J. Phys. Chem. 1996, 100, 13979-13984
13979
Dichlorobenzene Ionization Energies V. G. Zakrzewski and J. V. Ortiz* Department of Chemistry, UniVersity of New Mexico, Albuquerque, New Mexico 87131-1096 ReceiVed: April 2, 1996; In Final Form: June 4, 1996X
Electron propagator calculations on the lowest 14 vertical ionization energies of the para, meta, and ortho isomers of dichlorobenzene are performed using the OVGF and P3 approximations, where Feynman-Dyson amplitudes are equivalent to canonical molecular orbitals. Cl p orbitals destabilize the e1g set of benzene to produce the molecular orbitals associated with the two lowest ionization energies. Holes corresponding to four higher final states have mostly Cl 3p character. The remaining molecular orbitals strongly resemble their benzene counterparts, but significant Cl admixtures are present in most cases. Previous assignments for m-dichlorobenzene are confirmed, and remaining uncertainties in the ortho and para spectra are resolved. Basis sets with up to 304 contracted functions are used. Agreement with experimental ionization energies is close.
Introduction
Computational Methods
Photoelectron spectroscopy has long been a useful tool for investigation of molecular electronic structure.1 Assignment of observed bands to one-electron states has been facilitated chiefly by molecular orbital (MO) theory and Koopmans’s theorem, but the reliability of these models is limited by their neglect of electron correlation and final state orbital relaxation. Electron propagator theory (EPT)2 is a superior vehicle for interpreting photoelectron spectra, for it systematically includes relaxation and correlation effects while retaining an orbital picture of photoionization. Because propagator poles and residues are electron-binding energies and Feynman-Dyson amplitudes (or Dyson orbitals), respectively, it is possible to depict orbitals that are associated with correlated energy differences. Until recently, ab initio implementations of EPT usually have been limited to basis sets smaller than 120-140 functions.3 Applications were limited to small molecules with basis sets designed to give an accurate account of electron correlation or to somewhat larger systems described by less complete basis sets. With the development of new algorithms, it has become possible to study larger systems with greater accuracy. These capabilities are applied here to the three isomers of dichlorobenzene. Photoelectron spectra (PES) of the three isomers (para, meta, and ortho) of dichlorobenzene were considered in several papers4-7 and in a compendium.8 Penning ionization electron spectroscopy (PIES) measurements on the 14 lowest cationic states9 were used to assign PES of dichlorobenzenes. Assignments in ref 7 assumed the validity of minimal basis, Koopmans’s theorem results, and a regular hexagonal structure for the benzene ring. (No assignments accompany the spectra in ref 8.) PES were assigned in ref 9 using PIES results, canonical orbital energies from 4-31G Hartree-Fock calculations, and some empirical arguments. There are, however, plentiful examples (for example, ref 10 and references therein) of incorrect final state assignments based on Koopmans’s theorem, even when good basis sets are employed. Therefore, we performed electron propagator calculations to clarify previous assignments based on PES and PIES results, to provide a detailed description of the electronic structure of these molecules and to study the influence of basis set effects on theoretical results.
Propagator methods2,10-15 are ideal for the study of PES. They provide accurate predictions16,17 when flexible basis sets are used. A semidirect version of the outer valence Green function approximation (OVGF) was reported recently3 and incorporated in Gaussian 94.18 (For a detailed discussion of OVGF, see ref 10.) In this algorithm, terms requiring certain types of transformed electron repulsion integrals (ERIs) in the canonical molecular orbital basis are determined without their explicit evaluation and storage on disk. Transformed integrals with four virtual indices are handled in this manner, and there is an option for transformed integrals with one occupied and three virtual indices as well. Semidirect OVGF is a powerful tool for computation of outer valence ionization energies when combined with the ability of Gaussian 94 to run direct SCF and semidirect integral transformations. Because OVGF calculations require a pole search, direct evaluation of contributions from transformed integrals with four virtual indices must be repeated for each energy. This step obviously necessitates reevaluation of ERIs in the atomic basis. Two or three iterations per state are needed in most cases. The slowest step of the semidirect procedure, direct integral evaluation, uses Gaussian 94 routines adapted for parallel execution. Many of the present calculations were executed in this semiparallel mode at the Maui High Performance Computing Center. An alternative propagator method,19 known as the partial third order approximation (P3), has important advantages over OVGF. Its average errors are slightly smaller. It does not require transformed ERIs with four virtual indices. Intermediate sums dependent on transformed integrals with one occupied and three virtual indices can be done in a direct way. Only one contraction of this kind is required, for the intermediates in question are not energy-dependent. P3 calculations were performed using a modified version of the OVGF code found in Gaussian 94. Three types of basis sets were used: correlation-consistent, valence double ζ (cc-pVDZ), correlation-consistent, valence double ζ augmented by diffuse s, p, and d atomic functions (aug-cc-pVDZ), and correlation-consistent, valence triple ζ (ccpVTZ).20 In the case of dichlorobenzenes, these choices entail 140, 228, and 304 contracted basis functions, respectively. All the MOs, except those corresponding to 1s carbon and 1s, 2s,
X
Abstract published in AdVance ACS Abstracts, August 1, 1996.
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© 1996 American Chemical Society
13980 J. Phys. Chem., Vol. 100, No. 33, 1996
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TABLE 1: Para OVGF Ionization Energies (eV) 1 2 3 4 5 6 7 8
MO
cc-pVDZ
aug-cc-pVDZ
cc-pVTZ
expt8
3b2g 1b1g 3b3u 6b2u 5b3g 2b2g 10ag 4b3g
8.70 9.75 11.30 11.36 11.50 12.81 12.89 13.08
8.90 9.90 11.53 11.61 11.74 13.04 13.12 13.25
9.03 9.90 11.52 11.59 11.72 13.00 13.02 13.21
8.94 9.84 11.37 11.49 11.64 12.78 12.97 13.1
and 2p chlorine atomic orbitals (AOs), were retained in the propagator calculations. Geometries of the three dichlorobenzene isomers were optimized at the SCF level with the cc-pVDZ basis set. Fourteen ionization energies were calculated in each case. OVGF calculations on p-dichlorobenzene were done with several basis sets to establish the stability of the results. Calculations were performed in our laboratory on IBM RS6000/37T and RS6000/550 workstations and on the SP-2 at the Maui High Performance Computing Center. The largest calculation on p-dichlorobenzene (with the cc-pVTZ basis set) was done on an RS6000/550 with 128 MB of memory and 4 GB disk space. CPU times were 7 h and 55 min for the SCF, 13 h and 46 min for the integral transformation, and 56 h for OVGF calculations on 14 states. Some data on serial and semiparallel jobs are noteworthy. Test calculations were undertaken on p-dichlorobenzene with the cc-pVDZ basis set. Real execution time for the OVGF part of the code on one processor is 120 min and on four processors is 62 min. CPU time on one processor is 6931 s and on four processors is 2146 s. Thus, semiparallel OVGF runs about 3 times faster in CPU time and 2 times faster in real time. This discrepancy is expected because all I/O operations are executed in serial mode on one processor. Speedups are far from linear with respect to the number of processors, but the advantages of parallelism remain appreciable, especially for a code that was written for serial applications. Results and Discussion Table 1 compares OVGF results with experiments on p-dichlorobenzene.7-9 Average absolute errors are approximately 0.1 eV for all basis sets. A good compromise of accuracy and efficiency is the cc-aug-pVDZ basis. Propagator methods not only provide information on ionization energies but also give Feynman-Dyson amplitudes, φFDA, where
φFDA(x1) )
∫Ψ*N-1(x2,x3,x4,...,xN) ΨN(x1,x2,x3,...,xN) dx2 dx3 dx4 ...dxN Because OVGF and P3 methods assume the diagonal form of the propagator self-energy matrix in the canonical MO basis, the corresponding Feynman-Dyson amplitudes are identical with the canonical MOs. OVGF and P3 approximations remain valid only for final states where the pole strengths (PSs) are greater than 0.80-0.85. Three-dimensional MO plots, based on cc-pVDZ results, were obtained with the MOLDEN program.21 The 0.05 electron bohr-3 contours are displayed in Figures 1-4. p-Dichlorobenzene. Because all PSs exceed 0.8 and all except the ninth exceed 0.85, the qualitative validity of the Koopmans description of ionization energies is confirmed. Perturbative arguments underlying the OVGF and P3 approximations are quite likely to be valid. For this reason, orbital
Figure 1. Canonical molecular orbitals (Dyson orbitals) for benzene.
labels will be used instead of state labels for each vertical ionization energy. Final state labels coincide with the assignment presented in Table 2 of ref 9 except that another choice of coordinate system leads to permutations between b2g and b3g and between b2u and b3u labels. (The conventions adopted in the text, figures, and tables of ref 9 are not consistent.) The first two bands originate from the splitting of benzene’s degenerate HOMO: e1g f b1g + b2g. For dichlorobenzene, the HOMO consists of a benzene π3 pattern (Figure 1) with significant admixtures from chlorine pπ orbitals. (See Figure 2.) Antibonding character on four bonds (two C-Cl and two C-C bonds) explains the relative instability (low ionization energy) of this one-electron state. The second band in the PES refers to 1b1g, a benzene π2 orbital that has negligible chlorine contributions. It can be seen from the plots in Figures 1 and 2 that this MO remains almost unchanged when compared to its benzene counterpart even though the ionization energy is larger than benzene’s first ionization energy, 9.25 eV.8 This contrast is probably due to depletion of electron density in the ring produced by the Cl substituents. Each of the first two bands in the PES displays vibrational structure, in agreement with the π
Dichlorobenzene Ionization Energies
J. Phys. Chem., Vol. 100, No. 33, 1996 13981
Figure 2. Canonical molecular orbitals (Dyson orbitals) for p-dichlorobenzene.
delocalization seen in the two highest occupied MOs. The third band (3b3u) originates from the Cl lone pairs (n⊥) which are perpendicular to the plane of the ring. Next, two bands (4 and 5) of the spectra pertain to ionization from 6b2u and 5b3g. The evident similarity of these two MOs explains why the PES bands were considered to have the same energy in ref 7 and to differ by only 0.15 and 0.14 eV in refs 8 and 9, respectively. Three closely spaced, but sharp, peaks in the PES are compatible with the present results for bands 3-5. The sixth band pertains to ionization from the 2b2g MO, which consists of Cl p orbitals perpendicular to the plane of the ring (n⊥). This MO also has significant π C-Cl bonding character. (It was considered to be another Cl lone pair orbital perpendicular to the ring in ref 9). Some vibrational structure is present for this feature as well. Bands 7 and 8 originate from splitting of a degenerate set of benzene σ orbitals: e2g f ag + b3g. It should be noted that the authors of ref 9 have the same assignment of bands 6 and 7 in their Table 3 but a reversed order in their text and in their Figure
3. They argued that 2b2g consists of Cl lone pairs and should correspond to a sharp peak in their spectra. On the other hand, the bars indicating positions of the vertical ionization energies are placed in ref 8 in a different way compared to ref 9, showing band 6 as a sharp peak and bands 7 and 8 as high-energy shoulders. Furthermore, in ref 9, the largest sharp peak is considered to be band 7 with low-energy and high-energy shoulders. Here, bands 7 and 8 instead derive from a degenerate benzene MO that is associated with complex features in its PES, suggestive of final state vibronic interactions. Our calculations produce three bands of g symmetry within 0.2 eV of each other; one may therefore expect vibronic interactions to be important. Band 9 can be assigned to ionization from 2b3u, an orbital which is built from a2u of benzene (π1) and bonding contributions from Cl atoms. OVGF and P3 calculations show that ionization from this MO has the lowest pole strength (0.81-0.83), and it is likely that the band has satellites. This result also explains why agreement between theoretical and experimental results is worst
13982 J. Phys. Chem., Vol. 100, No. 33, 1996
Zakrzewski and Ortiz
Figure 3. Canonical molecular orbitals (Dyson orbitals) for mdichlorobenzene.
in this case. The next two bands (10 and 11) represent the splitting of another degenerate σ level in benzene: e1u f b2u + b1u. In band 12, ionization takes place from a distorted b1u benzene MO in which there is large C-H σ bonding character. These assignments are in agreement with conclusions made about bands 9 and 10 in ref 9 and contradict ref 7. Band 13
Figure 4. Canonical molecular orbitals (Dyson orbitals) for odichlorobenzene.
pertains to ionization from a b2u orbital that is practically unchanged from a benzene MO with σ C-C bonding character. In benzene, however, these last two MOs have the reversed
Dichlorobenzene Ionization Energies
J. Phys. Chem., Vol. 100, No. 33, 1996 13983
TABLE 2: Para aug-cc-pVDZ Ionization Energies (eV) MO 1 2 3 4 5 6 7 8 9 10 11 12 13 14
3b2g 1b1g 3b3u 6b2u 5b3g 2b2g 10ag 4b3g 2b3u 9b1u 5b2u 8b1u 4b2u 9ag
Koopmans OVGF 9.28 10.06 12.47 12.59 12.74 14.07 14.37 14.76 15.55 16.13 16.95 18.0 18.52 19.29
8.90 9.90 11.53 11.61 11.74 13.04 13.12 13.25 13.97 14.90 15.13 16.17 16.22 17.40
PS
P3
expt8
expt7
expt9
0.90 0.89 0.88 0.90 0.90 0.89 0.90 0.90 0.81 0.89 0.88 0.89 0.86 0.85
9.08 9.99 11.26 11.28 11.43 12.79 13.14 13.27 13.83 14.83 15.17 16.08 16.39 17.33
8.94 9.84 11.37 11.49 11.64 12.78 12.97 13.1 13.47 14.56 15.00 15.74 15.9 16.98
8.97 9.84 11.37 11.50 11.50 12.78 12.91 12.91 13.44 14.54 15.02 15.75 15.92 16.97
8.95 9.84 11.37 11.46 11.60 12.65 12.77 12.96 13.46 14.55 15.03 15.75 15.95 16.96
TABLE 3: Meta aug-cc-pVDZ Ionization Energies (eV) MO 1 2 3 4 5 6 7 8 9 10 11 12 13 14
3a2 4b1 13b2 3b1 17a1 2a2 12b2 16a1 2b1 11b2 15a1 14a1 10b2 13a1
Koopmans OVGF 9.46 9.82 12.58 12.61 12.80 13.96 14.44 14.64 15.59 16.43 16.66 17.71 18.50 19.68
9.10 9.49 11.59 11.67 11.81 12.96 13.13 13.21 14.01 14.94 15.04 16.00 16.20 17.66
PS
P3
expt8
expt7
expt9
0.90 0.89 0.90 0.88 0.90 0.89 0.90 0.89 0.82 0.88 0.88 0.87 0.86 0.85
9.28 9.69 11.28 11.44 11.49 12.70 13.15 13.23 13.88 14.89 15.08 15.93 16.38 17.58
9.26 9.66 11.47 11.56 11.71 12.77 12.77 13.0 13.50 14.54 14.8 15.72 16.1 17.03
9.14 9.70 11.47 11.58 11.73 12.80 12.92 12.92 13.57 14.62 15.00 15.78 16.04 17.08
9.28 9.65 11.46 11.58 11.70 12.77 12.84 12.98 13.55 14.56 14.95 15.76 16.02 17.03
TABLE 4: Ortho aug-cc-pVDZ Ionization Energies (eV) MO 1 2 3 4 5 6 7 8 9 10 11 12 13 14
4b1 3a2 15b2 16a1 3b1 2a2 15a1 14b2 2b1 14a1 13b2 12b2 13a1 12a1
Koopmans OVGF 9.40 9.72 12.28 12.95 12.94 13.40 14.53 14.45 15.71 16.32 16.59 17.77 18.43 19.44
9.04 9.41 11.33 11.88 11.95 12.44 13.08 13.13 14.11 14.95 15.00 16.01 16.16 17.47
PS
P3
expt8
expt7
expt9
0.90 0.89 0.90 0.90 0.87 0.89 0.89 0.90 0.82 0.88 0.88 0.87 0.86 0.85
9.24 9.61 10.97 11.61 11.77 12.13 13.09 13.15 13.99 14.90 14.95 15.93 16.32 17.41
9.23 9.63 11.23 11.77 11.77 12.38 12.63 13.3 13.71 14.50 14.8 15.69 16.0 16.98
9.08 9.64 11.25 11.70 11.75 12.37 12.70 13.35 13.69 14.56 14.93 15.71 15.90 16.99
9.24 9.65 11.26 11.76 11.76 12.37 12.65 13.28 13.70 14.56 14.85 15.70 15.95 16.99
order. The last MO, 9ag, is descended from benzene’s a1g and is distorted by Cl AOs. m-Dichlorobenzene. Our results for m-dichlorobenzene are in complete qualitative agreement with the assignments in the text and in Table II of ref 9, but there appear to be contradictions with the qualitative descriptions of orbitals in Figure 2 of the latter report. Koopmans’s theorem predicts the correct order of states for m-dichlorobenzene with the aug-cc-pVDZ basis set. (See Table 3.) The HOMO, 3a2, is formed from the π2 (instead of π3 as was stated in ref 9) MO of benzene and chlorine pπ orbitals. (See Figure 3.) 4b1 is formed from the π3 of benzene and smaller contributions from Cl pπ orbitals. This MO has more C-Cl antibonding character compared to the second highest occupied MO in the para isomer; the gap between this final state and the lowest cation state is smaller in the meta isomer. In the PES, the first two bands display extensive vibrational structure.8 The third band represents ionization from Cl lone pairs (13b2, n|) parallel to the ring plane. It is more destabilized than its para counterpart, 5b3g. 3b1 (n⊥) contains Cl lone pairs perpendicular to the ring. It also has a π bonding
contribution from three nonadjacent C atoms, but is not as destabilized by C-Cl antibonding interactions as the 3b3u MO of the para isomer. The fifth MO (17a1, n|) represents Cl lone pairs parallel to the plane of the ring and is more stable than its para counterpart, 6b2u. Three sharp, closely spaced features8 in the PES correspond to states 3, 4, and 5. 2a2 (n⊥) contains chiefly Cl lone pairs perpendicular to the rings that are significantly delocalized onto the adjacent carbons in a π bonding relationship. A nearly identical ionization energy is obtained in the analogous para case, 2b2g. Bands 7 and 8 (MOs 12b2 and 16a1) are the results of splitting a degenerate benzene σ level: e2g f b2 + a1. Note the opposite order of the patterns in the 10ag and 4b3g MOs of the para isomer. In the ninth case, 2b1 resembles benzene’s a2u distorted by a bonding interaction with Cl pπ orbitals. The low pole strength here indicates that stronger correlation effects demand a treatment of higher order corrections to produce closer agreement with experiment. Bands 10 and 11 originate in the splitting of a lower benzene σ pair: e1u f b2 + a1. The twelfth band’s MO displays a pattern similar to benzene’s b1u MO, but with C-Cl bonding components. 10b2 is a slightly perturbed version of benzene’s b2u MO, while 13a1 is similar to benzene’s a1g. o-Dichlorobenzene. In the case of o-dichlorobenzene, the order of cationic states 1-8 is the same as in ref 9 except for two pairs of states. States 4 and 5 (3b1 and 16a1) are switched by correlation corrections. Experimental results from refs 8 and 9 do not distinguish between these states, but in ref 7, the gap is 0.05 eV. Another Koopmans misordering occurs with states 7 and 8 (15a1 and 14b2). The HOMO, 4b1, is composed of the benzene π2 orbital with an antibonding contribution from Cl π orbitals. 3a2 is chiefly a π3 benzene orbital with a small contribution from Cl π orbitals. Note that closer Cl-Cl contacts produce ordering opposite of the meta case, but similar ionization energies. Extensive vibrational structure appears in the first two bands of the PES.8 The third final state’s MO (15b2, n|) is almost entirely Cl lone pairs parallel to the ring plane. This final state is destabilized with respect to its meta counterpart and corresponds to a simple, sharp peak in the PES.8 In the fourth MO (16a1, n|), Cl lone pairs parallel to the ring constructively interfere, but are destabilized by antibonding interactions with adjacent carbon contributions. The fifth band’s MO, 3b1 (n⊥), contains Cl lone pairs perpendicular to the plane of the ring and extensive delocalization onto all four nonadjacent carbons. Experimental and calculated ionization energies are higher for this case than for the corresponding meta MO, 3b1. Final states 4 and 5 contribute to the large peak observed at 11.77 eV.8 2a2 displays C-Cl bonding and is less stable than its meta counterpart with the same label. Bands 7 and 8 (MOs 15a1 and 14b2) pertain to the splitting of benzene’s e2g into a1 and b2. Band 9 (2b1) represents ionization from benzene’s a2u (π1) distorted by bonding interactions with the Cl atoms. Splitting of benzene’s e1u into a1 and b2 produces the MOs associated with the next two states. Band 12’s MO is the result of an interaction of s and pσ Cl orbitals with benzene’s b1u. Slightly distorted benzene b2u and a1g MOs appear as 13a1 and 12a1, respectively, for the ortho isomer. Conclusions The lowest ionization energies of dichlorobenzenes correspond to MOs that are chiefly benzene e1g (π2 or π3) levels with antibonding admixtures from the chlorines. Four states follow whose MOs consist primarily of Cl p orbitals that are parallel or perpendicular to the benzene ring plane. Orderings of these states are affected by bonding and antibonding
13984 J. Phys. Chem., Vol. 100, No. 33, 1996 interactions with carbon p’s. The seventh and eighth final states’ MOs strongly resemble benzene e2g levels, but with C-Cl interactions that may be bonding or antibonding. In the ninth state, the π1 MO of benzene is delocalized in a bonding fashion onto the chlorines. The five remaining states correspond to MOs that bear strong resemblances to deeper benzene levels, but with varying degrees of Cl delocalization. Electron propagator theory implemented with advanced algorithms is a valuable tool for assignment of PES. Accurate correlation corrections to canonical orbital energies, produced with flexible basis sets, can be calculated efficiently for dichlorobenzene isomers. Some remaining uncertainties in the assignment of PES have been clarified. Because the propagator approximations employed here retain the equivalence of Feynman-Dyson amplitudes and canonical MOs, orbital interpretations of the spectra are especially facile. Pole strengths are above 0.8 for all final states, thus confirming the qualitative validity of the Koopmans description. The computationally advantageous P3 approximation provides accuracy comparable to and sometimes better than OVGF. Acknowledgment. Mr. Mark Enlow provided technical assistance in the preparation of the figures. Discussions with Dr. Olga Dolgounitcheva improved our analysis of the MOs. This work was supported by the National Science Foundation under Grant CHE-9321434, the Petroleum Research Fund under Grant 29848-AC6, Gaussian, Inc., and the Maui High Performance Computing Center. References and Notes (1) Turner, D. W.; Baker, A. D.; Baker, C.; Brundle, C. R. Molecular Photoelectron Spectroscopy; Interscience: London, 1970. (2) Linderberg, J.; O ¨ hrn, Y. Propagators in Quantum Chemistry; Academic Press: New York, 1973.
Zakrzewski and Ortiz (3) Zakrzewski, V. G.; Ortiz, J. V. Int. J. Quantum Chem., Quantum Chem. Symp. 1994, 28, 23. Zakrzewski, V. G.; Ortiz, J. V. Int. J. Quantum Chem. 1995, 53, 583. (4) Kimura, K.; Katsumata, S.; Achiba, Y.; Yamazaki, T. Monograph Series of Research Institute of Applied Electricity; Hokkaido University, 1978; Vol. 25. (5) Streets, D. G.; Caesar, G. P. Mol. Phys. 1973, 26, 1037. (6) Potts, A. W.; Lyus, M. L.; Lee, E. P. F.; Fattahallah, G. H. J. Chem. Soc., Faraday Trans. 2 1980, 76, 556. (7) Rusˇcˇicˇ, B.; Klasinc, L.; Wolf, A.; Knop, J. V. J. Phys. Chem. 1981, 85, 1486. (8) Kimura, K.; Katsumata, S.; Achiba, Y.; Yamazaki, T.; Iwata, S. Handbook of HeI Photoelectron Spectra of Fundamental Organic Molecules; Tokyo Halsted Press: New York, 1980. (9) Fujisawa, S.; Oonishi, I.; Masuda, S.; Ohno, K.; Harada, Y. J. Phys. Chem. 1991, 95, 4250. (10) von Niessen, W.; Schirmer, J.; Cederbaum, L. S. Comput. Phys. Rep. 1984, 1, 57. (11) Pickup, B. T.; Goscinski, O. Mol. Phys. 1973, 26, 1013. (12) Cederbaum, L. S.; Domcke, W. AdV. Chem. Phys. 1977, 26, 206. (13) Simons, J. Theor. Chem. AdV. Persp. 1978, 3, 1. (14) Herman, M. F.; Freed, K. F.; Yeager, D. L. AdV. Chem. Phys. 1981, 48, 1. (15) O ¨ hrn, Y.; Born, G. AdV. Quantum Chem. 1981, 13, 1. (16) Zakrzewski, V. G.; von Niessen, W.; Boldyrev, A. I.; Schleyer, P. v. R. Chem. Phys. 1993, 174, 167. (17) Zakrzewski, V. G.; Ortiz, J. V.; Nichols, J. A.; Heryadi, D.; Yeager, D. L. Int. J. Quantum Chem., in press. (18) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T. A.; Peterson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; HeadGordon, M.; Gonzales, C.; Pople, J. A. Gaussian 94; Gaussian, Inc.: Pittsburgh, PA, 1995. (19) Ortiz, J. V. J. Chem. Phys. 1996, 104, 7599. (20) Dunning, T. H. J. Chem. Phys. 1989, 90, 1007. (21) Schaftenaar, G. MOLDEN; CAOS/CAMM Center: The Netherlands, 1991.
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