J . Phys. Chem. 1992, 96,428-437
4%
the vq) = 3 level is 0.68 ps. Similarly, the lifetimes of levels with vl' = 1 and vq) = 0, 1, and 2 are 0.97, 0.66, and 0.14 ps, respectively.26 This reduction in lifetime as a function of excitation of the bending mode is indicative of an increase in IVR or intersystem crossing. Thus, if the continuum were associated with either of these processes rather than d d a t i o n , one would expect the continuum absorption would be found under the entire AIZ:,XIZg+ absorption region. Moreover, if one takes the decrease in radiative lifetimes as a measure of the crossing rate, the calculated broadening estimated from the uncertainty principle would be substantially less than a wavenumber. The resolution of the doubled excimer pumped dye laser was not sufficient to excite single rotational levels of the C2N2spectrum. The overall symmetry of the Q branch AIZ-, XIZ+g 101410 band is Z ?r. The peak of the Q branch will be at J = 25 for a thermally excited population of C2N2. The excitation laser was fixed at the Q band maximum. The A I B , v'~= 1, vh = 0 level lies 47 625 cm-I above the ground state. The N = 16 level of C N (X2Z+) has 517 cm-l of rotational energy. This corresponds to a C2N2dissociation threshold of 47 108 f 10 cm-I or 212.28 nm. The corresponding bond strength for C2N2is 5.84 eV and AHfo(CN) is 435.5 f 2.0 kJ/mol. Experiments on C2N2 photolysis at higher energy are well modeled by a statistical theory that conserves angular momentum.12J3 The details of that calculation show that the rotational levels of the two C N fragments are not locked to one another. Rather the orbital angular momentum of the dissociating fragments takes on values which conserve total angular momentum while the rotational state of the partner can assume all energetically possible values with equal weight. Therefore, it is reasonable to assume that in the experiment described here the last observed rotational level of the C N fragment is an energetic upper limit set by the total energy available after dissociation. By comparison with BrCN photolysis at the same wavelength, the quantum yield for dissociation of C2N2excited on the 101410 line is about 0.05. The first dissociative state is reached by the 201403transition and lies 47070 cm-I above the ground-state origin. The next lowest level is excited via the 201412band. This hot band is seen in
-
-
-
(26) Huang, Y.; Barts, S. A,; Halpern, J. B., manuscript in preparation.
absorption and emission at about the same level as the 20'403 transition. No C N is observed following excitation of any rotational line in the 201412band. The frequency of the excited state vq) bending mode, 274 cm-I, is comparable to the average amount of rotational energy a t room temperature, 200 cm-I. If the dissociation limit was between the A'Z-, state 01020 and 01030 levels, it should have been possible to observe C N following absorption on some rotational lines of the 201412band. This is not the case. Thus, the dissociation limit should lie in the 20'40~band. Unfortunately, the low C N quantum yield a t threshold and the resolution of the photolysis laser make it impossible to directly determine where in this band dissociation is first seen. The energy needed to excite the rotationless 201403line, 47 070 f 100 cm-', can therefore be taken as an estimate for breaking the ethanedinitrile CC bond. The uncertainty includes a factor to compensate for the rotational energy of the parent C2N2. The dissociation threshold would then be 212.45 nm, the bond strength 5.84 eV, and AZ-Zf."(CN) 435.2 f 2.3 kJ/mol. This C N heat of formation is slightly lower than but within the error of the other two measurements. On the other hand, if rotation were ignored and it was assumed that the dissociation limit lay between excited states reached via the &I403 and 201412bands, 435.2 f 2.3 kJ/mol would be an upper limit. Averaging the three determinations yields for the heat of formation of C N a t 0 K H,'(CN)
= 435.4 f 2.0 kJ/mol
and an average bond strength for fracture of the CC bond in C2N2 of 5.84 f 0.02 eV. While this is close to the JANAF value, the agreement of our three measurements significantly reduces the uncertainty. It is worthwhile to recall that the uncertainty was based on a wide variation in measured values and the inability of the JANAF board to find a basis of choosing between them. Moreover, many workers have been using lower values re"mended by the shock tube and the photodissociative excitation experiments.
Acknowledgment. This work was supported by the National Aeronautics and Space Administration under grant NAGW-785 and by Howard University. Registry NO. CN, 2074-87-5.
Theoretical Study of the Thermochemistry of Molecules in the Si-C-H System Mark D. Allendorf* and Carl F. Melius* Combustion Research Facility, Sandia National Laboratories, Livermore, California 94551 -0969 (Received: June 24, 1991)
Ab initio electronic structure calculations coupled with empirical corrections are used to obtain a self-consistent set of heats of formation for molecules in the series H,,Si(CH,), and H,,SiCH, (n,m = 0-4). Heats of formation are also reported for silylethylenes and silylacetylenes in the series H2C=CHSiH, and H m S i H , (n = 0-3), and for H(CH3)Si=CH2, (CH&3i=CH2, and 1.2-dimethyldisilane. Gibbs free energies as a function of temperature and standard entropies are given for all molecules in the study.
I. Introduction The reactions of organosilicon compounds are of considerable interest in the field of organometallic ~hemistryl-~ due both to the parallels with the analogous hydrocarbon chemistry and to (1) Patai, S., Rappoport, Z . , Eds. The Chemistry of Organic Silicon Compounds; Wiley: New York, 1989. ( 2 ) Gaspar, P . P . In Jones Jr., M., Moss, R. A,, Eds. Reacfiue Intermediates; Wiley: New York, 1985; pp 333-427. (3) Baldridge, K. K.; Boatz, J. A.; Koseki, S.;Gordon, M. S. Annu. Reo. Phys. Chem. 1987, 38, 21 1-252.
their own unique properties. Organosilicon compounds are also of key importance to gas-phase reactions occurring during the chemical vapor deposition (CVD) of silicon carbide (Sic). Typical starting compounds used in this process are mixtures of silane and hydrocarbons4-' or organochlorosilanes such as methyltrichloro(4) Liaw, P.;Davis, R. F. J. Electrochem. SOC.1985, 132, 642. (5) Nishino, S.; Suhara, H.; Ono, H.; Matsunami, H . J . Appl. Phys. 1987, 61, 4889. ( 6 ) Powell, J. A.; Matus, L.G.; Kuczmarski, M. A. J. Electrochem. Soc. 1987, 134, 1558.
This article not subject to US.Copyright. Published 1992 by the American Chemical Society
Thermochemistry of the Si-C-H System silane,8-I2 which are decomposed in hydrogen at high temperatures (typically above 1500 K) to produce Sic. Decomposition of these reactants leads to reactive silicon-containing species such as silylenes (SiXY; x , Y = H, C1, or CH3).13,14Silylenes are known to be highly reactive toward unsaturated hydrocarbons such as ethylene and acetylene, which are also formed during reactant pyr~lysis.'~-'~ These reactions can thus lead to the formation of gas-phase organosilicon species that may be reactive with the deposition surface. Computational models are now available that can simulate the complex gas-phase chemistry occurring during CVD.I4q1* However, a base of thermodynamic data is required for their implementation. Although this data base exists for most of the species involved in silane and hydrocarbon decomposition, it is not available for many organosilicon compounds. The high-temperature decomposition of S i c precursors involves reactions of large numbers of species, many of which are short-lived and difficult to detect. It is thus difficult to experimentally obtain thermodynamic data for many of the species of interest. In this paper, we report results of ab initio electronic structure calculations using the empirical bond-additivity correction (BAC) m e t h ~ d 'to~ .determine ~~ thermodynamic parameters for compounds in the Si-C-H system. Data are reported for all compounds in the H,Si(CH3), and H,SiCH, systems. Several silylethylenes and silylacetylenes are also included, since these compounds are expected to be the initial products of rapid reactions between silylenes and unsaturated hydrocarbons.16 This extends our previous investigations into the thermochemistry of gas-phase silicon compounds, which have so far included the Si-H-Cl,21 Si2H,,22 Si-H-F,20 and Si-N-H-FZ3 systems. 11. Theoretical Methods
Detailed presentations of the theoretical methods used in these calculn tions have been already presented e l ~ e w h e r e . ' ~A*general ~~ discussion is provided here, however, for the reader who is not familiar with the computational technique. Ab initio electronic structure calculations using the Gaussian series of codes developed by Pople et were carried out to provide molecular geometries, vibrational frequencies, and electronic energies. In determining the equilibrium molecular geometry, restricted Hartree-Fock (RHF) theory was used for closed-shell molecules and unrestricted Hartree-Fock (UHF) theory for open-shell molecules. The electronic wave function is described by a 6-3 lG* split-valence basis set with polarization functions on the heavy atoms. Vibrational frequencies obtained at this level of theory are known to be systematically larger than (7) Balog, M.; Reisman, A.; Berkenblit, M. J . Electron. Mater. 1980, 9, 669. (8) Motojima, S.; Hasegawa, M. J . Vac. Sci. Technol. A 1990, 8, 3763. (9) So, M. G.; Chun, J. S. J . Vac. Sci. Technol. A 1988, 6 , 5. (IO) Cheng, D. J.; Shyy, W. J.; Kuo, D. H.; Hon, M. H . J . Electrochem. SOC.1987, 134, 3145. ( 1 1 ) Muench, W. v.; Pettenpaul, E. J . Electrochem. SOC.1978, 125, 294. (12) Kemenade, A. W. C. V.; Stemfoort, C. F. J. Cryst. Growth 1972,12, 13. (13) Stinespring, C. D.; Wormhoudt, J. C. J . Cryst. Growth 1988,87,481. (14) Allendorf, M. D.; Kee, R. J. J . Electrochem. SOC.1990, 138, 841. (15) Safarik, I.; Ruzsicska, B. P.; Jodhan, A.; Strausz, 0. P. Chem. Phys. Lett. 1985, 113. 71. (16) Safarik, I.; Sandhu, V.; Lown, E. M.; Strausz, 0.P.; Bell, T. N. Res. Chem. Intermediates 1990, 14, 105-131. (17) Chu, J. 0.;Beach, D. B.; Jasinski, J. M. J . Phys. Chem. 1987, 91, 5340. (18) Coltrin, M. E.; Kee, R. J.; Evans, G. H. J . Electrochem. SOC.1989, 136, 819. (19) Melius, C. F. In Bulusu, S. N., Ed. Chemistry and Physics of Energetic Materials; Kluwer Academic Publishers: Dorderecht, 1990; p 21. (20) Ho, P.; Melius, C. F. J . Phys. Chem. 1990, 94, 5120-5127. (21) Ho, P.; Coltrin, M. E.; Binkley, J. S.; Melius, C. F. J . Phys. Chem. 1985, 89, 4647. (22) Ho, P.; Coltrin. M. E.; Binkley, J. S.; Melius, C. F. J . Phys. Chem. 1986, 90, 3399. (23) Melius, C. F.; Ho, P. J . Phys. Chem. 1991, 95, 1410-1419. (24) Frisch, M. J.; Binkley, J. S.; Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; DeFrees, D. J.; Seeger, R.; Whiteside, R. A,; Fox, D. J.; Fluder, E. M.; Topiol, s.;Pople, J. A. GAUSSIAN 86; Camegie-Mellon Quantum Chemistry Publishing Unit: Carnegie-Mellon University, Pittsburgh, 1986.
The Journal of Physical Chemistry, Vol. 96, No. 1, 1992 429 TABLE I: Parameters for Bond Additivity Corrections for BAC-MP4(SDTQ) Level of Theory bond A ref species &b
Si-C Si-H C-H 'In
A-'.
841.99 91.19 38.61
H3SiCH3 SiH4 CH4
2.5 2.0 2.0
bBased on related classes of compounds.
experimental valuesZ5and so were divided by a factor of 1,12. Higher levels of theory incorporating electron correlation must be used to obtain accurate electronic energies. For this purpose, calculations employing fourth-order Mdler-Plesset perturbation theory with single, double, triple, and quadruple excitations were performed (MP4(SDTQ)), using a split-valence basis set with polarization functions on all atoms (6-3 lG**). Molecules with as many as 11 heavy atoms have been treated at this level of theory with existing computer technology. The electronic energies obtained from MP4 calculations are not sufficiently accurate, however, to provide useful heats of formation. This is primarily a result of the finite basis set. The errors incurred are found to be systematic, however, and can be removed by the application of empirical correction factors. In the method used here these factors are called bond additivity corrections. Their values depend primarily on bond type and bond distance but are also a function of the identity of neighboring atoms. The form of the BAC for a molecule Xk-Xj-Xj is given by EBAC(Xi-Xj) = fijgkij
(1)
r;l = Aii exp(-aiiRii)
(2)
where (3) hik = Bk eXp(-a;k(& - 1.4 A)) (4) A, and aii are empirically derived parameters that depend on the Xi-Xj bond type and R, is the bond distance (angstroms). The factor Bk in eq 4 depends on the identity of atom k. For molecules with an additional heavy atom I and structure Xk-Xi-Xi-X,, an additional correction factor is required, leading to EBAC = higkjgbi. The values of A , and aii used in these calculations are listed in Table I. The A, factors were obtained by fitting the BAC-MP4 heats of formation for reference compounds to their respective experimental values; only compounds with well-established heats of formation were used as reference compounds. The correction for the Si-C single bond, ASiC,was based on the heat of formation for the reference compound Si(CH3)4measured by Steelez6and preferred by W a l ~ h . * For ~ C-H bonds, the reference compound CHI was used to determine ACH. As in previous calculations, the BACs for Si-H bonds were determined from the SiH4 heat of formation.*O The exponents aii were determined by comparison with correction factors obtained for related classes of molecules for which many reference compounds are available. Since thermodynamic data for compounds with multiply bonded Si-C bonds is limited, however, asic was determined by assuming that this exponent should lie between the values of cysisi and acc. Neighboring-atom Bk factors used in this work are BH = 0.00, Bc = 0.31, and Bsi = 0.20. A correction was also made in the case of open-shell molecules for spin contamination of the ground state by excited electronic states. The error in the electronic energy caused by this effect was estimated using the approach of SchlegelZ8and is given by EBAC(spins2)= E(UMP3) - E(PUMP3) (5) where E(UMP3) is the third-order M P energy using the U H F wave function and E(PUMP3) is the projected UMP3 energy. This correction is generally small (10.5 kcal mol-') but may (25) Pople, J. A.; Schlegel, H. B.; Krishnan, R.; DeFrees, D. J.; Binkley, J . S.;Frisch, M. J.; Whiteside, R. A. Int. J . Quanfum Chem. 1981, SI5, 269. (26) Steele, W. V. J . Chem. Thermodyn. 1983, 15, 595. (27) Walsh, R. Organometallics 1989, 8, 1973-1978. (28) Schlegel, H. B. J . Chem. Phys. 1986, 84, 4530.
430 The Journal of Physical Chemistry, Vol. 96, No. 1, 1992
Allendorf and Melius
TABLE II: Bond Additivity Corrections for the MP4(SDTQ) Level of Theory (kcal mot’)
Si-C bond lengtha (no.)b 1.888
BAC 7.97
Si-H bond length (no.) 1.478 (3)
BAC 4.82
1.890 (2)
7.87
1.481 (2)
4.80
1.891 (3) 1.893 1.894 (3) 1.894
7.78 7.67 7.67 7.84
1.483
4.78
1.480 (2)
4.81
1.896 (2)
7.75
1.483
4.78
1.898 (3)
7.65
1.914
7.47
1.917 (2)
7.35
SiCH3
1.917
7.40
H3SiCH2
1.860
8.54
H2Si(CH3)CH2
1.863 1.888
8.41 7.89
species
1.866 1.890 (2) 1.870 1.895 1.892 (2) 1.694 1.693 1.879
8.27 7.79 8.12 7.64 7.69 12.95 12.79 8.04
1.693 1.882 (2)
12.61 7.92
HSiCH2
1.767
10.79
SiCH2 H3SiCH
1.702 1.840
12.69 8.99
H2SiCH
1.781
10.41
SiCH H3SiC
1.722 1.847
12.07 8.84
H2SiC HSiC H3SimH H2SiC4H HSiCdH SiCeH H2C=CHSiH3
1.797 1.750 1.838 1.821 1.847 1.816 1.873
10.00 11.26 8.61 8.99 8.43 9.12 8.06
H2C=CHSiH2
1.849
8.57
H,C=CHSiH
1.882
7.90
H2Si=CH2 H(CH3)Si=CH2
H2C=CHSi
1.843
8.70
CH3SiH2SiH2CH3
1.897 (2)
7.79
a In
1.513
4.50
1.480 1.447 (2) 1.482 1.480
4.81 4.84 4.79 4.81
1.485
4.76
1.467 (2) 1.471
4.93 4.90
1.475
4.86
1.474 1.477 (2) 1.474 1.471
4.87 4.83 4.86 4.89
1.474 1.474 (2) 1.473 (2) 1.483 1.472 (3) 1.473 (2) 1.506
4.87 4.87 4.87 4.78 4.88 4.88 4.57
1.477 1.478(2)
4.84 4.83
1.476 1.477 1.512
4.85 4.84 4.51
1.483 (4)
4.78
C C bond length
Si-Si bond length
spin or UHFunstable correctionC
C-H bond length (no.) 1.086 1.086 (2) 1.086 (2) 1.087 (4) 1.087 (9) 1.087 (1 2)
BAC 4.40 4.40 4.40 4.39 4.39 4.39
1.087 1.085 (2) 1.086 (4) 1.088 (2) 1.086 (6) 1.089 (3) 1.090 (2) 1.084 1.085 (2) 1.090 (2) 1.092 (2) 1.094 1.087 (2) 1.078 (2)
4.39 4.41 4.40 4.38 4.40 4.38 4.36 4.41 4.41 4.37 4.35 4.33 4.39 4.47
1.078 (2) 1.086 (2) 1.087 1.079 (2) 1.087 (6) 1.079 (2) 1.087 (8) 1.088 1.076 (2) 1.076 (2) 1.085 1.086 (2) 1.077 (2) 1.085 (2) 1.086 (4) 1.078 1.076 1.082 (2) 1.073
4.47 4.40 4.39 4.46 4.39 4.46 4.39 4.38 4.49 4.49 4.41 4.40 4.48 4.41 4.40 4.47 4.49 4.44 4.52
1.071
4.53
9.86 u
1.070
4.54
7.59 u 0.21 u
BAC
BAC
0.16 u 0.14 u 0.13 u
3.55 s 3.46 s 0.59 u 0.66 u 0.65 u 0.64u 0.63 u 3.03 s 1.84s 0.43 s 7.45 u 2.84 s 0.92u
4.98 u 10.21 u 1.058 1 .OS8 1.058 1.059 1.080 1.077 1.078 1.080 1.077 (2) 1.079
1.078 (2) 1.086 1.076 I .077 1.086 (6)
4.65 4.65 4.65 4.65 4.45 4.48 4.47 4.45 4.48 4.46 4.47 4.40 4.49 4.48 4.40
1.194 1.203 1.200 1.216 1.325
14.78 14.27 14.47 13.60 9.17
2.53 u 2.91 s 4.53 u
1.353
8.26
4.64 u
1.334
8.88
2.31 s
1.367
7.81
6.08 u 2.357
5.72
angstroms. *Number of bonds. c ~UHF-unstable , correction; s, spin-contamination correction.
become large for molecules containing a high degree of unsaturation or low-lying electronic excited states. Closed-shell molecules that are UHF-unstable, such as SiH2, also require an additional correction. The form of the correction is EBAC(SPinUHF-unstable) = KUHF.IS(S + 1) (6) where KUHF., is 10.0kcal mol-’ (based on the heat of formation
of 03) and S is the spin obtained from the UHF/6-31G** calculation. Application of this correction yields reasonable heats of formation for singlet SiH2and CHI. The BACs for all molecules in the study are given in Table I1 with the associated bond length, spin contamination, and UHF-unstable corrections. The values of thermodynamic parameters are derived from the BAC-MP4(STDQ) energy, which, when combined with the
Thermochemistry of the Si
