rate constant limits and thermochemistry. Ab initio and DFT

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The insertion of germylene into the H—H bond; rate constant limits and thermochemistry. Ab initio and DFT calculations on the reactions of GeH2 and SiH2 with H2 Rosa Becerra, Sergey E. Boganov, Mikhail P. Egorov, Valery I. Faustov, Oleg M. Nefedov, and Robin Walsh

Abstract: The technique of laser flash photolysis in the gas-phase has been used to set limits on the rate constants for the bimolecular reaction of germylene (GeH2) with deuterium (D2) at both ambient and elevated temperatures (585 K). These limits show that the activation energy for the insertion of GeH2 into the H—H bond is at least 19 (±6) kJ mol–1. Thermochemical arguments place the activation energy approximately in the range 63–84 kJ mol–1. DFT B3LYP/6– 311++G(3df,2pd) and ab initio QCISD(T)/6–311G++(3df,2pd)//QCISD/6–311G(d,p) calculations have been carried out on the potential energy surfaces of reactions ZH2 + H2 → ZH4 (Z= Ge, Si). Both methods predict the same mechanisms for germylene and silylene insertion which include formation of loose prereaction complexes and transition states of similar structure. The prereaction complex is only about half as strong in the case of germylene (∆H (298 K) = –9 (–11) kJ mol–1) as in the case of silylene (∆H (298 K) = –16 (–21) kJ mol–1) (QCISD values cited with B3LYP values in parentheses). The differences in activation energies are even more significant. Germylene insertion has a very high barrier of 58 (56) kJ mol–1 compared to that of silylene 13 (6) kJ mol–1. Calculated activation parameters for both reactions are in reasonable consistency with experimental results. Reasons for the enhanced H-H insertion barrier for germylene compared with silylene are discussed. Key words: laser flash photolysis, germylene, silylene, deuterium, activation energy, thermochemistry, ab initio calculation, DFT B3LYP calculation. Résumé : On a fait appel à la technique de la photolyse éclair au laser pour déterminer les limites des constantes de vitesse de la réaction bimoléculaire du germylène (GeH2) avec le deutérium (D2) à des températures tant ambiantes qu’élevées (585 K). Ces limites montrent que l’énergie d’activation pour l’insertion du GeH2 dans la liaison H—H est d’au moins 19 ± 6 kJ mol–1. Des arguments thermodynamiques suggèrent que la valeur de l’énergie d’activation est de l’ordre de 63 à 84 kJ mol–1. On a effectué des calculs DFT B3LYP/6–311++G(3df,2pd) et des calculs ab initio QCISD(T)/6–311G ++(3df,2pd)//QCISD/6–311G(d,p) sur les surfaces d’énergie potentielle des réactions ZH2 + H2 → ZH4 (Z = Ge, Si). Les deux méthodes prédisent les mêmes mécanismes pour la réaction d’insertion du germylène et du silylène; ils comportent la formation de complexes préréactionnels lâches et des états de transition de structure similaire. La force du complexe préréactionnel du germylène est approximativement la moitié (∆H (298 K) = –9 (–11) kJ mol–1) que dans le cas du silylène (∆H (298 K) = –16 (–21) kJ mol–1) (dans lesquelles la valeur citée correspond à QCISD et la valeur entre parenthèses aux calculs B3LYP). Les différences dans les énergies d’activation sont plus significatives. La valeur de la barrière pour l’insertion du germylène est très élevée 58 (56) kJ mol–1 par comparaison avec celle du silylène 13 (6) kJ mol–1. Les paramètres d’activation calculés pour les deux réactions sont en accord raisonnable avec les résultats expérimentaux. On discute des raisons de la barrière d’insertion H—H plus élevée pour le germylène par comparaison avec le silylène. Mots clés : photolyse éclair au laser, germylène, silylène, deutérium, énergie d’activation, thermochimie, calculs ab initio, calculs DFT B3LYP. [Traduit par la Rédaction]

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Received July 5, 1999. Published on the NRC Research Press website on October 25, 2000. This paper is dedicated to Adrian Brook in recognition of his special contribution to organosilicon chemistry R. Becerra. Instituto de Quimica-Fisica “Rocasolano,” C.S.I.C., C/Serrano 119, 28006 Madrid, Spain. S.E. Boganov, M.P. Egorov, V.I. Faustov, and O.M. Nefedov. N.D. Zelinsky Institute of Organic Chemistry, Russian Academy of Sciences, Leninsky Prospekt 47, 117913 Moscow, Russian Federation. R. Walsh.1 Department of Chemistry, University of Reading, Whiteknights, P.O. Box 224, Reading RG6 6AD, U.K. 1

Author to whom correspondence may be addressed. Telephone: +44 (0)118 931 6347. Fax: +44 (0)118 931 6331. e-mail: [email protected]

Can. J. Chem. 78: 1428–1433 (2000)

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Introduction Germylene(GeH2) is thought to be an important intermediate in the chemical vapour deposition (CVD) of semiconductor germanium from GeH4 (1, 2). It is certainly the key intermediate in the thermal decomposition of GeH4 (3). Interest in this species has grown, not only because of its involvement in the materials formation process, but also because in recent years it has become accessible to direct monitoring by laser resonant absorption (4–7). Studies in our laboratories have shown that GeH2 inserts into Ge—H bonds with a negative activation energy which is greater (i.e., more negative) for the Ge—H bond in Et3GeH (5) than that in GeH4 (6). In this respect the kinetic and mechanistic behaviour of GeH2 parallels that of SiH2 (8–10) which undergoes the equivalent Si—H bond insertion processes. However GeH2 is less reactive than SiH2 in its counterpart reactions and shows greater selectivity (alkyl substituents enhance the reactivity of Ge—H bonds to GeH2 more than of Si—H bonds to SiH2). This can be explained in terms of the involvement, and binding strengths, of the H bridged complexes formed as intermediates, whose relative stabilities have been calculated by ab initio methods (6). The question naturally arises of the ability of GeH2 to insert into the H—H bond, viz. [1]

GeH2 + H2 → GeH4

This is arguably the simplest insertion reaction of all and is potentially of great significance in CVD systems where H2 is present. The kinetics of the silylene analogue of [1] were first investigated by Jasinski (11), viz. [2]

SiH2 + H2 → SiH4

This study made a dramatic impact. Not only was it amongst the earliest of absolute rate measurements for SiH2, but the rate constant obtained (2.6 × 10–12 cm3 molecule–1 s–1 for SiH2 + D2) was more than 104 times greater than expected from earlier indirect experimental measurements (12) or available theoretical calculations (13–16). Thus, this paper caused a significant re-evaluation of the reactivity and thermochemistry of SiH2. At the present time there has been no reported (or attempted) measurement of the rate constant of rxn. [1] nor any published calculation of the energy barrier of reaction [1]. Thus unlike for rxn. [2] there is no prior history. The reaction is however ripe for investigation. It is an important point to note that we have chosen to study the deuterium variant of [1], following the logic of Jasinski (11) who studied the deuterium version of [2] (viz. SiH2 + D2). The reason for this is straightforward; it is to avoid the potential complications arising from studying a third-body assisted association process at pressures below the high-pressure (true bimolecular) limit. The reaction of GeH2 with D2 can be described by the mechanism shown in Scheme 1. In this reaction the initial insertion product is vibrationally excited GeH2D2*. This species can then either be collisionally stabilized by the third body, or decompose unimolecularly by one of the three pathways shown. Of these three pathways, assuming there are no unexpectedly large isotope effects, reversion to GeH2 + D2 is only one, and indeed on probability grounds represents only one in six of the possible decompo-

1429 Scheme 1.

sition channels for GeH2D2*. Thus the monitoring of the disappearance of GeH2 (with its unique isotopic absorption signature) should correspond, to a good approximation, to the rate constant k1 for the true bimolecular process. We have also carried out ab initio QCISD and DFT B3LYP calculations on the potential energy surfaces of both rxns. [1] and [2]. Silylene insertion [2] was naturally chosen as a reference reaction, not only because of the intrinsic interest in comparing Ge with Si, but also because there is a wealth of experimental (8, 9) and theoretical data (13–17) for [2]. Both reactions may be considered as test systems for comparison of the accuracy of various levels of quantum chemical calculations against kinetic and thermochemical data.

Experimental Rate measurements Germylene kinetic studies have been carried out by the laser flash photolysis technique, details of which have been published previously (4–6). Only essential details are therefore included here. GeH2 was produced by photodecomposition of 3,4-dimethylgerma-cyclopentene-3 (DMGCP) using the 193 nm line of a pulsed excimer laser (Coherent Compex 100). GeH2 was detected and monitored in real time by use of a single mode dye laser (Coherent 699–21) pumped by an argon ion laser (Coherent Innova 90–5), tuned to a known strong vibration–rotation transition at 17 111.31 cm–1 in the visible A ← X absorption band. Experiments were carried out in a variable temperature spectrosil quartz vessel with demountable windows which were regularly cleaned. Signal decays from 3–10 photolysis laser shots (at 60 mJ/pulse) were averaged and found to give good first order linear fits (ln (abs) vs. t plots up to 90% signal decay). These experiments yielded values for the first order rate coefficient, kobs, for removal of GeH2 in the presence of known partial pressures of D2. Gas mixtures for study consisted of a few mtorr (1 torr = 133.322 Pa) of DMGCP and various amounts of substrate D2 (limited by pressures which caused signal quenching). DMGCP was synthesised by us previously (4). Deuterium (British Oxygen Co) was 99.8% pure (0.2% of HD). It contained no GC detectable impurities and was handled carefully to avoid contamination by non-condensibles (air). Ab initio and DFT calculations In the ab initio calculations geometry optimisations, vibrational analyses and reaction paths were performed at the frozen core, QCISD/6–311G(d,p) level (18). All the structures obtained here were verified, by examination of the frequency matrix, as minima (all frequencies real) or transition © 2000 NRC Canada

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Can. J. Chem. Vol. 78, 2000 Table 1. First order rate constantsa for GeH2 decay in the presence of D2. Temp (K)b 293

D2 (torr) (1 torr = 133.322 Pa)

kobs (104 s–1)

Temp (K)c

0d 9.4 29.4 79.4

4.2 5.5 6.2 6.6

585

± ± ± ±

0.4 0.3 0.1 0.2

D2 (torr) (1 torr = 133.322 Pa)

kobs (104 s–1)

0d 9.5 51.0 —

2.3 ± 0.4 2.1 ± 0.4 3.4 ± 0.3 —

a

Average of three or four measurements. Precursor (DMGCP): 3.0 mtorr. c Precursor (DMGCP): 5.0 mtorr. d Pressurized to 10 torr with SF6. b

states (TSs) (one imaginary frequency). Final energies were refined by single point QCISD(T)/6–311G++(3df,2pd) calculations, which are denoted subsequently in this paper as QCISD(T)/6–311G++(3df,2pd)//QCISD/6–311G(d,p). The DFT calculations, including the finding and verification of stationary points, were done with the B3LYP functional (19) using the 6–311++G(3df,2pd) basis. Energies from both levels of theory were corrected to include zero point vibrational energy contributions. For all stationary points we also calculated enthalpies and Gibbs free energies at 298 K. For these other thermodynamic functions, harmonic oscillator and rigid rotor models were used throughout, employing geometries and frequencies (unscaled) from the appropriate set of calculations. Transition states were confirmed by calculations along the minimum energy paths (intrinsic reaction coordinate, IRC) connecting them with local minima. Most of the calculations carried out here were performed using GAUSSIAN 94 (20) on the SGI POWER CHALLENGE L supercomputer at the computer center of IOC RAS, Moscow.

Results and discussion Kinetics and thermochemistry The reaction was studied at 293 K and 585 K at several partial pressures of D2. The results are shown in Table 1. It is clear from the extremely small variation in values of kobs under the operational conditions that there is very little if any reaction. Even at the maximum pressures of D2 at each temperature the values of kobs are barely beyond the uncertainties of the measurements without D2. At intermediate pressures of D2 the values are consistent. It is certainly possible that the small increases observed could have been caused by as little as 0.01% of an impurity reacting at the collision rate. To obtain an upper limit to the true secondorder rate constants, the maximum values of kobs at the highest D2 pressures were combined with the zero D2 values and the difference attributed to reaction. This yielded for k1, maximum values of 1.0 × 10–14 cm3 molecule–1 s–1 at 293 K and 1.7 × 10–14 cm3 molecule–1 s–1 at 585 K. The difference between these values, which for the reasons given only represent upper limiting values, is not significant, and we therefore saw no point in investigating intermediate temperatures (or further D2 pressures). Because these measurements have only given limiting values, the magnitudes of the true rate constants remain to be obtained. Nevertheless each value can be used independently to obtain a lower limiting value for the activation

Table 2. Limiting values for rate constants and derived activation energiesa for GeH2 + D2 Temp (K) 293 585 a

k1 (cm3 molecule–1 s–1) –14

< 1.0 × 10 < 1.7 × 10–14

Ea[1] (kJ mol–1) > 10.8 (±3) > 19.2 (±6)

Based on assumed A factor (see text).

energy Ea[1] through the use of an estimated A factor, A1 = 10–12.07 cm3 molecule–1 s–1. This is obtained by analogy with the measured A factor (8,9) for SiH2 + D2 (deuterium analogue of rxn. [2]). Use of this value leads to the activation energy values shown in Table 2. Clearly the advantage of the higher temperature study is to have provided a better (higher) limit. While the value of A1 has been assumed by analogy with A2, it is worth noting that the values of the A factors for the reverse reactions, A–1 and A–2, obtained by study of the thermal decompositions of GeH4 (3) and SiH4 (21) respectively, are both 1015.5 s–1. Since the entropy changes for these isostructural reactions are likely to be close to one another, this adds weight to the assumption of similar forward reaction A factors. The activation energies quoted in Table 2 nevertheless allow for an uncertainty of 10±0.5 in the estimate of A1. There are no previous measurements of this activation barrier by direct means. However this result can be illuminated by consideration of the expected value based on thermochemistry. For the reverse reaction, viz. [–1]

GeH4 → GeH2 + H2

∆H° may be estimated from ∆Hf°(GeH4) = 90.4 ± 2.1 kJ mol–1 (22) together with ∆Hf°(GeH2) = 237.2 ± 12 kJ mol–1 by experiment (6), or 250–258 kJ mol–1 (6, 23, 24) by theoretical calculation. This puts ∆H°[–1] in the range 147–168 kJ mol–1; at the lower end from experimental data alone, at the higher end using theoretical information. The thermal decomposition of GeH4 in static systems is highly perturbed by surface reactions (for previous studies of the kinetics of GeH4 decomposition see ref. 3). Only one study by Newman et al. (3) in a shock tube in the temperature range 950–1060 K yields reliable kinetic measurements of rate constants of the purely homogeneous rxn. [–1]. Under these conditions the reaction is in its unimolecular fall-off region and RRKM modelling was required to obtain the true infinite pressure value of Ea[–1] for which a figure of 227 kJ mol–1 was obtained (error limits are not quoted). If this value is assumed reasonably independent of temperature, then Ea[1] can be © 2000 NRC Canada

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Fig. 1. Stationary points of reactions [1] (Z = Ge) and [2] (Z = Si) calculated at the QCISD/6–311G(d,p) and B3LYP/6– 311++G(3df,2pd) levels. The symmetry group is given below each structure.

Table 3. QCISD/6–311G(d,p) and B3LYP/6–311++G(3df,2pd) calculated geometric parameters (R, A) and the lowest harmonic wavenumber (ν (cm–1)) of stationary points of reactions ZH2 + H2 → ZH4 (Z = Si, Ge). Distances R are in Angstroms, angles A in degrees. For atom numbering see Fig. 1.a Structure Z = Si Complex

TS

Z = Ge Complex TS

Method

ν (cm–1)

R(Z-H1)

R(Z-H3)

R(Z-H4)

R(H3-H4)

A(H1-Z-H2)

Reference

QCISD B3LYP MP2 QCISD B3LYP MP2 MRD-CI HF

437 493 609 –1272 –1172 –1205 — —

1.509 1.513 1.505 1.479 1.484 1.477 1.494 1.484

1.936 1.870 1.858 1.661 1.647 1.636 2.001 1.691

1.859 1.778 1.787 1.522 1.522 1.515 1.548 1.547

0.783 0.805 0.792 1.117 1.140 1.135 1.974 1.103

95 95 94 110 110 110 118 113

This This 17 This This 17 16 15

work work

QCISD B3LYP QCISD B3LYP

261 330 –1347 –1252

1.589 1.590 1.539 1.539

2.276 2.108 1.742 1.721

2.225 2.033 1.573 1.568

0.758 0.773 1.215 1.250

92 92 111 111

This This This This

work work work work

work work

a For reagents and products calculated QCISD (B3LYP) parameters are: H2, R(H—H) = 0.744 (0.743); GeH2, R(Ge—H) = 1.592 (1.596), A(H-Ge-H) = 91.8 (90.9); GeH4, R(Ge—H) = 1.535 (1.534); SiH2, R(Si—H) = 1.516 (1.523), A(H-Si-H) = 92.6 (91.6); SiH4, R(Si—H) = 1.476 (1.480).

obtained via Ea[1] = Ea[–1] – (∆H° – RT). From the figures cited this puts Ea[1] in the range 63–84 kJ mol–1 (estimated at a temperature of 500 K). Because of the assumptions concerning Ea[–1] the uncertainty must be considered slightly larger than this. Nevertheless this thermochemical estimate is well above the limit set by experiment and therefore shows that unless the thermochemical data are seriously in error, a fast reaction between GeH2 and H2 is not to be expected. Quantum chemical calculations Apart from the reactants, GeH2 + H2, and the product, GeH4, we find two stationary points on the potential energy surface (PES) corresponding to a local minimum and a transition state, both of Cs symmetry. These are shown in Fig. 1. The same set of stationary points was found for the silylene rxn. [2]. For the latter reaction this agrees with earlier studies at the MP4(SDQ)/6–31G*//HF/3–21G level (15), MRD-CI/TZ+P level (16) and MP4/6–

311G++(3df,3pd)//MP2/6–311G(2d,2p) level (17). The geometrical parameters of these structures are shown in Table 3, including comparisons with earlier work in the silylene case. The geometries from the B3LYP and QCISD calculations are in good agreement with each other not only for the stable species (reagents and products) but also for the TSs and complexes. The bigger differences found between silylene and germylene complexes reflect the rather loose nature of these structures. The calculated energies are shown in Table 4. The prereaction complex in the germylene reaction is only about half as strong (∆H (298 K) = –9 (–11) kJ mol–1) as that in silylene case (∆H (298 K) = –16 (–21) kJ mol–1). Both here and subsequently the QCISD values are given first, with the B3LYP values following in parentheses. Despite the weakness of these species the interactions of the two fragments are significant enough to stretch the H—H bond (H4—H3) by 0.015 (0.030) Å in the germylene complex and by 0.039 (0.062) Å in the silylene complex. The © 2000 NRC Canada

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Can. J. Chem. Vol. 78, 2000

Table 4. QCISD(T)/6–311G++(3df,2pd)//QCISD/6–311G(d,p) and B3LYP/6–311++G(3df,2pd) calculated energies (E /hartree, ∆E, ∆H, ∆G in kJ/mol) of stationary points on the PES of reactions [1] and [2].a Z = Si

Z = Ge

Complex

TS

SiH4

Complex

TS

GeH4

QCISD(T) E ∆E ∆E + ZPE ∆E 298 K ∆H 298 K ∆G 298 K

–291.35054 –28 –9 –13 –16 15

–291.34032 –1 13 7 5 38

–291.43606 –252 –226 –232 –234 –194

–2077.74926 –17 –4 –6 –9 19

–2077.72484 47 58 53 50 84

–2077.81231 –183 –160 –165 –168 –128

B3LYP E ∆E ∆E + ZPE ∆E 298 K ∆H 298 K ∆G 298 K

–291.83611 –32 –14 –19 –21 12

–291.82650 –7 6 0 –2 33

–291.91909 –250 –225 –231 –234 –198

–2079.34896 –20 –5 –9 –11 20

–2079.32428 44 56 50 48 83

–2079.40668 –172 –150 –155 –157 –122

a Calculated QCISD (B3LYP) total energies of reagents (hartree): H2, –1.17235 (–1.180013); GeH2, –2076.57037 (–2078.16115); SiH2, –290.16762 (–290.643748).

characteristics of the silylene complex are in close similarity to those of the previous highest level of calculation by Gordon et al. (17) although our complex is slightly looser especially in the QCISD calculations. According to our calculations rxns. [1] and [2] have similar TSs. The distinction between them is only of the degree to be expected from the characteristic differences in Ge—H and Si—H bond lengths. The breaking H4—H3 bond of the germylene TS is stretched by 0.472 (0.508) Å compared to 0.373 (0.398) Å for the silylene TS. This implies that the PES maximum in the germylene insertion [1] is shifted towards the product compared to the silylene case [2] in agreement with expectations from Hammond’s postulate (25) for a less exothermic process. The TS structure for the silylene insertion [2] found here is very similar to those calculated earlier by Sosa and Schlegel (15) and Gordon et al. (17) but differs somewhat from that of Sax and Olbrich (16) (Table 3). The latter has a much more extended H4—H3 bond, which looks (with hindsight) out of keeping with the early nature of the transition state (based on energy). This was probably a deficiency of the calculation. The values for ∆H°[1] calculated by the QCISD and B3LYP methods are –168 and –157 kJ mol–1, respectively, (Table 4). Both fall within the range –147 to –168 kJ mol–1 estimated from thermochemistry and indicated above, and are consistent with our ab initio calculations on the reaction of GeH2 with GeH4 (6). The ab initio barrier (Ea = ∆E + ZPE) of 53 (50) kJ mol–1 at 298 K is slightly lower than the thermochemically estimated range of 63–84 kJ mol–1 at 500 K. However for the reasons given in the previous section this must be considered quite good agreement. The calculations may be judged by the results for the silylene case for which both methods give the same value of ∆H°[2] of –234 kJ mol–1 (Table 4). This compares well with the current best value of –239 ± 3 kJ mol–1 (derived from ∆Hf°(SiH4) = 34.3 ± 1.2 kJ mol–1 (26) and ∆Hf°(SiH2) = 273.2 ± 2 kJ mol–1 (8, 10)). The QCISD barrier, ∆E[2] of 7 kJ mol–1 is slightly higher than the measured Ea of – 2 kJ mol–1 (8, 9) but as reasonably

close as the previous best calculation of Gordon et al. (17) who also obtained 7 kJ mol–1 (the other earlier calculations (13–16) gave significantly higher barriers). Even better agreement for the barrier ∆E[2] was obtained in B3LYP calculations (0 kJ mol–1). It appears that DFT methods, with their markedly lower computational demands, can produce good results for these quite large systems. Thus B3LYP may be considered as the best choice for studying this type of reaction. The calculations carried out here show that, despite the mechanistic similarity, rxn. [1] has a significant barrier compared with rxn. [2] and so a fast reaction between GeH2 and H2, like that between SiH2 and H2, is not to be expected. It prompts the question as to why there is a significant increase of activation barrier from [2] to [1]. Sax and Olbrich (16) actually predicted this qualitatively on the basis of a valencebond configuration mixing (VBCM) model (27, 28) which was employed to explain the differences between the silylene and methylene (1A1 states) reactions with H2. The VBCM model involves energy surface mixing with surfaces derived from triplet state species. Despite the slight deficiencies of structure and energy in the calculations mentioned above (16), Sax and Olbrich make their prediction for GeH2 + H2 on the basis that the singlet-to-triplet excitation of GeH2 is ca 17 kJ mol–1 higher than that of SiH2. Whatever the merits of this argument we would point out that our calculations show unequivocally the extra extension of the H—H bond in the TS for rxn. [1] compared to [2] and this is consistent with the need to satisfy the less favourable H···Ge overlap compared to that of H···Si, due to the more diffuse nature of the germanium atomic orbitals. This reasoning also qualitatively supports a more demanding energy requirement for germylene than silylene in reaching the transition state. The existence of pre-TS complexes of GeH2 and SiH2 with H2 as predicted here, presents a challenge to experiment. The possibility exists of direct spectral observation at low temperatures. In this respect, the germylene complex may be more amenable to isolation than its silylene counterpart, © 2000 NRC Canada

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despite its weaker binding. This is because of the existence of the substantial barrier to formation of GeH4, in contrast to the low barrier separating the silylene complex from SiH4. The positive ∆G of complexation at 298 K makes equilibrium detection of either species totally unlikely. We finish by noting the contrasts between GeH2 and SiH2 insertion reactions. Both species insert readily and rapidly into Ge—H bonds (5, 6) and also Si—H bonds (29).2 Activation energies for these processes are all negative but are more negative for GeH2 than for SiH2 insertions although potential energy surfaces show many similarities. For H—H bond insertion, despite some similarity of the potential energy surfaces, GeH2 requires significant activation whereas SiH2 does not. For C—H bond insertion, reactions of both GeH2 and SiH2 with CH4 require significant activation. For GeH2 a recent DFT calculation gives a barrier of 138 kJ mol–1 (30), whereas for SiH2 + CH4 the best estimate of the barrier is 59 kJ mol–1 (31).

Acknowledgements We wish to thank the following: (i) the Royal Society of Great Britain for support under its joint project scheme with States of the Former Soviet Union (Grant P851); (ii) INTASRFBR (Grant N IR-97-1658); (iii) the Russian Foundation for Basic Research (Grants N 00-03-33001 and N 00-1597387); (iv) the Russian Academy of Sciences for a young scientists grant 1998, for support to S.E.B.; (v) the CACR Computer Center at the Zelinsky Institute for computer time on the SGI Power Challenge L; and (vi) the Direccion General de Investigacion Cientifica y Technica (DGICYT), Spain, for support to R.B. under project PB97-1214.

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R. Becerra, S.E. Boganov, M.P. Egorov, V.I. Faustov, O.M. Nefedov, and R. Walsh. Submitted to Phys. Chem. Chem. Phys. © 2000 NRC Canada

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