5860
J. Phys. Chem. 1993,97, 5860-5863
Ab Initio Characterization of Novel Gaseous (PO)*+Species C. Sarasolat, X. Lopegt A. Arrieta,t C. Barrientos,t A. Largo,'**and J. M. Ugalde'vt Kimika Fakultatea..Euskal -Herriko Unibertsitatea, P.K. 1072, 20080 Donostia, Euskadi, Spain, and Depatamento de Quimica- Fisica y Anafitica, Universidad de Oviedo, 33006 Oviedo, Spain Received: November 17, I992
Ab initio molecular orbital theory has been used to characterize gaseous doublet (P0)2+ species. Eight stable molecular structures were found, two planar cyclic structures, two bicyclic "butterfly" structures, two covalent hemibonded structures, and two ion-dipole structures. A planar cyclic D2h symmetry structure has been found to be the most stable at all levels of theory. The PO'PO+ ion-dipole complex is calculated to be the next most stable structure and then come the covalent hemibonded trans OPPO+ and POOP+structures. The ion-dipole complex P+*OPOlies higher in energy at the MP4SDTQ//MP2 level of theory with the 6-31G*basis set. However, our calculations predict that this structure has the greatest binding energy.
1. Introduction In recent years, considerablework has been done on both neutral and charged small phosphorus oxide complexes. In fact, the chemistry of low-coordinated phosphorus compounds has been the subject of a recent review.' Also, research of the combustion of phosphorus and phosphorus-containing species has raised a considerableamount of interest among both experimentalists and theoreticians. Thus, small neutral phosphorus oxide complexes of the form (P2)x(02)y(x = 1, 2; y = 2-5) have recently been found to be involved in the combustion of P2 in argon matrices.2 This reaction is also found to yield several less common phosphorus oxides like the oxo-bridged P203 and two isomers of the oxobridged P2O4 molecules. Some of these molecules, including the oxo-bridged species, have been characterized by ab initio calculations,3-5 Both open structures3 and bicyclic and bipyramidal structures4 have been discussed from the standpoints of both structural chemistry and IR spectroscopy. It is remarkable that the bicyclic form of P202 is found to be 2217 cm-l lower in energy than the planar C2h trans-OPPO isomer. However, a recently characterized planar D2h structure has been found to be the lowest energy s t r u c t ~ r e . ~ Trigonal bipyramidal forms are bound to be only 2000-6000 cm-I higher in energy than the open O==POP=O,O2POP=O, and 02POP02 forms, respectively, which is a clear indication that any of these isomers should be considered as possible P20x
structure^.^ Pyykko and Zhao have studied the bonding trends of X=Y and X=Y=Z species containing phosphorus.6 They concluded that OPO+ could be considered as a possible synthetic target. According to their calculations, it should have a short bond length between 1.4 and 1.47 A. However, they recall that due to the large electron affinity of its short-livedneutral parent OPO (2AI), it might be difficult to isolate. The rich structural diversity of neutral phosphorus oxide complexes is also encountered for the ionized species. In this research, we present ab initio results for the geometries, energies, vibrational frequencies, and vibrational intensities of the diphosphorus oxide cations (PO),+. A total of eight equilibrium structures will be discussedfrom the standpoints of both structural chemistry and IR spectroscopy. 2. Computational Method
Molecular geometries were initially optimized at the unrestricted Hartree-Fock (HF) level of theory with the 6-3 lG* basis Euskal Herriko Unibertsitatea. Universidad de Oviedo.
0022-3654/93/2097-5860$04.00/0
set,7 which contains polarization functions for both oxygen and phosphorus. Vibrational frequencies were calculated at all HF/ 6-3lG* stationary points from analytical second derivatives.Then geometries of the equilibrium structures were reoptimized at the MP2/6-31G* level, as a consequence of which a reduction in 0-P-O bond angles was observed. Notice that the same behavior hasbeenencountered ingoingfromHF/3-21G* toHF/6-31G*.3s8 Electron correlation effects have been accounted for using fourthorder Maller-Plesset (MP4) perturbation theory with the 6-3 lG* basis set on the MP2/6-31G* optimized geometries. These calculations were made by using the GAUSSIAN 90 program system.9
3. structures Figure 1 shows the MP2/6-31G* and the HF/6-31G*, in parentheses, optimized geometries for the eight stable molecular structures that we have been characterized on the potential energy surface of doublet (P0)2+. The order is in terms of increasing energies (decreasingstability). We have been able to locate seven more stationary points, at the same levels of theory, which turned out to correspond to transition states, for their frequency analysis revealed one mode of imaginary frequency. These molecular structures will be discussed elsewhere.IO The D2h symmetry cyclic structure I has been calculated to be the most stable isomer of (P0)2+. Its electronic configuration is
....b,,2b,,2b,,' ('B
I)
where the unparied electron occupies a molecular orbital which is essentially a 2p (P) perpendicular to the molecular plane. This structure can be thought of as arising from the ionization of the D2h symmetry cyclic 3Bluneutral (P0)2 characterized recently.5 Indeed, the HF/6-3 lG* optimized structure of I has one mode of imaginary frequency. Displacing along its corresponding eigenvector leads to a lower energy structure of C2" symmetry, with long PO bond length of 1.73 A, short PO bond length of 1.56 A, and POP bond angle of 96.3', with all its frequencies real. However, reoptimization of this structure at the MP2/6-3 lG* level of theory collapses into the D2h symmetry isomer. Subsequent frequency calculation, analysis of this D2h structure at the MP2/ 6-31G* level, shows that it is a stable structure, for all its frequencies are real. We have not been able to locate such a C2" stationary point at the MP2/6-31G* level of theory. Note that Luna et a1.lr have found a similar behavior for the distonic H2COS+. The P-P distance is calculated to be 2.48 A (2.44 A) at the MP2/6-3 lG* (HF/6-3 1G*) level. Subsequent Bader's charge density analysisr2showed no bonding along the P-P 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 22, 1993 5861
Characterization of Gaseous (P0)2+ Species
DIH= 89.4 (93.1)
(VI)
1.82
(1.42) ( III )
(1 79)
(VI)
2.20 (2.15)
DIH= 112.77 (124.44)
Figure 1. Optimized geometries at the MP2/6-31GS and HF/6-31GS, in parentheses, levels of theory. Distances are in angstroms and angles in degrees.
direction. Instead, a (3,+1) ring critical point was found in the middle of this planar cyclic structure. Structure VI1 of Figure 1 is also found to be planar and cyclic. Its corresponding neutral species has been studied by Lohr3 (see structure V of ref 3). It is remarkable that while all other parameters do not change very much, the P-P distance elongates from 2.00 A in the neutral to 2.15 A in the cation, at the HF/ 6-31G*level. In fact, inspectionof the molecularorbitals indicates that the P-P bond of the cation is a one-electron hemibond.13 Therefore, this structure, whose electronic state is 2B1, can be thought of as arising from the neutral species by removing one electron from the P-P bond. We have also found, at the HF/ 6-31G* level of theory, a 2Al stable electronic state for this structure which lies 35.0 kcal/mol higher. Our calculations predict that both electrostatic and covalent ion-molecule complexesexist for (P0)2+. Thus, structure I1 may be viewed as the Po'PO+ complex. Its geometry reveals the existence of two different moieties, one neutral and one cationic. This is further confirmed by the Mulliken population analysis which shows that one of the moieties bears almost a full unit charge, namely +0.8e-. Structure VI should correspond to a P+*OPOion-molecule complex, for the P+ moiety bears a charge of 0.7e-. The neutral OPO, which is a short-lived species known spectros~opically,~~ has been studied earlier by Lohr.ls He found a *A ground state, in good agreement with the experiment, with a PO distance of 1.45 A and a bond angle of 134.4' at the HF/ 6-31G* level of theory. In the OPO moiety of structure VI, both the bond length and the bond angle have changed substantially. Thus, at the same level of theory, we find both a wider bond angle and larger PO bond distances (see Figure 1). Finally, we would like to point out that the bond distance between moieties is shorter for the P+'OPO complex than for PO*PO+. For the covalent complexes,i.e., structures I11 and IV of Figure 1, it is worth pointing out that the P-P interaction is predicted to be favored with respect to the 0-0 interaction. This is in
contrast with the (SO&+ complex, which is predicted to be held by a three-electron hemibond between oxygen atoms and not sulfur atoms.16 The P-O bond lengths for the P-P-bonded and the 0-0bonded complexes are calculated to be similar, and they lie between the bond lengths of the ground states of PO, 1.46 A, and PO+, 1.4 A, at the MP2/6-31G* level of theory.I7 However, the bond angle is considerably larger for the 0-0-bonded complex than for the P-P-bonded complex. Both of the large P-P and 0-0 distances of structures I11 and IV, respectively,suggest that these bonds possess quite hemibond character. We have also located two minima for (PO),+ having a nonplanar bicyclic structure ("butterfly") with C2, symmetry. Seestructures V and VI11 of Figure 1. Analysis of the topology of their charge density, p(r), and its associated negative Laplacian, -V2p(r), revealed that structure V has a formal covalent P-P interaction and that for structure VIII, the oxygens are bonded also by a covalent bond, namely, a three-electron two-center (3e,2c) hemibond.13 The calculated HF/6-3 lG* dihedral angle of structure V is substantially smaller than the corresponding dihedral angle of the neutral species at the same level of theory. Thus, the former is 93.1 ', while the latter has a value of 1 11.2'.4 Also, it is worth noting that at the same level of theory, the P-P distance increases from 1.997 A for the neutral to 2.06 A for the cationic species V and that the P-0 distance increases 0.032 A for structure V with respect to its neutral ~pecies.~Further inspection of the molecular orbitals of structure V shows that the unpaired electron corresponds to a P-P *-bonding orbital, thus confirming further that this interaction corresponds to a oneelectron two-center hemibond. Allowing for electron correlation effects in the geometry optimization process has the effect of increasing all bond distances, in good accord with the general trend described earlier' for elements at the right of the periodic table. Significant correlation effects are noted mainly for the bond lengths of the relatively long bonds. Thus, inclusion of electron correlation lengthens the P-P and 0-0 hemibonds of structures I11 and IV by 0.15 and 0.1 3 A, respectively. For structure 11, the central P-0 bond is lengthened by 0.17 A, while the increase for the P+*OPObond is substantially smaller, namely, 0.03 A shorter. Other bond lengthenings on the order of a few hundredths of an angstrom are common. Modifications on bond angles and dihedrals as a consequence of including electron correlation are also small and lie in the range of 1-10' (see Figure 1). This is again in good agreement with the known fact7 that the HF/6-31G* structures of molecules incorporating second-row elements give reasonably good accord with experiment so that equilibrium geometries described within the framework of Hartree-Fock theory will be altered only slightly. 4. Vibrational Spectra
The calculated vibrational spectra are summarized in Table I. The theoretical vibrational transitions should be greater than the experimental values, as the calculated spectrum is harmonic whereas the experimental values include anharmonicity. Also, it should be mentioned that in many cases, discrepanices between computed and observed vibrational frequencies arise due to approximations in the harmonic force constant calculations. However, it has been well established7 that the discrepancies between theoretical and experimental frequencies reveal systematic differences that may be corrected empirically. Thus, Pople et al.18suggest that presumably correct frequencies can be found, scaling by the empirical factor of 0.8929 the calculated frequencies at the HF/6-31G* of theory, and DeFrees and McLeanlg have proposed a scale factor of 0.94 for the MP2/ 6-3 1G* level of theory frequencies. Hence, the frequency entries of Table I have been scaled accordingly. Inspection of Table I reveals that structure I has only two modes with appreciable IR intensity, namely, its breathing bl,
Sarasola et al.
5862 The Journal of Physical Chemistry, Vol. 97, No. 22, 1993
TABLE I: Vibrational Frequencies (in cm-’) and Intensities (in km/mol) for (PO)z+, at tfie HF/631G* Level of Theory structure 10
I1
I11
IV
V
VI
VI1
VI11
symm
mode
Y
IR
340 564 599 730 826 1974 40 103 334 381 1051 1365 20 108 123 234 1289 1340 31 66 80 204 1323 1527 256 472 494 586 839 953 88 164 368 413 868 1096 298 363 580 707 926 1176 162 252 412 475 882 945
21.2 0.0 0.0 93.0 0.0 23692 32.3 4.7 233.4 141.1 640.6 88.1 37.0 23 0.0 0.0 741 0.0 132 39 0.0 0.0 0.0 16878 0.0 19.9 38.6 6.0 64.3 940.4 5.4 17.1 45.8 102.7 76.9 748.0 0.0 339.4 1.1 178.2 99.6 19.4 16.4 20.6 0.0 10.8 0.3 5686.8
Raman 0.0 0.0
0.0 0.0 0.0 0.0 0.1 1.3 6.4 1.5 18.0 16.9 0.0 0.0 413 564 0.0 546 0.0 0.0 1171 1247 7178 0.0 30.4 8.1 1183.7 258.6 273.0 70.2 0.8 0.0 2.1 1.o 3.0 46.0 0.3 0.1 1072.8 6.8 129.3 433.4 371.5 0.3 575.0 574.8 39.3 130.6
MP2/6-3 1G* frequencies and intensities.
mode at approximately 1974cm-I and its bzupartner at 730 cm-I. For structure 11, we have calculated that the longest terminal P-0 bond stretching at 1051 cm-I has the largest IR intensity. Notice that experimental values for the 211ground state of P020 and for the ‘2ground state of PO+ 2 1 are 1220 and 1405 cm-], respectively. The shortest terminal P-O bond stretching at 1365 cm-1 is predicted to have considerably lower IR intensity, i.e., 88 km/mol. The central long P-0 bond stretching mode is found, as expected,in the range of small frequencies,Le., at approximately 334 cm-1, with the measurable IR intensity of 233 km/mol. For the covalent ion-molecule complexes I11 and IV, the IR-active P-0 stretch modes are calculated at 1289 and 1527 cm-1, respectively, and their Raman-active ag partners at 1351 and 1334 cm-I, respectively. However, absorption intensities of structure IV are substantially larger than those of structure I11 (see Table I). The IR spectrum of the P-P-bonded bicyclic structure V is found to be dominated by its bl mode with an estimated frequency of 953 cm-I. Its Raman-active a l partner has a frequency of 494 cm-I. The 0-0-bonded bicyclic structure VI11 has a b2 mode at 945 cm-1 with the highest IR intensity, and its active a2 partner is found at 412 cm-1. Inspection of Table I reveals that the intensities are appreciably higher for the 0-0-
bonded bicyclic conformer. The most intense vibrational transition of the ion-molecule complex VI is found to be associated with thecentralP-0 stretchingmodeat 1096cm-I. Theterminal P-0 bond stretching mode of the OPO moiety of structure VI is at 868 cm-1, with an IR intensity 10 times smaller than that of the former. The P+*OPOstretching has a frequency of 413 cm-I, in accord with its relatively weak bond strength and small IR intensity, i.e., 102 km/mol, as shown in Table I. Finally, our calculations predict that the planar cyclic structure VI1 has an antisymmetric P-O stretching vibrational b2 mode with a measurable IR intensity of 339.4 km/mol. Also, its P-Pstretching mode appears to have a measurable Raman intensity of 1072.7 km/mol. These two vibrational modes may help in its detection.
5. Stabilities Single-point calculations were made at the full MP4/6-3 1G* level of theory on the previously optimized MP2/6-3 lG* molecular structures. It has been found22 that comparison of relative energies of open-shell species which differ in the amount of spin contaminationmay be misleading. In such cases, projected Maller-Plesset energies23 are needed. Table I1 shows the projected Maller-Plesset energies along with the expected values of S2before and after, in parentheses, projecting out the largest spin contaminant. Inspection of these figures shows that spin contamination is projected out reasonably well in all cases except for structure VI, where substantial spin contamination remains even after removal of the largest spin contaminant. Note that UHF theory predicts this ionic structure, VI, to be lower in energy than covalent structures I11 and IV so that at this level of theory, electrostatic ion-molecule complexes are predicted to be more stable than covalent ones. However, allowing for electron correlation effects through optimization at the MP2 level and Maller-Plesset-type single-point calculations on this geometry up to the fourth order reveals that then only the ion-molecule electrostaticcomplex I1is more stable than the covalent structures; structure VI appears then to be even more unstable than the short P-P distance butterfly structure V. This trend is observed along all the perturbational series as shown in Table 11. Bonding energies and electron affinities of the various (P0)2+ structures are collected in Table 111. Note that five different reference systems were chosen, all of which are indicated in the third column of Table 111. Thus, for the cyclic structures I, V, VII, and VIII, their corresponding neutrals were selected as reference systems, so their electron affinities were calculated. It is immediately observed that the electron affinity trend parallals that of the increasing energy order trend. For structures 11,111, and IV, PO+(IZ) + PO(2II) was chosen as the reference system. Calculations predict that the electrostatic POPO+ complex has a substantially larger binding energy than either of the covalent complexes I11 and IV. However, it is worth noting that P’OPO+ appears to have the largest of all the calculated binding energies. For this species, the P+(’P) OP0(2AI) reference system was chosen. The resulting binding energy at the MP4STDQ//MP2 level of theory with the 6-31G* basis set was 46.31 kcal/mol. This suggest that electrostatic P-0 interactions are favored in the primary interactions between neutral and ionized phosphorus oxides. This is in contrast with the behavior found for the sulfur dioxide ionized dimer (S02)2+. In this case, both experiment and theoryI6 confirm that the complex is bound by a oxygenoxygen two-center three-electron covalent bond with an experimental binding energy of 21.8 kcal/mol which agrees well with the calculated figure of 27.0 kcal/mol.
+
6. Conclusions
Eight stable molecular doublet (PO),+ structures were characterized by ab initio molecular orbital calculations. Among them, we have found two planar cyclic structures, two bicyclic “butterfly” structures, two covalent hemibonded structures, and
Characterization of Gaseous (PO),+ Species
The Journal of Physical Chemistry, Vol. 97,No. 22, 1993 5863
TABLE Ik Ab Initio Energies (in au) and Energy Differences (in kcal/mol) in Parenthesea for (PO)*+ mol sym
state symm
UHF//UHF
PMP2//MP2
PMP3//MP2
PMP4//MP2
D2h
2B2g 2AI
-830.884 50 -830.870 91 -830.830 56 -830.803 42 -830.761 43 -830.839 55 -830.7 1 1 44 -830.585 04
-83 1.443 96 -83 1.426 03 -831.405 50 -831.391 71 -831.336 59 -831.32677 -83 1.274 69 -831.162 09
-831.442 57 -831.415 52 -831.392 03 -831.371 92 -831.335 80 -831.345 39 -83 1.28 1 22 -831.159 04
-831.485 14(0.0) -831.472 99(7.6) -831.451 93(20.8) -831.438 96(29.0) -83 1.386 99(61.5) -831.379 53(66.3) -831.329 18(97.9) -831.215 38(169.3)
I I1 I11 IV V VI VI1 VI11
Cs C2h
2A, 2A,
c 2h
2B~
c2u
cs
2Alf
2B~ 2B~
Cz, C2"
TABLE III: Binding Energies and Electron A m t i e s with the 6-316' Basis Set binding electron energy, affinity, kcal/mol eV
I I1
111 IV V VI VI1 VI11
7.76 39.83 24.03 17.09
ref state
level of thcory
neutral, ref 5 HF//HF PO+('.Z) + PO(2l-I) MP4SDTQ//MP2 PO+('.Z) PO(2l-I) MP4SDTQ//MP2 PO+('Z) PO(2l-I) MP4SDTQ// MP2 neutral, ref 4 MP4SDTQ/ / MP2 P+(3P) OP0(2A~)MP4SDTQ/ IMP2 neutral, ref 3 MP4SQTD/ IMP2 neutral, ref 4 MP4SDTQ//MP2
+ +
9.65 46.31 8.86 14.32
+
two ion-dipole structures. The planar DZh cyclic structure I was found to be the most stable at all levels of theory. However, UHF theory predicts ion-dipole structures to be more stable than hemibonded covalent ones. If electron correlation effects are included, through the M~rller-Plessettheory, then the POPO+ ion-dipole complex is found to lie lower in energy than both the P-P-hemibonded and the 0-0-hemibonded covalent complexes, but the P'OPO+ ion-dipole complex is found to rise in energy substantially above the covalent complexes. We have also been able to characterize two stable butterfly cyclic structures. The 0-0-bonded one is calculated to be the most unstable of all our eight molecular structures at all levels of theory. The P-P-bonded butterfly structure V is predicted to be more stable than the P'OPO+ ion-dipole complex at the MP2/6-3 1G* level of theory, but it lies higher in energy than both the trans-OPPO+ and the trans-POOP+ hemibonded covalent complexes. Inspection of the binding energies calculated at the MP4SDTQ//MP2 level of theory with the 6-3 1G*basis set reveals that ion-dipolecomplexes have larger binding energies than the covalent complexes. It is remarkable that the P ' O P O (2A" ) ion-dipole complex has a calculated binding energy of -46.31 kcal/mol with respect to P+(3P) OPO(ZA,), which clearly suggests a likely process for the formation of such a complex. Also, it is found that the P O PO+ ion-dipole complex I1 has a substantially larger binding energy with respect to PO+('Z) PO(,lI) than covalent complexes I11 and IV. Therefore, according to the data of Table 111, one should expect that the ion-dipole complex POP0+(2A,) be formed from PO+(IZ) PO(211) rather than either of the hemibonded complexes I11 or IV.
+
+
+
(S*) 0.82(0.75) 0.76(0.75) 0.85(0.76) 0.82(0.75) 0.81(0.78) 1.79(0.88) 0.77(0.75) 0.78(0.75)
Finally, analysis of the vibrational transition energies and associated IR and Raman intensities indicates that detection of these species is possible.
Acknowledgment. Support by the Basque Country University (EuskalHerrikoUnibertsitatea),Grant No. UPV/203.215-E171/ 91, and the Provincial Government of Gipuzkoa (Gipuzkoako Foru Aldundia) is gratefully acknowledged. References and Notes (1) (2) (3) (4)
Markowski, L. N.; Romanenko, V. D. Tetrahedron, 1988,45,6019. McCluskey, M.; Andrews, L. J. Phys. Chem. 1991,95, 2988. Lohr, L. L., Jr. J . Chem. Phys. 1990, 94, 1807. Lohr, L. L., Jr. J. Chem. Phys. 1992, 96, 119. (5) Lopez, X.; Largo, A,; Barrientos, C.; Ugalde J. M. J . Phys. Chem. In press. (6) Pyykk6, P.; Zhao, Y.-F. Mol. Phys. 1990, 70, 701. (7) A complete discussion of the basis and methods used in this paper may be found in: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.;Pople, J. A. Ab initio Molecular Orbital Theory; Wiley: New York, 1986. (8) Ewig, C. S.;Van Wazer, J. R.;J. Am. Chem. SOC.1985,107,1965; 1986,108,4354; 1988,110,79. (9) GAUSSIAN 90: Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M.; Binkley, J. S.; Gonzalez, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.;Topiol, S.;Pople, J. A. Gaussian 90, Revision I, Gaussian, Inc., Pittsburg PA, 1990. (10) Lopez, X.; Largo, A., Barrientos, C.; Ugalde J. M. To be published. (11) Luna, A.; M6,O.; YaAez, M. Chem. Phys. Lett. 1992, 197, 581. (12) Bader, R. F. W. Atoms in Molecules; Oxford University Press: New York, 1990. (13) Gill, P. M. W.; Weatherall, P.; Radom L. J . Am. Chem. Soc. 1989, I l l , 2782. (14) Kabbadj, Y.; Lievin, J. Phys. Scr. 1989, 40, 259. (15) Lohr, L. L., Jr. J . Phys. Chem. 1984,88, 5569. (16) McKee, M. L. J . Phys. Chem. 1990, 94,8553. (17) Redondo, P. Ph.D. Thesis, University of Valladolid, Spain, unpublished. (18) Pople, J. A.; Schlegel, H. B.; Krisham, R.; DeFrees, D. J.; Binkley, J. S.;Frisch, J. S.;Whiteside, R. A.; Hout, R. F.; Hehre, W. J. Int. J . Quantum Chem. Symp. 1981, 15, 269. (19) DeFrees, D. J; McLean, A. D. J . Chem. Phys. 1985, 32, 33. (20) Butler, J. E.; Kawaguchi, K.; Hirota, X . J . Mol. Spectrosc. 1983, 101, 161. (21) Grein, F.; Kapur, A. J. Chem. Phys. 1983, 78, 339. (22) McKee, M. L. J . Phys,Chem. 1986, 90,2235. (23) Sosa, C.; Schlegel, H. B. Int. J . Quantum Chem. 1986, 29, 1001. Schlegel, H. B. J . Chem. Phys. 1986,84, 4530.
