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J. Phys. Chem. 1996, 100, 8250-8253
Ab Initio Molecular Orbital Study of the GeH7+ Cation Suk Ping So Chemistry Department, The Chinese UniVersity of Hong Kong, Shatin, N.T., Hong Kong ReceiVed: October 11, 1995; In Final Form: January 2, 1996X
The geometries of the various isomeric structures of GeH7+ have been optimized using the 3-21G(*), a double-ζ plus polarization (DZP), and a triple-ζ plus polarization (TZP) basis set, and their vibrational frequencies have been computed. Electron correlation errors are corrected up to the MP4SDTQ level. GeH7+ has been predicted to exist, like SiH7+, in the H2‚‚‚GeH3+‚‚‚H2 structure rather than the GeH5+‚‚‚H2 one, the global minimum being a C2-symmetry structure with two symmetry-equivalent H2 subunits weakly bound to the GeH3+ cation. The dissociation energy D0 of GeH7+ into GeH5+ and H2 has been computed to be 5.21 kcal mol-1 at the MP4SDTQ/TZP//MP2/TZP + ZPE(MP2/TZP) level. This value is comparable to that for SiH7+. It is thus believed that GeH7+ should be stable enough for experimental detection and characterization. The next equilibrium structure is predicted to be a GeH5+‚‚‚H2 complex lying 3.73 kcal mol-1 higher in energy and with a dissociation energy D0 of only 1.49 kcal mol-1 close to that of CH5+‚‚‚H2.
Introduction Spectroscopic studies1 show that SiH3+ has a classical trigonal planar structure like CH3+. The methonium ion CH5+ was first discovered2 by mass spectrometry in 1952, but its experimental geometrical parameters have not been reported until now. Theoretically, CH5+ was previously predicted to have a global minimum of Cs symmetry, in which a H2 subunit is attached sideways to the CH3+ ion through a three-center-two-electron bond. However, a recent theoretical study with a large basis set at a highly correlated and vibrationally corrected level shows that this structure is nearly isoenergetic with two other (one Cs and one C2V) of the various structures and the energy barriers among these three structures are essentially zero, i.e., hydrogen scrambling around the molecule is virtually unrestricted.3 However, the situation is different for the corresponding heavier group IV protonated hydrides, namely the silonium ion SiH5+ and the germonium ion GeH5+. For these ions, complete hydrogen scrambling does not occur, since the energies of the above C2V structures are higher than their dissociation energies.4-6 The best theoretical estimates of their dissociation energies D0 (9.66-10.0 kcal mol-1 for GeH5+ and 10.3 kcal mol-1 (obs., 15 kcal mol-1)7 for SiH5+) are almost the same but much smaller than that (42.0 kcal mol-1)8 for CH5+. Hence, the GeH3+-H2 and the SiH3+-H2 bonds are significantly weaker than the CH3+-H2 bond. Recently, Cao et al.9 reported the first spectroscopic observation of SiH7+. Their IR data suggest that SiH7+ is a symmetric complex of the structure H2‚‚‚SiH3+‚‚‚H2, markedly different from CH7+, which has been concluded, from both its IR spectrum10 and ab initio calculation,11 to have a structure consisting of a H2 subunit weakly bound to one of the two hydrogen atoms of the three-center-two-electron bond in the Cs CH5+ subunit, i.e., CH5+‚‚‚H2. Theoretically,12,13 SiH7+ has been shown to have an equilibrium structure of C2 symmetry consisting of weakly bound SiH3+ and H2 subunits. The dissociation energy D0 of SiH7+ to SiH5+ and H2 is about 4.6 kcal mol-1, while the corresponding value11 for CH7+ is only about 1.46 kcal mol-1. To the author’s knowledge, there is no information, either experimental or theoretical, about the corresponding hydride X
Abstract published in AdVance ACS Abstracts, April 15, 1996.
S0022-3654(95)03020-6 CCC: $12.00
cation of the next group IV element, viz., GeH7+, reported in the literature. Hence, it is thought desirable to carry out a theoretical study of this ion. Calculations The vaious isomeric structures of GeH7+ were optimized under the specified symmetries by the energy gradient method at the SCF and the MP2(FU) levels, using the GAUSSIAN 92/ DFT programs14 implemented on our IBM RS/6000 workstations (Models 320H and 340). Three basis sets were employed. The smallest is the 3-21G(*) set (with d polarization functions of orbital exponent Rd ) 0.264 on the germanium atom only) as proposed by Dobbs and Hehre.15 The second one is the medium sized double-ζ plus polarization basis set (DZP) derived from Dunning’s Ge (14s11p5d) and H(4s1p) primitive sets contracted to Ge(7s5p2d) and H(2s1p), denoted as Ge(14s11p5d/7s5p2d) and H(4s1p/ 2s1p) and augmented by a set of d-type and p-type polarization functions of orbital exponents Rd(Ge) ) 0.25 and Rp(H) ) 0.75, respectively.16,17 The third basis set is of triple-ζ plus polarization (TZP) quality. It consists of Partridge-Vacek’s Ge(15s12p7d/10s8p3d)18,19 and Huzinaga-Dunning’s H(5s/3s)20,21 contracted functions augmented with a set of d-type polarization functions with Rd(Ge) ) 0.19 and two sets of p-type polarization functions with Rp(H) ) 1.5 and 0.375.22 The d-type polarization functions used are the six-component Cartesian functions. Vibrational frequencies were determined by the analytical evaluation of the second derivatives of energy to verify the nature of the stationary point structures, to examine zero-point energy corrections, and to predict vibrational frequencies for the unknown stable species for the sake of its (their) future experimental identification by infrared spectroscopy. The energies of the various species at the optimized MP2(FU) geometries were recalculated by the fourth-order perturbation theory with the Møller-Plesset partitioning of the Hamiltonian in order to take into account electron correlation.23 The fourth-order calculations done in this work (MP4SDTQ) are complete in the sense that the effects of single, double, triple, and quadruple excitations are all included.24 The MP4SDTQ calculations were done with the frozen core approximation. In addition, dissociation energies were also calculated at the G2 level25 using the basis sets of Curtiss and co-workers.26,27 © 1996 American Chemical Society
GeH7+ Cation
J. Phys. Chem., Vol. 100, No. 20, 1996 8251
Figure 1. Some isomeric structures of GeH7+.
TABLE 1: Some Optimized Structuresa of GeH7+ species 1
2
3
4
a
DZP
TZP
geom param
SCF
MP2
SCF
MP2
R12 R13,R14 R15 R16 R56 A215 A314 A516 R12 R13,R14 R15,R16 R56 A215,A216 A314 A516 R12 R13,R14 R15 R16 R56 A215 A216 A314 A516 R12,R13,R14 R15 R56
1.512 1.511 2.262 2.264 0.756 79.8 120.3 19.2 1.511 1.511 2.267 0.756 90.4 119.7 19.2 1.511 1.511 2.268 2.266 0.756 83.0 96.8 120.0 19.2 1.513 2.400 0.750
1.508 1.507 2.166 2.168 0.767 79.3 120.5 20.4 1.507 1.508 2.167 0.767 90.5 119.5 20.4 1.508 1.508 2.167 2.166 0.767 82.9 97.3 119.9 20.4 1.510 2.130 0.759
1.512 1.511 2.307 2.309 0.747 80.1 119.9 18.6 1.511 1.511 2.309 0.747 90.6 119.8 18.6 1.511 1.511 2.307 2.308 0.747 82.5 97.3 119.9 18.6 1.513 2.417 0.736
1.506 1.505 2.201 2.203 0.754 79.5 120.4 19.7 1.505 1.506 2.202 0.754 90.6 119.6 19.7 1.506 1.506 2.203 2.201 0.754 81.6 98.0 120.1 19.7 1.508 2.136 0.742
Bond lengths are in angstroms and bond angles in degrees.
Results and Discussion The geometries of 14 isomeric structures (1-4 for H2‚‚‚ GeH3+‚‚‚H2 and 5-14 for GeH5+‚‚‚H2) of the GeH7+ cation as depicted in Figures 1 and 2 were optimized under the specified symmetries. The geometries of structures 1-4 optimized at the SCF and the MP2(FU) levels with the DZP and the TZP bases and their energies are given in Tables 1 and 2. (To save space, the 3-21G(*) values are not listed but can be obtained from the author upon request.) It is found that these three basis sets give very similar values for the corresponding bond angles, while the 3-21G(*) bond lengths are generally longer than those of the DZP and the TZP. The inclusion of electron correlation at the MP2 level with the larger basis sets is seen from Table 1 to generally leave the bond angles practically unchanged but to shorten the Ge-H distance by ∼0.006 Å for the GeH3+ subunit and by ∼0.1 Å (but as large as ∼0.27 Å for 4) between the GeH3+ and the H2 subunits. On the other hand, when the smaller 3-21G(*) basis is used, the Ge-H bond of the GeH3+
Figure 2. Some optimized HF/DZP isomeric structures of GeH7+. Bond lengths are in angstroms and bond angles in degrees. (HF/TZP and MP2/TZP values for 7 are in round and square brackets, respectively.)
subunit is elongated by ∼0.01 Å instead and the GeH3+‚‚‚H2 distance is decreased by a somewhat larger value, viz., ∼0.13 Å. It is significant to note also that the geometries optimized with the DZP and the TZP bases are nearly the same. This suggests that these geometries are more accurate than those obtained with the smaller 3-21G(*) set and that they will not be changed too much by using more extended basis sets. Accordingly, the 3-31G(*) basis set was not used in the study of the structures 5-14. The structures 5-14 of GeH7+ were optimized and their vibrational frequencies calculated first at the SCF level with the DZP basis set. The predicted results are given in Figure 2 and Table 2. It is seen from Table 2 that all the H2‚‚‚ GeH3+‚‚‚H2 structures 1-4 are more stable than those of GeH5+‚‚‚H2 5-14 except 4, which is found to have four imaginary vibrational frequencies, and that only 7 and 11 among 5-14 are equilibrium structures with the former lying lower in
8252 J. Phys. Chem., Vol. 100, No. 20, 1996
So
TABLE 2: State Energies (au)a at Optimized SCF and MP2(FU) Geometries DZP species 1 2 3 4 5 6 7 8 9 10 11 12 13 14 a
level SCF MP2 MP4b SCF MP2 MP4b SCF MP2 MP4b SCF MP2 MP4b SCF SCF SCF MP2 MP4 SCF SCF SCF SCF SCF SCF SCF
SCF geom 8.948 054 (2)
TZP MP2 geom
c
SCF geom
MP2 geom
9.088 215 (1) 9.430 464 (1) 9.274 759
8.948 054 (2)
9.817 105 (1) 9.479 510 9.088 214 (1)
9.430 462 (2) 9.274 757 8.948 069 (0)
9.817 103 (2) 9.479 510 9.088 226 (0)
9.430 495 (0) 9.274 789 8.931 758 (4)
9.817 394 (0) 9.479 552 9.072 217 (4)
9.412 356 (4) 9.257 268 8.942 684 (1) 8.942 589 (2) 8.942 965 (0)
9.800 103 (4) 9.463 137 9.083 306 (0) 9.810 273 (0) 9.472 785
8.942 758 (1) 8.942 276 (1) 8.941 738 (3) 8.942 272 (0) 8.942 684 (1) 8.878 701 (1) 8.878 692 (2)
Energy ) -(2070 + value listed). b MP4 represents MP4SDTQ(FC). c Numbers of imaginary vibrational frequencies are in parentheses.
TABLE 3: MP2(FU)/TZP Harmonic Vibrational Frequencies (cm-1) and Zero-Point Vibrational Energies (kcal mol-1)a species
frequencies
ZPE
1 2 3
63i, 16, 273, 279, 301, 522, 614, 616, 725, 734, 798, 832, 833, 2173, 2210, 2216, 4053, 4071 63i, 16i, 276, 276, 302, 522, 613, 617, 724, 734, 798, 832, 833, 2173, 2210, 2215, 4053, 4071 41 (0.03)b, 65 (0.20), 276 (9.31), 277 (6.66), 303 (165.54), 520 (0.00), 614 (0.16), 616 (0.33), 732 (27.00), 736 (11.63), 798 (72.48), 833 (39.55), 833 (36.82), 2172 (0.00), 2210 (0.94), 2212 (1.18), 4051 (370.78), 4069 (0.04) 536i, 536i, 531i, 531i, 161, 161, 273, 371, 437, 437, 769, 841, 841, 2163, 2209, 2209, 4185, 4201 93, 103, 128, 196, 211, 352, 553, 567, 613, 809, 842, 842, 946, 2167, 2204, 2211, 3891, 4263
30.40 30.38 30.53
4 7
27.53 30.01
a Frequencies have been uniformly scaled by a factor of 0.95 and imaginary frequencies neglected in calculating zero-point energies. b Infrared intensities (km mol-1) are in parentheses.
energy. The infrared spectra observed9,10 for CH7+ and SiH7+ indicated that these species are the CH5+‚‚‚H2 and H2‚‚‚ SiH3+‚‚‚H2 complexes. This has been supported by ab initio calculations,11-13 which predict an equilibrium structure analogous to 5 for CH7+ and 3 for SiH7+. (No calculations on the corresponding structures 1-4 for CH7+ and 5-14 for SiH7+ have been reported in the literature.) In addition, germanium compounds generally resemble their silicon analogues more than their carbon analogues. It is thus anticipated that the yet unknown GeH7+ cation would have a H2‚‚‚GeH3+‚‚‚H2 rather than a GeH5+‚‚‚H2 structure, in line with the above SCF results. Furthermore, the present calculation has shown that the inclusion of electron correlation and the extension of the basis set from DZP to TZP do not change the nature (equilibrium or nonequilibrium) and the order of relative stability of the H2‚‚‚ GeH3+‚‚‚H2 structures 1-4 (Table 2). This is believed to be also true for 5-14. Consequently, the various GeH5+‚‚‚H2 structures except the equilibrium structure 7 will not be considered further, since this work is meant to study mainly the global minimum equilibrium structure of GeH7+. Data in Table 1 show that the GeH3+ subunits in the structures 1-4 are almost trigonal-planar, like their silicon analogues, having HGeH angles very close to 120° with a deviation of 0.5° or less. The Ge-H bond lengths of GeH3+ in the structures 1-4 are nearly all equal with a difference of not larger than 0.001 Å and are slightly shorter than those (1.510 Å at the MP2(FU)/TZP level) of free GeH3+. The GeH3+‚‚‚H2 distances of GeH7+ are over 2 Å (between 2.361 and 2.136 Å, depending on the levels of theory and the basis sets used). The calculated
H-H distances of the H2 subunits are around 0.75 Å (0.7420.754 Å at the MP2(FU)/TZP level), only slightly longer than that of an isolated H2 molecule (0.737 Å at the MP2(FU)/TZP level). Thus, GeH7+ is predicted here to be a weakly bound complex between a GeH3+ and two H2 subunits, again similar to SiH7+ whose H2‚‚‚SiH3+‚‚‚H2 structure has been confirmed spectroscopically9 and theoretically.12,13 As for structure 7, the MP2(FU)/TZP H-H distance (0.739 Å) of the H2 subunit bonded to a H atom of the GeH5+ subunit is closer to that of a free H2 molecule, indicating an even weaker bonding between the subunits H2 and GeH5+. Vibrational frequency calculations reveal that only 3 of the four H2‚‚‚GeH3+‚‚‚H2 structures is an equilibrium structure, while 1 is a transition state (with one imaginary vibrational frequency) for the H2 subunit rotations, and 2 and 4 are energy maxima with two and four imaginary frequencies, respectively (Table 2). The MP2(FU)/TZP harmonic vibrational frequencies uniformly scaled by a factor of 0.95 and the zero-point vibrational energies for 1-4 and 7 are summarized in Table 3. It is interesting to note that the asymmetric combination of the H-H stretches of the two H2 subunits of 3 has the largest infrared intensity (370.78 km mol-1 at the MP2(FU)/TZP level Table 3), while the corresponding symmetric combination is essentially infrared inactive (0.04 km mol-1) because it causes no change in the electric dipole moment of the molecule. Results similar to the above have also been found12 for the case of SiH7+. At the MP2(FU)/TZP level of theory, the H-H stretching mode of a free H2 molecule and of the H2 subunits in GeH5+
GeH7+ Cation and in 3 and 7 of GeH7+ are predicted here to have frequencies (scaled by 0.95) of 4303, 3911, 4051, and 4263 cm-1, respectively. Thus, the complexation with a GeH3+ ion causes this mode to have a frequency drop of 392 cm-1 in GeH5+ and 252 cm-1 in 3, while the complexation with a GeH5+ ion yields a frequency drop of only 40 cm-1 in 7. These indicate that GeH3+ forms a tighter complex with only one hydrogen molecule and that the bonding between the H2 and GeH5+ subunits is even much weaker. The corresponding frequency drops in SiH5+, SiH5+‚‚‚H2, and CH5+‚‚‚H2 are 420, 259 (obs., 295 cm-1), and 83 cm-1 (obs., 83.6 cm-1) at the CCSD/TZ2P level.11,13 The dissociation energies De of the structures 3 and 7 of GeH7+ into GeH5+ and H2 are, respectively, 5.74 and 1.50 kcal mol-1 at the MP4SDTQ/TZP//MP2(FU)/TZP level. (The state energies for GeH5+, GeH3+, and H2 at this level of theory are -2078.300 257, -2077.111 809, and -1.170 145 au, respectively.) Inclusion of the MP2(FU)/TZP zero-point vibrational energy correction reduces these values to D0 ) 5.21 and 1.49 kcal mol-1. The dissociation energies of GeH5+ into GeH3+ and H2 are much larger, viz., 11.49 (De) and 8.05 (D0) kcal mol-1. This is in line with the above finding that the complexation is weaker, similar to the silicon analogues, in GeH7+ (3) than in GeH5+ and stronger in 3 than in 7. At the G2 level of theory25 and with the basis sets of Curtiss and co-workers,26,27 the dissociations of 3 and 7 into GeH5+ and H2 were calculated to be exothermic with dissociation energies D0 equal to -0.33 and -4.62 kcal mol-1, respectively, which are very different from the MP4SDTQ/TZP results obtained above, namely, endothermic with dissociation energies D0 of 5.21 and 1.49 kcal mol-1. (The corresponding dissociation energies become 1.19, -3.04, 5.27, and 1.47 kcal mol-1 when the germanium 3d electrons are also frozen in the evaluation of all the postSCF energies.) The above MP4SDTQ/TZP theoretical dissociation energies De and D0 of GeH7+ (3) are comparable to the corresponding values of SiH7+, viz., 6.87 and 4.65 kcal mol-1 obtained by Liu et al.12 and 7.2 and 4.6 kcal mol-1 by Hu et al.13 In addition, MP2(FU) optimization with the 641(d) basis set26,27 (used in G2 calculation) yields a GeH bond length of 1.543 Å for GeH4+, which is far more different from the experimental value of 1.514 Å than the MP2(FU)/TZP value of 1.524 Å. Furthermore, Curtiss et al.27 have found, in the testing of their basis sets for molecules containing third-row nontransition elements Ga-Kr, that 19 G2 atomization energies calculated have an average absolute deviation of 1.24 kcal mol-1 from experiment and that the only one atomization energy having a deviation larger than 2.4 kcal mol-1 is that for GeH4 (+5.3 kcal mol-1). Hence, with the lack of other experimental data for comparison, we tend to think, in contrast to common practice, that the geometries and dissociation energies of GeH7+ computed with the TZP basis functions may be more realistic than the G2 values. If this is really the case, then GeH7+ (3) should exist long enough for experimental detection and characterization, since SiH7+ has been spectroscopically observed recently.9 On the other hand, both methods have predicted very low dissociation energies D0 for 7, and thus, its detection should be much less readily accessible if not impossible. The equilibrium structure of the SiH7+ cation (H2‚‚‚ SiH3+‚‚‚H2)12,13 is very different from that of the CH7+ cation (CH5+‚‚‚H2).10 Hu et al.13 have attributed this difference partly to the greater stability of SiH3+ in comparison to CH3+ because CH5+ has a much larger dissociation energy (42.0 kcal mol-1)8 for the loss of the H2 subunit than SiH5+ (10-15 kcal mol-1).4,7 In addition, a silicon atom is larger than a carbon atom in size and hence has a larger surface to which the H2 subunits can
J. Phys. Chem., Vol. 100, No. 20, 1996 8253 attach. Furthermore, carbon is more electronegative than silicon, and as a result, CH3+ is only able to bind one H2 subunit strongly, leaving the second H2 subunit to bind indirectly to the electron-deficient hydrogens of the three-center-twoelectron bond. The atomic radius and the electronegativity of a germanium atom and the dissociation energy of GeH5+ (8.05 kcal mol-1 obtained above) are much closer to the corresponding values of the silicon rather than the carbon analogues (Pauling’s covalent radius28/electronegativity29: C ) 0.772 Å/2.55, Si ) 1.17 Å/1.90, and Ge ) 1.22 Å/2.01). It is thus concluded that the above arguments are also valid for GeH7+, in line with the very low dissociation energies D0 predicted above for 7 at both the MP4SDTQ/TZP and the G2 levels. Acknowledgment. I thank the Hong Kong Research Grant Council for its financial support in the acquisition of an IBM RS/6000 Model 340 workstation and Dr. G. Vacek for sending me the DZP and TZP basis sets for germanium. References and Notes (1) Smith, D. M.; Martineau, P. M.; Davies, P. B. J. Chem. Phys. 1991, 96, 1741. (2) Field, F. H. Acc. Chem. Res. 1968, 1, 42, and references cited therein. (3) Schreiner, P. R.; Kim, S. J.; Schaefer, H. F.; Schleyer, P. v. R. J. Chem. Phys. 1993, 99, 3716, and references cited therein. (4) Hu, C. H.; Shen, M.; Schaefer, H. F. Chem. Phys. Lett. 1992, 190, 543. (5) Schreiner, P. R.; Schaefer, H. F.; Schleyer, P. v. R. J. Phys. Chem. 1994, 101, 2141. (6) Archibong, E. F.; Leszczynski, J. J. Phys. Chem. 1994, 98, 10084. (7) Boo, B. H.; Armentrout, P. B. J. Am. Chem. Soc. 1987, 109, 3549. (8) Schleyer, P. v. R.; Carneiro, J. W. M. J. Comput. Chem. 1992, 13, 997. (9) Cao, Y.; Choi, J. H.; Haas, B. M.; Johnson, M. S.; Okumura, M. J. Phys. Chem. 1993, 97, 5215. (10) Boo, D. W.; Lee, Y. T. Chem. Phys. Lett. 1993, 211, 358. (11) Kim, S. J.; Schreiner, P. R.; Schleyer, P. v. R.; Schaefer, H. F. J. Phys. Chem. 1993, 97, 12232. (12) Liu, R.; Zhou, X. J. Phys. Chem. 1993, 97, 9555. (13) Hu, C. H.; Schreiner, P. R.; Schleyer, P. v. R.; Schaefer, H. F. J. Phys. Chem. 1994, 98, 5040. (14) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92/DFT, Revision F.2; Gaussian, Inc.: Pittsburgh, PA, 1993. (15) Dobbs, K. D.; Hehre, W. J. J. Comput. Chem. 1986, 47, 359. (16) Dunning, T. H. J. Chem. Phys. 1970, 53, 2823. (17) Schreiner, P. R.; Schaefer, H. F.; Schleyer, P. v. R. J. Chem. Phys. 1994, 101, 2141. (18) Dyall, K. G.; Taylor, P. R.; Faegri, K.; Partridge, H. J. Chem. Phys. 1991, 95, 2583. (19) Vacek, G. Private communication. (20) Huzinaga, S. J. J. Chem. Phys. 1965, 42, 1293. (21) Dunning, T. H. J. Chem. Phys. 1971, 55, 716. (22) Archibong, E. F.; Leszczynski, J. J. Phys. Chem. 1994, 98, 10084. (23) Møller, C.; Plesset, P. S. Phys. ReV. 1934, 36, 618. (24) Krishman, R.; Pople, J. A. Int. J. Quantum Chem. 1978, 14, 91. (25) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J. Chem. Phys. 1991, 94, 7221. (26) Binning, R. C., Jr.; Curtiss, L. A. J. Comput. Chem. 1990, 11, 1206. (27) Curitss, L. A.; McGrath, M. P.; Radom, L. J. Chem. Phys. 1995, 103, 6104. (28) Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Cornell University Press: Ithaca, NY, 1960. (29) Allred, A. L. J. Inorg. Nucl. Chem. 1961, 17, 215.
JP953020+
