Journal of Molecular Structure (Theochem), 282 (1993) 51-57 0166-1280/93/$06.00 0 1993 - Elsevier Science Publishers B.V., Amsterdam

51

An MCSCF+ CI calculation of the H,C-AlH and H, CAl-H bond dissociation energies

Soraia Costa Silva, Marco Antonio Chaer Nascimento* Institute de Quimica, Departamento de Fisico-Quimica, Universidade Federal de Rio de Janeiro, Cidade Universitriria, CT, Bloco “A”, Rio de Janeiro, RJ 21910, Brazil

(Received 1 November 1991)

Abstract

Results of MCSCF(GVB)+CI calculations are presented for the H,C-AlH and H,CAl-H bond dissociation energies. Using the AlH, molecule as a test case it is shown that reliable bond energies can be obtained by considering only the differential correlation effects on the chemical bond being broken and the relaxation effects on its neighbouring bonds. The Al-H bond (39.32 kcal mol-‘) is found to be stronger than the Al-C bond (33.36 kcal mol-‘), but both bonds are weaker than the HAl-H bond.

Introduction

The reaction of matrix-isolated aluminium atoms with methane has been the subject of many experimental studies [ 1,2], mainly because it serves as a model for metal-centered catalysis systems.

Klabunde and Tanaka [l] were the first to study the Al/CH, system and concluded that the insertion of the aluminium atom into the C-H bonds was a thermally induced reaction. The fact that the elec- tronic configuration of the ground state aluminium atoms (‘P3s23p’) is similar to that of the photo- excited Cu atoms (*P3dl”3p’), which are known to react with methane, was used by those authors in support to their conclusion of a thermally induced reaction.

However, Parnis and Ozin, in a series of papers [2-4], reinvestigated the Al/CH, system and found no evidence for a thermally induced ground-state reaction. Instead, they found the reversible photo- chemically induced reaction, Al+CH,*

*Corresponding author.

CH,AlH, to be the only significant pathway involv- ing the methane molecule and the aluminium atoms. They also established, from their analysis of the ESR spectra, that the sole product of the reaction (H,CAlH) is non-linear, i.e. the C, Al and H atoms are not along the same bond axis.

The non-linear geometry was confirmed by the theoretical calculations of Quelch and Hillier [5] at the Hartree-Fock (HF) level. Those authors [5] also computed scaled harmonic frequencies in close agreement with the experimentally observed IR bands attributed by Parnis and Ozin [2] to the H, CAlH molecule.

In an attempt to establish possible mechanisms for the insertion of the aluminium atoms into the methane C-H bonds, Parnis and Ozin [4] tried to perform a thermochemical analysis. However, in the absence of experimental or theoretical data, they were forced to use estimated values for some bond dissociation energies. Thus, comparing the available theoretical results of bond energies for the Al-H (approximately 70 kcal mol-‘) [6-l l] and Al-CH, (67.8 kcalmol-‘) [12], they assumed that

52 XC. Silva and M.A.C. NascimentolJ. Mol. Struct. (Theochem) 282 (1993) 51-57

these bonds in comparable chemical environments should have roughly the same bond strengths. Similarly, the theoretical value of the HAl-H bond energy (45.6 kcal mol-’ ) [6] was used as an estimate for the H3 CAl-H and HAl-CH, bond energies, and the total bond dissociation energy of the H,CAlH was taken to be equal to that of the AlH, molecule. Based on those numbers they concluded that both proton abstraction and metal insertion should be thermodynamically favoured reactions but that an insertion/fragmentation reaction should also occur.

In this paper we present the results of MCSCF (GVB) [ 131 plus configuration interaction (CI) cal- culations for the H,CAl-H and HAl-CH, bond energies. Only the differential correlation effects on the chemical bond being broken and the relaxation effects on its first-neighbour bonds are considered. The AIHz molecule was used as a test case and the results obtained clearly indicate that such an approach can produce quite reliable values of dissociation energies with very little computational effort. A detailed analysis of the possible reaction pathways is the subject of a forthcoming publica- tion. Basis sets

Computational details

In this section we briefly describe the wave-

All the calculations were carried out using the Dunning [14] double-zeta (DZ) contraction of the Huzinaga gaussian basis set [15], augmented with polarization functions: (9s,5p)/[3s,2p] + cd = 0.75 for the carbon atom; (1 ls,7p)/[6s,4p] + cd = 0.25 for the aluminium atom; (4s/2p) + &, = 1.0 for the hydrogen atom.

functions and the approach used to calculate the bond dissociation energies. Basis sets and geometry optimization information are also presented.

Wavefunctions

We are interested in describing the bond breaking processes, so it would be convenient to use wavefunctions which have the correct functional form for proper dissociation. The GVB wave- function [13] is particularly suitable to study such processes because it is formally the same as the VB wavefunction, and therefore dissociates into the correct fragments, but the orbitals are optimized self-consistently, allowing for proper shape readjustments on bond breaking or formation.

Therefore we use GVB-type wavefunctions as the starting point in our calculations. However, because we are focusing our attention on the dif- ferential effects, only the orbitals comprising the breaking bond are treated as GVB pairs [13]. Thus, if all the other electrons of the molecule are desig- nated by {core}, the GVB wavefunction which properly describes the dissociation of one chemical bond can be written as

l(lovB = ANcore1{X,(l)X,(2) + xa(2)xb(l))

x 0x8 - B41 (1) where xa and x,, are variationally optimized non- orthogonal one-electron GVB orbitals. The other electrons are described at the HF level. Equation (1) is a special case of a GVB function, called the GVB-PP (perfect pairing) wavefunction.

For computational purposes it is more con- venient to replace the non-orthogonal GVB orbitals by the corresponding pair of orthogonal natural orbitals [ 131 I#J, and &

(2)

Geometries

Except for the fragment -CH,, for which the experimentally determined geometry was used [16], all the other geometries were optimized self- consistently using the HONDO 8 program [17] with an energy gradient threshold of lop4 hartree. Table 1 shows the geometry of all species formed in the two dissociation processes, together with the one for the AlH2 molecule used as calibration for the method.

XC. Silva and M.A.C. NascimentolJ. Mol. Strut. (Theochem) 282 (1993) 51-57 53

Table 1 Table 2 Optimized molecular geometries (in angstroms and degrees) of the AlH, AlH,, H,CAl and H,CAlH molecules

Total electronic energy E of the AlH molecule and dissocia- tion energy D, of the HAl-H bond compared to other theoretical results

Molecular Molecule parameter

AlH AlH, H,CAl H,CAlH

Al-H 1.670 1.588 1.595 Al-C 2.013 1.979 c-c 1.093 1.086, 1.090 AlCH 111.9 112.9, 108.8 HAlC 119.2 HAlH 118.3

Calculation E (hartree) D,(kcal mol-‘)

GVB(2/4) - 243.0328 CIGVB(2/4) - 243.0477 41.74 CIGVB( l/2) - 243.0384 43.16 MP4 - 243.078Sb

- 243.0839’ - 243.0875d - 243.0942’ 45.60

The dissociation process

In order to describe the dissociation process in a consistent way, one should treat the correlation and relaxation effects equivalently at both the equilibrium (R,) and infinite (R,) internuclear distances. However, because the dissociation energy is calculated as the difference in energy AE of the system at R, and R, , a consistent treatment of the differential correlation and relaxation effects should furnish reliable dissociation energies inasmuch as the other effects cancel out when AE is computed, and need not be considered.

For the dissociation process

H,CAl-H + H,CAl + H

the main differential correlation effect is associated with the electrons involved in the breaking bond. However, as the Al-H bond is stretched one should expect shape readjustments of the orbitals involved in the adjacent bonds. Therefore, a consistent treat- ment of the differential effects present in that dissociation process should consider the corre- lation of the two electrons involved in the breaking bond plus the readjustment of the orbital describ- ing the C-Al bond, at both endpoints R, and R,. It is true that, owing to the shape readjustment of the C-Al bond orbital, the corresponding intra- pair (C-Al) electron correlation will be different at R, and R, but this difference is small and can be neglected when compared to the differential cor- relations effects associated with the breaking bond. For the non-adjacent bonds it can be shown that

“The remaining bond is also treated at the GVB level. See text for discussion. bRef. 1 with 6-31G + (d,p). ‘6-31G + (2d,p). d6-3 1 G + (df,p). ‘6-31G + (2df,p).

both correlation and relaxation differential effects can be neglected. Also neglected are the inter-pair correlation effects between the electron pair of the breaking bond and each one of the adjacent bonds. However, the contribution of those effects to the total differential correlation effects can be minim- ized by using strongly localized molecular orbitals.

The dissociation process is therefore described by building the above mentioned effects into the wavefunctions at R, and R,. The breaking bond is first treated at the GVB-PP level, but afterwards the PP restriction is removed by allowing the GVB pair to have all three possible occupations (20, 02 and 11) for the two electrons in the pair. Using these three configurations as reference we allow full correlation of the electrons in the pair, i.e. all single and double excitations to all the other orbitals defined by the basis set used. In order to take into account the orbital shape readjustment we add to the previous list all the configurations generated by allowing single excitations from the electron pairs of the adjacent bonds to all orbitals defined by our basis set. (These calculations are referred to as CIGVB in Tables 2-4.)

More elaborate procedures have been used by Bair [18], Carter and Goddard [ 191 and Das and Wahl [20]. As will be shown, this simple approach

54 XC. Silva and M.A.C. Nascimento/J. Mol. Struct. (Theochem) 282 (1993) 51-57

Table 3 Total electronic energy of the H,CAlH molecule

Calculation E (hartree)

This work HF - 282.068 1 GVB(S/lO) -282.1324 CIGVB( l/2) - 282.0953 CIGVB(S/lO) -282.1398

ReJ P HF - 282.0558 CI( SD) - 282.3213

“Using a triple-zeta basis set without polarization functions.

can lead to dissociation energies comparable to those obtained from large scale CI and MBPT calculations.

Results and discussion

The procedure just described is very general and should be applicable to any system. However, depending on the nature of the atoms involved in the bond breaking, electronic recoupling becomes very important and must be included in the descrip- tion of the dissociation process.

The processes which we want to describe involve breaking a bond to a divalent aluminium atom; the dissociation process of the AlH2 molecule to AlH + H can be used as a test for the procedure.

AlH,

The GVB description [21] of the AlH2 molecule is schematically shown in Fig. l(a). Figure l(a) represents a GVB(2/4)-PP wavefunction, each bond being described by two GVB orbitals.

Table 4 H,CAl-H and H,C-AlC bond dissociation energies D,

Calculation D,, (kcalmol-‘)

Al-H C-Al

CIGVB( l/2) 39.40 34.61 CIGVB(S/lO) 39.32 33.36

“Including single excitations from non-adjacent bond pairs.

As the molecule dissociates, the electron in the lobe orbital involved in the bond being broken becomes singlet paired to the electron in the singly occupied lobe orbital (Fig. l(b)), while the remain- ing Al-H bond now involves a “p” orbital of the aluminium atom. The singlet-paired lobe orbitals also rotate back in order to reduce the interaction with the remaining bond pair. Therefore, besides the correlation effects in the breaking bond and shape readjustments in the adjacent bonds, in the case of the Al atom electronic recoupling must also be considered. This is accomplished by introducing this recoupling into the wavefunction at R,, as shown in Fig. l(b).

Table 2 shows the results obtained for the AlH, molecule compared to other theoretical calcula- tions. Figure 2 shows the GVB orbitals for the Al-H bond and the singly occupied orbital. For the differential zero-point energy correction (AZPE) we used the harmonic frequency results of Pople et al. [6] for the AIHl and AlH molecules, scaled by 0.89 [6]. The agreement with the results of an MBPT to fourth order calculation [6] is quite good and is an indication that reliable results can be expected using this procedure for the dissociation processes of the H,CAlH molecule. From Table 2 it can also be seen that treating the remaining bond pair at the HF level increases the dissociation energy by only 1.4 kcal mol-‘. Thus, for more complex systems, it is expected that treating the adjacent bonds at the HF level would not introduce appreciable errors.

H3 CAlH

For the H,CAlH molecule we considered two dissociation processes

H,C-AlH+H,C+AlH (process 1)

H&Al - H -, H,CAl + H (process 2)

In each case the breaking bond was treated at the GVB(l/Z) level. Following the procedure, only shape readjustments of orbitals in adjacent bonds should be considered. This implies allowing single excitations from the Al-H and C-H electron pairs to all orbitals for process 1, but only from the C-Al

S.C. Silva and M.A.C. Nascimento/J. Mol. Struct. (Theochem) 282 (1993).51-57 55

(0) AIH;! (b)HAl-H

Fig. 1. (a) GVB(2/4) wavefunction for the AlH, molecule, at the internuclear equilibrium distance; (b) GVB(2/4) wavefunction for the system HAl-H at R,; D represents a lobe orbital; 0 represents a single electron; a line between dots indicates singlet

pairing of the two orbitals.

electron pair for process 2. However, in order to test the hypothesis, we have also considered shape readjustments of the C-H orbitals as the Al-H bond was broken in process 2.

Table 3 shows the results obtained for the

H,CAlH molecule compared to other theoretical calculations [5]. In this case the differential AZPEs were computed using the harmonic frequencies given by Quelch and Hillier [5] for the H,CAlH, H, CA1 and AlH molecules, also scaled by 0.89 [6].

6.0 _ (0)

\

\

X

-6.O(

@n (W

-6.0 Z 6.0

-6.0: -6.0 Z 6.0

Fig. 2. GVB ((a) and (b)) orbitals for the Al-H bond and the singly occupied orbital (c) of the AlH, molecule: (- - -), zero amplitude; (- ), positive amplitudes; (- - --), negative amplitudes. The increment between contours is 0.05 au.

56 XC. Silva and M.A.C. Nascimento/J. Mol. Struct. (Theochem) 282 (1993) 51-57

Comparison of the two HF results suggests that, at least at this level of calculation, the inclusion of polarization functions is more important than extending the s and p atomic basis sets. It is also interesting to mention that Quelch and Hillier [5] concluded from a Mulliken population analysis that the singly occupied orbital has a strong (s + p) character and is localized in the Al atom. This same conclusion can easily be anticipated merely by inspection of the GVB description of the AlH, molecule (Fig. l(a)) because the lobe orbitals are just a combination of atomic s and p orbitals of the Al atom.

Table 4 shows the results of the dissociation energies for the two processes considered. The first feature to be noted on comparing the two results for process 2 is that orbital shape readjustments of non-adjacent bonds to the breaking bond can be safely neglected. This is an important result if one considers applying this procedure to more complex systems. The other important conclusion is that the Al-H bond is at least x 6 kcal mol-’ stronger than the C-Al bond in the H,CAlH molecule. Further, both bonds are weaker than the HAl-H bond (in fact the C-Al bond is w 10 kcal mall’ weaker than the HAl-H bond), showing that Al-H and Al-C bonds in comparable chemical environments may differ appreciably. Taking the value of 73.84 kcal mall’ for the dissociation energy of the AlH molecule [22], a value of 108.51 kcalmol-’ is obtained for the total bond dissociation energy of the H,CAlH molecule (CH, + H + Al), a result which does not differ significantly from the value of 116.9 kcal mall’ estimated by Parnis and Ozin [3].

Conclusions

The results for the AlH, molecule clearly indicate that bond dissociation energies comparable to those predicted by more elaborate calculations can be obtained merely by taking into consideration the differential correlation effects on the chemical bond being broken and relaxation of the other bonds.

The study of the H,CAl-H dissociation process also shows that only relaxation effects in the bonds

adjacent to the breaking bond need to be con- sidered if localized molecular orbitals are used.

Following this procedure, we find the Al-H bond to be x 6 kcal mall’ stronger the C-Al bond in the H,CAlH molecule, and both bonds weaker than the HAl-H bond. The Al-C bond is z 10 kcalmoll’ weaker than the HAl-H bond, showing that these two bonds in comparable chemical environments may differ appreciably.

Acknowledgements

The authors thank CNPq, Finep and FAPERJ for financial support.

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