11373
J. Phys. Chem. 1994, 98, 11373-11378
Donor-Acceptor (Push-Pull) Ethanes: Possible Bond Stretch Isomers of 1,l, l -Triamino-2,2,2-tricyanoethane and 1,1,1-Triamino-2,2,2-trinitroethane Michelle A. Pietsch and Michael B. Hall* Department of Chemistry, Texas A&M University, College Station, Texas 77843 Received: May 30, 1994@ Previous work has shown that limited basis set self-consistent field calculations on the title compounds yield structures with two stable minima. One minimum corresponds to a covalent isomer while the second minimum corresponds to an ionic one. In this work, we show that even with larger basis sets and perturbation corrections for electron correlation two minima are still apparent. Since frequency calculations produced only real frequencies for both minima for the tricyano molecules and produced only a pair of imaginary frequencies corresponding to a degenerate set of rotations for the trinitro molecules, it was concluded that both stationary points on each potential surface are true minima. The minima corresponding to the ionic isomers are much more stable than the ones corresponding to the covalent isomers, which are barely bound with respect to the barrier separating them. Thus, the latter could be detected only spectroscopically if at all. The structure of several other possible isomers and dimer were also investigated. These calculations suggest that the solid material will be mainly ionic with a network of hydrogen bonds.
Introduction Isomers that correspond to two potential energy minima differing by only the length of one bond are termed bond-stretch isomers. This term was coined in 1972 when Strohrer and Hoffmann studied hypothetical structures of the (CH)s+ ion.’ In this particular case, the two minima arose from the “forbidden” crossing of a symmetric and an antisymmetric orbital. More recently, ab initio quantum chemical calculations were used to study the question of bond-stretch isomers in vac-WOCl2(N&)3]+ and cis-mer-M0OC12(PH3)3.~ Song and Hall determined that neither an orbital crossing nor the second-order Jahn-Teller effect could explain the experimentally reported bond-length changes associated with these so-called bond-stretch isomers. There seemed to be no way to accommodate the existence of these isomers in the theory, and it is now known that the reported observations were due to impurities in the crystals used in the structural determinati~n.~ The hexasubstituted ethanes, Y3CCX3, offer another class of molecules where bond-stretch isomers may exist. Although the a-electron-donating and a-electron-withdrawing properties of Y and X can contribute to the charge separation between central carbons, the x-bonding effects are essential for the stability of large charge separations (ions). However, when both Y and X are n-donors or both Y and X are n-acceptors, a single minimum is predicted for the central C-C bond with a typical covalent bond length. When Y or X is a x-donor and the other one is a n-acceptor, two minima may arise from the crossing of two potential energy surfaces, one for a covalent species and one for an ionic species (Figure 1). Using restricted Hartree-Fock (RHF) calculations with a 6-3 lG* basis set, Mixon and Cioslowski4 performed calculations on a series of hexasubstituted ethanes with Y = NH2 and X = F, NOz, CN. As expected, (NH2)3CCF3, in which NHz and F are both n-donors, had one minimum with a central C-C bond length of 1.534 A, a value corresponding to a covalent geometry. The molecule (NH&CC(N02)3, where X is now the n-acce tor NO2, optimized with a central C-C bond length of 3.187 a value corresponding to an ionic geometry. Calculations for (NH2)3CC(CN)3, where CN is also a n-acceptor, generated two
1,
@
Abstract published in Advance ACS Abstracts, October 1, 1994.
Covalent minima
Ionic minima
Figure 1. Potential energy curves for the dissociation of Y3C’ -CX3 and Y3C”CX3. Figure is not drawn to scale.
stable bond-stretch isomers. The covalent isomer with a central C-C bond length of 1.595 A was 21.7 kcallmol less stable than the ionic isomer with a central C-C bond length of 3.102 A. This latter molecule, (NH&C(CN)3, was the only one found by Mixon and Cioslowski to have two minima. Krishnan et also published RHF calculations with a 4-31G basis set on the hexasubstituted ethanes: (NH2)3CC(N02)3 and (NH2)3CC(CN)3. For (NH2)3CC(N02)3 an optimized central C-C bond length of 1.60 A, a value significantly shorter than that reported by Mixon and Cioslowski,4 was the only minimum reported by Krishnan et al. Together the results of these two groups suggest that (NH2)3CC(N02)3 may also have two minima, corresponding to a covalent and ionic geometry. For (NH&CC(CN)3, the only minimum found by Krishnan et al. corresponded to the covalent geometry reported by Mixon and CioslowskiP Thus, hexasubstituted ethanes with n-donor ligands at one end and n-acceptor ligands at the other end may form a general class of molecules which display bond-stretch isomerization. Since bond-stretch isomerization remains a chemically unusual phenomenon, we undertook this study to determine if electron correlation and basis set improvements6 might modify the results of these initial predictions. Theoretical Details Calculations were performed with the GAMESS-UK and Gaussian92 packages7 at the Come11 National Supercomputer
0022-3654/94/2098-11373$04.50/0 0 1994 American Chemical Society
11374 J. Phys. Chem., Vol. 98, No. 44, 1994
Covalent Isomer 0 0
0-
Ionic Isomer
0
-
-
3.070 A (3.009 A)
1.626A (1.612 A)
pKKEFl H-N-H
Pietsch and Hall
pTFCGTl
117.77' (1 14.83")
H-N-H 116.61' (117.08')
1.140 A
(1.196A)
-,
I
C-C2-C 109.80° (110.46") C2-C-N 177.85' (177.59")
I.466A (1.482 A)
I
1.401 A (1.416 A)
_- . I
*a. C-C2-C 119.07'' (119.00") C2-C-N 173.18' (170.02")
Figure 2. Optimized geometries of the covalent and ionic isomers of ( N H & C C ( C N ) 3 at the RHF level using a 4-31G basis set. Values in parentheses are from MP2 optimizations with the same basis set.
Facility (CNSF) on an IBM 3090-600VF, at the Supercomputer Center of Texas A&M University on a Cray Y-MP2/116, at the Supercomputer Center of Cray Research, Inc., Eagan, MN, on a Cray Y-MP8V8128-2, and on the Chemistry Department's Cray SMP. The Laplacian of the electron density was calculated with the use of the MOPLOT program.8 All calculations employed either a 4-31G basis set90n all atoms or a 6-31G** basis set9 on all atoms with an additional diffuse sp functionlo (exponent = 0.0438) on the two central carbon atoms, denoted as 6-31(+)G** for this study. Results and Discussion Geometry Optimizations for (NH2)3CC(CN)3. Ionic and covalent isomers for the hexasubstituted ethane, (NH&CC(CN)3,were optimized at the RHF level with the 4-31G basis set and C3 symmetry. At the same level of theory, the separated radicals, *C(NH2)3and *C(CN)3,and the ions, [C(NH2)3]+ and [C(CN)3]-, were optimized by assuming central C-C bond length of 10 A and a triplet state for the radicals. The optimized covalent and ionic isomers of (NH2)3CC(CN)3 have central C-C bond lengths of 1.63 and 3.07 A, respectively, with the ionic isomer 24.7 kcaYmol more stable than the covalent isomer (Figure 2). In addition to the differences in the central C-C bond length, the two isomers differ in the rotation of the NH2 groups and the bending of the C(CN)3 group. The ionic isomer optimized with the C(NH2)3 group almost planar and the C(CN)3 group bending toward the C(NH2)3 group. This last feature has been referred to as an inverted umbrella
~tructure.~The covalent isomer optimized with both the C(NH2)3 and C(CN)3 nearly tetrahedral and with the C-NH2 plane tilted about 45" with respect to the plane containing the two central carbons and the amine nitrogen (Figure 2b). Mailer-Plesset (MP) perturbation corrections with frozen cores (1s) on carbon and nitrogen were calculated for the optimized RHF geometries of (NH2)3CC(CN)3 (Table 1). Application of the MP2 correction decreased the difference in energy between the ionic and covalent isomers from 24.7 kcaY mol at the RHF level to 12.3 kcaYmol at the MP2 level. With increased correlation (MP4DQ), the difference in energy between the ionic and covalent isomers decreased to 10.9 kcaY mol. The ionic and covalent isomers of (NH&CC(CN)3 were reoptimized at the MP2(full) level using the 4-31G basis set. The reoptimized geometries of the ionic and covalent isomers resembled the structures of their RHF counterparts shown in Figure 2. At this level of theory, the ionic isomer was 11.7 kcaYmo1 more stable than the covalent isomer, a value slightly less than the difference at the MP2 level with the RHF geometry; see Table 1. To verify that the covalent and ionic isomers are true minima on the potential energy surface, frequency calculations were completed for the optimized geometries of both the covalent and ionic isomers of (NH&CC(CN)3 with the 4-3 1G basis set. For the RHF optimized geometries, RHF frequency calculations produced only real frequencies for both isomers. Likewise MP2 frequency calculations for the MP2 optimized geometries produced all real frequencies for both isomers. Therefore, it was concluded that both isomers are local minima on the potential energy surface. The biradical (NH2)3C"C(CN)3 was optimized at the RHF level in a triplet state with an unpaired electron located on each central carbon, which were separated by 10 A to simulate two separate radicals (Figure 3). The 'C(CN)3 fragment optimized to an almost planar structure, maximizing the n overlap between the central carbon orbital containing the unpaired electron and the corresponding CN n* orbitals. The *C(NH2)3 fragment optimized to a nearly tetrahedral structure, minimizing the n destabilization between the unpaired carbon electron and the nitrogen lone pairs, with the NH2 groups at a rotation angle similar to ones found for the covalent isomer. The ions, [(NH2)3C]+ and [C(CN)3]-, were optimized in singlet states at 10 A separation with both (previously C-C bonding) electrons located on the [C(CN)3]- central carbon, (Figure 3). Like 'C(CN)3, [C(CN)3]- optimized planar. The optimized [(NH&C]+ fragment is also planar, which maximizes the overlap of the empty central carbon p orbital and the orbitals containing the lone pairs on the nitrogens. At 10 A, the optimized singlet ionic states were 28.7 kcaYmol more stable than the triplet-coupled radical states. In addition, MP2 energies were calculated for both the biradical and the separated ions at their RHF geometries. The separated ions were still 25.91 kcaY mol lower in energy than the biradical. Assuming that beyond 10 A the biradical energy equals the fully separated radicals and that the ionic curve follows a point charge (lh), we can
TABLE 1: Energy of the Optimized Covalent and Ionic Isomers at the RHF' Level and MP Energies of the Covalent and Ionic Isomers in Atomic Units" covalent ionic ion-cov a
RHF
MP2
MP3
MP4D
MP4DQ
-518.6869 -5 18.7262 24.65
-519.8082 (-519.8476) -519.8278 (-519.8663) 12.30 (1 1.73)
-5 19.7833 -519.8057 14.08
-5 19.8241 -519.8429 11.78
-519.8781 -5 19.8362 10.93
The difference in energies is given in kcaymol. The MP2 optimization energies are given in parentheses.
J. Phys. Chem., Vol. 98, No. 44, 1994 11375
Donor-Acceptor (Push-Pull) Ethanes
Ions
Radicals 0
Ionic Isomer
Covalent Isomer
*sa-
a
-l
1.660 A (1.590 A)
IO A
(2.886 A)
-8-8N-CI-CZ-c 6i.xno
0
0
V
0.993 A
0
0
0.996A
0.993 A
-1.411
A
1.323 A
pH-N-H 7 i z117.12' Tq
N-Cl-N 112.66" ( I 12.15") H-N-H 120.05" ( 1 16.82")
-1.153
i-1.411
A
a -,
1.401
A
1.216A (1.524 A)
1.253 A (1.130 A)
A
1.493 A (1.281 A)
1.388 A (1.416 A)
1.210 A (1.275 A)
1Figure 3. Optimized geometries of the radicals, (NH2)?CnC(CN)3, and the ions, [(NH2)3C]+ [C(CN)3]-, at 10 %, apart using a 4-31Gbasis set at the RHF level.
I 220 A
@
O(1.293 A)
Figure 4. Optimized geometries of the covalent and ionic isomers of ( N H 2 ) 3 C C ( N 0 2 ) 3 at the RHF level using a 4-31Gbasis set. Values in parentheses are from MP2 optimizations with the same basis set.
determine that the crossing point where the biradical is finally more stable than the separated ions occurs at approximately 45
A.
Geometry Optimizations for (NH2)3cc(No2)3Optimizing . the structure of (NH&CC(NO2)3 from the covalent5 and ionic4 starting geometries at the RHF level with a 4-31G basis set gave central C-C bond lengths of 1.594 and 3.064 A, respectively, with the ionic isomer 32.5 kcal/mol lower in energy than the covalent isomer (Figure 4). The ionic geometry optimized with a nearly planar C(NH2)3 group similar to that for (NH&CC(CN)3. The corresponding C(NO2)3 group optimized with the central carbon and the nitrogens of the C(NO2)3 group planar and the C-NO;! plane tilted about 45" angle with respect to the plane containing the central carbons and the nitro nitrogen. For the covalent isomer, both the C(NH2)3 and C(NO2)3 optimized to a nearly tetrahedral geometry with both the C-NH2 and C-NO2 planes tilted about 45" with respect to the plane containing the central carbons and the amine nitrogen or the nitro nitrogen, respectively. MP2(full) optimizations were completed for the ionic and covalent isomers of (NH2)3CC(N02)3. Like (NH2)3CC(CN)3, the MP2(full) optimizations yielded structures very similar to their RHF counterparts (Figure 4). At this level of theory, the ionic isomer was only 7.7 kcdmol more stable than the covalent isomer. RHF frequency calculations were completed for the RHF optimized geometries for both the ionic and covalent isomers. In agreement with Mixon and Cioslowski's results: the frequency calculation for the ionic isomer produced a degenerate pair of imaginary frequencies which correspond to the rotation of the nitro groups. The frequency calculation for the covalent isomer also produced a pair of imaginary frequencies; however, these imaginary frequencies corresponded to the rotation of the amino groups. Although appearance of the imaginary frequencies suggest that neither the ionic isomer nor the covalent isomer is a true minimum on the potential energy surface, reducing the symmetry from C3 to Csor C1 would permit free rotation
of the nitro and amino groups in the direction suggested by the imaginary frequencies. This reduction in symmetry would remove the imaginary frequencies associated with the nitro and amino group rotations but most likely would not affect the rest of the structure significantly. Potential Energy Curves. Potential energy curves of (NH2)3CC(CN)3 were constructed by fixing the central C-C bond length fixed and optimizing the remaining parameters in C3 symmetry. At the RHF level, the structures were optimized using a 4-31G basis set. In general, as the central C-C bond length increases, the C(CN)3 group changes from a pyramidal structure to an inverted umbrella while the C-NH;! planes rotate from almost parallel to the plane containing the central carbons and the amine nitrogen (a tetrahedral structure) at short central C-C distances to almost perpendicular to the same plane (a planar structure; Figure 2). For RHF geometry optimizations with the 4-31G basis set, two minima, corresponding to the covalent and ionic isomers, and one maximum are observed (Figure 5). The maximum is found at approximately 1.9 A and is approximately 2.1 kcaY mol higher in energy than the covalent minimum. When this potential energy curve is recalculated by determi9ing the MP energy at each point, this maximum shifts to 2.1 A (Figure 5). Although the energy difference between the covalent and ionic isomers decreases with MP corrections (Table 1 and Figure 5 ) , the energy difference between the covalent isomer and the maximum increases to 5.2 kcaVmol at the MP4DQ level. The contribution to the zero-point energy from the central C-C stretching frequency is 1.9 kcaYmo1, very close to the 2.1 kcaV mol energy barrier found at 1.9 A but significantly less than the MP4DQ barrier. To examine the barrier between the covalent and ionic minima further, a MP2(full) optimization with the 4-31G basis set was completed for the central C-C bond length of 2.1 A. Although this barrier is only 2.5 kcaYmol at the MP2(fc) level with the RHF geometry, it increased to 3.6 kcal/mol at the MP2 level
Pietsch and Hall
11376 J. Phys. Chem., Vol. 98, No. 44, 1994 -519.6
1
4
-519.9 1 .o
1
2.0
3.0
_---_
4.0
C-C bond length (A) Figure 5. Potential energy curves for the stretchingof the central C-C bond for (NH&CC(CN)3. The geometries were optimized at the RHF level and MP corrections were completed for the RHF optimized geometry using a 4-31G basis set.
Figure 7. Laplacian of the charge density plotted in the plane containing both central carbons and a carbon of a CN group for the (a, top) ionic and (b, bottom) covalent isomers. Regions of charge concentration (-VQ > 0) are denoted by solid lines and regions of charge depletion (-Ve < 0) are denoted by broken lines. -519.6
4
1
2
3
4
C-C Bond Length (A)
Figure 6. Potential energy curves for the stretching of the Cl-C2 bond for (NH&CC(CN)s. The geometries were optimized at the RHF level using a 6-31(+)G** basis set. MP2 corrections were completed on the optimized RHF geometries. with the MP2 geometry. Thus, the maximum found at a central C-C bond distance of 2.1 A does not disappear when MP2(full) optimizations are completed. Even though the central C-C stretching frequencies increase to 2.6 kcaVmol at the MP2 level with the MP2 geometry, the contribution to the zero-point energy from this stretching frequency is still not large enough to overcome the barrier that exists at 2.1 A. RHF geometry optimizations with the larger 6-3 l(+)G** basis set were used to construct a potential energy curve similar to that described above; again, two minima and one maximum were found (Figure 6). The minima (1.6 and 3.0 A) and maximum (1.9 A) for these two curves correspond to the same central C-C distances found at the RHF level using the 4-31G basis set. In addition, MP2(full) corrections to the RHF energy were calculated. The maximum is 5.0 kcdmol greater in energy than the covalent isomer at the FU-IF level and 4.0 kcal/mol higher in energy at the MP2 level. The ionic isomer is 21.8 kcal/mol more stable than the covalent isomer at the RHF level and 8.9 kcaVmol more stable at the MP2(full) level. Charge Density Analysis. The Laplacian or second derivative of the total charge density, denoted v e , measures the curvature of the total charge density. A negative curvature, Le., ve < 0, indicates an area of charge concentration and a positive curvature, ve > 0, indicates an area of charge depletion. The Laplacian of the total charge density (ve)is plotted in Figure 7 in the plane defined by the central C-C bond and a cyano carbon. For the ionic structure, central carbon with the attached CN groups has five concentrations of charge in its valence shell.
TABLE 2: Locations and Values for the Laplacian of the Total Charge Density Where C1 Is the Central Carbon of C(NH~)Jand C2 Is the Central Carbon of C(CN)3 ionic isomer covalent isomer no. dist, 8, VQ no. dist, 8, VQ C1 alongC1-NH2 3 0.507 -1.195 3 0.524 -0.164 0 alongCl-C2 1 0.497 -1.007 C2 alongC2-CN 3 0.532 -0.750 3 0.516 -0.824 alongCl-C2 1 0.494 -0.689 1 0.525 -0.590 behingCl-C2 1 0.491 -0.784 0 Three of these maxima are associated with the bonding between the central carbon and the cyano groups (Figure 7 and Table 2), with the other maxima situated along and behind the central C-C bond. As expected from the inverted umbrella geometry, more charge is concentrated behind the central C-C bond, than along the central C-C bond; see Table 2. Only three maxima were found for the central carbon with the attached N H 2 groups. All three of these maxima are associated with the bonding of the central carbon to the nitrogen of the N H 2 groups. Unlike the ionic isomer, the covalent isomer has four charge concentrations on each central carbon. The central carbon of C(CN)3 has three maxima associated with the bonding between the central carbon and the CN groups. The remaining maximum is along the central C-C bond (Figure 7 and Table 2). Likewise, the central carbon of the C(NH2)3 group has three maxima associated with the bonding between the central carbon and the NH2 groups and one maximum along the central C-C bond. For the central carbon of C(CN)3 in the ionic isomer, the two concentrations in the charge density along and behind the central C-C bond are a consequence of a completely filled p orbital. The central carbon of the C(NHz)3 group has no maximum of charge density associated with the central C-C bond, because of its empty p orbital. For the covalent isomer, both central carbons have a charge density maximum along the
J. Phys. Chem., Vol. 98, No. 44, 1994 11377
Donor-Acceptor (Push-Pull) Ethanes 1.152 8, 0.992 8, 122.7” 1.322 8,
0
122.7” 0.992 8,
d
1.398 8,
a
...”., ‘.
-
I
TOP
1.424 A
122.4”
0
1.653 A 106.59’ 1.397 A
b I
w
~ 1 . 3 9A 7
1
SIDE
120.6’
i,/
0.995 A 0.995 A 1.325 8, 120.6“
0 w
109.59”
Figure 9. Optimized structures of the covalent dimer using a 4-31G basis set. The top view and the side view of the dimer are shown. * 0.994 8,
I
1.152 A 1.398 8,
C
Figure 8. Optimized structures of possible “hydrogen bonded” isomers at the RHF level using a 4-31G basis set. (a) One cyano group is pointing toward one amine group. (b) Two cyano groups points toward two different amine groups. (c) One cyano group points toward two amine groups.
central C-C bond, corresponding to half-filled sp3 hybrid orbitals on both central carbons. Other Possible Isomers. Three structures consisting of one C(CN)3- ion “hydrogen bonded” to one C(NH2)3+ ion (Figure 8), were optimized with the 4-3 1G basis set. The first structure (Figure 8a) has one cyano nitrogen pointing toward two hydrogens on a single amine. This nitrogen is 2.29 8, away from both hydrogens and is 13.7 kcaVmol higher in energy than the ionic structure at the RHF level. The second “hydrogenbonded” structure involves two identical hydrogen bonds 2.14 8, from two cyano groups and two amine groups. Each “hydrogen bond” consists of a nitrogen from a cyano group pointing toward a hydrogen from an amine group (Figure 8b). This structure with two “hydrogen bonds” is only 3.0 kcaVmo1 higher in energy than the ionic isomer at the RHF level. The third “hydrogen-bonded” molecule has the nitrogen of the cyano group pointing toward two hydrogens, each hydrogen belonging to a different amine (Figure 8c). The nitrogens optimized to a distance 2.01 8, away from both hydrogens. Unlike the other structures which have rather long “hydrogen bonds”, this distance is within the range of a typical “hydrogen bond”. Although this last structure was only 0.14 kcaVmo1 higher in energy than the ionic isomer at the RHF level, the energy difference increased to 5.0 kcallmol when a MP2(fc) correction was completed on the RHF optimized geometry. All “hydrogenbonded” ion pairs were lower in energy than the covalent isomer at the RHF level but all were higher in energy than the ionic isomer. Dimers. Two dimers were formed, a covalent dimer (Figure 9) and an ionic dimer (Figure 10). The covalent dimer was formed by optimizing two covalent isomers so that the two ethane units are parallel and two amine groups on the first unit “hydrogen bond” to one cyano group on the second unit, in a fashion similar to the third hydrogen-bonded structure described above, and two amine groups on the second unit “hydrogen bond” to a cyano group on the first unit (Figure 9). The distance
1.152 A
d 1.323 8,
TOP 5.988 A
3.314 A
f
I
90.24” 89.24’
SIDE Figure 10. Optimized structures of the ionic dimer using a 4-31G basis set. The top view and the side view of the dimer are shown.
from one central carbon atom belonging to a C(CN)3 group on one isomer to the central carbon atom belonging to a C(NH2)3 group on the other isomer was optimized to be 6.26 8, (Figure 8c). The energy for the covalent dimer with the 4-31G basis set at the RHF level was 9.5 kcal/mol more stable than the two individual covalent isomers. A similar ionic dimer was constructed and optimized (Figure 10). This ionic dimer was 30.8 kcaVmol more stable than two ionic isomers and 70.6 kcaV mol more stable than the covalent dimer at the RHF level. Thus, as one would expect from the low ionization potential for C(NH2)3 and high electron affinity for C(CN)3 the solid material would be most stable as an ionic solid. Conclusion Even with basis set improvements and the addition of electron correlation, both (NH&CC(CN)3 and (NH2)3CC(N02)3continue to exhibit two minima on their respective potential energy surfaces, one representing the covalent isomer and the other representing the ionic isomer. The ionic isomer is more stable and the covalent geometry is barely bound with respect to the zero-point energy. In addition to the ionic and covalent structures, “hydrogen-bonded” structures and dimers for (NH2)3CC(CN)3 were also studied. All three “hydrogen-bonded”
11378 J. Phys. Chem., Vol. 98, No. 44, 1994 structures were lower in energy at both the RHF and MP2 levels than the covalent isomer. The solid phase would most likely be an array of ions with a network of “hydrogen-bonds”, because of the large contributions of the ionic terms to the lattice energy. The key characteristic of a system that displays this behavior will be z-electron-donor groups at one end and n-electronwithdrawing groups at the opposite end. Acknowledgment. We thank the Robert A. Welch Foundation (Grant A-648) and the National Science Foundation (Grant CHE 91-13634) for financial support. We also thank Drs. M. F. Guest and P. Sherwood for providing the GAMESS package of programs. We also thank Chris Hempel and Cray Research Inc. for providing the opportunity of using the Cray Y-MP8U 8128-2. References and Notes (1) Stohrer, W.-D.; Hoffmann, R. J. Am. Chem. SOC. 1972, 94, 779. Stohrer, W.-D.; Hoffmann, R. J. Am. Chem. SOC. 1972, 94, 1661. (2) Song, J.; Hall, M. B. Inorg. Chem. 1991, 30, 4433. (3) Parkin, G. Chem. Rev. 1993, 93, 887. Desrochers, P. J.; Nebesny, K. W.; LaBarre, M. J.; Bruck, M. A.; Neilson, G. F.; Sperline, R. P.;
Pietsch and Hall Enemark, J. H.; Backes, G.; Weighardt, K. Inorg. Chem. 1994, 33, 15. (4) Mixon, S. T.; Cioslowski, J. J. Am. Chem. SOC. 1991, 113, 6760. Ciolowski, J.; Mixon, S . T. Chem. Phys. h r r . 1990, 170, 297. (5) Krishnan, A. M.; Sjoberg, P.; Politzer, P.; Boyer, J. H. Chem. SOC., Perkin Trans. 2 1989, 1237. (6) Richardson, N. A.; Hall, M. B. J. Phys. Chem. 1993, 97, 10952. (7) (a) Guest, M. F.; Shewood, P. Daresbury Laboratory, Warrington, WA44AD, U.K. (b) Frisch, M. J.; Trunks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson,B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S . ; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S . ; Gonzales, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92, Revision B, Gaussian Inc.: Pittsburg, PA. (8) Interactive MOPLOT: a package for the interactive display and analysis of molecular wave functions incorporating the program MOPLOT (D.Lichtenburger), PLOTDEN (R. F. W. Bader, D. J. Kenworthy, P. M. Beddal, G. R. Runtz, and S . G. Anderson), SCHUSS (R. F. W. Bader, G. R. Runtz, S . G. Anderson, and F. W. Biegler-Koenig), and EXTREM (R. F. W. Bader and F. W. Biegler-Koenig). P. Shenvood and P. J. MacDougall, 1989. (9) Frisch, M. J.; Pople, J. A.; Binkley, J. S . J. Chem. Phys. 1984, 80, 3265. (10) Clark, T.; Chandrasekhar, J.; Spitznatal, G. W.; Schleger, J. Comput. Chem. 1983, 294.
