J. Phys. Chem. 1991, 95,8609-8613
8609
Ground-State and Vertical Ionization Energies versus SI-SI-Si and C-C-C Bond Angles in Si3H8and C3H8 J. V. Ortiz* Department of Chemistry, University of New Mexico, Albuquerque, New Mexico 87131
and J. W.Mintmire Chemistry Division, Naval Research Laboratory, Washington, D.C. 20375 (Received: February 9, 1990)
Geometry-optimized ground-state energies of Si,H8 are calculated as a function of Si-Si-Si bond angle from 109.471" to 120° with the 6-31G(d) basis and second-order many-body perturbation theory. A structure with the Si-Si-Si angle equal to 120' lies 0.44 kcal/mol higher than the global minimum. Effects on vertical ionization energies are calculated with electron propagator theory. The same bond angle distortion causes the vertical ionization energy to the 2B2 final state to increase by 0.09 eV, while the vertical ionization energy to the 2Al final state decreases by the same amount. When the same procedures are applied to C3H8,the ground-state energy change accompanying the bond angle distortion is 1.29 kcal/mol. Three cation final states are very close at the equilibrium geometry of the neutral. Distortion of the C-C-C angle to 120' causes the 2B2ionization energy to increase by 0.22 eV, the 2AIionization energy to decrease by 0.21 eV, and the 2B1ionization energy to decrease by 0.15 eV. Good agreement with experiment is obtained in the propagator calculations on vertical ionization energies for molecules in their equilibrium geometries. Contour plots and expectation values of the Feynman-Dyson amplitudes provide an interpretation of the ionization energy trends.
Introduction Electronic structure underlies the many applications and unusual properties of polysilanes.' Submicron lithography with dry processes takes advantage of the self-developing photoresist properties of these materials2 The search for polymer photoconductors has also awakened interest in saturated Si c h a i n ~ . ~ Organopoiysiianes are useful as precursors in mild syntheses of silicon carbide.' Applications such as these are intimately related to the unusual properties of these polymers. Although the Si backbone is built entirely from u bonds, there is strong absorption in the near-ultraviolet region for ~ligosilanes.~Abrupt bathochromic spectral shifts with decreasing temperature accompanying rod-toooil structural transitions imply that conformations influence electronic propertiesab Photochemical degradation gives rise to a variety of products in which various Si-Si bonds are broken and formed.' All of these effects are governed by the nature of bonding along the Si chain. Understanding how steric factors affect the structure and spectra of Si-containing chains is a prominent issue in polysilane research.+13 Long alkyl chains and various aryl substituents are ( I ) West, R. J. Orgonomet.Chem. 1986,300.327. Miller, R. D.; Michl, J. Chem. Reo. 1989, 89, 1359. (2) Hofer, D. C.; Miller, R. D.; Willson, C. G.; Neurather, A. Proc. SPIE, Ado. Rests? Technol. 1984,469, 108. Zcinler. J. M.; Harrah. L. A.: Johnson. A. W. Proc. SPIE, Ada Resist Technol:1985, 539, 166. (3) Kepler, R. G.;Zcigler, J.; Harrah, L. A.; Kurtz, S. R. Phys. Rev. B. 1987, 35, 2818. Fujino, M. Chem. Phys. Lett. 1987, 136, 451. (4) West, R. In Ultrastructure Processing of Ceramics, Glasses and Composites; Hench, L.. Ulrich. D. L., Eds.; Wiley: New York, 1984. (5) Pitt, C. G. In Homoatomic Rings, Chains and Macromolecules of the Main Group Elements; Rheingold, A. L.; Ed.; Elsevier: New York, 1977. (6) Harrah, L. A.; Zeigler, J. M. J . Polym. Sci., Polym. Lett. Ed. 1985, 23,209. Trefonas 111, P.; Damewood, J. R.; West, R. Organometallics 1985, 4, 1318. Miller. R. D.; Hofcr, D.; Rabolt, J.; Fickes, G. N . J . Am. Chem. Soc. 1985, 107, 2172. (7) Trefonas 111, P.; West, R.;Miller, R. D. J . Am. Chem. Soc. 1985, 107, 2737. McKinley, A. J.; Karatsu, T.; Walraff, G. M.; Miller, R. D.; Sooriyakumaran, R.;Michl, J. Organomrrallics 1988, 7, 2567. Karatsu, T.; Miller, R. D.; Sooriyakumaran, R.; Michl, J. J . Am. Chem. Soc. 1989, 1 1 1 , 1140. (8) Ortiz. J. V.; Mintmire, J. W. Ado. Chem. Ser. 1989, 224, 543. Mintmire, J. W.; Ortiz, J. V. Adu. Chem. Sei. 1989, 224, 551. (9) Mintmire, J. W. Phys. Reu. E 1989, 39, 13350. Mintmire, J. W. Mater. Res. Soc. 1989, I l l , 235. (IO) Teramae, H.; Takeda, K. J . Am. Chem. Soc. 1989, 111, 1281. Teramae, H. J . Am. Chem. Soc. 1987,109,4140. Takeda, K.; Teramae, H.; Matsumoto, N . J . Am. Chem. Soc. 1986, 108, 8186.
0022-3654/91/2095-8609$02.50/0
typical side groups. Spectra will depend on the choice of side groups for two reasons. First, side-group orbitals mix into the highest occupied and lowest unoccupied orbitals, which are dominated by bonding between Si chain atoms. Second, steric interactions between the side groups affect the structure of the Si chain. This, in turn, has an effect on the Si chain orbitals. To separate these effects, accurate calculations on small, saturated Si chains with H side groups should be attempted in order to show how the structure of the Si backbone affects spectra in the absence of any bulky side group. Results such as these comprise a standard for the creation of parametrized methods for the calculation of structures and spectra pertaining to less computationally feasible systems. An understanding of how dihedral angles affect ground-state energies and ionization energies has been obtained by doing a b initio calculations on the simplest relevant system, Si4H1,,.I4 Bulky substituents may be able to affect not only dihedral angles in polysilanes but Si-Si-Si bond angles as well. For example, experimental e ~ i d e n c e ' ~ suggests .'~ that the Si backbone bond angle is closer to 120', rather than being roughly tetrahedral, in ordered, low-temperature samples of poly(di-nhexylsilane). Therefore, calculations of similar quality are presently undertaken on the simplest relevant system, Si3H8. Ground-state energies will be calculated as a function of the Si-Si-Si angle, with the remaining geometrical parameters being reoptimized. Previous studies showed that changes in ionization energies as a function of dihedral angle can be large compared to corresponding ground-state energy changes.I4 Electron prop agator calculations on the reoptimized structures will be done to determine the spectral changes that accompany bond angle distortions. The results will be interpreted through an analysis of Feynman-Dyson amplitudes, the correlated generalizations of canonical molecular orbitals. Comparisons of total energies and ionization energies with analogous organic systems will show the ( 1 1 ) Nelson, J. T.; Pietro, W. J.; J . Phys. Chem. 1988, 92, 1365.
(12) Bigelow, R. W.; McGrane, K. M. J. Polym. Sci. E 1986, 24, 1233. (13) Klingensmith, K. A.; Downing, J. W.; Miller, R. D.; Michl, J. J. Am. Chem. Soc. 1986, 108.1438. (14) Ortiz, J. V.; Mintmire, J. W.J. Am. Chem. Soc. 1988, JJO, 4522. Mintmire, J. W.; Ortiz, J. V. Macromolecules 1988, 21, 1189. (15) Kuzmany, H.; Rabolt, J. F.; Farmer, B. L.; Miller, R. D. J. Chem. Phys. 1986,85,7413. (16) Lovinger, A. J.; Schilling, F. C.; Bovey, F. A.; Zeigler, J. M. Macromolecules 1986, 19, 2657.
0 1991 American Chemical Society
8610 The Journal of Physical Chemistry, Vol. 95, No. 22, 1991
unique properties of saturated Si chains.
Ortiz and Mintmire TABLE I: Si#* Energies versus Si-Si-Si (kul/mol) Si-Si-Si Hartree-Fock MBFT(2)
Methods
Full Hartree-Fock optimizations with the 6-3 1G(d) basis” are performed with GAUSSIAN 8218 and GAUSSIAN 88” subject to the constraint of C, symmetry. Si-Si-Si and C-C-C bond angles are then fixed at certain values, and all other geometrical parameters are rmptimized. Second-order many-body perturbation theory (MBPT(2)) optimizationsB are done with the same basis. Electron calculations of the vertical ionization energies at each structure are carried out. Correlation and relaxation corrections to Koopmans’s theorem26are contained in the self-energy matrix, Z(E),of the Dyson equation:
*13 [1!
Ionization energies and electron affinities are poles: values of E such that C ’ ( E ) has a zero eigenvalue. In the canonical molecular orbital basis
13
Z H-10.5
lGO-’(E)lij = ( E - ci)bij
m-ll.O
0.09 0.23 0.43
2-10.0 W
O
5 Z
Neglect of the self-energy matrix recovers Koopmans’s theorem, because zero eigenvalues obtain when E is set to a canonical orbital energy, c. When an ionization energy pole of an N-electron system is discovered, the Feynman-Dyson amplitude (FDA)
... d(N)
0 [1!
0)-12.0
I
----*--*--.
. 3 - - - - *
=
4FDA(1) is determined from the eigenvector corresponding to the zero eigenvalue. This eigenvector gives the linear combination of canonical molecular orbitals (CMOS) pertaining to a given final state: $FDA( 1) =
116
1 I8 120
0.04 0 0.03 0.11 0.25 0.44
-1
W
...,N) *N( 1,2,3,...,N) d(2) d(3) d(4)
0.09 0 0.01
P0 v
G - y E ) = GO-yE) - E ( E )
J-**,+l(2,3,4,
109.471 equil 1 I4
EXpy l)Cj i
FDA’s are generalizations of C M O S that describe the difference in electronic structure between a molecule and a cation. In the diagonal approximation, where the off-diagonal self-energy matrix elements are assumed to vanish, the FDA is equivalent to a CMO. (All of the Cts except one are zero.) This is also true when the self-energy matrix is neglected entirely. When diagonal and nondiagonal calculations are in close agreement, that is, when one orbital dominates the FDA and the poles obtained with the two methods are close, the Koopmans description of the ionization is retained except that the energy of the CMO is supplemented by relaxation and correlation terms in the diagonal elements of the self-energy matrix. This mixture of correlated and uncorrelated descriptions is generally successful for outer valence ionization energies of closed shell molecules. (The breakdown of this picture is discussed in ref 22.) (17) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J . Chem. Phys. 1972, 56, 2257. Hariharan, P. C.;Pople, J. A. Theor. Chlm. Acra 1973, 28, 213. (18) GAUSSIAN 82, Relcasc A. Binkley, J. S.;DeFrees, D.; Frisch, M.; Fluder. E.; Pople, J. A.; Ragavachari, K.; Schlegel, H. B.; Seeger, R.; Whiteside, R. Carnegie Mellon University: Pittsburgh, PA. (19)GAUSSIAN88, Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Ragavachari, K.; Binkley, J. S.; Gonzalez, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R.; Kahn, L. R.; Stewart, J. J. P.; Fluder, E. M.; Topiol, S.;Pople, J. A. Gaussian, Inc.: Pittsburgh, PA, 1988. (20) Bartlett, R.Annu. Reu. Phys. Chem. 1981,32, 359. Binkley, J. S.; Pople, J. A. Int. .IQuanrum . Chem. 1975, 9, 229. (21) Linderberg, J.; Ohm, Y. fropagators in Quantum Chemistry;Academic Press: New York. (22) von Niessen, W.; Schirmer, J.; Cederbaum, L. S. Compur. Phys. Rep. 1984, I , 57. Cederbaum, L.S.;Domcke, W.; Schirmer, J.; von Niessen, W. Ado. Chcm. Phys. 1986.65, 1 IS. (23) Simons, J. Theor. Chem. Ado. Persp. 1978, 3. (24) Herman, M. F.; Freed, K . F.; Yeager, D. L. Adu. Chem. Phys. 1981, 48, I . (25) Ohm, Y.; Born, G.Adu. Quantum Chem. 1981, 13, 1. (26) Koopmans, T.Physica 1933, I , 104.
108
110
112
114
116
S I - S I - S I ANGLE
118
120
122
DEGREES) Figure 1. Vertical electron binding energies of Si3H8as a function of Si-Si-Si angle. (
Several approximate propagators are employed in an effort to assess the treatment of relaxation and correlation. In one set of calculations, second-order diagonal, third-order diagonal, and partial fourth-order (P4)27-28 diagonal self-energy corrections to Koopmans’s theorem are determined. Second-order nondiagonal calculations are compared to their diagonal counterparts. Finally, a renormalized, nondiagonal self-energy is used to check whether higher order corrections are small. This renormalized approximation contains all the self-energy corrections present in the partial fourth-order expression and adds ring and ladder diagram terms through infinite order. All of the energy-dependent terms included in the so-called ADC(3), or extended 2p-h TDA, approximationU are retained. Iterations with respect to E are performed until the pole is found. Only core molecular orbitals are omitted from the summations required by the electron propagator theory calculations, which are executed with program links integrated into the Gaussian suites. The 6-31G(d) basis is used. This treatment of ionization energies of small silanes has been found accurate in previous studies.I4 FDAs are characterized through contour plots and evaluation of expectation values of one-electron operators:
14mA(1)*i)4FDA d(1) = ( 8 )
(n,
Examples of operators (8)include kinetic energy electronnuclear attraction (v), and electric potentials at the nuclear positions. Results Si-Si bond lengths and Si-Si-H angles in Si& are fairly independent of the Si-Si-Si bond angle. Differences in bond lengths between the equilibrium structure, where the Si-Si-Si angle is 112.4’ (112.7’ at the Hartree-Fock level), and the structure obtained when this angle is fixed at 120° are less than 0.01 A. Si-Si-H bond angles change by less than 2’. Har(27) Ortiz, J. V. Int. J . Quantum Chem. Symp. 1988, 22, 431. (28) Ortiz, J. V. J . Chem. Phys. 1988,89, 6348.
The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 8611
Si3H8and C3Hs TABLE II: SiIH. Vertical Ionization Enemies (eV)
~
state
Koopmans's theorem
second diag
third diag
'B,
10.51
'A; *BI
1 1.49
9.74 10.58 11.71 12.23
9.14 10.57 1 I .67 12.18
final
'A,
12.73 13.18
TABLE 111: C3H8Energies versus C-CC (kcal/mol) cc-c Hartree-Fock MBPT(2) 109.47 I 0.29 0.22 qui1 0 0 I14 0.04 0.06 I16 0.26 0.30 I18 0.67 0.7 1 I20 1.25 1.29
diag
second nondiag
renorm nondiag
exptZ9
9.74 10.56 11.63 12.13
9.75 10.58 11.71 12.23
9.75 10.55 11.60 12.11
9.87 10.72 1 1.65 12.17
P4
~~~~
s
J
H
L3
treeFock and MBPT(2) calculations are in close agreement for the energy difference between the structures: 0.43 and 0.44 kcal/mol, respectively. Differences between the Hartree-Fock and MBPT(2) optimized geometries are minor. Table I shows relative ground-state energies for several values of the Si-Si-Si bond angle. Propagator calculations of vertical ionization energies show large differences between uncorrelated (Koopmans's theorem) and correlated results. Discrepancies with experiment29are greatly reduced when the self-energy corrections are added. All of the propagator calculations are in close agreement for every cation final state at the equilibrium geometry. (See Table 11.) Diagonal results have essentially converged by second order. Differences between diagonal and nondiagonal results in second order are insignificant. Renormalized, nondiagonal calculations are quite close to the partial fourth-order diagonal results. In the nondiagonal calculations, each eigenvector has one coefficient that is nearly equal to unity. These data imply that the diagonal approximation is valid and that the convergence of the propagator perturbation series is nearly complete. Remaining errors originate from the incompleteness of the basis set. Identical conclusions follow when the propagator calculations are repeated for the 120° Si-Si-Si bond angle structure. A graph (Figure 1) of the vertical electron binding energies versus the Si-Si-Si angle is therefore generated from partial fourth-order diagonal calculations. These results show a steady increase in the lowest ionization energy as the Si-Si-Si bond angle increases. Just the opposite occurs for the next cationic final state. From the equilibrium geometry to the 120° case, the changes in both vertical ionization energies are about 0.09 eV. Smaller shifts, 0.06 and 0.04 eV, occur for the two remaining final states, 2B, and 2A2, respectively. A parallel set of calculations is now done on C3H8. When the C-C-C angle is distorted from its equilibrium value, 112.4O ( 1 12.8' a t the Hartree-Fock level), to 120°, changes in bond lengths and the other bond angles are as small as they were in Si3Hs. A total energy increase (Table 111) of 1.29 kcal/mol, about 3 times as large as the Si3H8 result, takes place. This ratio is approximately the same for each value of the central bond angle. MBPT(2) correlation corrections have little effect on the energy differences. Propagator calculations performed on C3H8contrast with their Si3Hs counterparts in several ways. Three final states are very close at the equilibrium geometry: 2Bl, 2B2,and 2A, (Table IV). Discrepancies between Koopmans's theorem results and secondorder results are large. Diagonal and nondiagonal second-order results agree closely. Third-order corrections are larger than they were for Si3Hs. Partial fourth-order corrections are smallest of all. Renormalized, nondiagonal calculations confirm the validity of the diagonal approximation and the convergence of the partial fourth-order results. Because the three states are so close in energy, there may be vibronic coupling accompanied by symmetry breaking in the final states. A recent theoretical studyMof propane
f, m-12.51
z
0 CL
F
0 W
1-13.0W
---*--
U
-13.5 108
110
112
C-C-C
W.;Feher, F.; Freund, R.J . Am. G e m . Soc. 1976,
116
ANGLE
120
118
122
DEGREES) Figure 2. Vertical electron binding energies of C,H8 as a function of C-C-C angle. (
0
...,I
9 ' P I
-6.0
I
I
-3.6
-1.2
I
1.2
I
3.6
6.0
Y Figure 3. Feynman-Dyson amplitude of *A, Si3HSt.
cations obtained several C, and C, structures within a 0.4 eV of each other that have either one imaginary frequency (indicative of a transition state) or a mode with a very low frequency. The lowest state had 2B2 symmetry in the C, p i n t group. He I photoelectron spectra" display broad peaks and shoulders whose values are listed in Table IV. Partial fourth-order diagonal calculations are carried out for the structures with nonequilibrium values of the C-C-C bond angle. These results are shown in Figure 2. From the equilibrium geometry to the 1 20° structure, the 2BIcurve rises by 0.15 eV, the 2B2curve falls by 0.22 eV, the 2AI curve rises by 0.21 eV and the 2A2curve falls by 0.09 eV. Correlated FDA's from the nondiagonal, renormalized prop agator calculations provide a one-electron picture of how electronic structure changes between initial and cationic states. Figures 3 (30) Lunell, S.;Feller, D.;
(29) Bock H.;Ensslin, 98, 668.
114
111. (31) Kimura,
Davidson, E. R. Theor. Chim. Acra 1990, 77,
K.; Katsumata, S.;Achiba, Y.; Yamazaki, T.; Iwata, S. Handbook of He I Photoelectron Spectra; Halsted Press: New York, 1981.
8612 The Journal of Physical Chemistry, Vol. 95, No. 22, 1991
Ortiz and Mintmire
TABLE I V C3H, Vertical Ionization Energies (eV)
final
state 2B7
2A;
2B, 2A2
Koopmans's theorem
second diag
third
P4
diag
diag
12.92 12.92 12.70 14.43
1 1.47 1 1.60 11.53 13.19
1 1.88
1 1.79 1 1.87
11.95 11.78 13.45
second nondiag
renorm nondiag
expt"
1 1.46 11.59 11.53 13.19
1 1.79 11.87 11.73 13.39
11.51 12.14 12.6 (sh) 13.53
11.73 13.40
d
YI
_ I
v
I
I .r N
9 0 N
N
9
c: ?
N
L7 I
-6.0
-3.6
I
v
1
-1.2
1.2
3.6
6.0
I
-4.5
-2.7
Y
1
I
1
-0.9
0.9
2.7
' .5
Y
Figure 4. Feynman-Dyson amplitude of 2B2 Si3Hs+.
Figure 6. Feynman-Dyson amplitude of 2B2 C&+.
Ln
TABLE V FDA Kinetic and Nuclear Attraction Energy Expectation Values (au)
ion
state
Tq
Si3Hg+ Si H Si:Hi+ Si3H8+ C3Hs+ C3Hg+
2B2
1.1644 1.0342 0.8415 0.8346 1.2559 1.1414 1.0280 0.9771
+
2Al
*B, 2A2 'B2
2Al
C3Hg'
2BI
C3Hst
'A2
TI 20 -15.1598 -14.3248 -12.5844 -12.3155 -10.5557 -9.9947 -9.2815 -9.2423
1.1686 1.0290 0.8425 0.8309 1.2484 1.1514 1.0358 0.9667
UIlQ -15.1353 -14.2636 -12.5894 -12.1992 -10.5327 -9.9663 -9.2698 -9.1591
TABLE VI: FDA Electric Potential Expectation Values at Various Nuclei (au)
-4.5
-2.7
-0.9
0.9
2.7
4.5
Y Figure 5. Feynman-Dyson amplitude of *Al C3H8+.
and 4 show the FDA's for the 2Al and the 2B2final states of Si3H8+. Contours in the plane defined by the three Si nuclei (squares) are plotted in intervals of 0.025. Solid (dotted) contours stand for positive (negative) contours, while dashed contours stand for nodes. Figures 5 and 6 display FDA contours for the analogous final states of C3H8+. Because of A relationships between px functions on the nonhydrogen nuclei, FDA's for 2B1and 2A2final states are not as easily represented through countour plots in a single plane. Constructive interference between these px functions and s functions on the hydrogens takes place. An antibonding phase relationship between neighboring pis obtains for 2B, FDA's, while for the 2A2FDA's there is an antibonding phase relationship between nonadjacent pis. Expectation values of the FDA's from diagonal and second order nondiagonal calculations are determined for the equilibrium geometries and for the structures where the central angle is 120O. At the equilibrium structures, FDA's resulting from renormalized, nondiagonal calculations are also obtained. Nondiagonal, secand nuclear attraction ond-order results for the kinetic energy (tr) operators, shown in Table V, differ by 1% or less from the renormalized results. Uncorrelated expectation values from the diagonal calculations have somewhat greater (1-2%) deviations
(n
nucleus Si, Si2 H2 H"l H'I
Cl c 2
H2 Hf',
H'I
2B2
-0.371 -0.293 -0.223 -0.196 -0.229 -0.472 -0.434 -0.284 -0.269 -0.389
2Al -0.377 -0.257 -0.319 -0.211 -0.168 -0.480 -0.381 -0.378 -0.296 -0.275
2BI
2A2
-0.316 -0.219 -0.388 -0.232 -0.158 -0.456 -0.328 -0.460 -0.309 -0.229
-0.181 -0.279 -0.143 -0.341 -0.171 -0.279 -0.416 -0.215 -0.410 -0.251
from those of Table V. FDA expectation values for electric potential operators from the renormalized calculations are given in Table VI, where Si2and H2 lie in the xz plane, both Si, nuclei and both HfI nuclei lie in theyz plane, and the four H'fI nuclei lie above and below the y z plane. Similar conventions apply to the nuclei of C3H8. These expectation values differ by less than 3% from the nondiagonal, second-order results. Discussion With H as the side-group substituent, steric consequences of increasing the central bond angle (Si-Si-Si or C-C-C) are small. Bond lengths and angles in the rest of the molecule remain approximately constant. Even when the bond angle is increased to 120°, there is no evidence that a major rearrangement of the bonds has taken place or that a qualitative change in electronic structure has occurred. Bulky substituents in an all anti chain could lead to such a bond angle opening because of 1,3 steric interactions.
Si3Hs and C3Hs Saturated C backbones will be much more resistant to bond-angle opening than polysilane backbones. Previous work on Si4Hloand Si5H1214 has shown that there is no electronic bias of the SI backbone respecting anti versus gauche rotational isomers, that is, the energy difference between the two forms is close to zero. A rotation barrier between the two minima of 0.6 kcal/mol was calculated for Si4Hlo. Bulky 1,3 steric repulsions may then be alleviated through rotations about single bonds. From the results of Table I, it is clear that bond angle opening will compete with rotations about single bonds in relieving steric congestion. Although energy differences along the ground state are in the 1 kcal/mol range, spectral shifts accompanying these geometrical distortions can be larger. The shifts are larger for the C case than for the Si case. This reflects what seems to be a generally greater sensitivity of electronic structure to bond angle changes in C3Hs. Changes in vertical ionization energies of small silanes with respect to dihedral angles along the Si chain amounted to several tenths of an e l e c t r ~ n v o l t .The ~ ~ rise and fall of the curves pertaining to Si-Si-Si bond angle changes (Figure I), by comparison, are about 0.1 eV for a bond angle opening from equilibrium to 120’. Opening of the Si-Si-Si bond angle will reinforce rotations toward gauche conformations in increasing the lowest vertical ionization energy. Because the diagonal approximation is accurate for all cation final states under consideration, CMO’s are an excellent approximation to the FDA’s Expectation values are stable to within 3% as one improves from C M O S to second order, nondiagonal FDA’s to renormalized nondiagonal FDA’s. In Si3Hs, FDA’s for the two lowest ionization energies are more concentrated in the Si-Si bond regions than the other FDA’s, which are more concerned with Si-H bonding above and below the yz plane. Relative magnitudes of electric potential expectation values at the H nuclei in Table VI illustrate the concentration of the 2BI FDA on the Si2-H2 bond regions and the concentration of the 2Bl and 2A2 FDA’s on the Sil-H”, bond regions. FDA’s of C3Hs are qualitatively similar in distribution to their Si3H8counterparts. Approximate formulations of the FDA’s follow from inspection of Figures 3-6. The contours in Figure 3 are compatible with the notion that constructive interference between two adjacent S i 4 bond functions is taking place. In the FDA of the lowest ionization energy (Figure 4), destructive interference takes place between two lobes localized in adjacent Si-Si bonding regions. Both FDA plots have nodes surrounding the Si nuclei that are characteristic of Si(3p) atomic orbitals. In the 2AI case, there is an accumulation of negative contours in the Si-Si bond regions and along the z axis just below the central Si nucleus. For 2B2)~ FDA, there are maxima and minima in the Si-Si bond regions as well. C3H8 FDA’s have similar patterns, but there are some important differences. For the 2B2FDA (Figure 6), there are two maxima in each C-C bond region, while in the C-H bond regions there are maxima on the H nuclei and near the C nuclei. In the 2AI FDA (Figure 5), three maxima are found close to the C nuclei in the C-C bond regions. The atomic orbital constituents of these FDA’s are easily discerned. Because C(2p) atomic orbitals have no radial nodes, there are no nodal surfaces that surround the C nuclei. It appears that building FDA’s from bond orbitals localized about bond midpoints is more appropriate for Si3H8than for C,Hs, where a linear combination of atomic (or hybrid atomic) orbitals
The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 8613 gives a better qualitative description. FDA expectation values provide trends in components of the ionization energy with respect to central bond angle changes. To some extent, the rise and fall of the electron binding energies in Figures 1 and 2 can be attributed to the nodal properties of the FDA. Because of destructive (constructive) interference in the xz plane, one expects electron binding energies to grow more negative (positive) for the 2B2and 2A2(2BIand 2Al) final states as the central angle increases. For all of the C3Hs+ final states and for the 2Bl and 2A2final states of Si3Hs+,there is a positive correlation of kinetic energy changes with changes in electron binding energies (Table V). In these cases, kinetic energy accounts for between 50% and 250% of the change in nondiagonal, second-order electron binding energies from the equilibrium to the 120’ structure. Similar trends obtain when the diagonal approximation is employed. For the ZA,final state of Si3H8+,there is still a positive correlation between the change in the electron binding energy and the change in the FDA’s kinetic energy, but the dominant energy change is the loss of 0.0968 au of potential energy stabilization between the electron and the terminal Si nuclei. Finally, for the lowest ionization energy of Si3Hs, kinetic energy increases while the electron binding energy falls. The change in electron-nuclear attraction energy is also positive from the equilibrium geometry to the 120’ structure. This implies that loss of electron repulsion energy underlies the overall trend. Electric potential expectation values of the FDA’s from renormalized, nondiagonal calculations reveal an important difference between the two molecules. Table VI shows these values for all final states at the neutral equilibrium geometries. In all cases, the electric potentials at the H nuclei are more negative for a given C3Hs FDA than for its Si3Hs counterpart. This indicates greater delocalization onto the H’s for C3Hs.
Conclusions To understand the effect of Si-Si-Si angle changes on the electron binding energies of polysilanes, accurate ab initio calculations have been performed on the smallest relevant system: Si3Hs. Comparisons with C3Hs illustrate the unique bonding properties of the Si chains. Increases in Si-Si-Si bond angles up to 120’ have an energetic penalty about a third of that encountered for the C analogue. Changes in ionization energies with respect to bond angle distortions are also smaller for the Si case. Shifts of about 0.1 eV obtain for the two lowest ionization energies when the Si-Si-Si angles are distorted from tetrahedral values to 120’. These shifts are smaller than the shifts that occur in Si4HI0when the Si-Si-Si-Si dihedral angle is changed from 180’ to 60’. FDA’s for Si3H8are approximately built from Si-Si bond orbitals, but for C3H8,a linear combination of atomic orbitals picture is superior. Nodal properties and kinetic energy trends are compatible with the changes in electron binding energies with respect to the central angle in some cases, but not all. Greater delocalization onto the H nuclei occurs for C3H8 FDA’s. Acknowledgment. This material is based on work supported by the National Science Foundation under Grant CHE-8723 185. The Government has certain rights in this material. Some of the calculations were performed at the Pittsburgh Supercomputer Center.
