adiabatic Bom-perimental one. This result questions of rourse the reliability Oppenbeimer functions: they are explicitly calculated as

[Reprlnted from the Joumal of the American Chomical&ciety, 100. 7841 {1978).j Copyright @il 1978 by the American Chomical Society and reprinted by pennission of the copyright owner 17

7842 Journal of the American Chemica/ Society/ 100:25 / December6, 1978

Ol bJ C)

fipre I. Reaction coordinates(<I>. M,and R) leadingto(a) bydroxycar­bene formation: (b) direct molecular dissociation; and (c) direct radical dissociation. In (b) the variable M denotes the distance from"the carbon to the midpoint of tbc H-H bond.

functions of tbe nuclear geometry, contrary to the conventional "Herzberg-Teller" -like approach, where one tries to include the dependence on the nuclear geometry by means of an ex­pansion around the equilibrium geomelry, i.e" an expansion in crude Born-Oppenhcimer functions. The geometries which were used as an input in the SCF-CI calculations were ob­tained from a comf.!etely optimized, single-configuration 4-31 G calculation.' These optimizations were made for dif· ferent values of the three reaction coordinates depicted in Figure 1: (a) leading to the hydroxycarbene, (b) leading di­rectly to molecular products, and (c) leading directly to radical products. With the SCF-CI program we calculated both the So and S1 surfaces. With the single determinant Gaussian 70 program, however, no reliable S1 calculations can be made for formaldehyde: the Si wave functions and geometries become unreliable because of spin contamînation from funetions of different multiplicity. Therefore we used for the S1 geometries the optimized T1 structures obtained from the Gaussian 70 program. The results of this procedure wil! be discussed in section II B.

18

The probability for the radiationless transition frorn S1 to . So is determined by the coupling between the S1 and So po­tential energy surfaces. This eoupling is caused by the impulse operator P of the nuclei. The electronic coupling.element is given by

C1o(Q) = {4>1(q.Q)IP/Ml<fio(q,Q))•P

Here, q and Q denote the complete sets of electron and nuc!ear coordinates, respectively; <t>1 and <fio are the electronic wave functions of excited and ground state; M denotes the set of nuc!ear masses, while the subscript q denotes integration over the electron coordinates. This integral can be rewritten7 as a linear combination of integrals of the electric field operator:

C1o(Q)

~7 D'}kZ. (4>1(q.Q)I~ -(q}- sj·)/r •• 'l<fio(q.Q))0

<l>o(Q)- 4'1(Q) p

(11.I)

Here, sj· and q} are the j'th Cartesian coordinate of nucleus n and eJectron e, respectively; z. stands for the charge of nu­cleus n; D'f. is an element of the Jacobian matrix, which transforms the Cartesian coordinates to the normal coordinates k, while <l>o(Q) and 4>1(Q) represent the adiabatic potential energy surfaces. At this point the methods used here and the one used for the calculation of the "statie" S1-S0 internal conversion 7 start to diverge. In the latter calculation the stan­ing point was a formaldehyde molecule "resting" in some vi­hrational state, x 11(Q), of the local minimum corresponding to H2CO (S1). In order to obtain the total coupling, u 11,o1• bet ween the prepared state and an element of the coupling So• manifold, the electronic coupling element C1o(Q) bas to be integrated over Q:

v11.01 = (x,,(Q)IC1o(Q)lxo;(Q))e (11.2)

whcre x 11(Q) and X!\l(Q) denote the (anharmonic) Yibrational wave functions involved. for the statie situatÏQll, these vibra­tional wave functions, corresponding to the normal Yibrations, can be calculated from the potential energy surfaces +o(Q) and \ll1(Q). forthedynamksituation,however, where the molecule does not just fluctuate around the equilibrium configuration, but instead wanders about on the potential energy surf ace. the vibrational part Of the coupling cannot be easily calculated. Therefore we only calculated at each point of the reaction coordinates the 12 integrals of the electric field operator:

Ej'n(Q) = (</>1(q,Q)lr'. (qi - sj-)/r.,.311/>o(q,Q))q . (11.3)

As a measure of the electronic eoupling wc can choose for in· stance the length of the vector E, defined by

E2(Q) = Ê È ZnlEJ'•(Q)I' {11.4) n=1r--1

We will return to this choice in the discussion in section llC.

Apart from an increasing E vector, the probability for the radiationless transition can also be enhanced becausc of the decreasingdistance, l\llo(Q) - 411(Q)I, between the potential energy surfaces. The total coupling due to electronic factors is then given by

vE(Q) = E(Q)/ll4>o(Q)- 4>1(Q)li (11.5)

B. Resulls. In Tables 1 and II we show the geometries and energies of the various formaldehyde states, For the sake of clarity we notc once more that we optimized the geometries with a single configuration 4-31 G program (method 1) and that

· these gcometries were used as input in the large basis set + Cl calculation (method Il). No further geometry search was at­tempted in the Cl study performed here, in contradistinction to what we did in a previoos paper7 for the H2CO (So) and H:iCQ (S1) states. The results from.ref 7 are also shown in Table 1 for comparison. The table soows that the H,CO (T1)

geometry from nn:thod I agrees reasonably well with the Cl optimization for H;iCO (S 1) from ref 7 and with the experi­mental data for H:iCQ (S1). The same hokls for the H;iCO (So) geometries. This indicates that the procedure for choosing the geometry input for method Il works satisfactorily, at least in the starting points for the potential energy surf ace scan. Fur­tber we sec from Table 1 that the unimolecular rearrangement occurs in one plane for the So case, leading to the hydroxy· carbene trans configuration. For the rearrangcment in the T1 state we find an increasing out of plane angle 8, leading to the HCOH (T 1 )·ga uche configuration. Table II shows the energies of the various states, relative to the H;iCO (So) values obtained by the same method. Concerning the value for H2CO (S1) we have to distinguish between the 71.9 kcal/mol for the opti­mized Si structure (bent) and the value of9L7 kcal/mol for the S1 geometry which is reached by a vertical (franck­Condon) transition from theSoequilibriumgeometry. Using a complete optimization in the Cl calculation, van Dijk8 found for these energies 74.2 and 91.7 kcal/mol, respectively. This similarity gives another positîve affirmation for the procedure used. The potential energy surfaces for the H2CO-HCOH rearrangement, obtained by method 11, are given in figure 2. In this figure the full lines represent the optimized So and Si surfaces, while the dotted lines, S0b and S 1P, represent the So surface with bent and the S 1 surface with planar geometry, respectively. The energy harrier for the unimolecular rear­rangement on the S0 surface is !02 kcal/mol. We sec from Table Il that the extension of method I to method Il dccreases this barrieronly by 8 kcal/mol. We do not expect thal a further geometry optimization in the Cl calculation wil! have a sub-

Kemper, van Dijk. Buck / Photochemistry of FQl'mofdehyde 7843

Table I. Optimized Bond Lengths (À) and Angles (deg) for H,CO, HCOH, and the Transition States (TS) for the Unimolecular Rearrangement

HCOH (So)·trans H,CO(So) method t• ref7• exp' H,CO (So)·TS method 1 method 1

co 1.204 1.23 1.2()8 co l.305 l.3211 CH =CH' l.081 l.10 l.116 CH' 1.087 1.098 LHCH' 116.2 116 ll6.5 CH l.266 1.936 fld 0 0 0 <!>'(• LHCO) 55 26.5

LH'CO 116.5 103.5 8 0 0

HCOH (T1)-gauche H2CO(T1) method 1 e•p H2CO (T1)·TS method 1 method 1

co l.367 , 1.307 co l.354 1.354 CH •CH' l.070 l.096 CH' l.072 1.072 LHCH' 121.0 118 CH l.448 l.782 e 32.3 37.9 l/>(=LHCO) 50 34.3

LH'CO 126.7 126.0 e 52.l 67.8

H,CO(S1) ref7 exp

co 1.36 1.325 CH =CH' l.06 1.095 LHCH' 112.S ll8

• Method 1: single configuration 4-3 IG. • Ascalculated in ref 7 with the (9s5p) [4s3p] basisset +Cl with geometry optimization. •· faper­imental data taken from ref 18. '8 deootes the out of plane angle. • <f> denotes the reaction coordinate for H2CO-HCOH. See Figure 1.

T.W. ll. Encrgies (kcal/mol) for the Various formaldehyde States. Relalive to the H2CO (Sol Value Obtained by the Same Method

method 1• metbod n• othcr work

HiCO(So) 0 (• -113.692 61)• O(• -113.86207) 0 ( • -113.863 54)1 H,CO{S,,)·TS' ll0.2 102.0 HCOH (S.,)-trans 51.2 52.5 51.712

H2CO(T1) 35.5 68.912

11,co (T1l-TS 100.9 HCOH !T1)-gauche 58.7 73.0"

71.9 (91.7)' 74.28 (91.7)• 153.4 123.7

• Method 1: singleconfiguration 4-JIG. • Method 11;(9s5p) (4s3p) +Cl, with the geometries from method 1.' TS ~ transition state. d The absolute energies are given in atomie units. ~The value in parentheses is the vertical ( f'ranck-Condon) energy difference. See tut.

stantial effect. Tb is can be seen, for instance, f rom the absolute energies for H2CO ($o) given in Table Il (second and third column): they are the same within 1 kcal/mol. The harrier on the S 1 surf ace is a little lower: 81.5 kcal/mol.

The calculated electronic couplings, uE(Q) (see eq 11.5), for this rearrangement are given in Figure 3. The most important resull for the unimolecular rearrangemcnt is given in Figure 4. Here we compare the electronic roupling, vE( Q), for the first part of the three reactioo coordinates, starting from the S1 equilibrium geometry. The calc;ulation for the two direct dis­sociations was done in the sa me way as for the H 2CO--HCOH rearrangement: calculate for sevcral values of the reaction coordinates Mand R (see Figure 1) the optimized triplet ge­ometry and use this geometry in the S 1 calculation with the large basis set +Cl program.

The direct dissociation paths have already been calculated on a Cl level by Hayes, Jaffe, and Morokuma.19-2t Our 4-31G results for the radical dissociation are the same as theirs: for the dissociation on the T 1 potential energy surf ace the out of plane angle increases remarkably; the leaving H atom is swung away from the rest of the molecule. For the direct molecular dissociation on the T 1 potential energy surface we also found an increasing out of plane angle (the angle between the CO

bond and the HCH plane in the coordinate system we used in this case), while the two H atoms depart in a slightly asym­metrie way from the carbon alom. This asymmetry is mnch less dramatic, however, as found by Hayes, Jaffe, and Moro­kuma20·l1 for the So dissociation.

C. Analysis and Discussion. We start oor discussion with the results given in Figure 4. We see there that the total coupling, vE(Q), given by eq 11.5 is unequal to zero in the starting poinL Tbis is because of the following reasons. In the first place. the starting point is the $ 1 equilibrium geometry, which differs from the So equilibrium structure. For this Jatter geometry the vibrational and translational components of the electronic coupling are zero because of symmetry reasons.7.S The most important contribution to the starting point coupling, however, comes from the rotational components. We conclude this from the following argumentation: as stated in section 1 IA, the electric field integrals (11.3) are transformed in the statie calculation from Cartcsian to normal coordinatcs by means of the Jacobian matrix elements DJk· lf the normal coordinate transformation is exactly known, it is possible7·' to distinguish completely between the vibrational, rotational, and transla­tional components of the electronic roupling. In the calculation reported here, the movement of the molecules is too far away

19

7844 Journa/ of the American Chemica/ Society/ 100:15 / Deeember6, 1978

160

100

"' 80 •o 20 0 , __ F"tgure 2. Calculated potentiai energy surfaces (method ll) för the H;iCO-HCOH rearrangement; q, denolés the reaction çoordinate. Sob = S. with bents, geometry: S1• s, with planar S. geometry. The zero point on the energy s.cale çorresponds with -113.862 07 au (see Table Il).

from the starting S1 equilibrium geometry to transform with one single, constant Jacobian: we end up at a completely dif­ferent (hydroxycarbene) (:Ollfiguration. Although, because of this reason, it is not possible here to exactly distinguish between the various kinds of couplings, we can perform the transfor­mation of the integrals (11.3) for the first part of the three re­action coordinates in order to get an approximate insight into the relative importance of the components. The result of this transformation is given in Figure 5. We only give five of the obtained nine curves because the translational vectors for the reaction coordinates (b) and (c) are almost the same as the one shown in the figure, while the rotational vectors become only slightly (<>< 10-4 au) larger for (b) and (c) at energies higher than l IO kcal/mol. So we see that the main difference between the couplings shown in Figure 4 is caused by the differences between the vibrational components for the three reaction coordinates. And only these eornponents can be responsible for înducing an internal conversîon. This is so because the trans­lational components have no physical relevance, being the consequence of keepîng the eleclron coordinates tixed while differentiating with respect to the translational coordinates.7

Concerning the rotational eornponents we note that, although they are dominant in the neighborhood of the S1 equilibrium geometry, they do not (:Olltribute much to the ra te of internal conversion. This is so because the electronic components have to be integrated between the vibrational and rotati<mal ei­genfunctions involved; see eq 11.2. This leads toa negligible contribution to the final coupling elements of the rotational components. 7 The result from these considerations is the conclusion that those electronic coupling components, which can effectively induce internal conversion, are larger for the H2CO-HCOH rearrangement than for the direct dissocia­tions. lt is hard to say exactly how much larger the possibility for internal conversion is for this rearrangement because of the

20

·-F"iguro 3. Calculated electronic oouplînp, v"(Q). for the H,CO-HCOH rcarrangement; tl> denoles the reaetion coon:lînatc.

uncertainties inherent in the method used; the obtaincd dif­ferences between the rearrangemenl and the direct dissoeia­tions are so systematic, however, that we have no doubt about the qualitative conclusîon made above. Unfortunately, tbisdoes not mean that the hydroxycarbene is the solution for the in­termediate state problem; we showcd earlier7 that the mag­nitude of the total S,,-S1 coupling elements is so low that in the statie situation there is not internal (:Ollversion at all. What we .have shown here is that the H~O-HCOH rearrangement leads to such a combination of normal mode movements that we have a favorable combination of coupling components. The increase of the coupling, relative to the statie calculation, is nol large enough, however, to explain the H2CO (S 1) decay. So we conclude that formaldehyde needs another molecule to induce the înternal conversion, a conclusion in agreement with the experimental findings mentioned before.5 Such a SC(:Olld

molecule is needed for another purpose too: as can be seen from Figure 2, the formaldehyde molecule wil! end up at the wrong side of the H2CO-HCOH energy barrier; it cannot reach the HCOH (S,,) local minimum on the potential energy surface. In principle there are two ways to lower this barrier (the pos­sibility that the hydrogen tunnels through the harrier is men­tioned brietly in the next section). The first way is an extensioo of the calculational method: il is well known that equilibrium structures can be described satisfactorily at a lower level of calculational sophistication than transition states. So an ex­tension of the method might lower the barrier.34 The second way to achieve this is introducing a second molecule; Ibis possibility is treatcd in the next seetion.

111. The Bimoleeular Rearrangement H,CO-HCOH

A. lntroductlou. As described above, the potential energy surfaces for both the So and S1 states show a large barrier for the unimoleeular rearrangement H2CO-HCOH. A second molecule is needed to lower the S,, harrier, in order to give the H~O (So*) molecule the opportunity to reach the HCOH ($o) minimum. Moreover, a second molecule is needed already for inducing the s,-So internal conversion. lt cannot even be excluded that there will be a much larger medium effect. Re­member, for instance, the well-known HCN-CNH rear­rangement. Calculations22 show that there is a large harrier for this reaction, and yet il takes place almost immcdîately in the laboratory. The hydrogen isocyanide was observcd for the

Kemper, OQll Dijk, lhlck / Photochemutry of F<>rmaldehyde

Fiptt 4. Calculaled eleclronic oouplings, v"(Q), fOf (al H,CO-HCOH rearra~ (b) direct molecular dissociation; and (c) direct radical dissociation. The cnergy scale is taken relativc to the H2CO (S,,) ener· gy.

first time in interstellar spacell where we have almost colli­siooless conditions; as soon as there is the possibility for colli· sions one obtains the "normal" HCN. The same holds for vinyl alcohol. Althoogh a 4-3 IG calculation predicts a harrier of 85 kcal/mol for its unimolecular rearrangement to acetalde­hyde, 24 it was only recently possible to detect vinyl alcohol in the gas phase.25 So for both the hydrogen isocyanide and the vinyl alcohol case we can expect a medium interaction which gives a large decrease of the harrier on the potential energy surface. The same may hold for formaldehyde.

B. MetW m Results. We treat the two formaldehydes as one super molecule using the Gaussian 70 program. We place the second formaldehyde as follows (see Figure 6 for the case where we try to lowerthe banier on the So surface): the oxygen 02 of the second molecule is placed on the line formed, in the unimolecular transition state, by C1 and the migrating hy· drogen H2• We then optimize on the STO-3G levelfor several positions (4>) of H2 at, and in the neighborhood of, the uni­molecular transition state (4>(TS)) the bond lengths C1 H2 and C102, and the angle a describing the position of the second (catalyzing) molecule relative to the first (migrating) one. Some·tests showed that the total energy was minimized upon keeping c" Hz, 02, and C2 in one plane. The remaining geo­metrical parameters were kept fixed at the 4-31G optimized values of the noninteracting molecules. With the optimized ST0-3G structures a 4-31G calculation was performed; a further 4-31 G optimization did not change anything consid· erably. We calculated at several positions.; in order to sec if the angle corresponding to the energy maximum shifts to an­other value, compared to the unimolecular case. This turned out not to be the case. We found the interaction bet ween H,CO · (TS) and H,CO to be attractive: !here is a shallo\v minimum in the potential energy curve as a function of the C,02 distance. This attractive character is in contradistinction to the (ST0-3G) curves for the H,CO-NH3 interaction;26 the situation reported here resembles more the hydrogen bond between H2CO and H,021 and the H2CO-H system. 2s Prom the op­timized position of the catalyzing molecule, the obtained MOs, and MuUiken population analysis we found that the interaction of the two molecules is mainly due to the interaction between the migrating hydrogen H 2 and the n orbital of the oxygen 0,. In Table lil we show the main results of the calculalion and compare them to the unimolecular rearrangement. We note

7845

., " ,,

,. •• 90 100 no ". ". Flpre 5. Lengtbs of vccton formed by !be vibrational oomponents for (a) H1CO-HCOH rearrangemcnt; (b) direct molec•lar dissnciat;..,; and (c) direct radical dissociatioo. Thè rotalional. R. and translational. T. vcctors for (a} are glven for comparison. The cnergy scale is taken rdative to the H,CO IS.)energy.

"•'-. c.,7To, /r(tp!TSI

"2 .

·. "' ·~/"'

c,

\ H3

Fiprt 6. Configuration used for calculatîng harrier 1owering, Sec text.

that the interaction does not lead toa hydrogen abstraction froll) the migrating to the catalyzing molecule: the C 1H2 dis­tance is increased relative. to the unimolecular case, bilt the hydrogen H2 stays with its original molecule. In Figure 7 we give as an illustration the obtained nel atomie charges for the T1 (migrating) + S0 (catalyzing) case; the other situations reported in Table 111 give the sa me picture. As can be seen from Figure 7, the amount of charge transfer between the molecules is negligible ("'0.02 electrons). Table lil shows that there is. indeed a harrier lowering effect; this effect, bowever, is rela· tively small, 6.5- IO kcal/mol. So we sec that we still have an energy harrier in the rearrangement: the unimolecular sin· gle-determinant harrier is l l0.2 kcal/mol; configuration in­teraction (sec Table Il) results in 102.0 kcal/mol, while the bimolecular interaction reported in this section gives a further lowering, resulting in a harrier of approximately 95 kcal/mol. Tuis is still aboul 2S kcal/mol above the vibrationless S1 level. The qualilative key to the solution of this kind of problem is of course tunneling. The problem with this mechanism, how­ever, is the fact that the calculated tunneling probabilities are

21

7846 J®roa/ oftlte American Chemica/ Society/ 100:25 / December6, 1978

•192 H "'51 -321

c=O H/

",92

+184

" ~20 -593 c=o

\ " •389

"

b H"''86 .fi1&2~1ey" ,,

\ "' +l~l

T1 lmlgr!+ S0 leatj

Flgure 7. Calcula1ed ( 4-31 G) net atomie charges 110-1 electrons).

extremely sensitive to the parameters involved (potentialen­ergy curves, energy of the state involved, etc.).29.30 So in principle it is probably possible to adjust or parametrize the (calculated) parameters in s11eh a way that the observed H,CO decay and also the differences between H,CO and D,CO are explaîned, but one never knows how reallstic such a treatment will be. These argumentations concerning tunneling hold, of course, for the unimolecular rearrangement too.

IV. Summary and Concluslon The H2CO-HCOH rearrangement shows a large barrie•

on both the So and S 1 potential energy surfaces. For the single determinant calculation with modest basis set this result was obtained already by Altmann et al.; 11 we showed that extension toa larger basis set+ Cl only slightly decreases this harrier. One of the main results of this work is the tinding that internal conversion to So* is more probable for the hydroxycarbene rearrangement than for the direct dissociation mechanisms. This is due to the fact that those coupling components which can effectively induce the radiationless transition are larger for the rearrangement than for the direct mechanisms. This indicates that the hydroxycarbene can serve as an intermediate state in the formaldehyde photochemistry. lnteractions with other molecules will be needed, however, to effect this lransi­tion and probably also to reach the intermediate state. The inclusion of a second molecule in the process complicates the description because of the numerous ways the molecules can interact. Apart from the possibility reported in section 111, which only leads toa relatively small decrease of the barrier, we can mention, for instance, hydrogen abstraction leading to HCO + H2COH. Another interesting possibility is a hydrogen exchange between two (excited) H2CO molecules leading to two hydroxycarbenes as indicated in a schematic way below:

H,CO

+ OCH2

' HCOH +

HOCH The energy harrier for this process might be lower than for the single hydrogen abstraction, in analogy with the bifunctional eatalyzed [ 1,3] hydrogen shift in propenel2 and the simulta­neously moved hydrogen atoms leading to double wel! poten·

22

Tûle 111. Calculated 4-3 JG Resolts for the lnteraction between a "Migmtin&''and a "Catalyzing" H,CO Molecule

migrating catalyzing harrier• c,tt" A• c,o" A a, deg

So So So T1 T1

T, So

So

110.2 99.9

102.5 65.4 59.0

1.266 1.391 4.002 116 1.319 3.361 118 1.448 1.472 3.754 112

0 In kcal/mol relative to two noninteracting molecules in their equilibrium OOJ'l:figuration. b Parameters from Figure 6.

tials in the guanine-cytosine pair and the formic acid dimer.33

Our final conclusion is that there area number of indications that the hydroxycarbene structure can play a key role in the H2CO (S1) decay, but that a lot of experimental and theoret­ica! work bas still to be done to come toa satisfactory under­slanding of the photochemistry of this seemingly simple mol­ecule. This future work might focus on the direct experimental contirmation of the hydroxycarbene structure and both ex­perimental and theoretica! work on interactions between formaldehyde and other quenching molecules.

References and Notes

(11 PlilllpsResear<hl.abor_E,_,The_ (2) DoGralf, B. A.; C41vert, J. G. J. Am. Chem Soc. 1"7, 89, 2247. (3) McOulgg. R. O.; C..!vert, J. G. J. Am. Chem. Soc. 1989, 91, 1590. (4) Y"""9. E. S.; Moore, C, B. J. Chem. Phys, 1973, 58, 3988. (5) Housloo. P. L.; Moore, C, B. J, Chem Phys. 1178, 65. 757. (8) van Oljk, J, M. F.; Kemper, M. J, H.; Kerp, J. H.M.; Viiser, G. J.; Buck, Il

M. Chem PhJ!s, l.ell. 1978, 54, 353. (71 van Dijk, J, M. F.; Kemper, M. J. H.; Kerp. J. H. M.; Buok, H. M. J. Chem.

PllJis"lnpreso. (81 """Dijk, J, M. F. Thesis, Eindhoven University o1 Teclvlology, Eindhoven.

The-.1977. (9) =· K. Y.; Fairchild, P. W.; lee, E. K. C. J, Chem. Phy$. 1977, 66,

(10) l.ahn, W. A.; Curtlss, L. A.; ._.,,W. J.; Lisle, J. B.; Poplo, J. A. !'rog, Phys, 0rg. Chem. 1974, 11, 175.

(11) -.J. A.;Csizmadla, l.G.; Yates,K.;Ya .... P.,J.(;hem, PllJis. 1977, 116,298.

(121 Lucchese, R. R.; -ter UI. H. F. J. Am. Chem. Soc. 1978, 100, 298. (13) The BCIL5)fpad<agewasde"9loped by Or. E. Clemenll andoo-workers;

the fOW'*lnde• tt~ prO(J'am was wrllten by Dt- Me van Hemert. WettlankOr.P.E.S.--ol~~kl<maklng­._prog<amsandOr. G.J. V'....,..kl< adaptionoflheseprogramo lolhe BurrougN 87700 compufer.

{14) lluMlng. T, H J. Chem. PflJis, 19711. 53, 2823. ( 15) Goscinski, O. and co-workers, u cbd in ref 7. (16) --K.; KonJsh;, H. J. Cl>em, ,,,,,., 1971, 55, 402, {17) - W. J. "al Gausslan 70, frwom 236. Qimlum Chemlslry ~

Exohange, -.a l.Wv<nily. llloomington. lnd. (18) Moule. 0. C.; Walsh, A.D. Chem. Rev. 1175, 75. 67. (19) Hayos, D. M.; - K. Chem Phys. Lolt. 1112, 12. 53&. {21)) Jallo. R. L; Hayo$, D. M.; -- K. J. Chem. ,,,,,._ 1974, 8(1,

5\08, {21) Jaffe. R. L; - K. J. Chem Phys, 1976, 6•, 4381. (22) Pea1soo, P. K.; Scilaefer lU, Il F. J. Chem Phys, 1975, 62, 350. (23) -·LE.; 8'ill, 0. Bull. Am. Astron. Soc. 1971, 3, 388. (24) - W. J,; Popplnger. O.;-. L. J. -· Chem. Soc. 1977, 99.

6443. (25) Sailo, S, Chem Phys. Lolt. 1978, •2. 399. {26) Mmaraj, U.; Csl!madia, I. G.; Wlnnlk, M. A. J. Am. Cl>em. Soc. 1977, 99,

946, (27) lwata, S.; Moro1wma. K. J. Am. Chem. Soc. 1973, 95, 7563. (28) Mizutanl, K.; lzumi. T.; -· S. Bull. Chem. Soc. Jpn. 1977, 511.

2113. {29} SrickmaM, J.: Zimtnermann, ... J. Chem. Pflys. 1Ht, 50, 1608. (30) Harmony. M.O. Chem, Soc. -- 1972, 1. 211. (31) Cllill<, J, H.; Moora, C, B.; Nogar, N. S. J. Chem. Phys. 1178, 68, 1264. (32) Niemayer, H. M.; Gooclnold. 0.; Ahlbefg, P. Te- 1175, 31.

1899. (33) Clementl, E.; Mehl. J.; von Nlessen, W. J. Chem Phr.J. 1971, 54, 503. (34) Aft8' lh8 monusorlpt was llnlshed a study oo 1he ~

rearrangement _.., {l)yl<Wa, C. E.; SChaefer Hl, H F. J, Am. Chem. Soc.1978, 100, 1378). TheaulllcrtshowthotforUVs,___in. duSiOnolpofaritatlonluncllcnsiS-.tequally~as~ ·-·

III. A THEORETICAL STUDY ON THE REACTIVITY

AND SP~CTRA OF HzCO and HCOH.

A DIMERIC MODEL FOR FORMALDEHYDE PHOTOCHEMISTRY.

23

A THEORETICAL STUDY ON THE REACTIVITY AND SPECTRA OF H2CO AND HCOH. A DIMERIC MODEL FOR FORMALDEHYDE PHOTOCHEMISTRY

* M.J.H. Kemper , C.H. Hoeks, and H.M. Buck

Contribution from the Department of Organia Chemistry, Eindhoven

University of Teahnology, Eindhoven, The Netherlands.

Abstract The reactivity and spectra of formaldehyde isomers and dimeric complexes between them are studied with ab-initio

methods. A large number of complexes between H2co, HCOH-trans, and HCOH-cis is calculated, and the suitability of minimal basis sets for this purpose is discussed. Infrared and Raman spec.tra of (H2Co) 2 are calculated with relatively simple methods using spectroscopie masses and scaled force constants. In this way, the structure of dimers in matrices can be deduced. Hydroxycarbene, HCOH, plays a key role in a model that expJains a large number of experimental facts of formaldehyde photochem­is try. Hydroxycarbene forms complexes with H2CO; the stabilization is due to hydrogen honds. HCOH is a new

example of an ambiphilic carbene. Addition products are formed from HCOH ... H2co complexes. The calculations show that, in agreement with matrix experiments, glycoaldehyde and methanol are easily formed. The formation of HCOH-trans occurs through a dimeric interaction with the shifting hydrogen. This bimolec­ular process is 9.6 kcal/mol (6-31Gx) in favour of the uni­molecular conversion. HCOH-cis might be formed via a non-planar transition state, where also stabilization at the carbenic center is possible. When higher concentrations of HCOH are available, a hydrogen exchange mechanism easily transfers hydroxycarbene back to H2co. Several experiments are suggested in this paper; notably molecular beam and isotopic-mixture experiments will give useful information. The involvement of HCOH in the light-induced formose reaction is suggested.

24

1. Introduction

During the last decade the study of the formaldehyde molecule has taken a central place in fundamental molecular photo­chemistry and photophysics. Formaldehyde owes this position to the fact that, on the one hand it can behave as a proto­type for the photochemistry and photophysics of larger mole­cules, and on the othev hand, it is amenable to detailed and well defined spectroscopie and theoretical studies. The experimental studies revealed a large number of phenomena. The overall process is seemingly simple: formaldehyde is pre­pared to the s1 state by light absorption, and the final products are molecular and radical fragments:

h -c H2+ CO H7COISol ~ t-tiCOIS,)

H + HCO

The detailed mechanism, however, is still a tantalizing problem. We will not try to discuss here in an extensive way all the existing literature on this subject. We will only mention in the following section some main results in order to define clearly the problem we are concerned with in this paper: the role of hydroxycarbene in formaldehyde photo­chemistry.

2. The problem

2.1. Gasphase and matrix experiments

The experiments on formaldehyde that are of interest here, can be placed in two categories: gasphase and matrix experi­ments. An important result in gasphase experiments is the finding by Houston 1 and Zughul 2 that a time lag is involved in the formation of CO photoproduct. At energi'es less than 1500 cm- 1

above the s1 origin, the appearance time of CO light absorption is much langer than the corresponding decay time of s1 formal­dehyde fluorescence. The appearance time is hardly dependent

25

on the formaldehyde isotope or the vibrational energy. Extra­polation of the results indicates that the zero pressure inter-

cept of the formation rate T~6 is at most 0.2 µsec- 1. This suggests that photochemistry cannot occur without collisions. As remarked by Weisshaar 3 , it is difficult to reconcile these results with the conclusions that have to be drawn from collisionless (p < 1 mTorr) decay experiments. At these low pressures a rapid collision-free decay channel is observed. This fast decay can be explained 3

, in principle, by a se­quential coupling mechanism. The prepared single rotational level in s1 is coupled with the set of high vibrational levels of s0 • These s0!t levels are broadened to a "lumpy" continuum because of coupling with the continuum of H2+CO dissociative levels. A level shift technique involving a uniform ex-ternal electric field enabled Weisshaar to obtain quantitative information about the molecular parameters that determine intramolecular decay rates. H is encouraging to see that the coupling elements obtained by this elegant method are in agreement with the calculations of van Dijk 4 and Heller 5 •

Weisshaar's conclusion is 3 that the only way to reconcile low and high pressure results is to claim that the s1 state can be quenched to a non-fluorescing intermediate state, X, which requires a subsequent collision to give products:

P=O / (1) ...

s, co ., 12) ...

P > 0.2 torr

The quenching (2) must dominate the collision-free channel (1)

for pressures above ~ 0.2 Torr. One of the main tasks of fundamental photochemistry is to unravel the nature of this intermediate state. Candidates are in short supply: high vibrational levels of the electronic

26

ground or triplet state (s0~ or T 1 ~. respectively), and the

hydroxycarbene isomer HCOH. It is difficult to dismiss definitively one of these possibilities; all of them have arguments pro and con. Moreover, the experimentally observed phenomena in formaldehyde photochemistry are so numerous and divers, that it is unlikely to find just one simple mechanism to explain everything. In this paper we concentrate on the involvement of the hydroxycarbene isomer, and we will only make some remarks'on the other possibilities. More de­tails , including the extensive literature on this topic, can be found in Weisshaar's work 8

• From a theoretical point of view, r 1 ~ has always been considered an unlikely candidate, because its vibrational level density near the s1 level is much too low. Experimentally, Tang 6 et al. showed, by exciting triplet perturbed s1 levels, that the triplet state plays no mechanistic role in the photochemistry of the 2341 and 2241

levels of formaldehyde. The recent and rather unusual results 3

of quenching experiments on D2co renewed the interest in this possibility. The main difficulty with s 0 ~ is probably the explanation of the time lag. It is hard to imagine how a very high vibrational state (28000 cm- 1) can resist energy re­laxation and randomization for one microsecond. Before going to the third candidate, HCOH, we have to mention the other type of experiment which is of interest here: photolysis of formaldehyde in low temperature matrices. These matrix experiments are complementary to gasphase work. It is for instance possible to study in a direct way in an inert­gas matrix the differences between monomeric and dimeric formaldehyde. Particularly, the work of Lee's group has to be mentioned here 1 - 9 • Diem7 photolyzed H2co in an Ar matrix. Infrared absorption before and after the photolysis showed that the dissociation of formaldehyde is effected by the cage dimer. The amount of photoproducts, CH30H plus CO, paralleled the amount of dimer present before photolysis. Surprisingly, the monomer peaks did not decrease at all after photolysis. So, matrix isolated H2co is not photochemically

27

dissociated. (Recall, that it is not yet clear at this moment, whether or not photoproducts are formed in gasphase experiments for p + 0. Extrapolation to zero-pressure has only given an

upper limit for TëÓ)· In more highly concentrated matrices, Sodeau 8 observed the formation of glycoaldehyde, methanol and carbon monoxide. Also some evidence for hydroxyketene, (CH(OH)CO), was reported. The intermediacy of hydroxycarbene in the formation of these addition products'was suggested. In the next section we will put together all these experimental facts and offer a model to explain them.

2.2. Hydroxycarbene

Houston and Moore 1 mentioned for the first time trans­hydroxycarbene as a possible intermediate in formaldehyde photochemistry. Extensive calculations by Goddard 10 and Pople 11 place HCOH (80) at energies of 52.8 and 56.6 kcal/mol, relative to the formaldehyde ground state. So, the local s 0-minimum which corresponds to HCOH is, in principle, accessible from the first excited singlet of H2co (Es 1 = 80.6 kcal/mol). In an earlier paper 12 , we reported calculations on the electronic coupling elements between the s 1 and s 0 surfaces. These elements, which induce s 1 "\J'V+ S~ internal conversion, increase as the molecule is distorted towards a HCOH-like geometry. The increase of the coupling elements for the reaction coordinates leading directly to molecular and radical products is much less dramatic. This suggests, that the H2co + HCOH reaction path is important, because it gives the molecule a maximal opportunity to leave the s 1 potential energy surface. We also showed 12 that bimolecular interaction between two H2co molecules lowers the energy harrier to HCOH rearrangement. In order to be acceptable as an intermediate in formaldehyde photochemistry, HCOH must give reasonable explanations for the main findings mentioned in Section 2.1: - The explanation for the time-lag is, of course, obvious.

Just as T1 would do, HCOH gives the formaldehyde molecule

28

a place to wait a while before giving photoproducts. - In gasphase experiments molecular and radical products are

formed. This process can be induced by collisions; zero­pressure dissociation is uncertain.

- Mainly the matrix experiments show that the unimolecular formation of HCOH either must be very difficult or it must be a very rapid reversible one.

- Cage dimers of H2co must lead, via HCOH, to the addition products glycoaldehyde and methanol.

This can be put together in Scheme I. Here, M is a second

matrix ~COIS1 1 + M--IHiCO···MI HCOH···M-products ""/. ( 11 12)

wf 131! gasphase

___..,H2 M + HCOH lS01 -_.H

Scheme I

+co

+ HCO

formaldehyde molecule in its electronic ground state. We will also pay some attention to CO, H2o, and H2 as a quencher. In the next three sections we give the results of a large number of ab-initio calculations on this model. In Section 3 we give calculated bimolecular complexes between molecules of tt 2co and HCOH. These complexes are used in Section 4 as a starting point for step (2) of the model: the formation of addition­products. In Section 5 we discuss the steps (1) and (3): the formation of hydroxycarbene. Finally we note that the reverse reaction (4) involves a larger energetic problem than transition (3). This is illustrated very schematically in Figure 1. The harrier to HCOH lies slightly above ihe s1 origin 13 • As will be discussed in Section 5 tunneling and/or bimolecular interactions give an effective lowering of this harrier beneath the s1 origin. If we start, however, with a Fischer-type transition metal­carbene complex like:

29

the carbene ligand can split off from the metal. Then imme­

diately a hydrogen shift occurs 14 , yielding an aldehyde; there

is no trace of RCOH at all. As remarked by Lucchese 15 , this

indicates that HCOH + H2co must be very easy. The carbene

ligand might have some internal energy after the split off,

but part of the HCOH molecules will relax to the vibrationless

:::::84 80.6 (3)

E H2CO 1511

(kcal/mol l 52.8

f HCOH ISol

0

H2CO 1501

Figure Energies (kcal/mol) involved in the rearrangernent HzCO <---> HCOH-trans

level at 52.8 kcal/mol. From there no unimolecular escape to H2co is possible because the energy harrier of ~ 31 kcal/mol

is too high. However, no HCOH is detected at all. The way to

escape is a bimolecular one and will be discussed in Section

5. 2.

All ab-initio calculations with ST0-3G and 4-31G basis sets

were done with the GAUSSIAN 70 program 16 ; for the 6-31G:t

calculations the GAUSSIAN 76 program 17 was used. A large

number of the calculations in Sections 3-5 concern interaction

energies; i.e. a calculated dimer energy minus the energies of the non-interacting molecules. In Table I we give all the

energies which are taken as a reference. 30

Table I. Calculated energies (a.u.), 'Which serve as a reference level

a / a SI'0-3G 4-31G SI'0-3G 4-31G 6-31G11/ 4-31G 6-31G*

H2CO -112.35435 -113.69171 -113.69262 -113.86555 -113.86633

l:IXl:l-trans -112.27841 -113.60763 -113.61107 -113.78168 -113.78351 ,

HCOO-cis -112.26909 -113.59684 -113.60005 -113.77253 -113.77449

a) SI'0-3G = geometry optimized with ST0-3G basis set; 4-31G/SI'0-3G =

4-31G calculation in ST0-3G optimized structure, etc.

3. Complexes of H6CO-isomers and their spectra

3.1. The complexes

In Table II we give the stable, dimeric complexes between formaldehyde isomers. All calculations were done with the ST0-3G basis-set; all intra- and intermolecular geometrical parameters were optimized with respect to the total energy of the system. The effect of optimizing intramolecular para­meters instead of holding them at their monomeric values is relatively small in case of weakly bonded complexes. If there is. however, a strong interaction or even a complete reaction between two molecules (as in Section 4), reoptimization is, of course, necessary. In order to treat all systems in an equivalent way, we decided to optimize all geometrical para­meters throughout this work. The intermolecular parameters are elucidated in Figure 2. Some remarks can be made for all

31

Table II. Sf0-3G calculated complexes between H2CO isomers. The inter-

molecular parameters are shown in Figure 2.

H-atoms R 1fi1 w2 +1 Energya

+2(kcal/mol)

HzCO + HzCO

1 1234 3.72 70 70 0 0 -0.94 (A -0.95)b "v

(D -0.63)b 2 1234 3.59 53 71 0 90 -0.87 1\,

(C -0.61)b 3 1234 3.44 0 180 0 0 -0.66 '\,

4 1234 4.07 101 48 0 0 -1.04 '\,

(B -1.04)b 5 1234 4.19 107 43 0 0 -1.04 1\,

(E -0.44)b 6 1234 3.92 54 54 90 90 -0.63 1\,

H2co + fl:(lf-trans

7 1238 4.06 74 56 0 0 -0.32 '\,

8 1238 3.91 65 46 90 0 -0.56 '\,

9 1247 5.93 0 0 0 0 -0. 15 '\,

10 1238 5.94 0 0 90 0 -0.11 '\,'\,

11 1247 4.51 191 322 90 0 -0.21 '\,I\,

12 1238 3.89 44 282 90 0 -4.41 '\,I\,

u 1247 4.14 54 18 0 0 -3.33

H2CO + HCOH-cis

14 1248 3.47 66 282 90 0 -3.24 '\,I\,

.u 1237 4.48 9 51 0 0 -6.14

16 1237 4.59 8 50 90 0 -4.71 1\,1\,

17 1248 4.53 32 304 0 0 -5.24 '\,I\,

18 1248 3.67 125 128 0 0 -1.54 '\,I\,

19 1248 3.55 176 116 90 0 -0.86 1\,1\,

20 1237 3.54 120 264 90 0 -0.82 '\,I\,

HC(lf-trans + HC(lf-trans

21 1674 2.77 68 68 0 0 -19.88 1\,1\,

22 2754 3.31 70 70 90 90 -0.77 1\,1\,

a)Relative to the sum of energies of the non-interacting molecules as

given in Table I. b)Related complexes and energies as given in ref. 18 32

Figure 2 Inte:rmolecular parameters for complexes between H2co isomers.

the complexes (except AlJ· The first column in Table II gives the hydrogen atoms which are actually present in each complex. The intermolecular parameters given in the next columns are optimized to~ 0.02 R in Rand~ 1° in the angles. The in­accuracy in these parameters is larger than for the intra­molecular ones, because the intermolecular potential energy surfaces are rather flat, as can be expected with these relatively small interaction energies. The intramolecular distances and angles differ only slightly from the values in the single molecules; therefore they are not shown in the Table.

H2CO + H2co

Our results on H2co dimers parallel qualitatively the results of Del Bene 18 • A rather detailed analysis of the factors which determine the small interaction energies can be found in her paper. There are, however, also some differences between her results and ours. Del Bene reports only two really stable dimers (:J.."and _rJ; the other dimers are nonequilibrium structures. when constraints on angular coordinates are relaxed. Contrary to Del Bene, we also optimized the intramolecular parameters. This results in a slightly (< 0.2 kcal/mol) larger stabili­zation energy for the complexes l•l and .t· These complexes

33

are, according to our results, equilibrium structures. We note, however, that the barriers leading from these structur~s to 1 are very small; probably the heights of these barriers

~

are even smaller than the inherent inaccuracy in the results (see also Section 3.2). So, the question whether or not l• 1• and 6 are real local minima on the potential energy surface

~

seems rather academie. In close proximity to the most stable dimer reported by Del Bene (,~),we found a new one C!) with the same interaction energy. We will return to these complexes

in Section 3.3.

H2CO + HCOH

There are seven complexes between H2co and HCOH with inter­action energies larger than 1 kcal/mol. We will discuss only these complexes. The stabilization energy is caused by the formation of a hydrogen bond. In the complexes ),l-J.Z we have a HCO-H •.• OCH2 bond. In complex].! formaldehyde is the hydrogen donor; this is the only complex where the carbon atom of hydroxycarbene serves as a hydrogen acceptor. We didn't find complexes with the carbene oxygen as an acceptor. That hydrogen bonding is important is suggested by several findings. In the first place, the equilibrium geometries of ~-J,2 show that the directed lone pair of the formaldehyde oxygen forms a nearly linear o ..• H-0 bond. This is consistent with the general hybridization model of Del Bene 19 , who studied ROH •.• OCH2 dimers, where R is H or one of the isoelectronic substituents ctt3 , NH2 , OH or F. Also ~ fits in this model; in this complex the formaldehyde C-H bond is nearly colinear with the non­bonding orbital on the hydroxycarbene carbon. The hydrogen ~ond character of the interaction is also shown by a small but significant interatomic electron density 20 {i.e.d.) for the 0-H .•• O and C-H ••. C bands. There is also a little charge transfer associated with the hydrogen bond formation. Complex Jj is shown in Figure 3 as a typical example; for all the other complexes the situation is qualitatively the same. The bridged

34

•165 H ~233 -262

·c=o / ·· .. H H • 256

•165 1

/0-233

H-C -178 -146

Figure 3 Changes in net atomie charges due to complex formation

(in 10-4 atomie units)

hydrogen donates electron density which is accepted by the

adjacent atoms. The hydrogen acceptor is polarized, and the

overall result is a charge transfer from the H acceptor to the

H donor. The amount of charge transfer varies from 0.008

electrons in ~to 0.043 electrons in J.2.; there is an

approximately linear correlation between the charge transfer

and the stabilization energy. These characteristics of the

hydrogen bonded HCOH-OCH2 complexes (charge redistribution,

H-bond directionality) are also found for H-bonds between

"normal" molecules 21•

HCOH + HCOH

There is a very large number of starting geometries if one looks for complexes between two HCOH (cis/trans) molecules.

We didn't make very extensive calculations in this region of the potential energy surface. Most calculations involved the

energetically favoured trans-isomer. Nearly all starting geometries we tried were either repulsive or they converged

to the highly stabilized complex ~ This complex plays a

central role in the rearrangement HCOH + H2co (reaction (4)

in Scheme 1), and will be discussed in Section 5.2. The weakly stabilized complex 22 can rearrange easily to 21 . ......._, ,.....,

35

3.2. Accuracy of structures and energies

In Section 4 we need the structures of the complexes as a starting point for the calculation of reaction harriers. For this purpose the H2co ... HCOH complexes will turn out to be the most important ones. Hydroxycarbene has not yet been detected experimentally, let alone complexes between formal­dehyde and hydroxycarbene. So, because of this lack of direct experimental data, we have to consider ether complexes to determine the usefulness of the ST0-3G basis set. Fortunately, it appears 21 that the general geometry of the complexes,which is the most important feature to us, is predicted rather well by minimal basis set calculations. The prediction of hydrogen bond energies (AE) however, is less satisfactory, because AE is more basis set-dependent than the structure. Perturbation theory studies 21 of weak molecular complexes have concluded that there are several main terms contributing to AE: electro­static energy, exchange repulsion, polarization energy, charge transfer contributions, and dispersion energy. The dispersion energy is essentially due to the intermolecular electron cor­relation; so,single-determinant methods are fundamentally incapable of yielding dispersion attraction between two molecules. The other terms, of which no one is predominating, cancel partially; partitioning of the hydrogen bond energy in the water dimer shows 22 that as a result the electrostatic contribution is on the same order as the bond energy itself. The terms contributing to AE are determined by molecular di­pole moments, statie polarizabilities, and ionization potent­ials. Every limited basis set gives typical errors in esti-:na t i ng these molecular properties 2 1

• Another difficul ty arises from the so-called basis set superposition effect 23 • If one calculates the total energy for a dimer, the complex is artificially stabilized because each monomer benefits from the basis functions of the other. This error can be estimated by recalculating the monomer with an additional set of basis ~unctions placed at the positions where, in the dimer, the ato•ns of the second molecule are. In their interesting study

36

on H2co.H2o and H2co.H2s complexes, Ahlström et aZ. 24 showed, that this basis set error is of the same magnitude as the dispersion energy; in their study these terms cancel partially. A detailed analysis of all these factors and the way they are over- or underestimated in different calculations is very difficult and tedious. So the best thing seems to be a com­parison between the final results of ST0-3G, near Hartree-Fock limit + CI, and experiment. This is done in Table III for the most extensively studied complexes: (H 2o) 2 and (HF) 2•

Table III. Dimerizationenergies (kcal/mol) for (H2o) 2 and (HF) 2

near Ha.rtree- correlation- total ST0-3G t.E Fock limit interaction exp.

CH20)2 3.9a 1.1b s.o 5.9c 5,4d

(HF)z 3.8e 0.3e 4. 1 s.sf 7.9g

a)ref. 25; b)ref. 26; c)ref. 27; d)ref. 28; e)ref. 29; f)ref. 30;

g)calculated from the t.Hzgs value in ref. 31 (see text)

For a comparison between theory and experiment, the experi­mental enthalpies of dimerization, AH, have to be converted to AE. These quantities are related by 22

:

AH= AE + AE (tr.) + AE (rot.) + AE (vib.) + A (PV)

In going from two monomer HF molecules to one (HF) 2 dimer three translational and one rotational degrees of freedom are lost, each of which contributes !RT to the enthalpy. So, in this case AE (tr.) + AE (rot.) = 2RT. Each vibration cöntri­

butes:

37

}hv + hv{exp(hv/RT)-1}- 1,

where the first term is the zero-point energy, and the second is due to the population of excited vibrational levels. The change in the intramolecular frequencies is relatively small. In the limit of low frequencies the contributions of each intermolecular vibration approaches the classica! limit, RT. For (HF)z also calculated values for these frequencies are available 29 • Using these numbers we calculate the AE value for (HF) 2 to be 7.9 kcal/mol. We note that, according to Kollman 21 , the experimental AH298 value ought to be re­examined, because it is certainly too high. Looking at the results in Table III, it is surprising as well as encouraging to see, that a small basis set can give a rather good final result. We realize, however, that it might be dangerous to extrapolate these results to the complexes studied in this paper. Therefore we investigate in the next section a much more refined consequence of ciimer formation.

3.3. Infrared and Raman spectra

Differentiation of the potential energy surface to the geometrical parameters gives the force field of a molecule. From these force constants the vibration frequencies can be obtained. Pulay 3 2 showed, that prediction of intern al coordinate diagonal force constants to experimental accuracy is not easily possible from single determinant Hartree-Fock wave functions. There are, however, near-systematic errors which allow for empirica! corrections to improve significantly the agreement with experiment. Theoretica! prediction of interaction constants is more successful. The predicting possibilities of a semi-empirica! calibration of force constants were recently shown by Bock et al. 33

•34 in studies on glyoxal and

and acrolein. They used a scale factor method35 for the adjust­ment of diagonal force constants; also they used the so-called spectroscopie masses 36 •

37 to allow for anharmonicity to some

38

extent. The agreement between calculated and experimental frequencies is to within 2%. Firstly, we will investigate on the basis of H2co how such a procedure must be done for ST0-3G calculated force constants; then we will calculate the spectra of (H 2Co) 2 and HCOH. Force constants can be calculated in internal coordinates (bond distances and angles), symmetry or local symmetry coordinates. We use internal coordinates because we want to calculate molecules of different symmetry. Throughout this paper we employ optimized geometries, rather than experimental geo­metries as suggested by Schwendeman 38

, since no experimental structures are available for (H 2C0) 2 and HCOH. The required force constants are obtained by quadratic fitting to points near the equilibrium structures. Diagonal terms are obtained from

F XX

the interaction terms are calculated from

Here, x0 and y0 are the values of the internal coordinates in the equilibrium structure. The displacements ~ are chosen neither too large for anharmonicity to matter nor too small for numerical inaccuracies to appear. The force constants are transformed to frequencies using the conventional FG method 39 •

H2CO and HCOH

The results for H2co are shown in Table IV. Column A gives the results obtained from pure ST0-3G force constants. As can be expected from the fact 42 that diagonal stretching and bending constants are overestimated in ST0-3G, typically by 20%-30%, these frequencies are much too high. In column B we

39

" 0 Table IV. Calculated vibrational frequencies (cm-1) for fonnaldehyde. The internal coordinates used in the

calculation are the CO- and CH-distances, the HCO-angles, and the angle of 0 out of the HCH-plane.

A B c D E F G

mode type exp.a unscaled unscaled scaledb Goddard&SchaeferlO D2CO HDCO atom. m. spectr. m. spectr. m. unsc. scaled

sym. CH-str. 2782.5 3500.0 3374.6 2701.7 3234 2749 2005.2 2778.6 2 CO-str. 1746.0 2101.2 2071.6 1754.2 2123 1805 1614.0 1665. 2

3 sym. bend 1500. 2 1797.0 1707.2 1562.4 1435 1435 1209.0 1478.5 4 out of plane 1167 .3 1074.9 1043.6 1043.6 1320 1320 845.9 949.9 s asym. CH-str. 2843.4 3647.0 3520.8 2841.0 3364 2859 2138 .1 2063.5

6 asym. bend 1249. 1 1395.7 1353.6 1240.5 1332 1332 990.6 1047.2

average deviation 19.0% 16. 1 'li 3.2% 13.4'1, 4.9% 4.6%a 4.4%a from experiment

a)Experimental frequencies from: HzCO reference 40; n2co and HDCO reference 41 b)Diagonal stretching and bending force constants scaled down by factors 0.65 and 0.9, respectively

used spectroscopie masses defined by 36,

37

1

Msp = M + 0.0795 M2

to allow for anharmonicity. As expected, the improvement is primarily in the CH stretching. Then, we scale down the dia­gonal constants; the interaction constants are left un­changed. We only use two scale factors: for the stretchings we use 0.65, and for the bendings we take 0.9. In their study on ethane, Blom and Altona 35 also found a ratio of 0.65 between the ST0-3G and the optimized C-C-stretch force constant. Our result is shown in column C; the agreement with experiment is good. For comparison we give in the next columns the results of Goddard and Schaefer 10 • They used the standard double zeta basis set of Huzinaga and Dunning; they scaled down by 15% the frequencies, rather than the force constants. In all vibrational calculations that follow, we use the same procedure as for H2CO: spectroscopie masses and scale factors of 0.65 and 0.9 for diagonal stretching and bending constants, respectively. Columns F and G show the results for deuterated formaldehyde. In Table V we give the frequencies for the most important HCOH structure: the trans isomer. The agreement

Table V. Calculated vibrational frequencies (cm-1) for HCOH-trans. The internal coordinates used in the calculation are CO-, CH-, and

OH-distances, the HCO- and COH-angles, and the torsion OH about the CO axis

mode type DCOD HCOD DCOH HCOH HCQHlO

OH-str. 2413.3 2412.9 3275.2 3275.4 3546(3464)a 2 CH-str. 1943.2 2615.4 1946.0 2615.0 2684 3 1266.6 1524.7 1512.8 1626. 1 1595 4 1188 .1 1194. 9 1214.2 1321.5 1264 5 946.2 1036.6 1031.2 1166.9 1101 6 tors ion 799.9 928.9 974.4 1082.8 1093

a)See text 41

with reference 10 is good, except for the OH stretching. We note, however, that the unscaled frequency reported by Goddard and Schaefer is 4075 cm- 1; sealing down by 15% results in 3464 cm- 1•

(H2

C0)2

From Section 2.1 it will be clear that cage dimers of for­maldehyde are very interesting: it was shown 7 that product formation is effected by the dimer; matrix isolated mono­meric formaldehyde is not photochemically dissociated. Infra­red and Raman spectra of formaldehyde in argon and nitrogen matrices were studied by Khoshkhoo and Nixon 43 • They concluded from the fact that only single i.r. and Raman lines occur for the dimer in each of the fundamental vibrational regions, that a plausible dimer structure would be one with a center of symmetry. These facts indicate that the complexes ,:t,,and _t are plausible candidates.

6 -The structures ,tand 2_, belong to the point group c2h; this results in sets of mutually exclusive i.r. and Raman bands.

We calculated the force fields for 1., and 2_,; only stretchings and bendings were taken into account, while the intermolecular internal coordinates are the same as in Figure 2 (R, $ 1 , and w2). From such a force field we obtain 13 frequencies; three of them are low-frequency intermolecular vibrations (< 75 cm- 1). The symmetry of the normal mode movement shows whether a vibration is i.r. or Raman active. Of course, these

42

calculated dimer frequencies cannot be compared directly with the experimental values. The experimental dimer frequencies are shifted from the monomer gas phase values not only because of dimer formation (effect A), but also because of the in­fluence of the matrix (effect B). These two effects can be separated in separated in

argon and nitrogen matrices; they cannot be solid formaldehyde,which can be considered as an

association of molecular dimers~~. Ina calculation only effect A, the difference between monomer and dimer frequencies, can be considered. Table VI gives the results for the infrared shifts. There is a good qualitative agreement between the A-shifts of the planar complex ,L and the experimental data for argon and nitrogen, with the exception of the mode 6 frequency. We note, however, that for modes 1 to 5 the results of A and B on the frequencies are similar: both shifts have

Table VI. Experimental and calculated shifts (cm-1) in infrared frequencies,

due to A: dimer fonnation (vdimer - "monomer)' and B: influence of matrix environment (vmonomer(matrix) - "monomer(gas))

Hf O D2CO

experiments calculated experiment calculated

solid44 · N 43 in Ar43 1 6 in Ar43 1 6 modea

m 2 "' "' "' "' A+B B A B A A A B A A A

1 54 17.3 8.8 14.7 12.5 4.2 -3.7 12 .o 9.9 2.3 -3.0

2 -32 -6.2 -3.3 -4.0 -3.7 -10. 7 -6.1 -3.0-6.1 -19.7 -11.5

3 -12 -0.6 -5.2 -1.3 -16.5 -6.8 -2.2 -2.0 -5.0 -1.5

4 10 0.2 6.6 0.9 0.5

5 16 21.4 6.2 19.6 10.0 2.9 -1.9 16.5 10.6 1.9 -1.5

6 -33 -4.9 3.6 -4.5 3.6 -11.4 0.7 -0.5 2.6 -9.1 0.6

a)The modes are derived from free H2co; the vibrations of (H2Co) 2 differ

only slightly from these

43

the same sign. For mode 6, A and B have an opposite effect. This might indicate that for this asymmetrie bending mode A and B influence each other; a separation of the total shift into two components and the comparison of one of these com­ponents to a calculated value is not permitted then. The solid phase results of Schneider and Bernstein44 agree for all modes wi th our calculation on complex ,l· We performed a number of numerical tests to investigate the uncertainty in the calculated shifts. It is well known 32

, for instance, that force constants are very sensitive to the choice of reference geometry. Our tests indicate that the signs of the calculated A-shifts are probably correct; the absolute values can have uncertainties as large as 50%. So, qualitative agreement with experiment is the best that can be expected. Fortunately, we found that the differences between i.r. and Raman frequencies in the complexes ,tand~ are almost insensitive to small changes in reference geometry. So, the numerical accuracy in

vdimer (i.r.) - vdimer (Raman) is much better than for the A-shifts. Our results are compared with experiment in Table VII. Unfortunately, in thi~ case the experimental data have a large uncertainty 43

• The measurement of adequate Raman spectra required a relatively wide spectrometer slit; the significantly poorer resolution than in the i.r. caused differences of up to 2 cm- 1 between the measured Raman and i.r. frequencies for the monomer fundamentals. This might also explain the strange qualitative difference between H2co and n2co. Table VII clearly shows that the planar complex 1., explains the experiments much better than complex !?..: Several conclusions can be drawn from this calculation. First of all it is seen that a simple minimal basis set calculation can reproduce rather subtle spectroscopie changes which are due to complex formation. This fact is quite surprising, because the interaction energies in (H2Co) 2 are low (< 1 kcal/ mol). The agreement between theory and experiment is at least

Table VII. Experimenta143 and calculated values (cm-1) for

vdimer(ir) - vdimer(Rarnan)

Hf O DzCO

modea experiments calculated experiment calculated in N2 in Ar 1 6 in Ar 1 6

"' "' "' "' -3.5 -0.4 0.3 -0.3 2.0 1.3 -2.5

2 4.6 6.3 5.7 -5.7 3.1 4.3 -11.9

3 -1 . 1 -8.9 -0.5 -0.6

4

5 -1.0 0.3 o.o 0.4 o. 1 o.o 6 -1.3 0.0 -1.7 o.o

a)The modes are derived from free HfO; the vibrations of (Hf0) 2 differ only slightly from these

as good as obtained with larger basis sets for stronger com­plexes29 •45•46, A reexamination of the experimental data is desirable. Such experiments should be done preferably with molecular beams to avoid the large (see Table VI, effect B) matrix-complex interactions. Such a molecular beam deter­mination of a dimer structure has already been done for water 47

• Our calculations show that fora reliable determi­mation of the complex structure, Raman frequencies are just as important as i.r. frequencies; i.r.-Raman differences are calculated more accurately than monomer-dimer shifts. The available data show that the planar complex ,tclearly is the best candidate for the (H2Co) 2 structure; this will be used in Section 5, where we study the formation of HCOH.

45

4. Formation of addition products

The thermal formation of addition products from H2co + H2co is difficult. Calvert and Steacie 48 report that methanol and carbon monoxide are the major products of a very slow reaction in the ternperature range 150 to 350 °c. So, there are high

activation harriers or difficult reaction paths to products. In Section 2 we mentioned that s1 excitation in matrices induces the formation of glycoaldehyde and methanol. We suggested in Scherne I, that HCOH is formed after such an excitation. Hydroxycarbene has an energy of about 55 kcal/mol, relative to the formaldehyde ground state 10 • 11 , So, the product formation can be easier if one starts with a complex between HCOH and H2co. In this Section we investigate this possibility. A number of test calculations showed that, in genera!, it is unwise to start with an intuitively estimated starting geometry for H2co ... HCOH. The most important reason for this is the difficulty to define a good react1on coordinate. We have to search. for a low energy path on an 18 dimensional energy surface; this reaction path has to be chosen as a function of one or, at most, two parameters. It turned out that the easiest way to do this, is to start from one of the complexes reported in Section 3; actually, this was the main reason for calculating these cornplexes. The se­lection of a particular complex is made by considering two aspects. Firstly, the geometry of the complex must be product­like; otherwise the reaction coordinate will be too long and uncontrollable. Secondly, the interatomic electron densities 20

(i.e.d.) in the complex can be taken as indication where bond forrnation can occur. So, the i.e.d. helps to define the reaction coordinate. Then, the energy is calculated as a function of this coordinate; at every point of the reaction the geometry is completely optimized.

46

GZyaoaZdehyde

Complex J.,t is an attractive candidate for the formation of glycoaldehyde. As indicated in Scheme II, we calculated several reactions for 12. ,.....,

11 b,

E:-4.41 kcal/mol

E =high

E =high

H4' ·c=o

/ . '• . ' 1 '

H • H ' : /"

c.:..:..:...:o' H/

-

E=+ 1.96 kcal/mol

Scheme II

/

47

The first main path (1) is the one which can be expected in carbene chemistry 49 • The reaction leads to the insertion into a C-H bond. We took two reaction parameters: the c1c3 and c3tt6 distances. A rather extensive scan of the 2-dimensional potential energy surface as a function of these parameters was performed; we note once more that all the other parameters were completely optimized. If we start from J..t, and decrease both parameters, we will obtain a 4-electron three-center, cyclic transition state (1a). Such a transition state was originally presumed for this type of reactions 50 • 51 • A second mechanism (1b) was suggested by Benson 52 • 53 • He proposed an abstraction-like insertion: the carbene initially attacks the hydrogen atom. Then, the two alkyl radicals give C-C bond formation. This mechanism was theoretically supported by Dobson 54 in his study on singlet methylene. We scanned the energy surface for reaction (1b). However, we didn't find low harriers for path (1): if we move into this direction, the energy increases steeply. We didn't determine the transition state energy exactly; it is, however, definitely larger than 60 kcal/mol. So, neither the three-center transition state (1a), nor the abstraction-like way (1b) is possible. Instead of that, we found that decreasing the c1c3 distance leads to an increasing i.e.d. for o2H8• This leads to reaction (2), where we have a 6-electron five-center, cyclic transition state. H8 is transferred from the hydroxy­carbene to the formaldehyde. In Figure 4 we give for this reaction the i.e.d. and energy as a function of c1c3 ; the picture given there is also typical for other reactions in this paper. In J.l the strongest intermolecular interaction is the o2H8-hydrogen bond. So, it is not surprising that for larger c1c3 values the energy surface is rather flat as a function of this parameter. A further decrease of c1c3 results in a simultaneous change of electron densities between c1c3, o2H8, and o4H8. This gives a real cyclic transition state. The energy harrier is small: starting from ~we need 6.37 kcal/mol.

48

t 0.3

l.e.d.

0.2

0.1

4.0 3.0 2.0

t +2

E 0 • kcal/mol • • -2 ' • •

-4 • .

4.0 3.0 2.0

Figure 4 Energy (kcal/mol) and i.e.d. for ,1,.t -l~l-> glycoaldehyde as a ftm.tion of c1c3 (.X). The energy reference level is the ST0-3G value for non-interacting H2CO + HC<:H-trans: -224.63276 a.u.

This harrier is 1.96 kcal/mol higher than the dissociation energy for !.6· The final products of (1) and (2) are the same; experiments with mixtures of, for instance, n2co + H2co might give, in principle, an experimental verification of the distinction between these two reaction paths. It is easily seen that, starting from n2co + HCOH; reaction (1) leads to a racemic mixture with c3 as the asymmetrie carbon, whereas in (2) chirality is absent.

49

There is one other interesting starting complex to form glycoaldehyde: fo_g. We found that, in this case, a C-H insertion is possible according to the abstraction-like path (1b): the hydrogen atom shifts towards the carbene before the C-C bond is formed. However, the energy harrier is still high: starting from 20 it demands 42.2 kcal/mol.

rv

H

' C=O '3 l /

H \\'"*"' C --/ OH

H

20 ,.,._,,

E = - 0.82 kcal/ mol E : + 41.4 k co 1 I mol

Methanol + aaPbon màno~ide

The complexes J...1 and !.§ are interesting possibilities for the. formation of methanol and carbon monoxide. Starting from the cis-complex J...1• we scanned the energy surface as a function of the o2H8 and c1H7 distances; all the other parameters were optimized. We found a transition state just 10.4 kcal/mol above the starting complex. The transfer of hydrogen atoms H7 and H8 occurs in a nearly simultaneous way; the increase

(41 +

co

E = - 3.24 kcal/ mol E= + 7.18 kcalfmol

50

in o2H8 i.e.d. is slightly ahead of the formation of the c1H7 bond. The transit.ion state is of the same type as for reaction (2): a 6~electron cyclic state. In complex J.é the CO bonds of formaldehyde and hydroxycarbene are antiparallel. For reaction (5) we couldn't find a low-lying transition state to products.

(Sl ? +

co

E = - 4.71 kcal 1 mol E = high

Methylformate

Methylformate is a third possible product from two formal­dehydes. Among the complexes from Section 3, there is no clear candidate as a starting geometry. In this case we put H2co and HCOH-trans as indicated below, and calculated

H~ "'·c-· o

H/\ \_H H O~

E =+ 35.1 kcal/mol

51

reaction (6). It was necessary again to take a combination of two reaction parameters: c1H7 and o2c3• If one only takes, for instance, the c1H7 distance as a reaction coordinate, the o2c3 distance will increase upon optimization, and no product formation occurs. The calculation showed that the addition reaction is abstraction-like (compare with (lb) and (3)). This fact is illustrated in Figure 5, where we give the most im­portant i.e.d. as a function of the o2c3 distance. In the

i.e.d.

0.5

0.4

0.3

0.2

0.1

o.o ex>

(co)

2.2 2.0 ( 1.981 ( 1.55 I

1.8 (1.381

1.6 1.4

Figure 5 Most important i.e.d. for HzCO + OCOO-trans J~2> methylfonnate as a famction of the o2c3 distance. Some optimized c1H7 distances are given between brackets. The arrow indicates the transition state (TS)

52

transition state (TS) electron density has shifted from o4H7 to c1H7, while the nature of the two CO bonds is intermediate between single and double bond. Most of the changes in i.e.d. occur after passage of the high energy harrier (35.1 kcal/mol, relative to tt2co + HCOH-trans).

The results are summarized in Table VIII. In our model, s1-excitation of formaldehyde produces a H2co ... HCOH complex. The energy of this complex, relative to 2H2co, is given in the first column. The second column gives AE: the calculated ST0-3G harrier to the addition product. For (2) and (4) we

Table VIII. Calculated energies (kcal/mol) for the fonnation of addition

products from HzCO + llXll

reactant product ~· reactant

AEb Ea product

12 _.en..,. glycoaldehyde 43.2 high -33.5 ""J

12 --'~1..,. glycoaldehyde 43.2(45.0f 6.4 ( 6.1)c -33.5 -20 _.(~1-> glycoaldehyde 52.7 42.2 -33.5 ,.._,.

14 _.(!1-> HfOH +CO S0.3(53.3f 10.4 (14.S)c -40.6 "" 16 _fäl-> H3CCll + CO 48.8 high -40.6 ,..._

H2

CO+HCOH _.(§1""> methylformate 47.7 35.1 -54.6

a)Relative to 2 HzCO (=-224.70870 a.u.); b) AE = E (Transition State) -

Er~actant; c)Recalculated with 4-31G basis set

recalculated the reaction using a 4-31G basis set. The Table shows that the results are virtually unchanged. We also calculated whether or not the basis set superposition effect (see Section 3.2) has an influence on the energy harrier. This could be the case because the error introduced by this

53

effect might be different in the starting complex and near the transition state. Fortunately, this turned out not to be the case; the superposition error as a function of the reaction coordinate is nearly a constant. All reported transi­tion states are genuine stationary points on the energy sur­face. This follows from the fact that a vibrational analysis according to the methods of Section 3.3 resulted in a single imaginary vibrational frequency. The calculated frequencies also showed that the differences in zero-point energy of reactants and transition state result in a small increase (< l kcal/mol) of the harrier heights. The results in Table VIII clearly show that hydroxycarbene indeed is an attractive precursor to glycoaldehyde and methanol. The formation of methylformate is much more di'ffi­cul t: it asks for a high activation energy. This gets support from the matrix experiments: glycoaldehyde and methanol are easily formed, hut no methylforrnate was detected. It is interesting to note that the activation energies for (2) and (4) are slightly higher than the dissociation energies of the starting complexes. This means that in gas phase the complexes will dissociate; free HCOH might give then molecular (Hz + CO) and radical (H + HCO) products. When the complex is confined to a rigid matrix, dissociation is not possible and the lowest activation energy is the one leading to an addi­tion product. Concerning the point that glycoaldehyde was only reported 7 in relatively concentrated matrices we note that it is possible that glycoaldehyde is also formed at higher dilutions, but that it is photolyzed itself 8 to carbon monoxide and methanol.

5. The rearrangement H2co~HCOH

In this Section we describe two types of bimolecular inter­actions which can be involved in the H2co + HCOH rearrange­ment: harrier lowering and hydrogen exchange. A discussion on the applicability in formaldehyde photochemistry will be given in Section 6.

54

5.1. Barrier lowering: H2co + M + HCOH + M

Very accurate calculations on the unimolecular rearrangement H

2co + HCOH were recently published by Goddard and Schaefer 10 • 1 ~

The energy relative to the formaldehyde ground state required for this reaction was calculated to be 84 kcal/mol at the Double Zeta + polarization + CI level with the inclusion of zero point corrections. This seems to be a rather ultimate value for the harrier. Unfortunately, this is still slightly above the s1 origin (80.6 kcal/mol), where photochemical dissociation definitely occurs. Recently 55,Miller showed in an elegant paper how to include tunneling corrections in uni­molecular rate constants. He suggests, that tunneling is quite significant in formaldehyde photochemistry, both for the direct molecular dissociation (H2co + H2 + CO) and for the hydroxycarbene rearrangement. As we wrote in an earlier paper 12 however, tunneling has the inherent difficulty of being extremely sensitive to the parameters involved (potential energy curves, etc.). So, it is probably possible to para­metrize these factors in such a way that the observed decays and also the differences between H2co and n2co can be ex­plained. It is difficult however, to judge how realistic such a treatment is. We also suggested in our earlier paper 12

an alternative (or additional) explanation for the harrier problem: we suggest that unimolecularly there is no rearrange­ment, hut a second formaldehyde molecule lowers the effective harrier. We took the flat transition state (HCOH) of the tt2co + HCOH rearrangement and placed the second (catalyzing) molecule in such a way that thè migrating hydrogen interacts with the oxygen lone pair of the catalyst (see also Figure 6b). The lowering effect from a partially optimized 4-31G calculation was reported to be 7.7 kcal/mol. This seemed to be much too small to form an attractive alternative, because our unimolecular harrier was as high as 102 kcal/mol. However, in view of Goddard's much lower harrier, a birnolecular effect of several kcal/mol is very substantial. Therefore we re­investigated the harrier lowering. We will improve two aspects

55

of our older study: all possible orientations of H2co, rela­tive to HCOH, will be studied and we will use, if necessary, a larger basis set and complete optimization. First, we calculated the energy surface for the unimolecular rearrange­ment H2CO-HCOH as a function of the angles e and ~ (see Figure 6a). The other parameters were optimized. The 4-31G result is shown in Figure 7. Optimizations in critical regions with 6-31G~ showed that the characteristics of the surface are unchanged if one uses this larger basis set. Modes with an inversion of H3 towards the other side of the molecule resulted in high energy barriers, as already found by Altmann et aZ. 56 • Contrary to her results, however, Figure 7 shows that a concerted rearrangement to cis hydroxy­carbene does not have a harrier much higher than the one leading to HCOH-trans. This is shown by the fact that the energy surface is relatively very flat for w between 55 and 65 degrees. For instance, an out-of-plane movement of H4 by 60 degrees costs only ~ 8 kcal/mol; this is in agreement with

oJ b)

Figure 6 Geometries for uni- and bimolecular rearrangements

56

the results of Goddard and Schaefer 10 • We note that with the ST0-3G basis set there even is no real stationary point at e = 0 degrees: the transition state lies at ~ = 62 and e = 70.

What is of special interest here is the fact that, although the energy of the transition state changes little upon in­creasing the out-of-plane angle, the character of the molecule changes remarkably. There are two ways to stabilize the car­benic-like transition states: at the carbenic centre and directly at the shifting hydrogen. Let us first see what a priori predictions can be made concerning these interactions and use for this purpose the results from Section 3. We start with the stabilization of the carbenic centre. Moss et al. 51

recently introduced the concept of ambiphilicity in the carbenic selectivity spectrum.They showed experimentally that

methoxy-chlorocarbene reacts in an electrophilic way with methyl-substituted ethene, while it acts as a nucleophilic carbene towards ctt2 = CHCOOMe and ctt2 = CHCN. This behaviour correlates very nicely with the HOMO-LUMO orbital energies of

f 160

8 120

80

40

0 F

120 100 80 60 40 20

"1-Figure 7 4-31G surface for HzCO --- HCOH. F = fomaldehyde, T = HCOH-

trans, C = HCOH-cis. The lines are in kcal/mol relative to F

57

carbene and reactant: if e.g. the difference LUMO-carbene/ HOMO-alkene is small, the reaction is an electrophilic addi­tion, and viae vePsa. According to these criteria, hydroxy­carbene is a second example of an ambiphilic carbene 58 • Let us now apply these simple principles to three structures: H2co, the planaP transition state HCHO (e = 0, and ~ = 55: TS-pl), and a non-planaP. structure (9 = 70, and~= 60: TS-np), which lies some kcal/mol above the transition state. The 4-31G HOMO energies are -11.99, -9.95, and -10.08 eV, and the LUMO's lie at 3.62, 3.01, and 1.90 eV, respectively. Simple subtraction shows now that TS-pl will preferentially have a nucleophilic interaction with H2CO, i.e. with the~~ molecular orbital 59 , The interaction between TS-np and tt2co is ambiphilic: the interaction with the formaldehyde n orbital is as large as the one with ~~. This predicts that for TS-np there are more orientations of H2co which lead to a stabilizing interaction with the carbenoid than for TS-pl. For the second source of stabilization, the direct interaction with the shifting hydrogen, another difference between TS-pl and TS-np is relevant. In Section 3 we showed that charge effects are important in the formation of complexes. The shifting atom H4 has a positive net charge in the transition states; with all basis sets this charge in the flat structure TS-pl is considerably higher than in TS-np. This agrees with the more nucleophilic character of the carbenic side of TS-pl, because a smaller electron density at H4 means, of course, a higher density at the other atoms. So, for TS-pl we expect a stronger interaction with an electron-rich side of H2co, especially with the oxygen !one pairs. The relative strength of the two interactions is difficult to predict. Recall from Section 3.1, however, that of the seven most stable complexes between H2CO and HCOH there is only one (J .. ~) where in the interaction the HCOH-carbon is involved. So, we expect that the direct inter­action with H4 gives rise to higher stabilization. These pre­dictions are completely confirmed by our calculations. We took TS-p!, TS-np, and an intermediate state between them

58

(0= 30, and w = 58); this third structure also lies on top of the "mountain ridge" between formaldehyde and hydroxycarbene. Then we placed at a large number of orientations a second molecule and optimized the structure while a and w were kept fixed. A stabilizing interaction between the transition state and the quencher gives an effective lowering of the harrier. To check if the ridge shifts to another value of w, we also calculated at several neighbouring points of the transition states. We conce?trated on formaldehyde itself as a quencher, but also did some calculations with H2o, CO, and H2 as a quenching molecule. We found a fairly large number of "com­plexes", most of them are stabilized by 0.5 to 3.5 kcal/mol. We discuss these structures only briefly. For the bent transition states (e = 30, and e = 70), there are indeed more orientations with a stabilizing interaction with the carbenic carbon than for TS-pl. With molecular hydrogen we didn't find interactions; with water or formaldehyde as a quencher the stabilization is slightly larger than with carbon monoxide.

When stabilization is due to the interaction with the shifting hydrogen, the harrier lowering indeed increases for lower e-values. Complexes stabilized by 1-4 kcal/mol were obtained with H2o, CO, and H2co. For this type of interaction we found one orientation which gives by far the largest energy lowering: it occurs when the planar transition state TS-pl interacts with the oxygen lone pair of a second formaldehyde. We discuss this structure, which was partially 4-31G optimized already in an earlier study 12 , in more detail. The structure is sketched in Figure 6b; the main features are given in Table IX. The Table shows that there is a substantial harrier lowering. The c1H4 distance is lengthened considerably by the interaction; we note_, however, that the energy surface as a function of this parameter is flat near the transition state.

59

Table IX. Uni- and bimolecular transition state tt2co ---> HCOH.

See Figure 6b for the atom numbering

ST0-3Ga 4-3lG/ST0-3Ga 4-31G 6-31G*/4-31G 6-31G*

unimolecular

E (kcal/mol)b 128.4 109.4 110 .2 105 .1 104.6

OzC1H4 57.3 57.3 55.0 55.0 56.3

C1H4 (~) 1.208 1.208 1.266 1.266 1.219

bimolecular

E (kcal/mol)b 117.4 98.7 94.0c 95.3 95.0

OzC1H4 60.4 60.4 55.0c 55.0 59.0

c1H4 (~) 1.272 1.272 1.645c 1.645 1.638

stabilization 11.0 10.7 16.Zc 9.8 9.6 in kcal/mol

a)As in Table I; b)Energies relative to HzCO;c) Partially optimized results

from reference 12: E = 102.5, o2c1H4 = 55, c1H4 = 1.319, stabilization = 7.7

The Table also shows that the transition state angle o2c1H4 shifts to a slightly larger value. The i.e.d. values for c1tt4 , o2H4 , and 0 3H4 show that i~ the transition state H4 is shared by c1 , o2 , and o3 : all three i.e.d. are about the same. There is a significant charge transfer from the catalyzing formaldehyde to HCOH (6-31Gx: 0.18 electrons). The analogous stabilization in the out-of-plane transition states is, as expected, considerably lower. We conclude here that this bimolecular interaction is strong enough to bring the harrier to trans-HCOH below the formal­dehyde s1 level. The formation of the cis-isomer costs a few kcal/mol more. Excitation with shorter wavelengths than corresponding to the lowest vibrational levels of H2co (S 1)

60

will be able however, to produce cis-HCOH; the larger number of stabilizing orientations can manifest itself then. In Section 4 we showed that trans-HCOH is a suitable precursor to glycoaldehyde, while methanol is easily formed from the cis-isomer. So, product formation studies as a function of excitation energy might give valuable information. Also the vibrational mode of the formaldehyde molecule will be im­portant: if the accepting mode which is reached after the radiationless transition is an in-plane mode, trans-HCOH will be formed via the planar transition state. If, on the other hand, the out~of-plane vibration is highly excited, more cis-HCOH will be produced via a non-planar transition state. Finally, if we recall the tt 2co + H2co complexes from Section 3.1, it is seen that the centrosymmetric complex ,.l is the most natural precursor to the transition state given in Figure 6b. In Section 3.3 we showed that ,lis the best candidate for the (H2Co) 2 structure in matrices. The fact that precisely this matrix structure leads to the highest harrier lowering is another indication for the involvement of dimeric interactions.

5.2. Hydrogen exchange: ZHCOH + 2H 2co

As described in Section 2.2 the dissociation of a transition

metal-carbene complex will result in the formation of HCOH. Part of these molecules will reach the vibrationless level at 52.8 kcal/mol. From there, unimolecular rearrangement to H2co is practically impossible. Experimentally, however, no hydroxy­carbene is detected. A bimolecular way to transform HCOH-trans into tt2co is a hydrogen exchange mechanism:

61

H

" c--o

" H

H

" o--c '\_H

(:::tronsition statel

In Section 3.1 we reported that two HCOH-trans forma very stabilized complex (complex ~ from Table II). This structure is very much like the transition state which we expect for 2HCOH ~ 2H2co. We took ~ as a starting point for our cal­culations. Table X shows the results. We calculated the potential energy surface as a function of the c1H6 and c3H8 distances. At each combinatiOn of these parameters we opti­mized, as usual, all other parameters. Two hydroxycarbenes give, without an energy harrier, complex ~· The stabilization energy is nearly the same in all basis sets: ~ 19 kcal/mol. A further decrease of the CH-distances leads to the transi­tion state between À.! and 2H2co. As shown in the last column of Table X, this transition state only lies a few kcal/mol above 21. So 21, (HCOH) 2, is a relatively shallow minimum on ,......,. ,...._,, the energy surface. This is illustrated in Figure 8. When two HCOH molecules form (HCOH) 2, the released stabilization energy will cause the system to overcome easily the harrier to formaldehyde. We note that the hydrogen exchange is nearly symmetrie (C 1H6 ~ c3H8 during the reaction). The ST0-3G harrier for the completely symmetrie (C 2h) exchange is only slightly larger than the asymmetrie one. For the larger basis sets we limited

62

Table X. Energies (kcal/mol) for the reaction 2 HCOH-tr. ---> (HCOH) 2 ---> 2 HCO 2

complex 21b harrier from 2 HCOH-tr.b

'VU

basis seta (HCOH)z ~to 2 HzCO

ST0-3G 95.3 75.5 1.4 (1.8)c 4-31G/ST0-3G 105.5 83.7 7.4

4-31G 102.3 84.8 2.9c

6-31G*/4-31G 105.3 88.3 5.7c

6-31G* 103.9 85.4

a)As in Table I; b)Relative to 2 H2CO; c) Fora symmetrically exchange. See text

kcal I Mol

901 94 . \\

80

78

76

74

12

10 2HCOH

• • •

( HCOH 12 ' ' ' ' '

~5 \-----·---· --·-5 J >·-1.80 1.60 1.40 1.20 2.00

CH(lJ

Figure 8 ST0-3G potential energy surface for 2 HCOH-trans ---> (HCOH) 2 ---> 2 H2co. The experimental s1 level of H2co is indicated

for comparison

63

our calculations to c2h symmetry. We also determined the i.r. and Raman frequencies of À.! according to the method described in Section 3.3. This confirmed that ~is a true stationary state (no imaginary frequencies). We merely remark, that the frequencies and modes are intermediate between the ones for H2co and HCOH; this agrees with the highly stabilized characte1 of 21. ,.....,

6. Conclusions and Discussion

We will now return to the model offered in Section 2.2. Our calculations show that unimolecular formation of HCOH is difficult; only tunneling 55 might give a possible way to reach HCOH from the vibrationless s1 level. The bimolecular interactions described in Section 5.1 lower the harrier to hydroxycarbene considerably (reactions (1) and (3) in Scheme I). Once HCOH is formed, the formation of addition products is easy (reaction (2)). Glycoaldehyde is formed via a five­center cyclic transition state and not via the expected CH­insertion; methanol and carbon monoxide are other possible products. In dissociation experiments with transition metal­carbene complexes the HCOH concentration can be relatively higl In that case a hydrogen exchange between two hydroxycarbenes occurs (reaction (4)). This offers a low energy path for

HCOH + H2co. If one irradiates H2co, the concentration of HCOH will be too low to make such an exchange likely. In that case the HCOH .. ~H2 co complexes can dissociate in gasphase experiments. The liberated HCOH then gives molecular and radical photoproducts. In a rigid matrix dissociation of HCOH .•. H2co is not possible; here the lowest harriers are the ones leading to the addition products. The easiest way to form HCOH is the harrier lowering des­cribed in Section 5.1. This mechanism approaches a collision complex (chemica!) model. Of course, also purely kinetic (physical) collisions can produce HCOH: Zughul 1 showed that He, Ar, and Xe give CO nearly as rapidly as collisions

with H2co itself. Houston 2 reported however, that Ar induces

64

photoproducts from n2co much slower than n2co itself. At excitation energies higher than = 90 kcal/mol a direct pro­duction of (HCOH) 2 becomes possible via the exchan~e mechanism (see Table X). We note that this mechanism also can play a role in "strange" hydrogen shifts as, for instance, vinyl­alcohol-acetaldehyde60. The high unimolecular harriers can be avoided by bimolecular hydrogen exchange. A similar problem exists in the H-shift of N2tt2

61 • 62 • Summarizing, the model offered in Scheme I explains a large number of experimental facts. Hydroxycarbene is a natural precursor to addition products. Although a tunneling-induced interconversion HCOH..,._...H2co might be rapid, the products will be formed from the most reactive isomer. Of course, calculations alone cannot prove the existence of HCOH. Weisshaar 3 measured i.r. fluorescence after 4ci excitation of H2co in order to observe the intermediate state. It was not possible, however, to detect the short-lived emission of the hydroxycarbene OH stretch. This was due to the "quasicontinuum" emissions of highly vibrational s0~ states, which are produced after non­reactive quenching. (The quantum yield for product formation was about 0.7). We suggest that hydroxycarbene might be detectable in interstellar space, where there are truly unimolecular conditions, without perturbations of emitting s0 ~ states. Formaldehyde is widely observed in the galaxy at radio wave lengths; it occurs in both high and relatively low density interstellar clouds 63 • The H2CO-HCOH situation can be analogous to the well known HCN-HNC case. Hydrogen isocyanide was observed for the first time in interstellar space 6 q; in the laboratory the molecule rearranges easily to HCN. Also some other experiments are suggested from our theoretica! results. Infrared and Raman frequencies of (H 2C0) 2 should be re-measured, preferably in a molecular beam. Matrix experiments with isotropic mixtures give information about the mechanism of addition reactions. Product formation as a function of excitation energy can clarify the relative im­portances of cis- and trans-HCOH. In this paper more attention

es

is given to trans-HCOH, because this is the energetically most favoured isomer. We feel that calculations on cis-trans interactions, as were done e.g. by Pasto 62 for N2tt2, have to wait until more experimental data are known. The uni- and bimolecular formation of gasphase photoproducts from HCOH is another interesting topic for calculations. To describe the

radical and molecular dissociation on an equivalent level, the inclusion of correlation effects will be necessary. We note that in matrix experiments 8 no indication for the in­volvement of radicals is reported. In this paper, we limited ourselves to relatively simple

ab-initio methods. For a starting point this is necessary, because fairly large sections of the potential energy surface of an eight-atom molecule have to be calculated. Fortunately, however, the experimentally verifiable results (stabiliza­

tion energies, i.r. and Raman spectra) are very good, while the cases where we used several basis sets show that the results essentially do not change in going from minimal ST0-3G to 6-31Gx.

Our results primarily concern gasphase and matrix studies. However, aqueous solutions of formaldehyde also show very interesting reactions. In the so-called formose reaction65

an aldol-type condensation results in the formation of hydroxy aldehydes, hydroxy ketones, and sugars. The interest in this reaction recently increased, because of its possible importance in the production of carbohydrates in spaceships 66 •

6

From this reaction some investigators even concluded 65 that

formaldehyde is involved in photosynthesis. Especially the origin of glycolate, H2C(OH)COOH, taxed many rninds 68 until the problem was solved by Tolbert 69 • In most formose experi­ments Ca(OH) 2 is used as a catalyst, but ultraviolet light can also be used for inducing the reaction. The mechanism is

an autocatalytic one; the slow primary formation of glyco­aldehyde is the rate determining step. Once this c2 fragment

is formed, more formaldehyde molecules can be added to it. It will be clear that our results suggest that HCOH can be

66

involved in these reactions, especially in the primary con­densation to glycoaldehyde. Theoretica! studies, however, will have to use semi-empirica! methods, because the situation in the liquid phase is much more complicated: the actual reactant in aqueous solution is not H2co, but hydrated formal­dehyde (methylene glycol).

REFERENCES AND NOTES

(1) Houston,P.L.; Moore,C.B. J.Chem.Phys. 1976,65,757

(2) Zughul,M.B. Ph. D. Dissertation. U.C. Berkeley 1978 (3) Weisshaar,J.C. Ph. D. Dissertation. U.C. Berkeley 1979

(4) van Dijk,J.M.F.; Kemper,M.J.H.; Kerp,J.H.M.; Buck,H.M.

J.Chem.Phys. 1978,69,2462

(5) Heller,D.F.; Elert,M.L.; Gelbart,W.M. J.Chem.Phys. 1978,69,4061

(6) Tang,K.Y.; Fairchild,P.W.; Lee,E.K.C. J.Chem.Phys. 1977,66,3303

(7) Diem,M.; Lee,E.K.C. Chem.Phys. 1979,41,373

(8) Sodeau,J.R.; Lee,E.K.C. Chem.Phys.Letters 1978,57,71 (9) Molina,L.T.; Tang,K.Y.; Sodeau,J.R.; Lee,E.K.C.

J.Phys.Chem. 1978,82,2575

(10) Goddard,J.D.; Schaefer III,H.F. J.Chem.Phys. 1979,70,5117

(11) Pople,J.A.; Krisfinan,H.B.; Schlegel,R.; Binkley,J.S. Int.J.Quant.Chem~ i978,14,545

(12) Kemper,M.J.H.; van Dijk,J.M.F.; Buck,H.M. J.Am.Chem.Soc. 1978, 100,7841 (13) Due to a calculational error, the reported value in reference 10 of

89 kcal/mol, is incorrect and should be 84 kcal/mol. H.F. Schaefer III

at the "Discussion meeting on photodissociation of polyatomic

molecules", Veldhoven, The Netherlands, december 1979.

(14) Fischer,E.O. Adv.Organomet.Chem. 1976,14,1

(15) Lucchese,R.R.; Schaefer III,H.F. J.Am.Chem.Soc. 1978,100,298

(16) Hehre,W.J. et.al. QCPE 1973,11,236

(17) Pople,J.A. et.al. QCPE 1978,11,368. We thank dr. G.J.Visser for adaption of this program to the Burroughs B7700 computer

(18) DelBene,J.E. J.Chem.Phys. 1974,60,3812

(19) DelBene,J.E. J.Chem.Phys. 1973,58,3139

(20) Our GAUSSIAN70 program calculates interatomic electron densities

(i.e.d.) between àtoms a and bas EE (E N.c .. ck.) s.k • Here j and k jk i 1 J1 1 J

68

are the atomie orbitals on the atoms a and b, respectively; i is a

molecular orbital with occupation number Ni and coefficients C; Sjk is the overlap integral <jlk>. This expression can be taken as a

measure of the strength of a bond between two atoms; it is half the

so-called Reduced Overlap Population as defined in:

A.G. Turner, ''Methods in molecular orbi tal theory", Prentice-Hall,

New Jersey, 1974.

(21) Kollrnan,P.A. in ''Modern Theoretica! Chemistry. Vol. 4", H.F. Schaefer

ed., Plenl.Dll Press, New York&London, 1977.

(22) Schaad,L.J. "Hydrogen bonding", Marcel Dekker inc., New York, 1974 , (23) Boys,S.F.; Bernardi,F. Mol.Phys. 1970, 19,558

(24) Ahlström,M.; Jönssen,B.; Karlström,G. Mol.Phys. 1979,38,1051

(25) Popkie,H.; Kistenmacher,H.; Clementi,E. J.Chem.Phys. 1973,59,1325

(26) Matsuoka,O.; Clementi,E.; Yoshimine,M. J.Chem.Phys. 1976,64,1351

(27) DelBene,E. J.Chem.Phys. 1971,55,4633

(28) Curtiss,L.A.; Frurip,D.J.; Blander,M. J.Chem.Phys. 1979,71,2703

(29) Lischka,H. Chem.Phys.Letters 1979,66,108

(30) Curtiss,L.A.; Pople,J.A. J.Mol.Spectry. 1976,61,1

(31) Franck,E.U.; Meyer,F. J.Electrochem. 1959,63,577

(32) Pulay,P. in ''Modem Theoretica! Chemistry. Vol. 4", H.F. &haefer ed.,

Plenum Press, New York&London, 1977.

(33) Bock,C.W.; George,P.; Trachtman,M. J.Mol.Spectry. 1979,78,248

(34) Bock,C.W.; George,P.; Trachtman,M. J .Mol.Spectry. 1979, 78 ,298

(35) Blom,C.E.; Altona,C. Mol.Phys. 1976,31,1377 and related papers.

(36) Rytel,A.; Rytel,M. Opt.Spektrosk. 1966,21,61

(37) Rytel,M. Opt.Spektrosk. 1964, 16,402

(38) Schwendeman,R.H. J.Chem.Phys. 1966,44,2085

(39) Wilson,E.B.; Decius,J.C.; Cross,P.C. ''Molecular vibrations",

Me Graw-Hill, New York, 1955. We thank dr. D.L.Vogel for making

available the necessary programs.

(40) Ramsay,D.A.; Till,S.M. Can.J.Phys. 1979,57,1224

( 41) Job,V .A.; Sethuraman,V.; Innes ,K.K. J .Mol.Spectry. 1969 ,30 ,365

(42) Newton,M.D.; Lathan,W.A.; Hehre,W.J. ~ Pople,J.A.

J.Chem.Phys. 1970,52,4064

(43) Khoshkhoo,H.; Nixon,E.R. Spectrochimica Acta 1973,29A,603

(44) Schneider,W.G.; Bemstein,H.J. Trans.Faraday Soc. 1956,52,13

(45) Curtiss,L.A.; Pople,J.A. J.Mol.Spectry. 1973,48,413

69

(46) Curtiss,L.A.; Pople,J.A. J.Mol.Spectry. 1975,55,1 (47) Dyke,T.R.; Mack,K.M.; M\ienter,J.S. J.Chem.Phys. 1977,66,498 (48) Calvert,J.G.; Steacie,E.W.R. J.Chem.Phys. 1951, 19, 176 (49) Bethell,D. Adv.Phys.Org.Chem. 1969,7,153 (50) Skell,P.S.; Woodworth,R.C. J.Am.Chem.Soc. 1956,78,4496 (51) von Doering,W.; Prinzback,H. Tetrahedron 1956,6,24 (52) Benson,S.W. Advan.Photochem. 1964,2, 1 (53) DeMore,W.B.; Benson,s.w. Adv.Photochem. 1964,2,219 (54) Dobson,R.C.; Hayes,D.M.; Hoffmann,R. J.Am.Chem.Soc. 1971,93,6188 (55) Miller,W.H. J.Am.Chem.Soc. 1979,101,6810 (56) Altmann,J.A.; Csizmadia,I.G.; Yates,K.; Yates,P.

J.Chem.Phys. 1977,66,298 (57) Moss,R.A.; Fedorynski,M.; Shieh,W.C. J.Am.Chem.Soc. 1979,101,4736 (58) This is easily seen by comparing our 4-31G calculated HCMO and UJMO

energies of trans-HCOH (-9.81 eV and 3.53 eV, respectively) with the values given in reference 57. For the reaction with CH2=CHCN the difference H(]v[)-carbene/UJMO-reactant is small, so the carbene reacts in a nucleophilic way. The reaction with Me2C=CMe2 is electrophilic. The same arguments hold for cis-HCOH.

(59) For an instructive illustration of these MO's, se for instance: Jorgensen,W.L.; Salem,L. '"The organic chemist 's book of orbitals", Academie Press, New York, 1973

(60) Bouma,W.J.; Poppinger,D.; Radom,L. J.Am.Chem.Soc. 1977 ,99,6443 (61) Parsons,C.A.; Dykstra,C.E. J.Chem.Phys. 1979,71,3025 (62) Pasto,D.J. J.Am.Chem.Soc. 1979,101,6852

The reaction 2 H2N2 <---> 2 HNNH-trans, whidi is completely analogous to 2 H2co <---> 2 HCOH-trans, is not reported by the author. Our preliminary calculations show, that this rearrangement occurs very easily.

(63) Watson,W.D. Rev.Modem Phys. 1976,48,513 . (64) Snyder,L.E.; Buhl,D. Bull.Am.Astron.Soc. 1971,3,388 (65) Walker,J.F. "Formaldehyde", Reinhold, New York, 1964 (66) Weiss,A.H. Sci.Tech.Aerosp.Rep. 1976,14,n76-16177 (67) Kolesnik,L.V.; Shul'gina,I.L. Aktual.Vop.Kosm.Biol.Med. 1971,137

70

(68) Gregory,R.P.F. "Biochemistry of photosynthesis", John Wiley, New York, 1977

(69) Tolbert,W.E.; Ryan,F.J. Proc.IIIrd.Int.Cong. on Photosynthesis, M.Avron ed., Elsevier, Amsterdam, 1974

71

72

IV. THE CALCULATION OF

RADIATIVE

TRANS IT ION S

IV .1

Ab initia Cl calculation of single vibronic level fluorescence emission spectra and absolute radiative lifetimes of H2CO (1AJ

M. J. H. Kamper, J. M. F. van Dijk,•> and H. M. Buck 0.partmtnt of Organic Chtm/Jtry, Eindltovtn Uniutrsity of Ttehno/og)I, Eindh0utn. The Netherlands (Received 26 September 1978)

Overlap intepals and dipole lnmlition moments wbich were obtained by an ab initio Cl calculation are used for the calculation of ftuorescence emission spectra and absolute radiative lifetimes of single vibronic levels of H200 (1 A,). The ..,..ment betwoon calculation and experiment is fairly good. The analysis of the results shows tbat a large fraction of the total emission intensity is due to low-intensity transitions and honds at wavelengths largor than 460 nm. The implicaticos of Ibis roswt for the dotonnination of fluoracenco qmntum yields and ndiativo lifotimes are discussod.

1. INTRODUCTION

The radiative transition between two single vibronic levels (SVL) of the electronic growld and first excited state of formaldehyde is described1 by the total dipole transition moment D:

D= J1 <x..CQ.)IDCQ.>lx"(Q.))o.<x..CQ.>lx1.<Q.)}o.• (1)

where D(Q.) is the electronic dipole transition moment, which induces the transition; x.,(Q•) is the qth vibra­tional wave function of normal mode k in the growld state, and x11(Q•) is the pth vibrational wave function of normal mode kin the first excited state. The subscript Q. denotes integration over normal coordinate Q., and the product runs over the normal coordinates. In a re­cent paper, 1 hereafter to be denoted as Paper I, we publlshed all the lntegrals occurring In Eq. (1) and cal­culated from them the "cold" (n,,.) absorption spec­trum, 1. e. , the absorptlon spectrum resulting from the vibrationless groilnd state level. The potentlal energy surfaces, which determine the vibratlonal wave func­tions, were obtained from an ab initio Cl calculation; the anbarmonic vibratlonal wave functions themselves were numerically determined on these potential energy surfaces. The most important quantlties in Eq. (1), the electronic dipole transition moments D(Q.), were expllcitly calculated as functions of the nuclear geom­etry. Tbrougbout the calculation we used the dipole lenglh expression for D(Q,)1:

where <Po and </> 1 are the electronic ground and first ex­cited state, reapectively; q1 stands for the Carteslan coordinates of electron i.

In Paper I, we sbowed lhat for the descrlption of radiative transitions, the dipole length expresslon Is superior to the dipole acceleration form of the elec­tronic transltion moment. Every nuclear geometry used in the calculation gives a D(Q.l value; cublc apllne func-

.,Present address: Philips Research Laboratories, Eindhoven, The Netherlands.

tions are fitted to these values and the result is sub­stituted In Eq. (1).

From the integrals obtained in lhis way, il is also possible to calculate the fluorescence emlssion spec­trum resulting from a SVL in lfaCOC'A2); a calculation completely analogous to the one given in Paper I for the cold absorption spectrum.

The lntenslties of the varlous translttons are propor­tional to the oscillator strenglhs,

/=~AEIDI',

where D is the total dipole transition moment from Eq. (1) and AE Is the energy corresponding ID the transl­tlon. Very recently,2 Shibuya, Harger, and Lee pub­lished· for the first time the lntenslty distrlbution of the fluorescence emlssion apectra of two SVL of H2C0(1A1):

4° and 41• In lhis paper, we give the results of the cal­

culation of the theoretica! spectra In order to lnvesti­gate, to what extent the integrals glven In Paper I can be used for predlctlng fluorescence spectra from other SVL and for lnterpreting ~erimental results.

It is also possible3 to calculate from the obtained D values the total radiative llfetime T, of a SVL:

(2)

where c is the velocity of light (= 137 a. u. ), and the summation is over all possible transitions from the SVL in question. Altbough lhis T, value, belng the combined result of a large number of transitions, is a mucb less rèfined quantity to cbaracterize the radiative properties of a SVL lhan its fluorescence emission apectrum, it is worth calculating T, because for most SVL of formal­dehyde T r values are known experimentally' contrary to the fluorescence spectra.

ll. RESUL TS AND DISCUSSION

A. Flu1>rescence emission spectra

In Table I, we give the calculated osclllalX>r strengths of the most intensive bands' occurring in the 41 and 4• fluorescence emlssion spectra for wavelengtbs smaller than about 460 nm, being the region for whlch the ex-

2854 J. Chem. Phys. 70(06), 15 Mar. 1979 0021-9606/79/062854-06$01.00 © 1979 American lnstitute of Physics

73

Kamper, van Dijk, and Buck: Fluorescance and llfetime of H:iCQ

TABLE L Calculated 08Cillator atrengtha of llle most ln-ve bands In the 41, and 1<• fluo-rescence emlsslon -tra.

41 llpeclrwn

Transllion t;.E (011.-•1 />< lo' {a. u.) Transllion

~ 28313 3.4 4f af~ 26812 0.8 <1o'sf 2f4l 26566 7.6 3f4! 4j 26001 26.6 t,'5t 4fst 25894 0.8 2f4f Z:al4' 25056 1.3 2ffM

2144 24820 8.8 < al4) 24500 4.6 4&f 4}51 24302 0.9 i:41 Z:4l 24232 59.5 3f4: Z:4:6: 24148 1.7 Z:<st 1:2:4' 23800 0.2 z:af4f 4l 23643 27.1 ' 2'<5f 4~6' 23560 0.6 *' z:af4 33320 1.5 ~""61 ll4) 23292 0.7 aM zl~ 23074 6,3 2'41 aM 23060 O • .f. 451 2iat4J 22814 10.3 2'4!&t 2f*l6! 226'7 0.3 41 2f41st 22556 2.1 2'aî4f zt4l 22486 87,4 aWst z:•IS: 22402 1,9 ., a:-ll 22143 "" 214M 1f*l 220H 0.2 Zl4,'s! ~: 21987 0.8

Z:.f.J 2189'/ 60.2

z!4M 21813 1.4

ZSaf4' 21574 1.1

l!Zf4l 21549 1.6

214' 21328 3.1

213W 21314 0.9

41 21309 10.7

perimental spectra• are krown. For the most Intensive transitions we compare in Fig. l ln a graphical way the expertmental" lntensity distribution wlth the calculated oscillalDr strqtlls. From the results we ca.n see that In genera! the agreement between experiment and cal­culatlon is qui.te satlsfaetory. We have taken the inten­sities relatlve ID the 2'41 transltion because a relatlvely large discrepancy between calcu1ation and experiment occurs for the ~ transitlon, wbich was u.nd by Sblbu)'ll et al. 1 as referenee.

As a.n illustralion for the applicalion of the calculated

4• llpeclrwn

t;.E (cm'"') /><101 (a.u.)

27021 18.0

26937 1.0

25520 3.1

25345 1.3

25275 40.3 26191 2.3

24886 18.9

24602 0.5

24254 O.li

24020 0.3

23844 0.2

23774 7.0

23599 2.9

23529 45,8

23446 2,8

23313 a.a 23068 42.3

23010 0.7

33856 1.2

22352 9,9

22028 7.9

21853 3.2

U782 33.3

218119 1.9

2126' 1.4

oseillalor strengtbs, we mention that Sblbnya et al.• worrled about the possiblllty that ~~ transitions might be overlapped by 2°,...14l5f. From the f va!Ues given in Table l it Is seen tbat the intensities of IC..,4\5t are much lower tban the ones of ~. We find tbat the ratio 4}st/2f~ = 0. 016, and 2'415'/21~ = O. 031, so this over­lap can be negleeted. The same holde for the possible overlap of ~~by ~4}~. The broken llnes In Fig. 1 are transitions, wbich are experimentally not reported, but which have, aecordingtoTableI, oscillatorstrqtlls comparable wlth the Z:,~ transltlons (the meas11recl transl.lions with the loweat lntensitlea). These unre-

J. Chem. Plv/t" Vol. 70, No. 6, 16 Match 1979

74

Kemper, van Dijk, and Buck: Fluorascence and llfetime of H;iCO

1.0

0.5 4)

·~ :zf~

28 27 26

1.0

4i exptrîmentol

:'l

2~4·

1

28 21 26

•' . 2~41

25 24

2f4~

2f4~

1

2S 24

2:3~4~

2:4 *' 23 22

•!

2;4~

1

23 22

•' :·

21

21

4 E • 101 c.m'"1

FIG. 1. Caloulated and exper!mental' fluorescence em!ss!on spectra from the 41 level. The intensltles are relattve to the 214l transltlon. The broken Itnes are the hlgbest calculated inteultles, wbieb are experimentally llOt found.

ported transitions sbould, aceording to the calculation, be measurable.

The low !ntensity bands, glven in Table I, glve rise to a IOw "background" emission spectrum with, owing to the increasing number of bands, an intensity s!owly increasing with the wavelength. As wlll be seen In Sec. II. B, these small bands represent a nonnegligible part of the total emisslon intensity. For the ~4~ and 2'/41 transitions, both lying in the reglon where the experi­mental determinatlons become more difficult because of spectra! congestion, tbere is a relatively large dil­ference between experiment and calculation. We note, tbal the experlmental intensity behavlor is peculiar for tb"'!" bands: theoretically, the ratio R=D'<:i:x~>I D"!~ral is 1. 2ll for all x~. For ra= 4i the experimen..: tal value" follows the tbeoretical prediction: R = 1. 31 ;,0.62. Forx:=4A, bowever, the experimental inten­silies", re sult in R = O. 63" o. 10, which is far out of the expected range. Also, the ~41 transitiOn is experimeo­tally lower lhan expected.

In Fig. 2, we eompare the experimenlal" and calcu­lated 4o fluoreseence emlssion spectra. Most of the remarks made for the 41 spectrum apply here too: Table I shows that the overlap of ~4' by 2"_15~ or ~&r

is negligibie; the transitions, indicated In !'"lg. 2 by broken llnes, should be detectable and the experimental intensity ralios :i;f4t/2'~ and 2f4g/~ are lower, than is expected on theoretica! grounds. The large nwnber of low intensity .bands glves rise again to a low background emission spectrum.

B. Absolute radlalion lifetlnws

In Table II, we give the absolute radiatlve llfet!mes, calculaled by means of Eq. (2), together with the ex­perimenta1• values. The results are compared in a ' graphical way in Fig. 3. The agreemeot between ex­periment and caiculation is qui.te satisfactory. A more detailed analysis shows that some remarks have to be made. Shibuya et nl.• measured r,(4°) relalive to r,(41

), using the experimental intensity dlstributions shown in Figs. 1 and 2. Tbey justlried their procedure by making two assumptiOns: first, that all the observed emission bands are progressions of 2~ built oo Av4 = odd; and second, that the fractiOn of the band inten­sitles at wavelengthe longer than 460 nm is either neg­ligible or the same for the 4° and 41 levels. We will show that these assumptions are questionable.

The calculaled absolute radiative llfetimes from Table II are obtalned by tak!ng into account In Eq. (2) all contributing transitions, includlng the many b~s

1.0

0.5

1.0 28 21

4° uperimentat

0.5

28 27 .! 26

25 24 23

25 23

22 21 3 ·1

A Ex fO em

22 21

4 Ex I03 em~1

FIG. 2. Calculated and experimentsl2 fluo~DCé emlulon spectra from the 4• level. The intenoltles are relative lo the 2~4 transllion. The braken lines are the bigbest calculated inlensltles, whlob are experlmentally not found.

J. Chem. Phys.. Vol. 70, No. 6, 15 Mm:h 1919

75

Kamper, van Dijk, and Buck: A-and lifetime of H,CO 2857

., µsec

8

40

Colculoted

43 21

43

22 41

22 43

2341 t s' s' 2' s'

4• 21 41

114

1 11

21

41 1

1 t 2

Tf

µsec

10

8

6

2

0

,o ,.

1

0

1000

Experimentol

,. 2

1 4

1

1000

2000 3000 4000

2243

234

1

2' ,.

2241

2'sï 1

1 2141

·{4' s'

2000 3000 4000

witb a relatively low oscl.Uator strength (see Table I), and also transttlons lying outside the experimental en­ergy reglon (e.g. , Il!. progressions built on 4l, ~. ot:, <lf, etc.). If we orûy take lnto account in Eq. (2) the caleulated D and AE values for those bands, wb1ch have been used by Sblbuya et al. In their experimentai deter­mination of T,.(41)/r,(4°}, we get T,(4')= 10.3 1aec and T.(41)= 15. 3 p.see. Tbe ratio of these vatues is 0.67, in excellent agreement with Sbibuya' s experimental value of O. 68 "'O. 12. Il is seen, ho wever, by comparing these -r • values witb the ones given In Table II, that the used experimental bands are just responsible for no more tb.an 33% (respectively, 28%) of the totai emisslon lntensity of the 41 (respectlvely, 4'l level. If we include all oontributing transltlons in the experimental spectra! reglon, 1. e; , the ones gtven In Table I, we obtaln T,(41)/r,(4°)•8.5 p.sec/10.6 µsee=0.80. Onlyifwe also take into account, in Eq. (2), the transitlons lor wavelengths larger than 460 nm do we arrive at the cor­rect lifetlmes gtven in Table II, witb T,(41)/-r,{4°) =0. 81. We flnd that these long wavelengtb transitlons repre­sent 60% of the total emtsslon intenslty.

-1 5000 e b(cm 1 vi

1 2's1

11

22

41

FIG. 3. Ca.lèulated and ex­pertmental' abaolute radlalive lifélimè• of SVL of u,co11A,).

TABLE ll. Caloulated and experlmental abeolute racllatlve llfetlmea of SVL af H1C0(1A,).

SVL

4• 4• 4• 2l4l 2•4• 2241 5• 114.' 2'4' 2'4' 2t5t 112141

2•s1

112•4•

0 124 948

1307 3152 2471 2968 2971 3343 3621 4147 4150 531ä 5818

"• (calc) -4.2 3.4 5.5 3.4 5.6 3.7 4.2 3.4 6.2 5.3 4.4 3.5 4.9 4.0

'Experlmental valu.e.o taken from Ref. 4. "Measured relall.ve to 411 aee text. 0Taken from Bef. 6. "raken from lief. 7.

Tr (exptl)' ,,. .. 3.3• 2.3 5.5 4.2 7.2 5.8 O.fl" l.4d

11.6 -10

}s.1 }-37

J. Chem. Phys., Vol. 70, No. 8, 15 Mon>h 1979

76

Kemper, van Dijk, and Buek: Ftuorescence and lifetime of H~

The conclwrion from Ibis caleulation is tbat the de­pendence of the result of a measurement of the emis­sion intenslty relative ID a reference emission inten­sity, upon both the sensitivity of the apparatus and the spectra! region wbich is viewed, can be quite iarge. The sensitivity determines to what extent the large nmnber of low intensity bands are taken into account, while the spectra! region bas ID be quite large to be sure that all the emissions are detected. In experi­ment& where the measurement takes place retative to another compound instead of another v!bronJc level of the sa.me molecule, these difficulties might cause even larger discrepancies than demonstrated above for the formaldehyde 41 and 41 levels. Thls Is because the emisslon spectrum of the standard compound w!U, in genera!, differ more from the emlssiOn spectra of the investigated molecule than the mutual differences in the emlssion spectra of 8VL In the sa.me molecule. In thelr determlnation of the 1', values of l'ormaldehyde, Miller and Lee• mention that "In some cases longer wavelength eutoff filters were used for viewing the emissiOn. " They conclude from the results (identical fiuorescence excltation spectra) that an equal fraction

of the emission Is deteeted l'or each 8VL of formal­dehyde. A more quantltative and systematic study con­cernlng this problem, lnchlding the fraction of emission of the reference compound (acetone), would be very ln­teresting.

1J. M. F. van Dijk, M. J. H. K-. J. H. M. Kerp. and H. M. Buck. J. Cbem. ~ 89, lM53 (1978).

2K. Sblbuya, R. A. Barger, and E. K. C. Lee, J, Chem. Phys, 89, 751 (1978>.

'J. M. F. van Dijk, Ph.D. thesis, Eindhoven Unlverslty of Teolmology, 1977.

'R. G. Miller and E. K. C. Lee, J. Cbem. P1>3'a. 68, 4448 (1978).

'The hot bands glven in Ref. 1 are lhe ones wblch C8D be ex­peotecl for an absorpt1on experlment-under normal conditions, i.e., transittons x:with ~=0, 1,2 for mode 4andb=O.1 for the other modes; in fiuoreseenoe emission experiments of course many more. bands Will ocour.

"R. G. Mlller and E. K. C. Lee, Cbem. P1>3'a. Lelt. 88, 104 (1975).

1K. Y. Tang and E. K. C. Lee, Chem. P1>3'a, Lett. 43, 232 (1976).

J. Chem. Phys.. Vol. 70. No. Il, 15 Malch 1979

77

IV.2 A COMPARATIVE STUDY OF THEORETICAL METHODS FOR CALCULATING FORBIDDEN TRANSITIONS

x M.J.H. Kemper , L. Lemmens, and H.M. Buck

Department of Organia Chemistry, Eindhoven University of TeahnoZogy, Eindhoven, The NetherZands

In this study simple calculational methods for forbidden transitions are tested. Using different methods we calculated vibrationally induced electronic transition moments. These D(Q) functions are, to a very good approximation, linear functions of the normal coordinates. A separate calculation of ground and excited state with a 4-31G basis set is the best alternative way to reproduce large basis set + Cl results on formaldehyde. Contrary to older results, we show that in formaldehyde mode 5 (and in a less degree mode 6) contributes largely to the total n~~ oscillator strength. It is argued that the experimental determination of f-values should be reconsidered.

78

1. Introduction

The calculation of the electronic oscillator strength and the vibrational structure of absorption and emission spectra in the visible-UV region is of great importance in several branches of chemistry and physics. Symmetry-aZZo~ed transitions are determined by purely electronic factors. Herzberg and Tellerl (HT) explained the occurrence of we.ak symmetry-forbidden

transitions by introduc1ng the coupling between the electronic and nuclear motions. A first assumption in their treatment is the adoption of the Born-Oppenheimer (BO) approximation. The molecular wavefunction (~) is presented as a product of an electronic wavefunction (@), depending parametrically on the nuclear coordinates (Q), and a vibrational wavefunction (x) :

1(1 •• ( q. Q) = ~. ( q 'Q) x .. ( Q) • 1) 1 1J

( 1)

q represents the set of electron coordinates, while i and j identify the electronic and vibrational states, respectively. Time-dependent perturbation theory gives for the oscillator strength of transition ij + kl (in atomie units):

(2)

where

D(Q) = <~-1 R l~k> 1 q

(3)

The subscripts q and Q denote the variable of integration, and àE is the energy difference between the states ij and kl. For R, the dipole-length operator q or the dipole-velocity operator V/àE can be chosen. If HT theory had been developed these days instead of almost 50 years ago, equation (2) might have been a terminal equation of the theory, because what rests is merely numerical quantum-chemistry. Almost any semi­empirical or ab-initio program calculates the dipole integrals

79

needed for (3). Then, the electronic transition moment D(Q) is obtained as a numerical function of the normal coordinates and is integrated between the vibrational functions X• This is what we call the direct method.

Not having available quantitative programs, HT expanded the electronic eigenfunctions in a Taylor series in nuclear dis­placements Q:

+ ( 4)

where summation over the nuclear displacements is understood ; ~O refers to the wavefunction in the equilibrium configuration, and ~'is a~/aQ. The electronic transition moment between the states i and k is then:

For symmetry-forbidden transitions the first term equals zero; the transition_ is induced by the vibronic terms ~l .and ~k' The early efforts to calculate HT intensities concentrated on the s0-s1 (nw~) transition of formaldehyde and the 1B2u and 1B1u transitions in benzene. The contribution of the ground state term (~ 0 ) was usually neglected because the excited states were supposed to be most susceptible to perturbations. Then,the theory becomes complicated: the excited state term c~;) is evaluated using perturbation theory in which the wave functions are mixed through the nuclear coordinate dependence of the nuclear-electron Coulomb term of the Hamiltonian. Most­ly, ~ 1 is mixed only with the nearest available upper state. In fact, this method is an expansion of adiabatic BO functions in crude BO functions. From this expansion the well known picture of "intensity borrowing" emerges. In order to improve convergence, Liehr 2 introduced the idea of floating orbitals (FO). For practical use at molecules other than the simple formaldehyde or the highly symmetrie benzene, however, these methods are hardly applicable. The conceptually simple and

80

straightforward direct method is much easier to use. Quantum­chemical calculations being what they are, however, a number of well known problems arises: how accurate must the wave­functions be; what is the influence of difference basis sets, correlation energy, et~? The aim of this paper is to start a systematic investigation of these points in order to develop a simple method, suitable for large organic molecules. In this study we concentrate on the first part of the problem: the electronic transition moment D (Q).

2. Methods

2.1. Choice of references

There is only a very limited number of quantitative studies on forbidden transitions which reflect the modern state of art in computational quantum-chemistry. The reason for this is to a great extent the fact, that it was difficult to judge the quality of the results. Equations (2) and (3) show that both the electronic and vibrational wavefunctions have to be calculated to obtain the vibrational structure of absorption and emission spectra. Most studies, however, concentrated on the totai oscillator strength f, because in that case the vibrational problem seemingly disappears. The f-value for the cold s0 + s1 transition is given by (writing x(Q) as x):

f = ~ foo, 1e 2 3

Since f lx 1e>} constitutes a complete set in the vibrational coordinates, use of the quantum mechanical sum rule,

I: 1X1e><x 1e1 = 1, resul ts in: e

f

(6)

( 7)

where ~Eav is some average energy difference. If for the vibrational function x00 the harmonie approximation is adopted,

81

the integration in equation (7) is a standard one 3 as soon as D(Q) is known numerically as a polynomial in Q. In this study we wil! only use equation (7) for the comparison with other calculations. Comparison with the experimental f-values is difficult, as will be discussed in section 4. For the formaldehyde molecule the vibrational intensity dis­tributions of absorption 4 and emission5 spectra, and especially radiative lifetimes6,? of single vibronic levels are known much better than total f-values. In a series of papersa-10 from our laboratory i t was shown that these spectra and life­times can be reproduced very accurately. The theoretica! results can even be used to identify unknown, observed spectra 11 •

So, it seems save to assume that both the vibrational and the electronic wavefunctions were calculated sufficiently correct. Therefore we take, instead of using equation (7), the D(Q) functions obtained by van Dijk9• 13 for formaldehyde as a reference to gauge the much simpler calculational methods used in this study.

2.2. Computational methods

The reference functions were obtained9,l3 with Clementis IBMOLS,H programl 4 • The main features of the method are as follows. The basis set was of double zeta quality: for carbon and oxygen a (9s5p){4s3p} set, for hydrogen a (4s){2s} set. The configuration interaction included the 175 most important configurations, selected with Morokuma's point system15 • 1 6. In order to keep the Cl manageable, ground and excited state had to be constructed from the same MO set. To describe both states with the same accuracy, Goscinski's transition operator method (TOM) was used 17 (see below). To be suited for molecules of larger size this computational scheme must be simplified considerably. We decided not to go as far as using semi-empirica! methods, because in that case the connection with the "correct" method would become very diffuse. Moreover, the number of available and essentially different semi-empirica! methods is discouragingly large.

82

In order to be practible, only single determinantal methods with not too large basis sets can be considered. So, we used the widely distributed GAUSSIAN?O program 18 , with standard ST0-3G 19 and 4-31G 20 basis sets. This program routinely calcu­lates dipole-length integrals. We will now describe several approaches to the calculation of ground and excited state, and of transition properties between them.

VOG (Virtual OrbitaZ of Ground State)

A RHF closed shell calculation gives the ground state <1> 0 as a normalized determinant of spinorbitals <P. a and <f>. ~:

l l

(8)

where N=16 for formaldehyde. The easiest and most crude way to construct <1> 1 is the replacement of the occupied orbital <f>s by the virtual orbital <Pg• which is obtained as a bonus when the Hartree-Fock equations are solved:

(9)

What follows is simple 21 :

(10)

The MO's are expanded in atomie orbitals; equation (10) then simply reduces to a summation over dipole integrals, multiplied by the appropriate MO coefficients.

VOE (Virtual Orbit.aZ of E:x:cited State)

GAUSSIAN?O enables an alternative for the calculation of <1> 1 :

the orbital occupation can be altered. This gives an UHF open shell wave function for <1> 1 • After this SCF procedure a similar replacement can be done as in the VOG method. In such a way the ground state is constructed from the <1> 1 molecular orbitals. The

83

electronic dipole transition moment is evaluated using equa­tion (10).

TOM (Transition Operator Method)

In the methods above, either the ground state MO's or the excited state MO's are actually used in the iterative SCF procedure. An intermediate situation occurs in the TOM method. In a normal RHF procedure the Fock operator has the form (schematically):

F = h + ~ (2J. - K.) J J J

(11)

where h, J, and K are the one-electron, the coulomb, and the exchange operator, respectively. If a transition is described in which an electron is promoted from molecular orbital i to molecular orbital a, the Fock operator is changed in:

(12)

The molecular orbitals resulting from this operator are used to construct ~O and ~ 1 states. In the original method 17 effec­tively one half electron is transfered from i to a; because of the RHF formalism this results in u=0.25. In principle however, u is an adjustable parameter; note e.g., that u=O results in the VOG method. The D(Q) function is obtained from equation

(10). We used this method only in the RHF formalism.

SIM (Separate Iteration Method)

The most direct method is a separate calculation of ~O and ~ 1 .

In this case however, the excited state molecular orbitals •' are not orthogonal to the ground state orbitals •· This causes the calculation of the transition moment to be a little more complex, namely21

:

84

D(Q) l: «P-1 q jqi'.> i,j=1 l J q ( 1 3)

where Mij is (-1)i+j times the ij-minor of the overlap matrix

<•il<Pj>. Because separate calculations for ground and excited state are needed, the SIM method.· is more costly than the other

ones.

It is important to note, that none of the four simple methods above, directly gives an ~xcited state, that is an eigenfunc­tion of s2 . To satisfy spin symmetry, linear combinations of Slater determinants (configuration state functions (CSF)) should be used. There are several general methods to construct

CSF's 22 ; widely used are projection operators and bonded functions. Configuration interaction programs like IBMOL use

such methods. In the bonded function method, matrix elements over spin-correct wave functions can be written in terms of integrals over molecular orbitals. We get 22 :

01 D(Q) = <~ol R 1~ 1 > = E a .. <<Pil q I•·> (14) q i,j lJ J q

where the coefficients a~] are called projective reduction coefficients. For the VOG and TOM methods, which both use the RHF formalism, it is simple to derive these coefficients 22 •

As a result, the spin syrnmetry constraint adds a multiplication factor zl to equation (10):

D(Q) (15)

Of course, the same result would have been obtained, in a less

genera! way, by taking 1 1 = z-!{!• 1a ...• 8a• 9B! - 1• 1a ...• 8B•9aj}.

In the VOE and SIM methods, which use the UHF formalism, no simple spin symmetry correction can be made; so, there we used

the equations (10) and (13), respectively~

The normal coordinates in our calculations were taken from

the force field of Duncan and Mallinson 23 • D(Q) was calcula­ted as a function of the modes 4 (out-of-plane wagging),

85

5 (asymmetrie CH-stretch), and 6 (asymmetrie bend). The other three modes do not disturb c2v symmetry, and, as a consequence, do not induce a transition dipole moment.

3. Results and discussion

Figure 1 gives the mode 4 components of D(Q), calculated with the minimal ST0-3G basis set. The first important conclusion is, that D(Q) is to a very good approximation a linear function in Q (correlation coefficients > 0.99) 24 • The same holds for most of the calculations on modes 5 and 6, both in the ST0-3G and in the 4-31G basis set . This allows to present the results in the very compact form given in Table I. The linearity of D(Q) was also found by Ziegler and Albrecht 25 in their CNDO/S study on benzene. This linearity shows, that the first order approximation of equation (4) is a correct one. Table I shows, that,relative to ST0-3G, the use of 4-31G increases the tran-si tion dipoles. This is not an unexpected effect; it also occurs with permanent dipoles 26

'26

• For instance, for the formaldehyde

ground state we get <~~I q l~g>q = 0.595 (ST0-3G), 1.181 (4-31G), 0.920 (experiment 27 ), and 1.114 (reference 13 ). Also,-in their study on calculational methods for symmetry-allowed transitions, Rauk et al 26 found that the transition moment D(QO) = <~~I R l~~>q (see equation (5)) increases in going from a single to a double zeta basis set. Of the four calculational methods, the VOE calculation has to be dismissed: the ST0-3G results on modes 5 and 6 are unsatis­factory. No further attempts were made with this method. Clearly, the best results, in the sense of reproducing the

reference curves, are obtained with SIM (4-31G). So, a separate

calculatinn of *o and *l is the best alternative for large basis set + configuration interaction. Because a construction of *o and ~ 1 from the same set of molecular orbitals would save computing time, some attempts were made to optimize the TOM method. From Table I it is seen, that the results of

86

t . 1 Q 4 I V 0 G ::::: T 0 M 10.2 5 )

(a.u.l 0.8

0.6

0.4

0.2

•

•

0.2 0.4 0.6 0.8 1.0 1.2

Q4 ...

Mode 4 components of D(Q) calculated with ST0-3G basis set. The results from TOM(a=0.25) are al.most the same as from VOG.

The straight lines are obtained from a regression analysis.

The values from the reference calculation (*) are indicated

for comparison.

•

1.4

87

(D (D Table I. Correlation coefficients (e.c.) and slopes of the normal mode components of the electron

dipole transition moment D(Q).

Sf0-3G basis set

mode 4 rode 5 JIDde 6

e.c. slope e.c. slope e.c. slope

VOG 0.999 0.615 0.999 0.178 0.986 0.085 VOE 0.996 0.350 0.644 0.005 0.998 0.004 TOM (0.25)a 0.996 0.666 0.999 0.104 0.999 0.083 SIM 0.999 0.208 0.975 0.030 0.999 0.044

4-31G basis set

VOG 0.999 0.709 0.996 0.452 0.996 0. 115 TOM (0.25)a 0.998 0.762 0.996 0.362 0.999 0. 117

SIM 0.996 0.230 0.999 0.132 0.999 0.066

Reference 9 , 1 3 0.970 0.160 0.999 0.272 0.998 0.124

a,.c,M (0.25) = standard TOM method with a= 0.25, (equation (12)).

TOM (0.25) hardly differ from VOG. A further increase of the

a parameter in equation (17) gives a decrease in the transition /

dipoles. Table II gives the 4-31G results. For higher values

of a serious convergence difficulties arise in the SCF proce­

dure. Table II shows, that variation of a does not improve

Table II. 4-31G slopes of D(Q) fl.lllctions for several values of the TOM variable a.

a mode 4 nnde 5 mode 6

0.25 o. 762 0.362 o. 117 0.50 0.468 0.192 0.088 0.70 0.357 o. 141 no convergence

the general applicability of the TOM method.

It is interesting to compare in Table !II the results of

several calculations on the s0-s1 transition of formaldehyde.

The Table uses total f-values obtained from equation (7) 36 '37

•

The main difference between the old results and ours is the

importance of modes 5 and 6. All our methods indicate, that

the inducing power of mode 5 is of the same order as mode 4.

The same holds, in a less degree, for mode 6. All the older

calculations predict mode 4 to be by far the strongest

inducing vibration; only Lins 32 calculation gives for mode 6 a large oscillator strength. The experimental results are

rather vague; this is caused by the overlapping of many

bands. What is known however, confirms our findings: Callomon

and Innes 38 report, that the type C subsystem (mode 5 and 6;

mode 4 gives type B bands) contributes as much as 25% to the

total intensity; Job et al 39 state, that the type C to type B ratio is at least 0.1. Our SIM (4-31G) results agree well

with Callomon and Innes: the SIM f-values in Table !II show,

that type C contributes 29% to the total intensity. It should

also be noted, that Miller and Lee 40 found that the vibronic-

89

co 0

Table III. Calculated total oscillator strength (x103) for the fonnaldehyde s0-s1 transition.

inducing Pople & 2 9 Roche & 3 0 Johnson 3 1 Linsz Kilin33 Pauzat34 van Dijk9 this work node Sidman Jaffé et al et al et al SIM (4-31G) Experiment35

(1957) (1974) (1975) (1976) (1976) (1980) (1978)

4 0.3 o. 13 o. 17 0.51

J Q.29

0.053 1.10 2.27

} Q.24 5 }8x1o-

4 6xl0-3

} 1.2x10-4 10-3.

} Sxl0-3 3. 17 0.74

6 '\JO 0.66 0.65 o. 19

f.D's estimated CNOO/S estimated estimated CN00/2 ab-initio ab-initio ab-initio +CI

Methoda Hr FO FO Hr Hr direct direct direct

a Hr = some level of H;rzberg-Teller theory; FO = floating orbital method

ally induced radiative s1-s0 transition is promoted more strongly by mode 5 than by mode 4. So~ we conclude that the semi-empirica! methods give qualitatively wrong results. A comparison with the experimental 35 absolute f-value should be made with care. Experimentally, the total absorption band has to be integrated. In this procedure atl absorption bands have to be taken into account, including the long mode 2

progressions (2~46, 2~56, and 2~66). These progressions have intensity up to 250 nm. We doubt whether this spectral range has been measured with the same sensitivity throughout. This situation is very much the same as recently discussed by us 10

for fluorescence emission spectra: if one takes into account in a radiative lifetime calculation only the "usually" obser­ved experimental bands, the calculated lifetimes are rnuch too long. Here, in absorption spectra, an incorrect measurement of the short wavelength bands results in a too small experi­mental f-value. Moreover, the ratio type C/type B will be measured too small, because the progressions of modes 5 and 6 lie at shorter wavelengths than the corresponding mode 4 bands. Anyway, the formaldehyde f-values should be remeasured.

91

92

REFERENCES AND Nffi'ES

(1) Herzberg,G.; Teller,E. z. Physik. Chem. 1933,B21,410 (2) Liehr,A.D. Z. Naturforschg. 1958,13A,311 (3) Wilson jr. ,E.B.; Decius,J.C.; Cross,P.C. ''M:llecular Vibrations",

McGraw-Hill, New York, 1955, Appendix III

(4) Lee,E.K.C. Acc. Chem. Res. 1977,10,319 (5) Shibuya,K; Harger,R.A.; Lee,E.K.C. J. Chem. Phys. 1978,69,751 (6) Weisshaar,J.C. Ph. D. Dissertation. U.C. Berkeley 1979 (7) Miller,R.G.; Lee,E.K.C. J. Chem. Phys. 1978,68,4448 (8) van Dijk,J.M.F.; Kemper,M.J.H.; Kerp,J.H.M.; Buck,H.M.;

Visser,G.J. Chem. Phys. Letters 1978,54,353 (9) van Dijk,J.M.F.; Kemper,M.J.H.; Kerp,J.H.M.; Buck,H.M.

J. Chem. Phys. 1978,69,2453 (10) Kempr,M.J.H.; van Dijk,J.M.F.; Buck,H.M. J. Chem. Phys • ..!222.,70,2854 (11) The identification of Hardwick and Tills 12 spectrum as 4 13 1 emission

is completely confinned by calculation (M.J .H. Kemper, unpublished'

results). This confinnation shows that Hardwick and Tills reassign-' nent of v3, that was predicted already theoretically8 ' 9 , is

correct. (12) Hardwick,J.L.; Till,S.M. J. Chem. Phys. 1979,70,2340 (13) van Dijk,J.M.F. Thesis, Eindhoven University of Te<;:hnology 1977 (14) A version, written by drs. van Hemert (Leiden University) and

l\brmer (Nijmegen University) was used. (15) M:irokuma,K.; Konishi,H. J. Chem. Phys. 1971,55,402 (16) Hayes,D.M.; M:irokuna,K. Chem. Phys. Letters 1972,12,539 (17) Goscinski,O. Int. J. Quanttun Chem. 1975,9,221 and related papers. (18) Hehre,W.J. et. al. Q:PE 1973,11,236 (19) Hehre,W.J.; Stewart,R.F.; Pople,J.A. J. Chem. Phys. 1969,51,2657 (20) Ditchfield,R.; Hehre,W.J.; Pople,J.A. J. Chem. Phys. 1971,54,724 (21) McWeeny ,R. ; Sutcliffe ,B. T. ''Methods of M:ilecular Quantum Mechanics",

Acádemic Press, London, 1969 (22) Roos ,B. in "Computational Techniques in Quantun Chemistry and M:ilec­

ular Physics", Diercksen,G.H.F.; Sutcliffe,B.T.; Veillard,A. edts., D. Reidel, Dordrecht, 1975

(23) Duncan,J.L.; Mallinson,P.D. Chem. Phys. Letters 1973,23,597

(24) We note, that the Q-values we u5ed are scaled ones: Q is just

an integration variable in <x(Q) 1 D(Q) 1 xCQ)>Q , that disappears in the final results. The only relevant demand is that D(Q) is

calculated in the whole Q-interval where x(Q) is significantly

unequal zero.

(25) Ziegler,L.; Albrecht,A.C. J. Chem. Phys. 1974,60,3558

(26) Hehre,W.J.; Pople,J.A. J • .Amer. Chem. Soc. 1970,92,2191

(27) Jones,V.T.; Coon,J.B. J. M::>lec. Spectry. 1969,31,137

(28) Rauk,A.; Barriel,J.M.; Ziegler,T. Prog. Theor. Org. Chem., Vol. 2,

Csizmadia,I.G. edt., Elsevier, 1977 (29) Pople,J.A.; Sidman,J.W. J. Chem. Phys. 1957,27,1270

(30) Roche,M.; Jaffé,H.H. J. Chem. Phys. 1974,60, 1193 (31) Johnson jr. ,W.C. J. Chem. Phys. 1975,63,2144

(32) Lin, S.H. Proc. R. Soc. Lond. 1976,A352,57 (33) Kilin,V.A.; Terpugova,A.F.; Cheglokov ,E.I. Opt. Spectrosc.

1976,41,456 (34) Pauzat,F.; Levy,B.; Millie,Ph. M::>l. Phys. 1980,39,375

(35) Duncan,A.B.F.; House,E.H. as cited in reference 29.

(36) We used in equation (7) the linear relationship between D and Q;

the use of higher polynomials did not significantly change the

results. This holds for the reference curves also.

(37) The mutual differences between van Dijks results and ours, are

larger in Table III than in Table II because the f-values are

proportional to the square of the slope of the D-functions.

(38) Callonnn.J.H.; Innes,K.K. J. M::>lec. Spectry. 1963,10,166 (39) Job,V .A.; Sethuraman,V.; Innes ,K.K. J. Molec. Spectry. l969,30 ,365

(40) Miller,R.G.; Lee,E.K.C. Chem. Phys. Letters 1975,33,104

93

V. SOME FUTURE DEVELOPMENTS

All the papers in this thesis carried their own conclusions. Here, we will try to give, in the light of the Scheme in Chapter I, a broad survey of the results. The main intention of this Chapter however, is to indicate some subjects, which might be a logica! and interesting continuation of the work presented in this thesis.

The calculation of emission/absorption spectra and radiative lifetimes (Chapter IV.1) has been quite successful. This shows, that ab-initio + CI methods give correct total transition mornents for formaldehyde. Then, the possibility is open for calculating Förster/Dexter energy transfer 1 -~ and collision

induced internal conversion (CIIC). These processes have, from a theoretica! point of view, very rnuch in cornrnon 5 • CIIC can be symbolized by:

or, by using electron ($) and vibrational (x) wave functions:

+ +

The subscripted letters at x denote the vibrational quantum nurnber. Energy transfer is given by:

+ + s,

In this notation, nothing seems to occur. If one writes however:

94

+ +

it is seen that initial and final state are differe71t: contrary to the electron energy, the vibrational endrgy did not exchange completely. The rate of CIIC is determined by:

(1)

H1 is the total interaction Hamiltonian between the two molecules. If these molecules are not too close to each other, it is clever to use a Taylor expansion for H1 . The first term of this series is a dipole-dipole interaction:

v

a and B are cartesian coordinates •. ral and r 82 are electric dipole operators, and TaB is a tensor containing the (time dependent) distance between the molecules. Now, equation (1)

reduces to a combination of Franck-Condon integrals (e.g.

<x 1j lxoj•>), dipole moments (<~ 0 1 ~ 1~ 0 >), and dipole trans­ition moments (<~ 1 1 r l$o>). The description of the energy transfer processes is completely analogous. Although these integrals are known for formaldehyde, the quantitative elaboration of the theory is not trivia!. The dynamics of the process gives complications 6 because donor and acceptor move relatively to each other. Simple models, using for instance average distances, are not satisfactory 7 • A correct calculation for formaldehyde would be desirable, because resonant energy transfer might explain the unusual fluores­cence quenching of formaldehyde at low pressures 9 • Below 1

Torr, extremely large quenching efficiencies are observed. When a long-distance Förster mechanism exchanges the electro­nic energy, a different set of rotational-vibrational states

95

is prepared. From these states, many will have an effective coupling with the "lumpy" continuum of dissociative states. In other words, Förster energy transfer has a considerable effect on the life time of a prepared rovibronic state. Another reason to study CIIC is, of course, the importance of the dimeric mechanism of Chapter III. In Chapter II we noted already, that the unimolecular internal conversion is too small; so,a second molecule is needed to induce the radia­tionless transition. A quantitative theory of energy transfer will be of wide importance in photochemistry. To be useful for large molecules however, simple calculational methods are needed. A start for this was given in Chapter IV.2; the next step will be a simple method for Franck-Condon integrals.

In Chapter III it was shown, that quantum chemical methods are useful in the study of reaction mechanisms. It was suggested, that hydrogen shifts in molecules like vinyl-alcohol and N2H2 can be explained by analogous mechanisms. Also, reactions of hydrated formaldehyde are worth studying. The bimolecular harrier lowering described in Chapter III resembles model calculations on enzyme catalyzed hydrogen transfer 9 • These calculations can be done with semi-empirica! methods (e.g. MIND0/3). Such methods however, give doubtful results for hydrogen bonded systems 10 • 11 • The ab-initio results of this thesis give a good reference to gauge the semi-empirica! calculations.

Returning to formaldehyde, we mentioned already collision induced radiationless transitions and energy transfer as important subjects for future investigations. Above all things however, new experiments are needed. Some examples were sugges­ted in Chapter III. Especially matrix studies with several isotopic mixtures can give valuable information. On the theor­etical front, the involvement of radical fragments has to be studied; for this purpose configuration interaction is neces­sary. The recen'tly available GAUSSIAN 80 program will be useful here.

96

REFERENCES

(1) Förster,T. Z. Naturforsch. 1949,A4,321 (2) Förster,T. Discuss. Faraday Soc. 1959,27,7 (3) Förster,T. Radiat. Res. Suppl. 1960,2,326 (4) Dexter,D.L. J. Chem. Phys. 1953,21,836 (5) Lennnens,L. Graduation Report, Eindhoven University of Technology 1980 (6) Allinger,K.; Blumen,A. J. Chem. Phys. 1980,72,4608 (7) Kemper,M.J.H. unpublishable results (8) Weisshaar,J.C. Ph. D. Dissertation, U.C. Berkeley 1979 (9) Niemeyer,H.M.; Goscinski,O.; Ahlberg,P. Tetrahedron 1975,31,1699

(10) Zielinski,T.J.; Brean,D.L.; Rein,R. J. Amer. Chem. Soc. 1978,100,6266 (11) Klopnan,G.; Andreozzi,P.; Hopfinger ,A.J.; Kikuchi,O.; Dewar ,M.J .S.

J. Amer. Chem. Soc. 1978, 100,6267

97

SUMMARY

During the last decade the study of the formaldehyde molecule has taken a central place in fundamental molecular photochem­istry and photophysics. In this thesis an integrated theoreti­ca! study of this molecule is presented. The relations between the various aspects, which are needed for such a theoretica! description are elucidated. Non-Born-Oppenheimer couplings

between ground and first excited singlet state are calculated as a function of several unimolecular reaction coordinates. These coordinates lead to hydroxycarbene (HCOH),and to molec­ular (H2+CO) and radical (H+HCO) dissociation products. The largest coupling is obtained for the reaction leading to hydroxycarbene. So, such a rearrangement gives the molecule an optima! change to leave the excited potential energy sur­face. Another argument in favour of this chemica! intermediate is its ability to explain the time-lag in the formation of photoproducts: it gives the molecule a natura! place to wait

a while before dissociation. The energetic harrier on s0 however, is too high to make the unimolecular formation of hydroxycarbene an easy reaction. Moreover, the increase of the coupling elements is too small to induce an effective, unimo­lecular internal conversion. Therefore, a dimeric mechanism is

developed for formaldehyde photochemistry. A large number of ab-initio calculations on this model, in which hydroxycarbene has a centra! position, is presented. The calculation of infra-red and Raman spectra of monomeric and dimeric for­maldehyde gives information about the geometry of matrix

dimers. From complexes between hydroxycarbene and formaldehyde, addition products are formed. In accordance with experiments, glycoaldehyde and methanol are easily formed; the formation of methylformate is difficult. In contrast with usual theories in carbene chernistry, CH-insertion is not possible. Hydroxy­carbene is formed via a dimeric interaction, which results in

98

a harrier lowering of~ 10 kcal/mol, relative to the uni­molecular case. This lowering makes the formation of hydroxy­carbene possible out of the vibrationless s1 level. At high concentration of hydroxycarbene, a hydrogen exchange mecha­nism occurs; this tranfers the molecules back to formaldehyde. The exchange mechanism explains why no hydroxycarbene is detected after the dissociation of transition-metal/carbene complexes.

Calculated Franck-Condon integrals and dipole transition moments are used to determine fluorescence emission spectra of single vibronic levels of s1• The radiative lifetimes of a large number of levels are calculated. The agreement between theory and experiment is striking. A critical analysis of the results shows, that long wave length emission contributes largely to the total decay. Experimentally, this part of the spectrum is usually neglected. An analogous situation occurs in absorption experiments: the modes 5 and 6 are normally considered to be neglectable as promoting vibrations for the forbidden s0-s1 transition. It is shown however, that a variety of calculational methods indicates, that these vibra­tions are just as important as mode 4. The capacity of rela­tively simple ab-initio methods for reproducing electronic transition moments of sophisticated calculations, is tested systematically. The results are very encouraging. It is shown, that these methods can be used to develop quantitative theories of Förster/Dexter energy transfer and collision­induced internal conversion.

99

SAMENVATTING

Het formaldehyde molekuul is gedurende de laatste jaren een van de belangrijkste modelstoffen geworden voor de studie van fundamentele fotochemische en fotofysische processen. In dit proefschrift wordt een samenhangende beschrijving van deze processen gegeven. De wijze waarop de diverse theoretische grootheden, die voor een dergelijk doel nodig zijn, samen­hangen, wordt duidelijk gemaakt. Koppelingselementen tussen de grondtoestand en de eerste aangeslagen singulet toestand zijn berekend als functie van een aantal monomolekulaire reaktiecoördinaten. Deze reakties geven enerzijds hydroxy­carbeen (HCOH), en anderzijds molekulaire (H2+CO) en radikaal­(H+HCO) dissociatieprodukten. De grootste koppeling treedt op voor de reaktie, die hydroxycarbeen als eindprodukt heeft. Dat betekent, dat juist deze reaktie het molekuul de beste mogelijkheid geeft, om het aangeslagen potentiaaloppervlak te verlaten. Een ander argument, dat voor dit chemische intermediair pleit, is de mogelijkheid om de tijdsvertraging bij de vorming van fotoprodukten te verklaren: het verblijf in een hydroxycarbeen energie-minimum geeft het molekuul de gelegenheid even te wachten, alvorens tot dissociatie over te gaan. De energetische barrière op het s0 oppervlak is echter te hoog, om de monomolekulaire vorming van hydroxycarbeen gemakkelijk te doen zijn. Bovendien is de toename van de kop­pelingselementen te gering, om een effectieve interne konver­sie mogelijk te maken. Daarom is een dimeer-mechanisme opge­steld voor de fotochemie van formaldehyde. Dit mechanisme, waarin hydroxycarbeen een centrale rol speelt, is onderzocht m.b.v. een groot aantal ab-initio berekeningen. Berekende infrarood en Raman spectra geven informatie over de geometrie van matrix-dimeren. Uit kompleksen tussen hydroxycarbeen en formaldehyde worden additieprodukten gevormd. Glycolaldehyde en methanol worden gemakkelijk gevormd; methyl formiaat is

100

veel moeilijker te bereiden. Deze resultaten zijn in over­eenstemming met matrix experimenten. De reakties gebeuren niet via CH-insertie, hetgeen betekent dat gangbare theorieën over carbeen.'chemie herzien moeten worden. Hydroxycarbeen wordt gevormd via een bimolekulaire interactie, die de mono­molekulaire energie barrière met ongeveer 10 kcal/mol ver­laagt. Hierdoor wordt het mogelijk om ook vanuit de vibratie­loze s1 toestand hydroxycarbeen te maken. Bij hoge hydroxy­carbeen concentraties vindt waterstof uitwisseling plaats, waardoor weer formaldehyde wordt teruggevormd. Dit verklaart waarom bij dissociatie-experimenten met overgangsmetaal-carbeen kompleksen geen hydroxycarbeen wordt waargenomen.

Met behulp van berekende Franck-Condon integralen en dipool overgangsmomenten worden fluorescentie emissie spectra van vibronische s1 toestanden gesimuleerd. Van een groot aantal niveau's zijn stralingslevensduren berekend, met een opmer­kelijke overeenstemming met de experimentele gegevens. Een analyse van de resultaten toont aan, dat emissie in het lange golflengte gebied niet verwaarloosd mag worden. Bij absorptie­metingen treedt iets soortgelijks op: de modes 5 en 6 zijn altijd verwaarloosd bij beschouwingen over vibrationeel geïn­duceerde s0-s1 overgangen. Een hele reeks berekeningsmethoden toont echter aan, dat deze vibraties net zo belangrijk zijn als mode 4. De mogelijkheden om op eenvoudige manieren nauw­keurige elektronische overgangsmomenten te berekenen worden systematisch onderzocht. Deze methoden, die bemoedigende re­sultaten opleveren, kunnen worden gebruikt om kwantitatief onderzoek te doen naar Förster/Dexter-energie overdracht en botsings-geinduceerde interne konversie.

101

102

24 juli 1951

1967

1967-1972

LEVENSLOOP

geboren te Heerlen

eindexamen MULO A + B

studie aan de H.T.S. Heerlen

augustus 1972 eindexamen chemische

techniek (met lof)

1972-1976 studie aan de T.H. Eindhoven, afdeling

der scheikundige technologie

januari 1975 kandidaatsexamen (met lof)

augustus 1976 ingenieursexamen (met lof)

oktober 1975 Unilever Chemie-prijs

1976-1980 wetenschappelijk ambtenaar in de vakgroep

Organische Chemie

december 1980 wetenschappelijk medewerker bij het

Philips' Natuurkundig Laboratorium

te Eindhoven

DANKWOORD

Er is geen moeilijker taak dan goed te bedanken.

Gilles Ménage (1613-1692)

Dankbaarheid is de herinnering van het hart.

Jean Baptist Massieu (1742-1818)

103

STELLINGEN

1. De bewering van Pauzat et al, dat Kobe heeft aangetoond,

dat oscillator sterkten moeten worden uitgerekend met de

dipool-lengte operator is weliswaar correct, maar in het

geheel niet van toepassing op het door hen bestudeerde

probleem.

F. Pauzat, Ph. Millie en B. Levy, Chem. Phys. Letters Z! (1980) 494, D.H. Kobe, Phys. Rev. A .:!Q (1979) 205

2. De mededeling dat de s0--..s16 overgang van [18] annuleen

symmetrie-verboden is, kan nauwelijks grensverleggend

genoemd worden.

U.P. Wild, H.J. Griesser, V.D. Tuan en J.F.M. Oth, Chem. Phys. Letters i! (1976) 450

3. De suggestie van Yau en Pritchard, als zou hun niet-itera-

tieve methode voor de berekening van niveaudichtheden

zonder ~oeite zijn toe te passen op niet-harmonische syste­

men, duidt op een schromelijke overschatting van ofwel de

intelligentie van hun lezerspubliek, ofwel hun eigen inzicht

in deze ingewikkelde problematiek.

A.W. Yau en H.O. Pritchard, Can. J.

Chem. 55 (1977) 992

4. De invloed van non-Born-Oppenheimer koppelingen op ORDCD

spectra is vanuit theoretisch oogpunt bijzonder interessant.

Helaas zijn deze effecten experimenteel voorlopig vrijwel

onaantoonbaar.

J.M.F. van Dijk, Thesis 1977, Eindhoven.

5. In zijn theorie van de optische activiteit rept Tinoco met

geen woord over de kern-kern repulsies tussen individuele

groepen. Hierdoor komt hij zijn belofte, elke impliciete

aanname te zullen waarmaken, niet na.

J. Tinoco jr. , Adv. Chem. Phys. ~ (1962) 113

6. Liehr beeindigt zijn klassieke werk over de floating

orbital methode met de zin:"In section 1.3, reference 11 ,

of reference 5 (pg. 316), must now be supplemented by

reference 6 of this paper". Helaas is deze mededeling

karakteristiek voor de leesbaarheid van het gehele werk.

A.D. Liehr, z. Naturforschg. 13a (1958) 311 en 13a (1958) 591

7. Het correct leren gebruiken van een kwantumchemisch

rekenprogramma kost ongeveer één dag; het zinvol leren

gebruiken daarvan, ongeveer één jaar. Dit feit leidt bij

veel chemici tot teleurstellingen en tot misvattingen

over de kwantumchemie.

8. Ter voorkoming van ongewild plagiaat dienen de mogelijk­

heden, om te achterhalen welke stellingen reeds gepubliceerd

zijn, sterk verruimd te worden.

9. Werner Heisenberg werd geboren omstreeks 5 december 1901

in de omgeving van Würzburg.

10. Het op de juiste wijze foutief ijken van thermometers, kan

een aanzienlijke energie-besparing opleveren.

11. Sinds het in de handel zijn van pacemakers e.d. is levens­

lange garantie geen waarborg meer voor de goede kwaliteit

van het betrokken product.

12. De bewering, als zouden er bij het alpinisme veel doden

vallen,is onjuist. Helaas berust deze onjuistheid slechts

op de tijdsvolgorde waarin gewoonlijk de diverse gebeur­

tenissen bij ongelukken in het gebergte plaatsvinden.

M.J.H. Kemper Eindhoven, 21 november 1980