The Journal of
Physical Chemistry
0 Copyright, 1990,by the American Chemical Society
VOLUME 94, NUMBER 19 SEPTEMBER 20, 1990
LETTERS Predicted Enthalpies of Formation for Silaethylene, Disilene, and Their Silylene Isomers Jerry A. Boatz*Vt and Mark S. Gordon* Department of Chemistry, North Dakota State University, Fargo, North Dakota 58105 (Received: April 16, 1990; I n Final Form: July 27, 1990)
Enthalpies of formation of silaethylene (SiH2=CH2), methylsilylene (HSICH,), disilene (SiH2=SiH2), and silylsilylene ( HSiSiH,) are predicted by using the recently developed GAUSSIAN-I method for computing accurate molecular energies. The predicted enthalpies of formation of the silylenes are compared with enthalpies of formation determined from isodesmic reactions. Very good agreement is found between these two methods and improved values for the enthalpies of formation of silaethylene and disilene are suggested.
Introduction Accurate enthalpies of formation are essential in understanding the thermodynamics of any given class of reactions. Furthermore, a knowledge of enthalpies of formation for a reaction or a group of related reactions is a necessary first step in the deduction of the mechanisms for these reactions. Unfortunately, the thermodynamic properties of many silicon compounds are not wellknown experimentally. In particular, the enthalpies of formation of the prototypical unsaturated silicon compounds silaethylene (SiH2=CH2)and disilene (SiH2=SiH2) and their silylene isomers (HSiCH, and HSiSiH,, respectively) are not well-known experimentally and continue to be debated.'+ Fortunately, for molecules with just 1-2 heavy atoms, theory is now able to provide quantitative guidance regarding thermodynamic quantities. Theoretical methods are used here to help unravel the thermodynamics of the four unsaturated silicon-containing compounds mentioned above. Several techniques for the theoretical prediction of enthalpies of formation of molecules have recently been developed.s-'O Among these is the GAUSSIAN-I methodology6 of Pople and coworkers (hereafter referred to as GI), which uses large basis sets 'Present address: Department of Chemistry, University of Utah, Salt Lake City, U T 841 12.
0022-3654/90/2094-7331$02.50/0
and quadratically convergent configuration interaction (QCI)" to predict enthalpies of formation and other properties of small (1)(a) Raabe, G.;Michl, J. Chem. Rev. 1985,85,419-509.(b) Gordon, M. S. Theoretical Studies of Multiple Bonding to Silicon. In Molecular Structure and Energetics; VCH Publishers: New York, 1986;Vol. 1, Chapter 4. (c) Apeloig, Y.Theoretical Aspects of Organosilicon Compounds. In The Chemistry of Organic Silicon Compounds; Patai, S., Rappoport, Z., Eds.; Wiley: New York, 1988;Chapter 2. (2)Walsh, R. Organometallics 1989,8, 1973-1978. (3) ONeal, H.E.;Ring, M. A.; Richardson, W. H.; Licciardi, G. F. Organometallics 1989,8, 1968-1973. (4)Gordon, M. S.; Boatz, J. A. Organometallics 1989,8, 1978-1980. (5) Pople, J. A.; Luke, B. T.; Frisch, M. J.; Binkley, J. S. J . Phys. Chem. 1985,89,2198-2203. ( 6 ) Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A. J . Chem. Phys. 1989,90, 5622-5629. (7)(a) Dewar, M. J. S.; Thiel, W. J . Am. Chem. Soc. 1977,99,4899.(b) Stewart, J. J. P. MOPAC. Quantum Chem. Program Exchange, Program 455; Department of Chemistry, Indiana University, Bloomington, IN 47405. (8)D i s h , R. L.; Schulman, J. M.; Sabio, M. L. J . Am. Chem. Soc. 1985, 107, 1904. (9)Ho,P.;Coltrin, M. E.; Binkley, J. S.; Melius, C. F. J . Phys. Chem. 1986,90,3399. (10)(a) Melius, C. F.; Binkley, J. S. ACSSymp. Ser. 1984,249,103. (b) Ho,P.; Coltrin, M. E.; Binkley, J. S.; Melius, C. F. J . Phys. Chem. 1985,89, 4641-4654. ( I I ) Pople, J . A.; Head-Gordon, M.; Raghavachari, K. J . Chem. Phys. i987,87,596a.
0 1990 American Chemical Society
Letters
7332 The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 molecules to within 1-2 kcal/mol of the experimental values. Binkley and MeliuslO apply empirical correction factors to fourth-order perturbation theory correlation energies to obtain enthalpies of formation for small compounds. For larger systems, the semiempirical methods of Dewar and Thiel and Stewart' can be used to predict enthalpies of formation. When enthalpies of formation are known for a subset of reference compounds, homodesmic reactionsi2may be used to predict enthalpies of formation of moderately sized compounds to within 2-3 kcal/mol, using split-valence plus polarization basis sets and a modest level of theory (Le., second-order perturbation theory) to determine correlation corrections.s Such reactions have been utilized in calculating enthalpies of formation of several highly strained organic molecules and their silicon analogs13as well as several alkyl silane^.^^*^^ Furthermore, recent studies have employed isodesmic reactions16 to predict the enthalpy of formation of (di)methylsilylene4 and methyl-substituted silenes and disilenes." Thus, once the enthalpies of formation for selected reference compounds have been established from experiment or with a reliable level of theory (e.g., GI), the analogous properties for larger related compounds may be predicted with the aid of isodesmic or homodesmic reactions. This combination of G1 theory and isodesmic/homodesmic reactions is thus a powerful tool for determining themodynamic properties. In the present work, G I 6 total molecular energies are used to compute enthalpy differences for reactions which relate the compound of interest to its constituent elements. By combining these computed reaction enthalpies with the known enthalpies of formation for the elements, one then obtains predicted enthalpies of formation for the compound of interest. For comparison, an isodesmic reaction (analogous to one from an earlier paper4 used to predict the enthalpy of formation of methylsilylene) is used to calculate the enthalpy of formation of silylsilylene. Computational Methodology The geometries for all compounds were initially optimized at the self-consistent field (SCF) level, using the 6-31G(d) basis setls and the analytical gradient routines in G A U S S I A N ~ ~ . ' ~All structures thus obtained were verified as local minima by demonstrating that their matrices of energy second derivatives are positive definite. The structures were then refined20 by using second-order many-body perturbation theory2' (denoted as MP2/6-31G(d)), as formulated by Pople and co-workers.22 The G I method of Pople et al.6 was then applied to obtain accurate molecular energies for the prediction of reaction enthalpies: the GI energies are obtained by assuming that, beyond the MP4/6(12) (a) George, P.; Trachtman, M.; Bock, C. W.; Brett, A. M. Tetrahedron 1976,32,317-323. (b) George, P.; Trachtman, M.; Brett, A. M.; Bock, C. W. J . Chem. Soc., Perkin Trans. 2 1977, 1036-1047. (13) (a) Boatz, J. A.; Gordon, M. S.; Hilderbrant, R. L. J . Am. Chem. Soc. 1988, 110. 352. (b) Boatz, J. A.; Gordon, M. S. J . Phys. Chem. 1988, 92, 3037. (c) Boatz, J. A,; Gordon, M. S. J . Phys. Chem. 1989, 93, 3025. (14) Gordon, M. S.; Boatz, J. A.; Walsh, R. J. Phys. Chem. 1989, 93, 1584-1585. (15) Boatz, J. A.; Gordon, M. S. J . Phys. Chem. 1990, 94, 3874-3876. (16) Hehre, W. J.; Ditchfield, R.; Radom, L.; Pople, J. A. J . Am. Chem. SOC.1970, 92,4796. ( 1 7) Gordon, M. S.; Boatz, J. A. Manuscript in preparation. (18) (a) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J . Chem. Phys. 1971, 54, 724-728. (b) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J . Chem. Phys. 1972,56,2257-2261. (c) Hariharan, P.C.; Pople, J. A. Theor. Chim. Acta 1973,28,213-222. (d) Gordon, M. S. Chem. Phys. Lett. 1980,76, 163-168. (19) Frisch, M. J.; Binkley, J. S.; Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohling, C. M.; Kahn, L. R.; DeFrees, D. J.; Seeger, R.; Whiteside, R. A.; Fox, D. J.; Fleuder, E. M.;Pople, J. A. GAUSSIANB~;Carnegie-Mellon Quantum Chemistry Publishing Unit, Pittsburgh, PA, 1984. (20) The MP2/6-31G(d) structures of disilene and silylsilylene were taken from ref 25. For silaethylene and methylsilylene, the MP2/6-31G(d,p) structures from ref 26 were used. Although the GAUSSIAN-I method assumes MP2/6-31G(d) geometries, the differences in the MP2/6-31G(d) and MP2/6-31G(d.p) structures are expected to be small. For example, the MP2/6-31G(d) [MP2/6-31G(d,p)] eometry of silaethylene is R SIC) 1.716 A [ 1.714A], R(CH) = 1.085 [1.080 A], R(SiH) = 1.482 [I.,; A], L(HSiC) = 122.5' [122.5"], L(HCSi) = 121.9' [121.9']. (21) Mdler. C.; Plesset, M. S. Phys. Rev. 1934, 46, 618. (22) Pople, J. A.: Binkley, J. S.; Seeger, R. Int. J . Quantum Chem. Symp. 1976, S10, 1-19
1
d
TABLE I: GI Total Energies a d Enthalpies of F o " W moleculeb
GI energy
AHr'm AGr"29~ as1'29a (0.0) (0.0)' (31.2)' (107.6)' (96.9)' (40.1)' (171.3)' (160.4)c (37.8)c 46Sd 49.4 -9.7 (37 f 5)t HSiCH, ('A') -329.405 39 50.d 52.5 -6.3 (44 f 3)C (48 f 2)g (53 i 4)* SiH2=SiH2 ('Ag) -580.43065 64.9' 66.5 -5.4 ( 1 6 2 f 2)c HSiSiH, (IA') -580.418 IO 72.V 73.9 -3.5 (75 f 2)t (75.3)'
H2 ('z:) -1.16500 Si (IP) -288.933 78 c(W -37.78464 SiH2=CH2 ( ' A l ) -329.41 I 5 2
'GI energies in hartrees, enthalpies and free energies of formation in kcal/mol, entropies in cal/(mol K). Experimental values in parentheses. *The electronic state is given below the structure. '(Gas phase): Chase, M. W. Jr.; Davies, C. A,; Downey, J. R. Jr; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. JANAF Thermochemical Tables, 3rd ed.;J . Phys. Chem. Ref. Data. 1985, 14, Suppl. 1. dFrom reaction la. CReference 24. fFrom reaction Ib. CReference 3. *Reference 29. I From reaction 2a. From reaction 2b. Reference 34.
3 1 IG(d,p) level of theory, additional improvements in basis set and level of correlation are additive. The resulting QCISD(T)/6-31 I+G(Zdf,p) energies are then modified for remaining basis set deficiencies6 Addition of scaled zero-point vibrational energies (ZPE) gives energy differences AE9. Finally, the reaction enthalpies are converted to 298 K as described previo~sly.~ The following isogyric reactions6 were used in predicting the G 1 enthalpies of formation of silaethylene, methylsilylene, disilene, and silylsilylene: 2H2 C Si H2Si=CH2 (la)
-
+ + HSiCH3 2H2 + C + Si H2Si=SiH2 2Hz + 2Si 2H2 + 2Si HSiSiH3
(lb) (2a) (2b)
The isodesmic reaction used to calculate the enthalpy of formation of silylsilylene is HSiSiH3 SiHl SiH2 + SiH3SiH, (3)
+
In this reaction, RHF/6-3 1G(d) structures and MP2/6-3 IG(d)//RHF/6-3 1G(d) energies (including ZPE corrections scaled by a factor of 0.8923) were used. Experimental enthalpies of formation for SiH4, SiH2, and SiH3SiH3were taken from W a l ~ h . 2 ~ Results and Discussion The GI total energies for all compounds considered in this paper are given in Table I. The experimental and predicted values for the enthalpies of formation are also listed here. (The MP2/63 1G(d) geometries have appeared elsewhere20*2s.26 and so will not be given here.) The predicted G1 enthalpies of formation for silaethylene and its isomer methylsilylene are 46.5 and 50.6 kcal/mol, respectively. The predicted 4.1 kcal/mol difference between these two, with silaethylene more stable, is 3 kcal/mol smaller than Walsh's experimental estimatez4but is within the stated experimental error bars. Most earlier theoretical studies,26-2sall of which use basis (23) Pople, J. A.; Schlegel, H. B.; Raghavachari, K.; DeFrees, D. J.; Binkley, J. S.; Frisch, M. J.; Whiteside, R. A,; Hout, R. J.; Hehre, W. J. Inr. J. Quantum Chem. Symp. 1981, S15, 269-278. (24) Walsh, R. The Chemistry of Organosilicon Compounds, Chapter 5, Thermochemistry, Patai, S., Rappoport, 2.;Eds.; Wiley: New York, 1988. (25) Gordon, M. S.; Truong, T. N.: Bonderson, E. K. J . Am. Chem. Soc. 1986, 108, 1421. (26) Gordon, M. S.;Truong, T. N. Chem. Phys. Lett. 1987,142, 110-1 14. (27) Luke, B. T.; Pople, J. A,; Krogh-Jesperson, M. B.; Apeloig, Y.; Karni, M.; Chandrasekhar, J.: Schleyer, P. v R.J . Am. Chem. Sor. 1986,108,270.
Letters
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7333
TABLE II: MP2/&31G(d)//RHF/&31G(d) Total Energies, Zero-Point Energies (ZPE), and Enthalpies of Formation for Reaction 3" electronic state
total energy
SiH2 SiH4 SiH,SiH,
'AI IAl
HSiSiH,
'A'
-290.069 36 -29 1.307 7 1 -581.46704 -580.23039
molecule
]Al,
ZPE 7.9 20.9 32.8 20.6
AH1°298 65.3' 8.2' 19.1' 75.8
"Total energies in hartrees; Z P E and enthalpies of formation in kcal/mol. *Reference 24.
sets of at least double-zeta plus polarization quality with correlation corrections, also predict silaethylene to be 2-4 kcal/mol more stable than methylsilylene (although a combined experimentaltheoretical study29predicts a somewhat larger energy difference of 10 kcal/mol). AMIm predicts silaethylene to be 23.4 kcal/mol more stable than its silylene isomer. Now let us compare the individual G I enthalpies of formation with the experimental values. For silaethylene the theoretical value is nearly 10 kcal/mol higher than that proposed by W a l ~ hwhile ,~~ for methylsilylene the GI enthalpy of formation is 6 kcal/mol above Walsh's result. For the latter isomer, there are other experimental estimates, in addition to the value of 44 kcal/mol from W a l ~ h These . ~ ~ are 48 f 23 and 53 f 429kcal/mol. If G I theory is indeed accurate to 1-2 kcal/mol, these results suggest that the preferred experimental enthalpy of formation is that from Ring et ale3 In addition, it appears that the experimental enthalpy of formation of silaethylene needs to be reexamined. These assertions are reinforced by the fact that the G1 enthalpy of formation for methylsilylene agrees very well with an earlier theoretical study from this laboratory4 which used an isodesmic reaction analogous to reaction 3 and MP2/6-3 IG(d,p)//RHF/63 lG(d,p) energies to obtain an estimated enthalpy of formation of 49.2 kcal/mol. The predicted G I enthalpies of formation for disilene and silylsilylene are 64.9 and 72.8 kcal/mol, respectively. This 8 kcal/mol energy difference is twice as large as that found for silaethylene and is somewhat smaller than the (at least) 13 kcal/mol difference suggested by the experimental results of W a l ~ h The . ~ ~GI difference is, however, in good agreement with several previous calculations2s~27~31~32 which predict disilene to be more stable by 6-8 kcal/mol. A notable exception is the study by Ho et a19 which predicts disilene to be 23 kcal/mol more stable than silylsilylene (which is similar to the AM130 value of 25 kcal/mol); however, the empirical scaling techniques used in deriving that value have recently been q u e s t i ~ n e d . ~ ~ ~ ~ ~ Of the two SizH4isomers, the G I enthalpy of formation is in better agreement with experiment for silylsilylene (75 f 2 kcal/mol from W a l ~ h75.3 ; ~ ~kcal/mol from Ring et al.34). The experimental estimate for disilene (162 kcal/molZ4)is in worse agreement and is the source of the disagreement in the isomer~~
~~~
~
~~
~
(28) Grev, R. S.;Scuseria, G. E.; Scheiner, A. C.; Schaefer, H. F. I11 J . Am. Chem. Soc. 1988, I IO, 7337. (29) Shin, S.K.; Irikura, K. K; Beauchamp, J. L.;Goddard, W. A. J . Am. Chem. Soc. 1988, 110, 24. (30) Dewar, M. J. S.; Jie, C. Organomerallics 1987, 6, 1486. (31) Samasundram, K.; Amos, R. D.; Handy, N. C. Theor. Chim. Acra 1986, 70, 393-406. (32) Olbrich, G . Chem. Phys. Lerr. 1986, 130, 115. (33) The enthalpies of formation obtained in this paper are computed after empirical bond energy correction factors have been applied to the MP4 energies. Using the uncorrected MP4 energies, one obtains a relative enthalpy difference between disilene and silylsilylene of about 6 kcal/mol (favorin disilene), which is in good agreement with other theoretical (34) Martin, J. G.; ONeal, H. E.; Ring, M. A. Inr. J . Chem. Kine?., in press.
ization energy noted in the previous paragraph. An earlier theoretical study9 (at the MP4/6-31 IG(d,p)//HF/6-31G(d) level) predicted the enthalpies of formation of disilene and silylsilylene to be 57 f 10 and 80 f 3 kcal/mol, respectively. From the isodesmic reaction 3, one obtains a predicted enthalpy of formation for silylsilyleneof 75.8 kcal/mol (see Table 11), in good agreement with the G1 result. The above summary indicates a fairly wide range of possible enthalpies of formation for the four compounds of interest. However, we believe the present predictions to be accurate within 1-2 kcal/mol, based on the following: 1. The GI method6 generally predicts thermodynamic properties (such as electron affinities, ionization potentials, and atomization energies) with an accuracy of 1-2 kcal/mol. Similar accuracy has been obtained for molecules containing two heavy atoms or a third-row element.35 2. The GI predicted enthalpies of formation of methylsilylene and silylsilylene are in very good agreement with the enthalpies of formation obtained from isodesmic reactions (which are generally accurate to within 3-5 k c a l / m 0 1 ) . ~ ~ ~ ~ * ' ~ 3. The GI relative enthalpies of formation are consistent with the results of several earlier high-level ab initio s t ~ d i e s . ~ ~ - * ~ * ~ ' , ~ ~ Therefore, we are confident that the G1 computed enthalpies of formation of these four molecules represent improvements to the currently accepted values, particularly for silaethylene and disilene, and for the first time provide a consistent set of values for the four molecules of interest here. To the extent that the G1 enthalpies are accurate to 1-2 kcal/mol, comparison of the experimental and GI enthalpies of formation suggest that, experimentally, only the enthalpy of formation of silylsilylene is accurately known. The experimental enthalpy of formation of difilene appears to be somewhat low and thus the energy difference relative to silylsilylene is overestimated. Although the enthalpy of formation of methylsilylene obtained by Ring et aL3 is consistent with the GI result, the agreement among the three experimental determinations is rather poor. Furthermore, the large difference between the experimental and theoretical enthalpies of formation for silaethyene is disturbing. With the exception of silylsilylene, the theoretical results presented here strongly suggest the need for futher experimental measurements of the enthalpies of formation of these compounds. Having established accurate enthalpies of formation of these four compounds, it is possible to design isodesmic and/or homodesmic reactions to predict the enthalpies of formation of several derivatives of the parent molecules. For example, the isodesmic reaction HRSi=SiH2 SiH4 H2Si=SiH2 SiH3R (4)
+
-
+
can be used to compute the enthalpy of formation of HRSi=SiH2 (where R denotes a general functional group), provided the enthalpy of formation of SiH3R is known. In a forthcoming paper," the enthalpies of formation of the methyl-substituted silaethylenes and disilenes, calculated by using isodesmic reactions and the enthalpies of formation of silaethylene and disilene computed in the present work, will be reported. Acknowledgment. This work was supported in part by grants from the National Science Foundation (CHE89-11911) and the Air Force Office of Scientific Research (90-0052). The computations were performed on the NDSU Quantum Chemistry Group VAX 8530 (provided with the aid of DoD grant 87-0237), Celerity C1260D (purchased with the aid of N S F grant CHE85-11697), and the Cary Y-MP at the San Diego Supercomputer Center. (35) Curtiss, L. A. Private communication.
