J . Phys. Chem. 1990,94, 5527-5530
ordinates that must remain constant, and I the identity matrix; then
Acknowledgment. This work was supported by a grant from the National Science Foundation (CHE-87-11901) and by the Pittsburgh Supercomputer Center.
+
Aq P(BAAxA BDAxD) (A21 Q(BAAxA + BDAXD)= 0 (A3) The displacement of the real atoms depend on the displacements of the variable internal coordinates. The displacements of the dummy atoms must be such that the remaining internal coordinates are constant. Since the number of fixed coordinates is greater than or equal to 3nD,eq A3 must be solved for AxD in a least-squares manner:
Appendix The use of dummy atoms in defining internal coordinates gives rise to some complications in converting mass-weighted Cartesian coordinates to internals. For a nonlinear molecule with nA real atoms and nD dummy atoms, there are only 3nA - 6 internal coordinates that may be varied independently and 3nD internal coordinates that must be fixed. Symmetry may require additional coordinates to be fixed. The conversion between Cartesian and internal coordinates is written in terms of Wilson's B matrix,
Aq = BAx
5527
AxD = -(BbQBD)-lBbQBAAxA Substitution into eq A2 yields Aqv = B'AxA, B' = PBA - PBD(BbQBD)-lBbQBA
(AI)
The B matrix can be partitioned into blocks dealing with the displacement of the real atoms, AxA,and the dummy atoms, AxD; let P be the projector for the internal coordinates that are independently variable, Q = I - P the projector for the internal co-
644) (A5)
This modified B matrix, B', can be used to compute the C matrix, C' = B'm-'Bn, since the masses of the dummy atoms are no longer involved.
Thermal Decomposition Processes for Sllanol Mark S. Gordon* and Lisa A. Pederson Department of Chemistry, North Dakota State University, Fargo, North Dakota 58105 (Received: November 1, 1989; In Final Form: March 2, 1990)
Six alternative decomposition modes of silanol are examined with ab initio electronic structure theory. Geometries determined at the MP2/6-3 lG(d,p) level of computation and single-point energetics obtained with MP4/MC-3 1 lG(d,p) wave functions predict that the 1,l- and 1,Zeliminations of molecular hydrogen are both thermodynamically and kinetically competitive, with all other processes requiring at least 10 kcal/mol more energy to occur. At the highest level of theory, silanone is predicted to be 2.7 kcal/mol lower in energy than hydroxysilylene.
I. Introduction The molecule silanol, SiH30H, is the simplest saturated species containing an S i 0 bond. It is, in addition, the simplest prototype for silicic acid, Si(OH)4, the starting molecule for siloxane polymerization processes to form (Si+), polymers. Silanol is also a candidate for an alternative to silane as a precursor to chemical vapor deposition.' It is of considerable interest to develop an understanding of the mechanisms and energetics of the processes summarized above. Previous papers from this2 and other3 laboratories have considered potential intermediate steps in the silanol and silicic acid polymerization process. A key step in gaining a full understanding of S i 4 reactivity and the nature of the S i 4 bond is to analyze the alternative thermal decomposition processes of the parent silanol. The thermal decompositions of a number of related compounds have already been investigated with theoretical techniques. These include silane,' ethane? methylsilane: disilane,' silylamine? methyl (1) (a) Coltrin, M. E.; Kee, R. J.; Miller, J. A. J. Electrochem.Soc. 1984, 131,425. (b) Steinwandel,J.; Hoewhele, J. Chem. Phys. Lett. 1985, 116,25. (2) (a) Gordon, M. S.;Davis, L. P.; Burggraf, L. W.; Damrauer, R. J. Am. Chem. Soc. 1986,108,7889. (b) Davis, L. P.; Burggraf, L. W.; Gordon, M. S. J . Am. Chem. Soc. 1988, 110, 3056. (c) Damrauer, R.; Davis, L. P.; Burggraf, L. W.; Gordon, M. S. J . Am. Chem. Soc. 1988,110, 6601. (3) (a) Burggraf. L. W.; Davis, L. P. Chemically Modified Surfaces; Gordon and Breach Sciencc: New York, 1986; pp 157-187. (b) Davis, L. P.; Burggraf, L. W. Science of Ceramic Chemical Processing Wiley: New York, 1986; pp 400-41 1. (c) Burggraf, L. W.; Davis, L. P. Mater. Res. Soc. Symp. Proc. 1986.73.529. (d) Davis, L. P.; Burggraf, L. W. Ultrastructure Processing of Advanced Ceramics; Wiley: New York, 1988; pp 367-368. (4) Gordon, M. S.; Gano, D. R.; Binkley, J. S.; Frisch, M. J. J. Am. Chem. Soc. 1986, 108, 2191. (5) Truong, T. N.; Gordon, M. S.;Pople, J. A. Chem. Phys. Lerr. 1986, 130. 245.
0022-3654/90/2094-5527%02.50/0
and ethyl mercaptan? ethylsilane,1° and chloromethylsilane." When one of the atoms in the parent molecule is a saturated Si, it is generally found that 1,Zelimination of molecular hydrogen to form a silene has a much higher barrier than the 1,l-H2 elimination from the silicon to form a silylene, even in those cases for which the 1,2-process may lead to thermodynamically favored products. It has also been found that the two hydrogens in the 1,Zelimination process prefer to leave in an asymmetric manner. Viewed in the reverse direction as an addition of H2across a double bond, the H2 tends to attack in such a manner that both H's are closer to the less electronegative partner in the double bond. In the present work, the following alternative decomposition processes of silanol are considered: SiH30H S i H 3 0 H (1)
----
+ SiHzOH + H SiHo + OH H2Si0 + H2 HSiOH + H2 SM2 + H 2 0
(2) (3)
(4) (5)
(6)
The first thy 4 of these reactions are homolytical cleavages of a (6) Gordon, M. S.; Truong, T. N . Chem. Phys. Lett. 1987, 142, 110. (7) Gordon, M. S.;Truong, T. N.; Bonderson, E. K.J . Am. Chem. Soc. 1986, 108, 1421. (8) Truong. T. N.; Gordon, M. S.J. Am. Chem. Soc. 1986, 108, 1775. (9) Baldridge, K. K.;Gordon, M. S.;Johnson. D. E. J. Phys. Chem. 1987, 91, 4145. (IO) Francisco, J. S.;Schlegel, H. B. J. Chem. Phys. 1988, 88, 3736. ( 1 1) Nagase, S.; Kudo, T. J . Chem. Soc., Chem. Commun. 1983,6,363.
0 1990 American Chemical Society
Gordon and Pederson
5528 The Journal of Physical Chemistry, Vol. 94, No. 14, 1990
a
0.962
a b
C*V
cs
c1
d C 0
0.973
CC
Figure 2. MP2/6-31G(d) structures for transition states (bond lengths in angstroms, angles in degrees): (a) reaction 4, (b) reaction 5, (c) e
reaction 6. 115.0'
1
94.7"
Figure 1. MP2/6-31G(d,p) structures for reactants and products (bond lengths in angstroms; angles in degrees): (a) siland, (b) water, (c) siloxy radical, (d) silanone, (e) hydroxysilyl radical, (f) hydroxysilylene.
single bond and are expected to occur with no barrier. Reactions 4 and 5 correspond to the 1,2- and 1,I-H2 eliminations discussed above, while reaction 6 is the extrusion of H 2 0 to form the simplest silylene. The isomerization reaction connecting the polyatomic products of reactions 4 and 5 has been studied by several groups.Iz 11. Computational Metbods Initial geometries for all species were obtained with the 631G(d) basis sett3at the selfconsistent-field (SCF)level of theory, using restricted and unrestricted wave functions for closed and open shells, respectively. The existence of minima and transition states was verified by diagonalizing the analytically computed matrix of energy second derivatives (hessian) and showing that the correct number of imaginary frequencies (zero for minima, one for transition states) was obtained. Subsequently, the geometries were reoptimized with the 6-31G(d,p) basis setI3 and with mnd-order perturbation theory (ME)." Since the refined geometries differed very little from those obtained at the SCF/ 6-31G(d) level (generally less than 0.02 A in bond lengths and less than 3' in angles), hessians were not computed at the higher level of theory. To estimate the zero-point vibrational energy corrections, the SCF/6-31G(d) frequencies were scaled by a factor of 0.89. To analyze the transition states obtained for reactions 4-6, the SCF/631G(d) minimum-energy paths (MEP) were obtained for these three reactions. The initial (harmonic) step off the saddle (12) (a Gordon. M. S.;George, C. J. Am. Chem. Soc. 19'84. 106,609. (b) Sakaicb.; Gordon, M. S.;Jordan, K. D. J. Phys. Chem. 1988,92,7053. (13) (aZHariharan. P. C.; Popk, J. A. Thew. Chim. Acra 1973,28,213. (b) Gordon, M. S.Chem. Phys. Lcrr. 1980, 76, 163. (14) Krishnan. R.; Frisch, M. J.; Poplc, J. A. J . Chem. Phys. 1980, 72, 4244.
point was 0.05 (amu)t/2-bohr. To follow the MEP, the Euler method with stabilization (ES2)I5-" was used, with a step size varying from 0.01 to 0.05 (amu)'12.bohr. The final energetics for all reactions at the MP2/6-31G(d) structures were obtained with the MC-311G(d,p) basis set,'* using fourth-order perturbation theory (MP4"), including triple excitations and excluding inner shells. The geometry optimizations and perturbation theory calculations were performed with G A U S S I A N ~while ~ , ' ~ the MEP's were obtained by use of GAMESS.~ 111. Results and Discussion
The structures of the MP2/6-31G(d,p) minima and for the three transition states are displayed in Figures 1 and 2, respectively. (The structures of SiHz, SiH3, SiH4, and OH have been reported previouslflz' and are not repeated here.) Note that the two isomers H S i O and HSiOH are both predicted to be planar, with the S i 0 bond length in the former isomer being 0.13 A shorter than that in the latter. (Since it is generally agreedI2 that the trans structure is the lowest energy isomer of HSiOH, this is the only isomer shown in Figure 1.) The S i 0 bond length in the doxy radical is slightly longer than that in the parent silanol, while the Si0 bond in SiH20H is virtually unchanged from the silanol value. In the transition state for the 1,2-H2elimination (reaction 4), the Si0 bond length has decreased 65% of the way from its value in silanol to the final value in silanone. This is suggestive of a rather late transition state. This is supported by the leaving SiH and OH bond lengths, which are stretched by 18% and 55%, (15) Schmidt, M. W.;Gordon, M. S.;Dupuis, M.J. Am. Chem.Soc. 1985, 107,2585. (16) Garrett, E. C.;Redmon. M.; Steckler, R.; Truhlar, D. G.; Baldridge, K. K.; Bartol, D.; Schmidt, M. W.; Gordon, M. S.J. Phys. Chem. 1988.92,
1476. (17) Baldridge, K. K.;Gordon, M. S.;Truhlar, D. G.; Steckkr, R. J. Phys. Chem. 1989, 93; 5107. (18) McLean, A. D.; Chandler, G. S. 1. Chem. Phys. 1980, 72, 5639. (19) Frisch, M. J.; BinWey, J. S.; Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Brobrowicz, F. W.; Rohlfmg, C. M.; Kahn, L. R.; DeFrees, D. J.; Sceger. R.; Whiteaide, R. A,; Fox, D. J.; Fluder, E. M.; Topiol, S.; Pople, J . A, GAUSSIAN8& Carnegie-Mellon
Quantum Chemistry Publlsbing Unit; Rttsburgh, PA. (20) (a) Dupuis, M.; Spangler, D.; Wendohki, J. J. NRCCSofnvarr Cat. Prog. 1981, QgOl. (b) Schmidt, M. W.;Baldridge, K. K.; Boatz, J. A.; Kcseki, S.;Gordon, M. S.; Elbert, S.T.; Lam,E. QCPE 1987, 7, 115. (21) Gordon, M. S.;Baldridge, K. K.; kmholdt, D.; Bartlett, R. J. Chem. Phys. Lett. 1989, 158, 189.
Thermal Decomposition Processes for Silanol
The Journal of Physical Chemistry, Vol. 94, No. 14, 1990 5529
* -365.13 -5.0 -365.97 1
-365.13 -5.0
0.0 A
0.0 B
\
5.0
5.0
Figure 4. Selected structures along the MEP for reaction 4.The top line shows H2approaching silanone; the middle line shows the transition state with mass-weighted arrows showing the atom motions in the normal mode corresponding to the imaginary frequency; the bottom line shows the formation of silanol.
Ga -365.13 -5.0
0.0 C
5.0
Figure 3. Minimum-energy paths for (a) reaction 4, (b) reaction 5, and (c) reaction 6. Energies (hartrees) on the vertical axis; reaction coordinate s ((amu)%ohr) on the horizontal axis.
respectively, relative to their values in silanol. Correspondingly, the forming H H bond is 25% longer than its final equilibrium value. Note also that the H2 leaves in a rather asymmetric manner. At the transition state, the hydrogen originally bound to 0 (H,) is actually closer to Si than is the H originally bound to Si (&); that is, the SiH, and Si& distances are 1.626 and 1.734 A, respectively. This is consistent with the point noted earlier, that in 1,2-eliminations the two hydrogens want to remain close to the less electronegative end of the X-Y bond. The transition state for the l,l-H2 elimination (reaction 5 ) is rather asymmetric, with the two leaving SiH bonds differing in length by 0.16 A. These two bonds are stretched by much smaller amounts than are those in the 1,Zelimination. The forming HH bond length is 1.152 A, much larger than the corresponding value in the 1,2-elimination. Thus, one would classify the 1,l-elimination transition state as earlier than the 13-elimination transition state. For reaction 6, the elimination of water to form silylene, the S i 0 bond in the transition state has stretched to 1.94 A, an increase of 0.27 A (16%) relative to the value of silanol. At the same time, the breaking SiH bond has stretched by about 10% and the forming O H bond length is still 32% longer than its final equilibrium value. So,this reaction also has a relatively early transition state. Since the imaginary normal mode does not always provide sufficient information to be certain that a transition state connects the correct reactants and products, SCF/6-3 1G(d) minimumenergy paths were obtained for reactions 4-6. Energy vs s (reaction coordinate) plots are displayed in Figure 3, where it is seen that the energy varies smoothly from the transition state in both directions for all three reactions. Selected structures along the MEP are displayed in Figures 4-6 for reactions 4-6, respectively. In each figure, the central structure is the transition state with mass-weighted arrows superimposed to illustrate the direction of the imaginary normal mode. In each case, the MEP illustrates the progression of the reaction from reactants through the transition state to products very nicely. The MC-31 lG(d,p) total energies and the (unscaled) SCF/ 6-31G(d) zero-point vibrational energies are listed in Table I, and the relative energies for the reactions of interest are summarized
Figure 5. Selected structures along the MEP for reaction -5. The top line shows H2approaching hydroxysilylene; the middle line shows the transition state with mass-weighted arrows showing the atom motions in the normal mode corresponding to the imaginary frequency; the bottom line shows the formation of silanol.
?
Figure 6. Selected structures along the MEP for reaction -6. The top line shows H20approaching silylene; the middle line shows the transition
state with mass-weighted arrows showing the atom motions in the normal mode corresponding to the imaginary frequency; the bottom line shows the formation of silanol. in Table 11. Thermodynamically, the most favorable processes are clearly the molecular eliminations of Hlr with all other processes being at least 20 kcal/mol more demanding energetically. Of the two H2eliminations, the 1,2-elimination, leading to silanone,
J. Phys. Chem. 1990, 94, 5530-5535
5530
TABLE I: Totrl (MP4/MC-311C(d,p); brmecCl) d Zero-Poiat (C31C(d); kerl/mol) Eaergia
species' SiHIOH SiH,O SiHzOH HzSiO SiHOH SiH4 SiH, SiH2 H20 OH
H2 H
o(3p)
TS4 TS5 TS6
total energy
ZPE 25.8 17.6 19.4 12.1 14.1 20.9 14.2 7.9 14.4 5.7 6.5
-366.528 89 -365.83644 -365.811 14 -365.290 61 -365.28841 -291.401 86 -290.15404 -290.138 51 -76.276 21 -15.588 33 -1 .I61 69 -0.499 8 1 -14.933 33 -366.41 5 16 -366.41 7 52 -366.401 29
+
22.6 23.1 23.3
+
aTSXrefers to the transition state for reaction X.
TABLE II: R e a c h hemetics (kcal/mol)
reaction products reaction products SiH,O + H
MP4/ 6-3lG(d)o AE 117.9
MP4/ MP4/MC6 - 3 1 G ( d , ~ ) ~ 311G(d*p)b AE A E A H 118.1
Of course, to assess the relative energy demands requires an examination of barrier heights and activation energies, as well as overall energy differences. The calculated activation energies for reactions 4-6 are 68.2, 67.5, and 77.8 kcal/mol, respectively. So the two H2 eliminations have virtually identical activation energies and very similar classical barrier heights as well. It is therefore likely that these two species will be seen with very similar probabilities, depending on the temperature at which the decomposition is carried out. The next lowest energy route is the elimination of water to form silylene, and this process is 10 kcal/mol higher in energy. All of the reactions obtained by homolytic cleavages are considerably higher in energy. Finally, note that the relative energy of SiH4 + O(3P) is listed in Table 11. Since this pair is very high in energy, the potential product pair SiH, O(lD) is estimated to be more than 150 kcal/mol above the parent silanol, using the experimental oxygen 'D-3P splitting.22 It is interesting to compare the results discussed in the previous paragraph with the analogous results obtained for silane4 and disilane.' Silane dissociates to SiH, H2 with a 61 kcal/mol endothermicity and essentially zero additional barrier. For disilane, dissociation to SiH2 SiH4has a slightly smaller (54 kcal/mol) energy requirement than dissociation to SiH,SiH + H2 (58 kcal/mol). The 1,2-H2elimination to form disilene has a much higher (89 kcal/mol) classical barrier height. Thus, there are several significant differences between the silanes and silanol: (1) the lowest energy processes in silanol are 10 or more kcal/mol higher than those in the silanes; (2) the 1,Zelimination of H2 from silanol has a much smaller barrier than does the analogous process in disilane (or methylsilane6); (3) elimination of silylene, the lowest energy process in silane and disilane, is disfavored in silanol.
120.9
113.6
SiHIOH + H 93.2 93.1 95.0 89.2 42.5 HSiO + H2 44.1 44.3 38.4 HSiOH + H2 42.2 42.0 45.7 41.1 121.2 121.5 117.2 SiH4+ O('P) 120.8 116.3 117.0 SiH, + OH 116.8 111.9 71.6 SiH2+ HzO 71.5 71.6 68.5 transition states 72.8 71.7 71.0 68.2 H2Si0 + H2 70.0 HSiOH + H2 70.3 69.9 67.5 79.4 SiH2+ H 2 0 80.0 80.1 77.8 'Calculated at the SCF/6-31G(d) geometry. bCalculatedat the MP2/ 6-31G(d,p) geometry.
is favored by 2.8 kcal/mol a t the highest level of theory. This prediction that silanone is slightly more stable than hydroxysilylene reverses the earlier predictions obtained with smaller basis sets and SCF geometries.I2
+
Acknowledgment. This work was supported by grants from the National Science Foundation (CHE86-40771) and the Air Force Office of Scientific Research (87-0049). All calculations were performed on the North Dakota State University IBM 3090/120E computer, under the auspices of the NDSU Computer Center and a joint study agreement with IBM. Registry No. SiH30H, 14415-38-8. (22) Kelly, R. L.,Ed. J Phys. Chem. Ref. Data 1987,16 (Suppl. No. I).
Analogy between Trivalent Boron and Divalent Silicon Eluvathingal D. Jemmis,*'la Bharatam V. Prasad,la Seiji Tsuzuki,lband Kazutoshi Tanabelb School of Chemistry, University of Hyderabad, Central University P.O..Hyderabad 500 134, India, and the National Chemical Laboratory for Industry, Ibaraki 305, Japan (Received: November 1, 1989; In Final Form: February 20, 1990)
The electronic configuration of divalent Si compounds with a u lone pair and an empty p orbital is similar to that of trivalent borane if a B-H bond is equated to the lone pair on Si. Following this analogy two novel compounds, :Si(p-CH)(p-H)Si:, 24, and :Si(pCH)fii:, 26, are proposed. The energetics and geometries of the two compounds and their isomers (24,2639, and 41-65) are studied by use of the MNDO and 3-21G* methods.
Introduction Group IV elements of the periodic table generally form tetrav&nt ampounds. valency in the heavier mmbem of the group beginning with Ge &awe of the inert pair effwt.2 (1) (a) University of Hyderabad. (b) The National Chemical Laboratory for Industry. (2) (a) Greenwood. N. N.; Earnshaw, A. Chemistry ofllemenfs; Pergamon: Oxford, 1984. (b) Cotton, F. A.; Wilkinson, G. Advanced Inorganic Chemisfry, 5th ed., Wiley-Interscience: New York, 1988.
In carbon chemistry, low valent species such as carbenes, carbaniom and carbonium ions are known, but they are highly reactive intermediates. Divalent silicon presents a different story. Even though silylenes such as SiCI2 and SiF23.4are highly reactive, many silylenes especially with organic substituents are very stable (3) Atwell, W. H.; Weyenberg, D. R. Angew. Chem., fnr. Ed. Engl. 1969, 8, 469. (4) Bock, H.; Solouki, B.; Maier, G. Angew. Chem., fnr. Ed. Engl. 1985, 24, 205.
0022-3654/90/2094-5530%02.50/0 0 1990 American Chemical Society
