J . Phys. Chem. 1994, 98, 5040-5043
5040
Structure, Infrared Spectrum, and Dissociation Energy of SiH7+ Ching-Han Hu, Peter R. Schreiner, Paul von R a p 6 Schleyer, and Henry F. Schaefer, 111' Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602, and the Computer Chemistry Center, Institut f i r Organische Chemie der Universitat Erlangen- Niirnberg, Henkestrasse 42, D- 91054 Erlangen, Germany Received: December 13, 1993; In Final Form: March 11, 1994"
Ab initio quantum mechanical methods, including the self-consistent field (SCF), single- and double-excitation configuration interaction (CISD), single- and double-excitation coupled cluster (CCSD), and the single-, double-, and perturbative triple-excitation coupled cluster [CCSD(T)] have been applied to three stationary points on the SiH7+ potential energy hypersurface. Double- (plus polarization (DZP) and triple-{plus double-polarization [TZ2P and TZ2P(f,d)] basis sets were employed. The C2 structure, where two symmetry-equivalent H2 subunits complex the SiH3+ cation, was found to be the global minimum, in agreement with the findings of Liu and Zhou ( J . Phys. Chem. 1993,97,9555). The bound vs free H2 harmonic vibrational frequency shift obtained a t the TZ2P C C S D level (259 cm-I) is 36 cm-l less than the experimental frequency shift (295 cm-I), compared with the shift obtained by Liu and Zhou with second-order perturbation theory, which was 33 cm-I higher than the value from experiment. The theoretical rotational constants are compared with the experiments of Okumura's group. The dissociation energy DOof SiH7+ to yield SiHS+ and H2 is sizable, 4.6 kcal/mol [TZZP(f,d)] CCSD(T) ZPVE(TZ2P CCSD)], much larger than the analogous value for CH7+.
+
Introduction The structures of silonium cations are attractive both theoretically and experimentally. Those hypercoordinate molecules provide insights into new structural features, and they are usually quite different from the analogous carbonium ion structures. The chemistry of silicon hydrides is also closely related to the ionmolecule reactions encountered in chemical vapor deposition processes. A major experimental breakthrough for the SiH7+ system was very recently made by Cao, Choi, Haas, Johnson, and Okumura.1 Their observed infrared spectrum for SiH7+displayed, in the 3500-4200-cm-1 region, a single band centered around 3866 cm-I, which was assigned to a perturbed hydrogen-hydrogen stretching motion. The frequency shift of 295 cm-I with respect to free hydrogen (H2) suggested that molecular hydrogen is a weakly bound subunit with a binding energy of 7-9 kcal mol-', but this is only an empirical estimate. The absence of a second band in theselected region furthermore indicated that themolecule must be symmetrical so that two hydrogen subunits become symmetry equivalent, and a C2 as well as a C2, structure was suggested.' It was also concluded that the rotations of the hydrogen moieties occur at very low barriers. From the 2-A distance of the H2 ligands from planar SiH3+, the rotational constant B of 0.85 cm-l was derived for this prolate top molecule. The C2, (two forms with the hydrogen subunits either in or out of plane, Figure l), D3h, and CZforms of SiH7+ were examined in a subsequent theoretical investigation2 up to the MP2/6-31G(dp) level of theory. Only the C2 structure has less than one imaginary vibrational frequency, and it is also lowest in energy. Further optimizations were carried out a t the MP2/TZ2P level, and energy single points were computed at the CCSD(T)/ TZ2P//MP2/TZ2P level. Thevibrational frequency (3861 cm-1, after scaling by 0.91) for the hydrogen subunit shift compares very well with the experimentally observed frequency (3866 cm-1) for the corresponding vibrational mode. A lower than experimental (7-9 kcal mol-') value was found for the zero-point vibrational energy corrected dissociation energy of SiH7+ into SiH5+ and H2 (4.7 kcal mol-I). The latter SiH5+-H2dissociation energy is less than half of that predicted theoretically for SiH5+ (10.3 kcal mol-').3 No estimates were made of the rotational constants of the structures considered. @
Abstract published in Aduance ACS Abstracts, April 15, 1994.
0022-3654/94/2098-5040$04.50/0
For the parent silonium cation SiHs+, ab initio theoretical methods3 have suggested a C, structure which involves an H2 subunit attached to the SiH3+ cation. Thus, the silonium cation reveals nonclassical three-center two-electron (3c-2e) bonding. The methonium cation CH5+ is more ~ o m p l e x . ~Hydrogen scrambling, which occurs with essentially no barrier in CH5+,4 apparently does not occur in S ~ H S + The . ~ best theoretical prediction for the dissociation energy Do of SiH5+was 10.3 kcal/ mol, which is 5 kcal mol-I lower than the experimental value5 of about 15 kcal mol-'. The binding interaction between the SiH3+ cation and H2 is significantly weaker than the binding energy of 42.0 kcal mol-' for CH3+ and H z . ~ The structure of CH7+ primarily consists of a H2 moiety which is very weakly bound to one of the two hydrogen atoms of the 3c-2e bond in the CH5+ C, structure. The binding energy7 is only about 1-2 kcal mol-'. This is very different from the SiH7+ structure which appears to have two equally bound H2 subunits. In the present study we discuss the structures, vibrational frequencies, and dissociation energies as well as the rotational constants of the C2, C, (I), and C2, (11) structures of the SiH7+ cation by applying high-level a b initio quantum mechanical methods. We also compare our results to the CH7+ cation and attempt to explain the origin of the differences in binding.
Theoretical Approach Geometries were optimized using the self-consistent-field (SCF),Bthe single- and double-excitation configuration interaction (CISD)? the single and double excitation coupled cluster (CCSD),"J and the single, double, and perturbative triple excitation coupled cluster [CCSD(T)]' 1 analytic gradient methods. One core orbital was kept frozen and one virtual orbital deleted at the correlated levels. Three different basis sets have been used, including the double-f plus polarization (DZP),l2 the triple-f plus double-polarization (TZ2P),l3 and the TZ2P(f,d) basis set which was obtained by adding a set of higher order polarization functions to the TZZP basis set. The DZP basis is (1 ls7pld/6s4pld) for silicon and (4slp/2slp) for hydrogen. The orbital exponents for the polarization functions were ad(Si) = 0.50andap(H) = 0.75. TheTZZPbasisset consistsof (12s9p2d/ 6s5p2d) for silicon and (5s2p/3s2p) for hydrogen, with polarization function orbital exponents of ad(Si) = 1.00,0.25 and ap(H) 0 1994 American Chemical Society
Structure of SiH7+
The Journal of Physical Chemistry, Vol. 98, No. 19, 1994 5041
TABLE 1: Total Energies (in hartrees) of Three SiH,+ Stationary Points and the Minimum Structures of SiHs+, SiHs+, and H2 with the Number of Imaginary Vibrational Frequencies Given in Parentheses c 2 Cb (1) c, (11) SiH5+ SiHB+ H2 -292.617 342 (1) -292.617 319 (2) DZP SCF -292.617 317 (3) -291.481 310 -290.335 324 -1.131 089 TZ2P SCF -292.647 989 (0) -292.647 962 (1) -292.647 961 (2) -291.508 278 -290.358 677 -1.132 992 TZ2P(f,d) SCF -292.650 102 (0) -292.650 073 (1) -292.650 072 (2) -291.510 325 -290.360 028 -1.133 006 DZP CISD -292.839 022 (0) -292.838 920 -292.838 916 -291.622 872 -1.1 66 708 -290.488 092 TZ2P CISD -292.942 082 (0) -292.942 024 -292.942 022 -291.658 874 -1.170 805 -290.580 122 DZP CCSD -292.854 408 (0) -292.854 290 -292.854 286 -291.680 800 -290.494 135 TZ2P CCSD -292.965 546 (0) -292.965 485 -292.965 484 -291.784 585 -290.591 274 DZP CCSD(T) -292.857 503 -292.857 374 -292.857 370 -291.683 627 -290.496 324 -292.969 855 -292.969 788 TZ2P CCSD(T) -292.969 186 -291.788 458 -290.594 293 The total energies of the SiH5+ + H2 supermolecule are DZP CISD, -292.832 269, and TZ2P CISD, -292.932 163. For the SiH,+ + 2H2 supermolecule the absolute energies are DZP CISD, -292.812 690, and TZ2P CISD, -292.910 139.
i'
78.8'
Results and Discussion
i'1
1.459
'H ;
Ctv 1
q2 90.7'
C t V I1
1.456
I"\ H4 '7.911'
Figure 1. Geometries examined in this study, including structural parameters obtained at the TZ2P CCSD(T) level of theory. Complete geometricalparameters for the C2 structure are summarized in Table 2.
= 1.50, 0.375. The TZ2P(f,d) basis set is designated as Si( 12s9p2dlf/6s5p2dlf) and H(5s2pld/3s2pld) with polarization function orbital exponents of a@) = 0.32 and ad(H) = 1.oo. Harmonic vibrational frequencies were determined via analytic second derivative technique^^^ at the SCF level of theory. At the correlated levels, harmonic vibrational frequencies were obtained from finite central differences of analytic energy first derivatives. All computations were carried out using the locally developed program PSI,l5 running on IBM RS 6000 workstations.
The absolute energies of the CZ,CZ,(I), and CZ, (11) forms of theSiH7+cation (Figure 1) and theSiH5+, SiH3+, and H2 minima are summarized in Table 1. The geometrical parameters and the harmonic vibrational frequencies of the SiH,+ minimum (C2) are summarized in Tables 2 and 3. The C2 structure of SiH,+ is the lowest in energy at all levels of theory. However, the energy differences of the three structures (Cz, Cz, (I) and Cz, (11) are less than 0.1 kcal mol-'. At the DZP SCF level of theory, all structures have at least one imaginary frequency. When we optimized the compound without symmetry constraint (Cl structure) a t the DZP S C F level, the global minimum was found to be very slightly different from the C2 structure, where the total energies differ only at the sixth decimal point in atomic units. However, when the triple-f basis sets were used, the number of imaginary frequencies for each structure decreased by one. The "missing" imaginary frequency in going from the double-{to the triple-{basis sets corresponds to a motion which leads to nonequivalent Si-HZ distances. Apparently, this is due to an inadequacy of the DZP basis set to describe SiH7+ correctly, since the less diffuse functions in the DZP basis do not allow a proper description of the rather long silicon-hydrogen subunit bonds. The triple-{basis sets also yield Si-H bonds which are always longer than the ones obtained with the double-{ basis set. Since the Czu(I) form is a transition state for the Hz subunit rotations, the rotational barrier is essentially zero. In Table 2 we have also summarized selected geometrical parameters of free Hz, SiH5+, and SiH3+. The geometrical parameters of SiH7+in Table 2 indicate that the molecule involves a SiH3+ cation weakly bound to two Hz subunits. Both basis set and method have the same effect on the bond lengths, which increase with enhancements in theoretical sophistication. Inclusion off functions on silicon does not alter the results significantly (TZZP(f,d) SCF, Table 2). The MP2 method in conjunction with a TZ2P basis set still seems to underestimate the bond lengths,2 which in turn overestimates the general trend of the vibrational frequencies, as we will discuss below. The Si-H bond distances of the SiHs+ counterpart in SiH7+ are slightly shorter than those of free SiHs+. The H2 bond length of SiH7+ is only slightly shorter than the bond length of free Hz, indicating a small perturbation of the hydrogen subunits through the cation moiety. It is remarkable, however, how little overall effect the basis set and theoretical method have on the geometries of the SiH7+ structures. The harmonic vibrational frequencies and intensities of SiH7+ are summarized in Table 3, together with the harmonicvibrational frequencies of free Hz as well as the H2 stretching frequency within SiH5+. As noted before, the only observable H2 frequency for SiH7+is the asymmetric combination of the two Hz moieties (wI0 mode). The mode involving symmetric combination of the two H2 vibrations does not change the dipole moment of the molecule, and thus has no I R intensity. The w10 mode has been observed experimentally by Cao, Choi, Haas, Johnson, and Okumural at 3866 cm-1. This yields a frequency shift of 295
5042 The Journal of Physical Chemistry, Vol. 98, No. 19, 1994
TABLE 2
Hu et al.
The Geometrical Parameters for the SiH7+ (CZ)Minimum (Bond Distances in angstroms (A), Angles in degrees)'
r12 rwr34
m.r68 r1s.r16 mr18 a21Sa216 a314 72175,72186 T3125974126
Si-H in SiH3+ H2 in SiHs+ H2
DZP SCF
TZ2P SCF
TZ2P(f,d) SCF
DZP CISD
TZ2P CISD
DZP CCSD
TZ2P CCSD
DZP CCSD(T)
TZ2P CCSD(T)
1.449 1.449 0.749 2.164 2.162 83.1 120.0 46.2 83.5 1.452 0.759 0.735
1.451 1.451 0.750 2.166 2.164 83.1 120.0 46.3 83.5
1.452 1.452 0.750 2.158 2.155 83.0 120.0 46.1 83.4
1.449 1.449 0.757 2.066 2.064 82.6 120.0 45.8 83.5
1.45 1 1.451 0.756 2.088 2.085 82.7 120.0 45.5 83.4
1.452 1.452 0.760 2.063 2.061 82.6 120.0 45.8 83.5
1.456 1.456 0.761 2.088 2.085 82.6 120.0 45.3 83.4
1.453 1.453 0.761 2.055 2.054 82.5 120.0 45.8 83.5
1.455 0.760 0.734
1.456 0.761 0.734
1.454 0.770 0.744
1.457 0.771 0.742
1.456 0.772
1.461 0.774
1.457 0.773
1.457 1.457 0.762 2.080 2.078 82.5 120.0 45.0 83.4 1.462 0.776
TZ2P MP2C 1.453 1.453 0.756 2.072 2.070 82.1 120.0 na na
The numbering of the atoms refers to Figure 1. Symmetry definitions used in this table: rij = distance between atoms i and j; aijk = angle between atoms i-k. q j k l = torsional angle between atoms i-1. Geometrical parameters taken from ref 2.
TABLE 3: Harmonic Vibrational Frequencies (cm-l) and IR Intensities (km/mol, in Parentheses) for the SiH,+ (C,) Global Minimum Structure DZP SCF
TZ2P SCF
TZ2P(f,d) SCF
DZP CISD
TZ2P CISD
DZP CCSD
TZ2P CCSD
TZ2P MP2a
4398 (0) 2507 (7) 2453 (0) 1009 (91) 810 (36) 726 (1) 423 (0) 327 (2) 50 (0) 4383 (310) 2507 (7) 1009 (91) 962 (218) 810 (38) 727 (1) 325 (3) 6 (8) 27i 4641 4247
4376 (0) 2473 (4) 2418 (0) 999 (66) 855 (23) 721 (0) 497 (0) 323 (4) 53 (0) 4360 (352) 2473 (4) 999 (66) 952 (203) 855 (25) 721 (0) 322 (18) 288 (250) 5 (0) 4589 4218
4371 (0) 2481 (5) 2426 (0) 997 (65) 876 (25) 729 (0) 497 (0) 327 (4) 55 (0) 4354 (350) 2480 (5) 997 (65) 954 (202) 876 (27) 729 (0) 326 (1 1) 275 (255) 4 (0) 4585 4210
4298 (0) 2480 (4) 241 1 (0) 967 (76) 845 (36) 769 (1) 547 (0) 369 (3) 102 (0) 4279 (274) 2479 (5) 967 (67) 940 (180) 845 (37) 770 (1) 366 (9) 256 (316) 3 (0) 4485 4059
4260 (0) 2428 (2) 2373 (0) 949 (56) 836 (26) 748 (0) 583 (0) 355 (5) 76 (0) 4240 (332) 2428 (2) 949 (57) 917 (166) 836 (27) 749 (0) 379 (249) 349 (25) 1 (0) 441 1 4038
4238 (0) 2453 (3) 2393 (0) 954 (72) 833 (35) 764 (1) 552 (0) 370 (3) 108 (0) 4220 (266) 2452 (4) 954 (72) 928 (169) 833 (36) 766 (1) 367 (10) 262 (315) 2 (0) 4485 4059
4172 (0) 2387 (1) 2330 (0) 928 (53) 813 (26) 741 (0) 587 (0) 354 (6) 78 (0) 4152 (366) 2386 (1) 929 (43) 898 (151) 813 (28) 742 (0) 383 (273) 349 (95) 77 (0) 441 1 3991
4246 (0) 2422 (1) 2366 (0) 945 (49) 859 (32) 754 (1) 589 (0) 363 (6) 77 (0) 4224 (358) 2422 (1) 945 (52) 909 (163) 860 (25) 755 (1) 382 (230) 358 (37) 19 (0) 4552
mode
(A)
wi w2 w3 w4 w5 w6
w7
w8 a9
IO
(B)
WI1
WI2
w 3 w14 WIS
@I6 all @I8
H2 H2 in SiH5+ a
Frequencies and IR intensities taken from ref 2.
TABLE 4 Dissociation Energies (kcalhnol) of SiH7+ and SiHs+. The Values in Parentheses Are the ZPVE-Corrected Dissociation Energies DO SiH,+ DZP SCFa TZ2P SCF TZ2P(f,d) SCF DZP CISD TZ2P CISD DZP CCSD TZ2P CCSD DZP CCSD(T) TZ2P CCSD(T) TZ2P(f,d) CCSD(T)*
-
SiH5+ + H2 SiHs+
3.1 (1.7) 4.2 (1.9) 4.3 (2.0) 4.2 (1.8) 6.2 (3.3j 4.3 (2.2) 6.4 (3.8) 4.5 (2.4) 6.7 (4.1) 7.2 (4.6)
-
-
SiHp+ + H2
9.4 (5.4) 12.4 (6.6) 10.9 (7.0) 12.3 13.8 12.5 14.1 12.9 14.7 16.2
+
a BSSE corrections for the reaction SiH7+ SiHS+ H2 at the DZP SCF, TZ2P SCF, and TZ2P+f SCF levels of theories are 0.18,0.05, and 0.03 kcalmol-l,respectively. Energy singlepoint on theTZ2PCCSD(T)optimized structures.
cm-1 compared to that for free hydrogen (4161 cm-1). Our theoretical vibrational frequency shift a t the TZ2P CCSD level of theory is 259 cm-I, in good agreement with the experimental hydrogen frequency shift. The previously determined2TZZPMP2 frequencies give a shift of 328 cm-1. Similarly, the H2 vibrational frequency shift from free H2 to the corresponding mode in SiH5+is 420 cm-1 a t the TZ2P CCSD level3 indicating a tighter complex of the silonium cation SiHs+ with the hydrogen molecule. Table 5 reports the equilibrium rotational constants Ae-Ce for
TABLE 5 Rotational Constants A-C (in cm-1) for the SiH7+ Structures at the TZ2P CCSD(T) Level C2 (prolate top) C2" (I) (asymmetric top) Ca (11) (asymmetric top) average
A
B
C
2.406 2.405 2.405 2.405
0.829 0.840 0.840 0.836
0.829 0.817 0.817 0.821
the three SiH7+ stationary points considered here. Of course, such a theoretical approach to the prediction of rotational constants for a molecule as floppy as SiH7+ is naive. The proper theoretical approach to the prediction of the rotational constants Ao-Co is clear but presently impossible. One should use the 18-dimensional ab initio potential energy hypersurface to solve the Schrodinger equation for the motion of the nuclei within the Born-Oppenheimer appoximation. This would give rotational constants directly comparable with the experiments of Okumura's group. The above discussion notwithstanding, the theoretical equilibrium rotational constants for the three stationary points are remarkably similar. And the theoretical values of Be all agree reasonably well withtheexperimentall30 = 0.85 cm-1. Avery crude procedure is to average the rotational constants for the three stationary points. This is done in Table 5 , and the resulting average Be is 0.84 cm-1. Our best prediction for the dissociation energy De of SiH7+ into SiHS+and H2is 7.2 kcal mol-1 at the TZ2P(f,d) CSSD level. Inclusion of the TZ2P CCSD zero-point vibrational energy correction decreases this value to DO = 4.6 kcal mol-'. This
Structure of SiH7+ SiHs+-H2 dissociation energy is more than twice as large as the previously predicted7bDo(CH5+-.H2) = 1.2 kcal mol-'. The geometry of the SiH7+ cation (H2-.SiH3+.-H2) is very different from the geometry of the CH7+ cation derived from the CHs+ moiety ( C H S + - . H ~ ) .These ~ ~ differences are in part due to the greater stability of the SiH3+ cation, which is reflected in the differences in the loss of H2 from CH5+ (42.0 kcal mol-l)6 and SiHs+ (10-15 kcal mol-l).3-5 Also, as a third-row element, silicon is much bigger than carbon, thus providing a large surface area where the hydrogen molecules can attach. In other words, H+3H3+--H2 is less crowded than a hypothetical HyCH3+.-H2. Also, carbon (2.5) is more electronegative than silicon (1.7). Consequently, CH3+ is only able to bind one hydrogen molecule strongly; thesecond H2 has to bind indirectly to oneof theelectrondeficient hydrogens of the three-center-two-electron bond.
Concluding Remarks The C2 structure of SiH,+, which consists of a SiH3+ cation weakly bonded to two equivalent hydrogen molecules, was found to be the global minimum on the potential energy surface. Nevertheless, the rotation of the hydrogen molecule moieties around an axis perpendicular to the main axis is essentially unrestricted since the energy differences between the minimum and the rotational transition structures C2, (I) and C2, (11) are negligible. The experimental asymmetric H2 stretching vibrational frequency shift (bound versus free) of 295 cm-l is well reproduced theoretically (259 cm-l). The SiH7+ dissociation energy DO into SiH5+ and H2 is 4.6 kcal mol-' [TZZP(f,d) CCSD(T) ZPVE(TZ2P CCSD)], much larger than the dissociation of CH7+ into CH3+ and H2 (1.2 kcal mol-').
+
Acknowledgment. The work in Georgia was supported by the U S . Air Force Office of Scientific Research, Grant AFOSR-
The Journal of Physical Chemistry, Vol. 98, No. 19, 1994 5043 92-5-0047. The work in Erlangen was supported by the Deutsche Forschungsgemeinschaft, the Fonds der Deutschen Chemischen Industrie (doctoral fellowship for P.R.S.), and the Convex Computer Corp.
References and Notes (1) Cao, Y.;Choi, J.-H.; Haas, B.-M.; Johnson, M. S.;Okumura, M. J . Phys. Chem. 1993, 97, 5215. (2) Liu, R.; Zhou, X . J. J. Phys. Chem. 1993, 97,9555. (3) Hu, C.-H.; Shen, M.; Schaefer, H. F. Chem. Phys. Lett. 1992,190,
543. (4) Schreiner, P. R.; Kim, S. J.; Schaefer, H. F.; Schleyer, P. v. R. J . Chem. Phys. 1993, 99, 3716. Also see refs 6 and 7b. (5) Boo, B. H.; Armentrout, P. B. J . Am. Chem. SOC.1987,109,3549. (6) Schleyer, P. v. R.; Carneiro, J. W. M. J. Comput. Chem. 1992.13, 997. (7) (a) Boo, D. W.; Lee, Y. T. Chem. Phys. Lett. 1993,211, 358. (b)
Kim,S.-J.; Schreiner, P. R.; Schleyer, P.v. R.;Schaefer, H. F.J. Phys. Chem.
1993, 97, 12232. (8) Pulay, P. In Modern Theoretical Chemistry, Volume 4;Schaefer, H. F.,Ed.; Plenum: New York, 1977; pp 153-185. (9) (a) Brooks, B. R.;Laidig, W. D.;Saxe,P.; Goddard, J. D.; Yamaguchi, Y.; Schaefer, H. F. J. Chem. Phys. 1980, 76, 4625. (b) Rice, J. E.; Amos, R. D.; Handy, N. C.; Lee, T. J.; Schaefer, H. F. J . Chem. Phys. 1986, 85, 963. (10) Scheiner, A. C.; Scuseria, G. E.; Lee, T. J.; Rice, J. E.; Schaefer, H. F. J. Chem. Phys. 1987,87,5361. Scuseria, G. E.; Janssen, C.; Schaefer, H. F. J. Chem. Phys. 1988,89, 7382. (1 1) Scuseria, G. E. J . Chem. Phys. 1991, 94, 442. (12) (a) Primitive basis sets: Huzinaga, S. J . Chem. Phys. 1965,42,1293. (b) For hydrogen: Dunning, T. H. Ibid. 1970, 53, 2823. (c) For silicon:
Dunning, T. H.; Hay, P. J. In Modern Theoretical Chemistry, Volume 3; Schaefer, H. F.,Ed.; Plenum: New York, 1977; pp 1-27. (13) (a) Primitive basis set for silicon: Huzinaga, S. Department of Chemistry, Department of Chemistry Report 11, University of Alberta, Edmonton, Alberta, Canada, 1971. (b) Contracted basis set for silicon: McLean, A. D.; Chandler, G. S. J. Chem. Phys. 1980, 72, 5639. (14) Saxe, P.; Yamaguchi, Y.; Schaefer, H. F. J . Chem. Phys. 1982,77, 5674. (15) PSI 1.1 1990; PSITECH Inc.: Watkinsville, GA 30677.
