ELSEVIER

THEO CHEM

Journal of Molecular Structure (Theochem) 398-399 (1997) 381-394

Ab initio calculations of the structural, energetic and vibrational properties of some hydrogen bonded and van der Waals dimers

Part 3. The formaldehyde dime?

T.A. Forda,*, L. Glasser22b

“Cenmfor Theoretical and Computational Chemistry, Department of Chemistry and Applied Chemistry, University of Natal,

Durban 4041, South Africa

hCentre for Mokcular Design, Department of Chrmisty lJnicersi@ of the Witwutersrand, Johannesburg, Wits 2050, South Africa

Abstract

The structures, energies and atomic charges of five dimers of formaldehyde have been examined by means of ab initio molecular orbital theory, using the Gaussian-90 computer program at the second-order level of Mflller-Plesset perturbation theory and the 6-3 1 G split valence Gaussian basis set, augmented with polarization and diffuse functions (6-3 l++G**). These dimers are distinguished by the relative orientations of the monomer planes (coplanar, parallel or perpendicular) and dipoles (collinear, parallel or antiparallel). Three of the dimers were found to be genuine minima on the potential energy surface. These are a C,, structure with its dipoles antiparallel and its molecular planes perpendicular; a coplanar species of C2,1 symmetry with antiparallel monomer dipoles; and a CzV adduct with the dipoles collinear and the molecular planes perpendicular.

The infrared spectra (wavenumbers and intensities) of these three dimers were computed, and the wavenumber shifts and intensity changes on dimerization were derived. The perturbations of these spectroscopic properties are compared with those observed for formaldehyde isolated in argon and nitrogen matrices at cryogenic temperatures, and the most probable structure is deduced in the light of all the available spectroscopic evidence. 0 1997 Elsevier Science B.V.

Keywords: Ab initio; Molecular complexes; Formaldehyde; Vibrational spectrum

1. Introduction

In an attempt to establish a unified theory of mole-

cular interaction, covering all types of interaction

from weak van der Waals bonding to relatively strong

hydrogen bonding, we have initiated a theoretical

study of a variety of dimers formed between some

small polyatomic molecules, including Hz0 [l],

* Corresponding author. E-mail: ford@che.und.ac.za ’ Presented at WATOC ‘96, Jerusalem, Israel, 7- 12 July 1996. ’ E-mail: glasser@aurum.chem.wits.ac.ra

ONF and ONCl [2], CO2 and N20 [3], SO2 [4],

NH3 [1,5,6], BFj [7-91 and NH20H [lO,ll]. These studies have been extended to include a number of heterodimers containing H20 [12-231, CO2 and NlO [20,21], NH3 [17,24,25], BF3 [16,25-281 and NHzOH [18,24]. In a number of cases we have con- firmed the predictions of the infrared spectra of these dimers and complexes by measuring the spectra, in

cryogenic matrices, of several aggregates of Hz0 [1,16,29,30], CO2 and N20 [31], SO1 [32], NH1

[1,25,29,33,34], BF3 [7,16,2.5,26,34-361 and

NHzOH [30,33,37]. This collection of aggregates

Ol66-1280/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved.

PII SO 166.1280(96)04929-9

382 T.A. Ford, L. Classer/Journal of Molrculcrr Structure IThrochem) 398-399 (1997) 381-394

illustrates a remarkable variety of types of interaction, including dipole-dipole, dipole-quadrupole and quadrupole-quadrupole, with interaction energies spread over a wide range.

The dimer of formaldehyde, H,CO, is intuitively predicted to belong to the set of dipole-dipole bonded

adducts, possibly stabilized by a weak hydrogen bond involving a CH group of one monomer unit and the carbonyl oxygen atom of the other. The structure of

the dimer has been determined in the gas phase by Lovas et al. [38], by means of pulsed beam microwave spectroscopy. These authors detected a non-planar dimer of symmetry C,, having a structure character- ized by internal rotation of the monomers, resulting in the interchange of the hydrogen bond donor-acceptor properties of the sub-units. In this structure, the mono- mer molecular planes are perpendicular to one another, with the monomer dipoles in an essentially antiparallel alignment. This proposed structure con- stitutes a cyclic arrangement with the heavy atoms

lying in the same plane, involving a single conven- tional, but bent CH...O hydrogen bond and a second interaction associated with the C and 0 atoms of the partner monomers. The torsional-rotational tunnel- ling motion proposed to occur in this dimer is analogous to that previously reported for the water dimer [39].

The formaldehyde dimer has also been observed in cryogenic matrices by infrared and Raman spectro- scopy [40-421. Khoshkhoo and Nixon observed only one infrared and one Raman dimer band in each monomer fundamental region in both argon

and nitrogen, and concluded that the dimer possessed a centre of symmetry [40]. They also interpreted the blue shifts of the CH stretching bands as being incom- patible with a hydrogen bonded structure, while the red shift of the CO stretching mode suggested inter- action through the CO groups [40]. Nelander, in a careful study of all possible combinations of deuter- ated and “C-substituted dimer species, also in argon and nitrogen, detected multiple absorptions in most monomer fundamental regions, which indicated a non-centrosymmetric structure [4 I]. Based on the intensity ratio of the two components of the CO stretching mode, Nelander calculated an angle of 140 t- 20” between the CO bonds, while he concluded that the almost equal intensities of the two compo- nents of the out-of-plane CH2 wagging band indicated

that the monomer planes were approximately perpen- dicular. He also estimated the separation of the transi- tion dipoles to be 250 or 270 pm, depending on the matrix material. Nelander’s interpretation of his results allowed for an exchange process between two equivalent potential energy minima separated by a small energy barrier, with splitting caused by the relative internal motions of the monomers, as

observed in the gas phase by Lovas et al. [38]. van der Zwet et al. [42], in studying the complex between formaldehyde and carbon dioxide in argon and nitro- gen, confirmed Nelander’s [41] observation of two bands in most of the intramolecular fundamental regions, apart from those which they assigned to the H2C0.C02 complex, which they attributed to a formaldehyde dimer, without commenting on the possible structure of the dimer.

The formaldehyde dimer has been studied theoreti- cally by a number of authors [43-461. Del Bene [43] considered six different structures at the self-consis- tent-field (SCF) [47] level, with the STO-3G basis set.

She found two of these to be genuine minima on the potential surface, a planar centrosymmetric species with an antiparallel orientation of the monomer dipoles (A) and a singly hydrogen bonded (CH...O) adduct (B). An aggregate of C, symmetry, similar in structure to the gas phase structure of Lovas et al. [38], and labelled D, was found to be a non-equilibrium species [43]. However, the non-equilibrium D struc-

ture is similar in energy to the more stable A and B, and it was predicted that interconversion could take place easily. Kemper et al. also used the SCF/STO-3G combination to examine six separate dimer structures [44]. Their results are qualitatively similar to those of

Del Bene [43]. Specifically they considered a dimer (1) of Czh symmetry analogous to Del Bene’s A, and a second species belonging to the same point group (6), similar to Del Bene’s E, with antiparallel dipoles and parallel molecular planes [44]. Like Del Bene, they found their dimer 6 to be less stable than 1. Kemper et al. computed the dimer-monomer wavenumber shifts of 1 and 6, and claimed good qualitative agree- ment in the case of 1 with the experimental data of Khoshkhoo and Nixon [40], apart from the result for the CH2 rocking mode. Zubkov employed both an ab initio and a semi-empirical approach to compute the interaction energies of a number of molecular dimers, including formaldehyde [45]. He considered

T.A. Ford, L. Gla.wer/Journal of Molecular Structure (Theochem) 398-399 (1997) 381-394 383

two alternative structures, with an antiparallel (similar

to Del Bene’s E [43], which he labelled s) and a per- pendicular dipole alignment (p). Zubkov consistently found the s conformer to be more stable, but the p structure to have the shorter interaction distance [45]. Hobza et al. [46] studied two stacked structures of the formaldehyde dimer, one parallel, of symmetry C2,,. and one antiparallel (Clh), equivalent to Del Bene’s E and Kemper et al.‘s 6, at the SCF and second-order Moller-Plesset (MP2) [48] levels, and

with basis sets ranging from STO-3G to 6-3 1 G*/2. At an intermolecular separation of 300 pm, Hobza et al. calculated repulsive SCF interaction energies of from 8.9 to 23.8 kJ mol-’ for the Czr structure, depending on the basis set, and found the attraction to be due solely to the correlation energy component. For the C2,, isomer, the SCF energy was found to be attractive, and to dominate the total interaction energy [46].

In this paper we report the results of an exploration

of the structures and vibrational spectra of five dimers of formaldehyde, and compare the results among the

various structures and with the experimental and pre- vious theoretical work described above.

2. Computational method

The calculations were performed using the Gaus- sian-90 program [49] installed on a Convex C210 computer, at the MP2 level of theory [48], with the 6631+tG** basis set [50,51]. Del Bene has shown that the use of a split-valence polarized basis set, with polarization functions on both hydrogen and

heavy atoms [52], augmented by diffuse functions on the heavy atoms [50,5 11, can yield optimized struc- tures and hydrogen bonded wavenumber shifts which

reproduce experimental data quite accurately [53- 561. She feels that adding diffuse functions to hydro- gen atoms is not necessary [57], however we have included this feature in our basis set in order to account as fully as possible for the subtle effects expected to be important in such potentially weakly hydrogen bonded systems. Full optimizations were carried out at the VERYTIGHT level [49] in each case, subject to the point group symmetries of the

individual dimer species. All molecular orbitals were included in the post-SCF calculations.

The interaction energies were corrected for basis

set superposition error (BSSE) [58] by the Boys-

Bernardi full counterpoise technique [59], and also for vibrational zero-point energy differences. The SCF interaction energies were decomposed according to the Morokuma scheme [60,61] using the Monster- gauss program of Peterson and Poirier [62]. Other details are as reported in our earlier publications in

this series [3,9].

3. Results and discussion

The results of the geometry optimization of the formaldehyde monomer are presented in Table 1. Comparison with the substitution geometry reported by Harmony et al. [63] shows the CO bond length to be overestimated by 1.7 pm and the CH bond lengths to be underestimated by 1 .O pm, while the HCH angle is computed to be slightly too small, by 0.1”. The corresponding percentage errors are 1.4, - 0.9 and - 0.1, respectively. The search for plausible dimers of formaldehyde yielded five stationary points on the

potential energy surface (see Fig. 1 and Table 2). The regions of the surface examined were dictated by the relative orientations of the monomer dipoles and planes. For example, we considered two struc- tures featuring collinear dipoles in a head-to-tail arrangement, one with planar and the other with perpendicular monomer planes (Del Bene’s structures C and F) (431. We also studied three structures which were characterized by an antiparallel alignment of the monomer dipoles, one with the planes coplanar, one

parallel and the third perpendicular (Del Bene’s A, E and D) [43]. An attempt to achieve convergence with a starting structure similar to Del Bene’s B isomer resulted in relaxation to her adduct A. A further struc- ture, having both its planes and its dipoles parallel,

Table 1 Optimized structural parameters of the formaldehyde monomer,

corresponding experimental values, and calculated - experimental

differences

Parameter Calculated Experimental” Difference h

r(CO)lpm 122.3 120.6 1.7 r(CH)lpm 109.8 110.8 - 1.0

Ht?H/deg 116.5 116.6 - 0.1

’ Substitution geometry; see ref. [63].

’ Difference = calculated - experimental parameter.

384 T.A. Ford, L. Gl~sser/Journal of Molecular Structure (Theochem) 398-399 (1997) 383-394

II

e c _ cl

0 0 D 0 D 0

0

T.A. Fml, L. GlassedJournal of Molecular Structure (Theochem) 398-399 (1997) 381-394 385

Structures, minimum energies and Hessian indices of the monomer, and of some dimers of formaldehyde

Species” (point group) Orientation of monomer Orientation of Energy/a.u. h Hessian index

planes monomer dipoles

Monomer (CL,) - 114.20088414867 0

Dimer I (C ,) Perpendicular Antiparallel - 228.40877555283 0

Dimer II (Cl),) Coplanar Antiparallel - 228.40759985270 0

Dimer III (Cz,) Perpendicular Collmear - 228.40607536471 0

Dimer IV (CZh) Parallel Antiparallel - 228.40596068297 3

Dimer V (C?,) Coplanar Collinear - 228.40593282733 I

’ See Fig. I for illustrations of dnner structures.

h MP2/6-3ItG**.

similar to the stacked C?,. structure of Hobza et al. [46], dissociated on successive cycles of the optimi- zation process. The descriptions of our five stationary point structures, with their point group symmetries and minimized energies, are listed in Table 2, which also includes the monomer energy and the Hessian index of each species. The optimized structures of dimers I-V are illustrated in Fig. 1.

The optimized geometrical parameters of the dimers are collected in Table 3, in which the number- ing of the atoms refers to Fig. 1. The changes in each of these parameters on dimerization are also listed; in each case the CO bond lengths are found to increase and the CH bond lengths to decrease relative to the monomer. The HCH angles in the centrosymmetric structures, II and IV, increase, while in the non- centrosymmetric structures, 1, III and V, the HCH

angle in the electron donor (ED) molecule opens up and that in the electron acceptor (EA) closes. Dimer I appears to provide the closest fit to the experimental structure of Lovas et al. [38]. These authors used two models to fit the structural parameters to the observed rotational constants; the preferred fit yielded a C2...01 distance of 298 pm and an 02...Hl bond length of 218 pm. Our corresponding values are 274.1 and 283.1 pm, indicating that our results underestimate the strength of interaction of the CH...O hydrogen bond. Their centre of mass separation distance is 304 pm, while ours is computed to be 342.5 pm, and the angles between the Cl01 and the C202 bonds and the line joining the monomer centres of mass are 95.7” and 102.5”, compared with our 76.2” and 94.3”

respectively. These discrepancies are clearly asso- ciated with our underestimation of the CH...O hydrogen bond strength, referred to above. While

structures II and IV, possessing centres of symmetry, have zero dipole moments, and structures III and V have dipole moment components only in the direction of the CO bond axis, dimer I has two components, one approximately parallel to the two CO groups (along

the x-axis) and the other lying in the plane of the heavy atoms (the x-z-plane), the calculated values being pL, =0.4465 and p: = 1.1258 D." The experi- mental values of these components are 0.027 and 0.858 D, respectively [38]. Although the agreement is quantitatively not very good, as is usually found to

be the case with predicted dipole moments, even with fairly large, flexible basis sets, our structure I is the only one we considered which possesses two non-zero components.

In Table 4 are shown the dimerization energies, corrected both for BSSE and for zero-point energy differences. In the case of dimers IV and V, which were found to have three, and one, negative eigen-

values respectively, the zero-point energy differences are naturally underestimated due to the exclusion of the negative wavenumbers. All five dimers have inter- action energies which cluster within a remarkably narrow range. Correction for BSSE alone preserves the sequence of the interaction energies, for the three structures, I-III, corresponding to true minima; however, inclusion of the zero-point energy differ- ence correction in addition reverses the order of the energies of I and II. This emphasizes the extremely

small spread of the dimerization energies among all five structures.

The SCF part of the association energy of each dimer was subjected to a decomposition analysis,

’ I D = 3.336 x 10~‘” C m.

386

Table 3

T.A. Ford, L. Glnssrr/Journul of Molecular Structure (Theochrm) 398-399 (1997) 381-394

Optimized geometrical parameters of some formaldehyde dimers

Dimer Parameter” Dimer value Difference’

r(CIOl)/pm 122.6

r(C I H I )/pm 109.6

r(C I H2)/pm 109.6

H Ii: I H2/deg 117.5

Ol~IHlideg 121.3

0 1 e I H2/deg 121.1

r(C202)lpm 122.6

r(C2H3), r(C2H4)/pm 109.6

H3c2H4Ideg 116.4

02e2H3,02i‘2H4/deg 121.8

r(CZ~~~Ol)lpm 274. I r(02,“Hl)/pm 283.1

Clfil.~~OZ/deg 123.3

C262.,.Hl/deg 96.4

Clbl...C2/deg 100.6

02e2...Ol/deg 98.4

r(ClOl), r(C202)/pm 122.6

r(CIHl), r(C2H3)/pm 109.8

r(C I H2), r(C2H4)/pm 109.5

HI i: I H2,H3c2H4/deg 117.6

Olel HI ,02(?2H3/deg 121.1

0 I c 1 H2,02c2H4/deg 121.3

r(Ol...H4), r(02...H2)lpm 253.5

Cl61 .“H4,C2(?)2...H2/deg 1 I I.3

Clfi2~~~02,C2fi4~~~0l/deg 127.5

r(C 10 I )/pm 122.4

r(ClHI). r(ClH2)/pm 109.7

HI C? 1 HZ/deg 116.8

r(C202)/pm 122.5

r(C2H3). r(C2H4)/pm 109.6

H3(?2H4/deg 115.9

r(Ol...H3), r(Ol..,H4)lpm 270.2

C2fi3.~~01,C2fi4~..01/deg 101.9

r(ClOl), r(C202)lpm 122.4

r(ClHI). r(ClH2), r(C2H3), r(C2H4)lpm 109.7

HI t I H2,H3c2H4/deg 116.6

r(C1.,.02), r(C2,‘.Ol)/pm 322.5

Cl~l~.~C2,C2~2..~Cl/deg 95.5

r(C 10 I )/pm 122.4

r(ClHI), r(ClH2)/pm 109.7

H I c I H2/deg 116.8

r(C202)lpm 122.5

r(C2H3), r(C2H4)lpm 109.6

H3c2H4ldeg 116.0

r(Ol..,H3), r(Ol.‘,H4)lpm 275.7

C2A3..,0l,C2A4...Ol/deg 102.3

0.3

- 0.2

- 0.2

I .o - 0.5

- 0.7

0.3 - 0.2

- 0.1

0.0

0.3

0.0

- 0.3

I.1

- 0.6

- 0.4

0. I - 0.1

0.3

0.2

- 0.2

- 0.6

0. I

- 0.1 0. I

0. I

- 0.1

0.3

0.2

- 0.2

- 0.5

‘See Fig. I for numbering of the atoms.

h Difference dimer - monomer parameter

T.A. Ford, L. Glasser/Journrrl of Moleculur Structure (Throchem) 398-399 (1997) 381-394 387

Table 4

MP2 dimeriaation energies, corrected for basis set superposition error and for zero point energy difference, of some dimers of formaldehyde

Dimer Energy/kJ mol-’

Uncorrected BSSE AEo Corrected” Correctedh

1 - 60.040 4.46 I 5.717 - 55.579 - 49.862

II - 57.080 3.282 3.569 - 53.798 - 50.229

III - 52.894 2.007 2.327 - 50.887 - 48.560

IV - 52.549 2.652 1.585’ - 49.897 - 48.312

V - 52.513 1.939 1.915d - 50.574 - 48.659

‘Corrected for BSSE only.

h Corrected for BSSE and AEo.

’ Neglecting three negative eigenvalues.

d Neglecting one negative eigenvalue.

according to the Morokuma partitioning scheme [60,61]; the results are presented in Table 5. The cor- relation energy, represented by the difference between

the MP2 interaction energy (Table 4) and the sum of the Morokuma components (the SCF interaction energy, Table 5), is in each case the largest attractive component, followed by the electrostatic term. The polarization and charge transfer contributions are rela- tively unimportant. Of the repulsive components the exchange term is consistently larger than the mixing, as is usually found to be the case. Among the three most probable structures, I-III, the absolute values of each of the five components decrease in the same sequence, I > II > III. This is the same order as that of the uncorrected MP2 interaction energies, and of those corrected for BSSE only.

Table 6 lists the Mulliken charges [64] for the

atoms of the monomer and of each of the dimers, along with the perturbations of the atomic charges on dimerization, and the amount of charge transferred from the ED to the EA fragments. The total charge

transfer is very small, varying from 3.6 me in I to 18.9 me in III. In dimer I the major charge shifts involve Hl, 01, C2 and 02, with the primary inter-

action being a weak non-linear hydrogen bond between Hl and 02, with a secondary interaction between C2 and 01 (see Fig. 1). The negligible charge shifts experienced by H3 and H4 and the relatively large positive difference associated with C2 confirm that the secondary interaction is C2...01, rather than the alternative bifurcated (H3,H4). .Ol . In dimers III and V the chief redistribution of charge occurs within the EA molecules; the main difference between the ED and EA fragments is that in the ED the carbon atoms donate charge, while there is a net acceptance of charge by the carbon atoms of the EA. Dimers II

and IV, being symmetrical, show no donor/acceptor distinction between the component monomers. In II the carbon, the oxygen and the non-bonded hydrogen

atoms are net electron acceptors, while only the bonded hydrogen atoms suffer electron depletion; in IV on the other hand, since the hydrogen atoms are

Table 5

Morokuma decompositions of the total interaction energies of some dimers of formaldehyde

Component Energy/kJ mol-’

Dimer I Dimer II Dimer III Diner IV Dimer V

Electrostatic

Polarization

Charge transfer

Exchange

Mixmg

Total SCF

Correlation Total MP2

- 32.166

- 7.249

- 8.139

27.092

5.216

- 15.246

- 34.616 - 49.862

- 22.587

- 3.556

- 3.863

13.093

I.526

- 15.387

- 34.842 - 50.229

- 14.533

- 1.508

- 1.278

5.592

0.179

- I 1.548

- 37.012

- 48.560

- 16.166

- I.841

- I.521

8.855

0.765

- 9.908

- 38.404 -48.312

- 14.024

- 1.387

- I.041

4.828

0.069

- Il.555

- 37.104 - 48.659

388 T.A. Ford, L. Glns.wr/fourt~al of Molecular Structure (Them-hem) 398-399 (1997) 381-394

Table 6

Computed Mulliken charges” of the formaldehyde monomer and of some of its dimers

Species h

Monomer

Dimer I (ED)

(EA)

Dimer II

Dimer III (ED)

WA)

Dimer IV

Dimer V (ED)

@A)

Atom’

C

H

0

Cl

HI

H?

01 c2

H3,H4

02

Cl,C2

HI,H3

H2,H4

01,02

Cl

HI,H2

01

c2

H3,H4

02

CI,C2

H 1 ,H2,H3,H4

01.02

Cl

HI,H2

01

c2

H3,H4

02

Charge/r

0.2732

0.0844

- 0.4420

0.2684

0.1219

0.0780

- 0.4647 0.3035

0.0857

- 0.4785

0.27 17

0.0738

0.1 I21

- 0.4575

0.2765

0.0938

- 0.4452

0.2493

0.0968

- 0.46 18

0.3088

0.0805

- 0.4699

0.2768

0.0923

- 0.4440

0.24 I9

0.1001

- 0.4595

Charge difference/u”

- 0.0048

0.0375

- 0.0064

- 0.0227 0.0303

0.0013

- 0.0365

- 0.001.5

- 0.0106

0.0277

- 0.0155

0.0033

0.0094

- 0.0032

- 0.0239

0.0124

- 0.0198

0.0356

- 0.0039

- 0.0279

0.0036

0.0079

- 0.0020

- 0.0313

0.0157

- 0.0175

Fragment charge/r

0.0036

- 0.0036

0.0000

0.0189

- 0.0189

0.0000

0.0 I74

- 0.0174

’ le = 1.602 x IO-‘“C.

h ED-electron donor; EA-electron acceptor.

‘See Fig. I for numbering of atoms.

d Difference dimer - monomer charge.

remote from the site of interaction, they experience little change, while the carbon and oxygen atoms lose and gain electron charge, respectively.

Table 7 lists the predicted wavenumbers of the for- maldehyde monomer, as well as those reported by Shimanouchi in the gas phase [65], and the ratios of the calculated to the experimental values. These ratios lie in a range between 1 .Ol 1 and 1.100, indicating that the monomer wavenumbers are overestimated by a typical average value of about 5%. The calculated intensities are reported in Table 8, and are compared with the gas phase values of Nakanaga et al. [66]. Agreement for this property is not as close as that for the wavenumbers, although all the computed intensities agree with the corresponding observed

ones within a factor of 2. Table 9 shows the computed wavenumbers for those dimers (I, II and III) which were found to be genuine minima. The assignments of the normal modes derived from the intramolecular modes of the monomers were quite unambiguous, and for I and III were found to be highly localized in either the electron donor (ED) or the electron acceptor (EA) monomer units. In II they represented in-phase and out-of-phase coupled vibrations of the two equivalent monomer units. The notation for describing the intermolecular modes was derived from that of Yeo and Ford [67], with 1 indicating the libration of one monomer unit as a whole and r the torsion, usually of a CH2 group, while the descriptions con and anti refer to those motions about a given axis

Table 7

T.A. Ford. L. Glasser/Journal of Molecular Structure (Theochem) 398-399 (1997) 381-394 389

Computed wavenumbers of the formaldehyde monomer, corresponding experimental values, and calculated/experimental wavenumber ratios

Symmetry species Mode Approximate description i),,,,/cm-’ i&p, /cm- ’ hc/kxpt

0 I VI v,(‘=z) 3041 2783 I.093

“1 v(CO) I765 I746 I.01 I

V? KHz) 1574 I500 I .049

h, p1 U&HZ) 3126 2843 I.100

Y KHz) 1285 1249 I .029

hz rJh wtCH2) 1215 II67 I.041

Mean I .054

‘See ref. [65].

either in the same or in the opposite sense. The inter- molecular motions of the dimers are referred to the Cartesian axes as defined in Fig. 1. The predicted

intensities of the infrared active bands of the three

dimers are collected in Table 10. In order to be useful in distinguishing among the

possible formaldehyde dimer structures, the indivi- dual infrared spectra should be sufficiently different that they are capable of eliminating one or more of the various options. The most reliable way of accomplish- ing this is through a study of the wavenumber shifts for each dimer, and a comparison with those observed experimentally [40-421. Table 11 shows the com- puted dimer-monomer shifts for the three preferred structures. All three predictions are agreed that both CH stretching modes should shift to the blue and that

these shifts are the largest in the spectra. Moreover, apart from some very small calculated shifts (~1 of I and vi and vs of III), which are probably not signifi- cant, the CO stretching and CH? bending modes are all predicted to shift to the red. The CH2 rocking and wagging vibrations appear to be the most fruitful for discriminating among dimers I, II and III. In the case of I, the two components of both the rocking and

wagging modes are predicted to shift to either side of the monomer absorptions; in dimer II all four wave-

number shifts are predicted to be positive; while for structure III, apart from a zero shift for the v r5 rocking

vibration, its partner is expected to shift to the red, and the two wagging modes are calculated to show small shifts to the blue. A more fundamental difference is expected between the dimer II spectrum on the one hand, and those of I and III on the other, in that only the a, and b, modes of II are expected to be observed,

since the a, and b, vibrations are infrared inactive, thus reducing the number of observable dimer bands for this species.

The wavenumber shifts of the formaldehyde dimer observed experimentally in argon and nitrogen matrices [40-421 are collected in Table 12. While Khoshkhoo and Nixon failed to observe any evidence of a second dimer absorption in any of the fundamen-

tal regions [40], both Nelander [41] and van der Zwet et al. [42] detected two bands in the symmetric CH2 and CO stretching, and in the CH2 wagging regions. This observation tends to eliminate the centro- symmetric structure II from further consideration. All three groups measured blue shifts for both the

Table 8

Computed intenstties of the infrared absorption bands of the formaldehyde monomer, corresponding experimental values, and calculated/

experimental intensity ratios

Symmetry species Mode Approximate description A,,,,/km mol-’ A&,,/km mol-’ A,,I&&

al PI ~,(cHd 62.4 75.5 0.826

U? v(CO) 68.9 73.99 0.93 I v1 KHz) 6.5 II.15 0.583

hl VJ v,,(CHL) 107.7 87.6 1.229 vs P(CH~) 7.7 9.94 0.775

h2 Bh N=z) 4.9 6.49 0.755

‘See ref. [66]

390 T.A. Ford, L. Glas.ver/Journal of Molecular Structure (Theochenz) 39X-399 (1997) 381-394

Table 9

Computed wavenumbers of some dimers of formaldehyde

Dimer Symmetry species Mode Wavenumberkm-’ Approximate description”

111

a”

0 2

b,

bz

3160 v,,KH:) (ED) 306X v,(CHz) (EA) 3064 v,(CHz) (ED) 1766 GO) (EA) 17.56 v(C0) (ED) I.572 6(CHz) (EA) 1567 NCHL) (ED) 1291 p(CH2) (ED) 1203 w(CH$ (EA)

188 1, (con) 137 I, (anti) 113 v(O,,.H)

3155 v<,(CHZ) (EA) 1281 P(CHI) (EA) 1218 w(CHz) (ED) 225 r(CHz) (ED) + r(CH?) (EA) (con) 143 r(CH2) (ED) + r(CH?) (EA) (anti) 60 I; (ant])

3162 u<,(CH~) 30.51 v>(CH:) 1745 v(CO) IS68 &CH?) I293 p(CH z)

126 v(O...H) 73 I> (con)

I226 ~(CHZ) 68 I; (anti) 57 I, (anti)

I224 PKH~

52 I; (con) 3160 v,,(CHz) 3050 v,(CHI) 1758 wx)) IS68 &CH:) 1292 P(CHZ)

134 I, (anti)

3060 “,(CH?) (EA) 3052 v,(CHI) (ED) 1765 v(C0) (ED) 1761 CO) (EN 1574 NCH:) (ED) I562 WHd W.)

81 u(O...H) 54 r(CHz) (EA) + r(CH2) (ED)

3154 v,,(CH:) (EA) 1272 PKW (EN 1218 w(CH 2) (ED)

100 I, (con) 45 w(CHz) (ED) + p(CH>) @A)

3142 v,,(CHZ) (ED) I285 PW~ (EDI

1220 4CHd (EN

52 l,(con)

4 P(CHZ) (EDI + 4CHd @A)

a ED-electron donor; EA-electron acceptor: I-libration ofa monomer unit as a whole; con, anti-senses of libration of monomer units or groups about a particular axis (x, J or z) with respect to one another (see Fig. I).

T.A. Ford. L. Glasser/Journal of Molecular Structure (Theochem) 398-399 (1997) 381-394 391

Table IO

Computed intensities of the infrared active bands of some dimers of formaldehyde

Dimer Mode (symmetry) Intensity/km mol-’ Mode (symmetry) Intensity/km mol-’

III

68.4

61.2

36.1

97.1

17.4

3.35

20. I

6.08

0.86

I I.3

40. I

0.1 I

102.1

158.8

50.0

80.4

70.9

83.7

I I.5

15.9

0.18

88.2

8.18

5.70

54.2

0.50

89.4

8.39

5.64

0.85

0.02

34.9

99.1

29.2

8.42

59.3

4.72

23.3

6.82

89.0

8.03

4.62

31.7

3.65

symmetric and antisymmetric CH2 stretching shift, which again is not helpful for diagnostic bands-as predicted for all three dimers. Both com- purposes. The CH2 rocking region also yielded only ponents of the CO stretching band are observed to one dimer absorption in each experimental report. The shift to the red-again as predicted for all three intensities of the modes predicted to suffer negative models. In the CH2 bending region, only one band wavenumber shifts (vi4 of I and vIo of III) are calcu- was observed by all three groups; it indicates a red lated to be small (see Table lo), therefore they may

Table I I

Computed dimer-monomer wavenumber shifts for some dimers of formaldehyde

Monomer mode Dime, mode and wavenumber shift/cm-’

Dimer I Dimer II Dimer III

~,,(cHd

v,(CH~)

v(CO)

6(CH 2)

P(CH 2)

w(CHz)

VICU’) 34 u,(a,) 36 Q(h,) 28

v,7(a”) 29 lJ I?(bJ 34 p 14(k) I6

0’) 27 Vz(Q,J IO VI@]) I9 V?(fl’) 23 p ,,(b,,) 9 @l) II v&J’) 1 Vi(fl,) - 20 PI(W) 0 v(fl’) -9 v ,,(b,,) -7 Vl(Q 1) -4 v&J’) -2 Y&J -6 YT(O I) 0 WI’) -7 y I&u) -6 JJf’(Q) -8 V&J’) 6 y&J 8 ho - I3 lJ ,&“) -4 v u(biJ 7 v ,s(N 0

vs(a’) - I2 u&J II vl,(b,) 3 v I&“) 3 v,,(b,) 9 v I&z) 5

392 T.A. Ford, L. Classer/Journal of Molecular Structure (Theochem) 398-399 (1997) 381-394

Table 12

Experimental dimer-monomer wavenumber shifts for the formaldehyde dimer in argon and nitrogen matrices

Monomer

mode

Wavenumber shift/cm-’

Argon

Ref. [40] Ref. [41] Ref. [42]

Nitrogen

Ref. [40] Ref. [41] Ref. [42]

~c,(cHd IO.0 9 _ _

vKHz) 12.5 12.4

_ 5.1

JCO) - 3.7 - 3.5

- 9.9

KHz) _ _

_

PKHz) 3.6 3.3 _ _

w(CHG _ 5.9

_ - 4.2

9 _

12.4

5.2

- 3.5 _

- 9.8

- 5.0 _

3.9 _

5.8

- 6.3

6.2 6 _ _

8.8 8.6

_ 5.9

3.3 - 3.5

_ - 8.9

5.2 - 5.1 _ _

3.6 6 _

6.6 6.2 _ _

4.6 _

8.7

5.7

- 3.2

- 10.8

- 5.0 _

4.9 _

4.2

- 5.8

easily have been overlooked in the experimental spectra, especially since they are predicted to show only small wavenumber displacements from the monomer vibrations. The CH2 wagging mode region indicates the first positive means of identifying the correct dimer structure. Structures II and III are

expected to have two dimer bands in this region, both of which are perturbed to higher wavenumber (and only one of which, in dimer II, is expected to be observable), while in dimer I v9 is shifted 12 cm-’ to the red and vi5 3 cm-’ to the blue. Both Nelander [41] and van der Zwet et al. [42], in argon, and van der Zwet in nitrogen, detected two bands, one on the high and one on the low wavenumber side of the monomer absorption; these shifts are sufficiently large that their assignments to the dimer are beyond

dispute. Table 13 reports the computed dimer/monomer

band intensity ratios. With very few exceptions none of these ratios lies outside the band of values between 0.5 and 2.0 representing perturbations of a factor of 2 or less. In particular, no large increases in the inten- sities of the CH stretching modes are apparent, which would be indicative of strong hydrogen bonding; this is consistent with the absence of any red shifts in the CH stretching wavenumbers on dimerization. We conclude that the intensity perturbations, by and large, are small, and that they confirm the evidence provided by the wavenumber shifts that the monomer units in the formaldehyde dimer are subject to rather

weak attractive forces, certainly not sufficiently powerful to cause dramatic changes to the monomer spectra on association.

4. Conclusions

We have found five possible dimers of formalde- hyde to be stationary points on the potential energy surface. Among these, the computed dimerization energies show very little variation, whether uncor- rected, or corrected for BSSE or zero-point energy difference, or both. Thus their calculated dimerization energies are not a sound basis on which to determine which is the preferred structure. Dimers I, III and V are non-centrosymmetric, and are therefore the only

species which would yield microwave rotational spec- tra [38]. Of the live, only three, I, II and III, were found to have no imaginary wavenumbers and are therefore the only three real minima on the surface. Structure IV may be transformed into I by a rotation of one of the monomer units through 90” about its Cz axis. Dimer V may be similarly converted to III by an equivalent rotatory motion. Moreover, while dimer II may be converted into I, again by rotating one of the monomers through 90” about its CO bond, its energy minimum is evidently sufficiently low with respect to the rotational barrier that it is quite stable. Of the unsymmetrical dimers, I and III, the amounts of charge transferred on association are minimal, and

T.A. Ford. L. Glasser/Journal qf Molecular Srrucrurr (Theochem) 398-399 (1997) 381-394 393

Table 13

Computed dimer/monomer intensity ratios of the infrared active bands of some dimers of formaldehyde

Monomer mode Dimer mode and intensity ratio

Dimer I Dimer II Dimer III

V&HZ) v,(a’) 0.64 rJ I?@,,) 0.95 v9(h,) 0.82 v ?(U”) I 0.83 Vi&Z) 0.83

v,(CHl) Vz(0’) 0.98 &‘,d(h,,) 2.54 vl(dl) 0.80 lJ i(& 0.59 vz(u I) I .29

KG) v&‘) 1.41 v ,,(h,,) I .44 iJ?(UI) I .03 us(a’) 0.25 v&1) 1.21

%CH 2) zJg(u’) 0.52 ” Ih(hil) 4.49 us(a I) 1.77 ?(Q’) 3.09 V&I) 2.45

PKH 2) Y&o 0.79 iJ ,,(bU) I .09 v,(,(b,) 1.05 lJ &“) I .09 v,&) I .04

w(CH 2) v&r’) 0.18 V&I,) 0.16 v,,(b,) 0.96

p I&f) I.15 iJ (h(k) 0.94

this property is therefore also not a good indicator of the correct structure.

Among structures I, II and III, II has no permanent

dipole moment, III has a dipole moment component along only one of its principal axes, and I has two such components. Only I is qualitatively consistent with the experimental observation [38], that in the gas phase the dimer has dipole moment components of cc, = 0.858 and ph = 0.027 D. The infrared spectra of dimers

I and III are calculated to have two infrared-active modes in each monomer fundamental region, while II, being centrosymmetric, has only one. The pre-

dicted spectrum of II is inconsistent with the spectra observed [41,42] in argon and nitrogen matrices. The major differences in the predicted infrared spectra of the three preferred structures are in the shifts of the monomer CH2 wagging modes; while for II and III both components of this vibration in the dimer are predicted to shift to higher wavenumber, in dimer I one component is predicted to be displaced in either direction. Only I has a spectrum consistent with the observed spectrum of the formaldehyde dimer in cryogenic matrices; shifts of between

4.2 and 6.6 cm-‘, and between -4.2 and -6.3 cm-‘,

are observed experimentally [41,42], thus eliminating structures II and III. Thus, dimer I remains as the

only structure for the formaldehyde dimer which is compatible with all the available spectroscopic evidence, and we therefore propose this structure as the definitive model for this simple molecular adduct.

Acknowledgements

The authors gratefully acknowledge the Foundation for Research Development and the Universities of Natal and the Witwatersrand for their ongoing financial support of this research.

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