4643
J . Phys. Chem. 1993,97, 46434646
Theoretical Study of the [Ge,H2,S] Potential Energy Surface: Comparison with [Ge,Hz,O] Suk Ping So Chemistry Department, The Chinese University of Hong Kong, Shatin, I?. T., Hong Kong Received: November 13, 1992
The geometries of seven structures on the singlet [Ge,H2,S] potential energy surface, triplet thiogermylene (HGeSH) and triplet germathione (H2GeS), and some other related species have been optimized using the HF/3-21G(*) and MP2/3-21G(*) methods, and their vibrational frequencies and the singlet-triplet energy differences in HGeSH, H2GeS, and H2Ge0 computed. Electron correlation errors are corrected up to the MP4SDTQ level. As in the case of [Ge,H2,O], the ground state of thiogermylene is the singlet trans-HGeSH and germathione (H2GeS) lies energetically higher than cis-HGeSH. With correction for zero-point vibrational energies, the MP4SDTQ hydrogenation energies of H2GeS and H2GeO and the activation energies for the reactions trans-HGeSH cis-HGeSH, H2GeS trans-HGeSH and H2GeS H2 GeS have been calculated to be 12.4, 19.2, 17.3, 50.5, and 63.7 kcal mol-', respectively. Through the various comparisons, it has been concluded that germanium is less reluctant to form double bonds with sulfur than with oxygen and Ge-S double bonds are thermodynamically and kinetically more stable than G e 4 double bonds.
-
-
-
+
trans-HGeOH cis-HGeOH (4G) and compared with that of [C,H2,O]. Germathione (H2GeS), on the other hand, is much less investigated. Its theoretical structure and vibrational frequencies have been reported by Trinquier et al.4 It is thus thought desirable to study the [Ge,H2,S] potential energy surface in comparison to our previous work3on [Ge,H2,O].
implemented on our MicroVAX 2000 computer and IBM RS/ 6000 workstation. The basis set used is the 3-21G(*)set (3d and 4d polarization functions on sulfur and germanium atoms, respectively) as proposed by Dobbs and Hehree6 These authors have examined the performance of their 3-21G(*)basis sets with regard to the calculation of equilibrium geometries, reaction energies, and vibrational frequencies of a variety of normal and hypervalent compounds containing third- and fourth-row maingroup elements. It has been found that bond lengths are generally well reproduced with a mean absolute deviation of about 0.020 A from experimental values, and hydrogenation energies for saturated compounds are reasonably well described with a mean absolute error (comparisons are to experimental data which have not been corrected for zero-point energies) of about 4 kcal mol-'. Calculated harmonic frequencies for one-heavy-atom hydrides are all larger than the observed values typically by 9%-12%, consistent with experience with compounds of first- and secondrow elements. Hence, the harmonic vibrational frequencies of the [Ge,Hz,X] (X = 0, S) species under study obtained by analytically differentiatingthe energies twice are uniformly scaled by the commonly used factor of 0.89. Vibrational frequencies were determined firstly to verify the nature of the stationary point structures,secondly to examine zero-point energy corrections on reaction energies and barrier heights, and thirdly to predict vibrational frequencies for the unknown stable species and their isotopomers for the sake of their future experimental identification by infrared spectroscopy and the assignment of the observed frequencies. The energies of the various species at the optimized SCF and MP2 geometries were recalculated by the second-order (MP2), third-order (MP3), and fourth-order (MP4) perturbation theory with the Merller-Plesset partitioning of the Hamiltonian in order to take into account electron correlation.' 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.8 All MPn calculations were done with frozen core.
Calculations
Results and Discussion
The equilibrium and the transition-state structures were optimized by the energy gradient method at the RHF and RMP2 levels for the singlet states and at the UHF and UMP2 levels for the doublet and triplet states, using the GAUSSIAN 90 programs5
Geometry optimization yields planar and nonplanar structures for the singlet and triplet [Ge,H2,S] isomers, respectively, as in the case of [Ge,H2,0].3 All these structures were computed to have no imaginary vibrational frequencies and thus are ther-
Introduction Silanone (H2Si0)and silanethione (H2SiS)have been studied theoretically and compared.' They are found to be kinetically stable toward their unimolecular destructions such as
and
-- ++ -
H2SiX
H
H,SiX
H,
HSiX
(1)
Six
(2)
H,SiX trans-HSiXH (3) Furthermore, H2SiSis found thermodynamicallyand kinetically more stable than H2SiO. Through these comparisons, it has been emphasized that silicon is less reluctant to form double bonds with sulfur than with oxygen. The singlet-triplet energy differencesin H2SiS and H2SiO are calculated to be considerably smaller than that in H2CO. Experimentally,Withnall and Andrew$ carried out an infrared investigationof the photochemical reaction of germane and ozone in solid argon. Using the techniques of isotopic substitution and filtered photolysis,they identified,among other species,hydroxygermylene (HGeOH) and, for the first time, germanone (H2GeO) and reported a completeassignmentof their infrared spectra. However, the experimental structures of these species are not yet known. Recently, So3 studied by means of ab initio molecular orbital calculations including polarization functions and electron correlationthe potential energy surface of [Ge,H2,0] with respect to reactions 2G, 3G (reactions 2 and 3 are hereafter known as 2G and 3G for the germanium analogues, respectively), and 4G
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0022-3654/93/2091-4643$04.00/0
0 1993 American Chemical Society
4644
so
The Journal of Physical Chemistry, Vol. 97, No. 18, 1993
TABLE I: Optimized SCF and MP2(3-21C(*))Equilibrium Geometriess ~
r(GeH)_ r(GeS) ~
r(SHI
_
LHGeS
LGeSH
rb/@
SCF MP2
1.595 1.607
2.243 2.226
cis-HGeSH (1) 1.328 94.5 1.340 91.1
102.0 101.0
0 0
SCF MP2
1.593 1.604
trans-HGeSH (2) 1.329 90.7 2.233 89.8 1.341 2.215
98.6 97.4
180 180
SCF MP2
1.544 (1.549) 1.556
SCF MP2
1.553 1.568
Triplet HGeSH (4) 2.230 1.329 117.6 2.218 1.342 117.8
SCF MP2
1.554 1.565
Triplet H2GeS (5) 2.237 106.8 2.219 106.4
110.7 110.2
SCF
1.556 (1.544) 1.567
Triplet H2GeO (6) 1.821 105.3 (1.850) (104.6) 1.832 104.9
111.3 (1 14.9)d 110.9
7 80
HzGeS (3)
MP2
2.020 (2.020) 2.033
124.6 (124.1) 124.3
110.8 (1 1 1.8)d 111.4 98.5 97.4
90.6 93.2
a Bond lengths are in A and bond angles in deg. S is replaced by 0 when triplet H2GeO is considered. T is the HGeSH dihedral angle for HGeSH. c 6 is the HGeH angle for H2GeS and H2GeO. Values from refs 4 and 9 are in parentheses.
modynamically stable, being at the minima of the potential energy surface. The optimized structures are listed in Table I in which the geometrical parameters of triplet H2Ge0and singlet H2GeS computed by Trinquier et al.4~9usingthe pseudopotentialmethodlo are included for comparison purpose. The agreement between their values and those of this work is seen to be good except for the bond lengths of triplet H2Ge0. Perhaps, it is important to point out that the S2 value obtained here for the triplet states of both H2Ge0 and H2GeS is 2.013, almost identical to the value 2 of a true triplet. Hence, the unpredictable spin contamination effect due to UHF wavefunctions on molecular geometry” may be neglected. No experimental geometries of the [Ge,H2,X] (X = 0, S) isomers are available for comparison. It is however noteworthy that the calculated Ge=O (SCFIMP2, 1.635 A11.634 A)3 and Ge=S (SCFIMP2, 2.020 A12.033 A) bond lengths of singlet H2Ge0and H2GeShave almost the same values as in the corresponding diatomics GeO (obs,I2 1.62 A; SCF/ MP2, 1.619 A11.693 A) and GeS (obs,I2 2.01 A; SCF/MP2, 2.004 A12.033 A). The triplet state of H2GeX (X = 0,S) studied is the (n T * ) 3A” state. Hence as expected, electronic excitation from the ]A, ground state to this 3A”state has been found to lengthen the GeX bond, viz. by 0.144 A for H2Ge0 and 0.186 A for H2GeS at the MP2 level. The out-of-plane angle 8 between the HGeH plane and the GeX axis is 62.1 O for triplet H2Ge0and 60.4O for triplet H2GeS. Thus, H2Ge0is more pyramidalized than H2GeS in the 3A” state. The n orbitals of H2GeX (X = 0, S) are strongly localized on the X atoms while the T* orbitals are associated with the Ge and X atoms. Accordingly, in the formation of the (n T * ) 3A” state, electrons are transferred to the germanium atom, thereby inducing sp3 hybridization on it. The greater out-ofplane angle 8 predicted for triplet HzGeO can therefore be accounted for in terms of a larger amount of electron transfer to germanium in this species, as is evidenced by the Mulliken atomic charges: +0.555/+0.362 (Ge), -O.546/4.349 (0),and -O.OOS/ +0.007 (H) for the 1A,/3A”states of H2GeO; +0.298/+0.151 (Ge),-0.321/-0.176 (S), +0.012/+0.012 for the IAI/~A”states of H2GeS. The present calculation yields a nonplanar saddle point structure 7 for the rrunr-HGeSH cis-HGeSH reaction 4G, a planar one 9 for the H2GeS H2 GeS reaction 2G, but a planar one
-
-
- -+
8b Figure 1. Transition state structures.
9
TABLE Ik Optimized SCF and MP2(3-21C(*)) Transition State Geometries. transition state geom param SCF MP2 7
r(GeH) r(GeS) r(W LHGeS LGeSH
8a/8b
r(GeH,) r(GeHt) r(G4 r(SHt) LH,GeS LH,GeS
9
r(GeH,) r(GeHt) r(GeS) r(H,Ht) LMGeSb LHIMGe
T
T
1.600 2.323 1.334 95.9 94.3 90.4 1.56411.573 1,62711,641 2.11412.147 1.87912.031 118.11104.8 58.6163.2 18011 14.7 1.554 1.790 2.044 1.339 124.6 101.1
1.618 2.306 1.366 96.7 90.5 90.1 1.59111.587 1,63411,648 2.14712.167 1,90611,865 115.31110.4 58.7156.6 1801114.5 1.561 1.804 2.052 1.432 123.4 100.8
Bond lengths are in A and bond angles in deg. M is the midpoint of the H,-H, distance.
-
8a and a nonplanar one 8b for the H2GeS trans-HGeSH reaction 3G. These saddle point structures are depicted in Figure 1 and their molecular constants listed in Table 11,while the energies of structure 1-9 are collected in Table 111. The inclusion of electron correlation at the MP2 level increases the bond lengths of the [Ge,H2,S] and [Ge,H2,0] equilibrium isomeric structures by about 0.05 A or less but decreases their bond angles by up to about 7O with respect to the corresponding SCF values (Table I and ref 3). It affects the saddle point structures in a similar way as well but, as expected, by larger amounts. However, the GeS double bonds of 1 , 2 , 4 , and 5 are shortened by correlation effects instead. The saddle point structures 7,8a, 8b, and 9 all haveone negative eigenvalue for the matrix of the second derivatives of the molecular energy with respect to the full set of molecular geometrical parameters. However, vibrational frequency calculation at the SCF geometries reveals that, unlike 7,8b, and 9, and in contrast to anticipation, 8a has two imaginary frequencies instead of one. This indicates that 7, 8b, and 9 are transition states but 8a corresponds to an energy maximum. Table I11 shows that 8a is less stable than 8b at all levels of theory considered. Besides, examination of the normal coordinates of vibrations reveals that
The Journal of Physical Chemistry, Vol. 97, No. 18, 1993 4645
[Ge,H2,S] Potential Energy Surface
TABLE III:
State Energies (au) at Optimized SCF and
MP2 Geometries
species level of theory 1
2
3
4
5
6
I
8a/8b
9
SCF MP2 MP3 MP4SDTQ SCF MP2 MP3 MP4SDTQ SCF MP2 MP3 MP4SDTQ SCF MP2 MP3 MP4SDTQ SCF MP2 MP3 MP4SDTQ SCF MP2 MP3 MP4SDTQ SCF MP2 MP3 MP4SDTQ SCF MP2 MP3 MP4SDTQ SCF MP2 MP3 MP4SDTQ
SCF xeom -2462.3495 1 -2462.55941 -2462.58545 -2462.59839 -2462.35261 -2462.56318 -2462.58901 -2462.60206 -2462.34248 -2462.56094 -2462.58082 -2462.59595 -2462.31262 -2462.50615 -2462.53030 -2462.54143 -2462.318 16 -2462.50 193 -2462.52176 -2462.53891 -2141.0161 5 -2141.24224 -2141.25589 -2141.26895 -2462.328 11 -2462.53348 -2462.56015 -2462.51265 -2462.230291.23935 -2462.416241.47854 -2462.491 101.50164 -2462.5 1 59 1 1.5 20 10 -2462.2 1012 -2462.44811 -2462.41142 2462.49054
MP2 geom -2462.55936 -2462.58543 -2462.59841 -2462.56346 -2462.58929 -2462.60231 -2462.56112 -2462.58101 -2468.59641 -2462.50638 -2462.53051 -2462.541 I1 -2462.502 10 -2462.52194 -2462.53921 -2 141.24236 -2141.25608 -2141.26928 -2462.53361 -2462.56094 -2462.51301 -2462.41101 1.41823 -2462.492081.49891 -2462.5 1 1611.5 1 825 -2462.44866 -2462.41 166 -2462.49 104
one of the imaginary vibrational frequencies of 8a is for the outof-plane vibration of the two hydrogen atoms. Accordingly, the nonplanar structure 8b is the transition state for the 1,Zhydrogen shift reaction 3G as in the cases of H2PP,I4H2Si0,I and H2SiS.I On the contrary, the transition states for the same reaction of H2Ge0,3H2CO,I3and H2CSI4 are all planar. The theoretical vibrational frequencies after being uniformly scaled by a factor of 0.89 and the zero-point vibrational energies of structures 1-9 and other species related to this work are given in Tables IV, V, and VI. It is unfortunate that there are no experimental data for comparison. The vibrational frequencies of H2Ge3*Shave also been predicted by Trinquier et al.4 Their values are scaled by 0.89 (somewhat arbitrarily as far as pseudopotential with DZ d frequencies are concerned) and reproduced in Table V. It is noted that, as in the case3of H2Ge0, their values agree quite well with the present ones except for the GeH2 out-of-plane wagging frequency vl(bl). The large discrepancy of 244 cm-I for v2 (reported/present = 802/558 cm-I; 873/574 cm-1 for H2Gel60) is quite unexpected and cannot be accounted for here because bond lengthsand bond angles obtained by Trinquier et al.4differ from the present values only by O.OO& 0.005 A and OS', respectively (Table I). Data in Tables IV and V show that the GeS stretching frequencies of HGeSH and H2GeS are much smaller than the values obtained from the GeO stretching frequencies of HGeOH and H2Ge0 by considering only the mass difference between the S and 0 atoms. This indicates that GeS bonds (T + a) are weaker than GeO bonds. In addition, H2Ge0 has a larger out-of-plane GeH2 wagging frequency. Thus germanium in H2GeO has a greater reluctance to leave planarity. It is seen from Table I11 that both HGeSH and HzGeS, like their oxygen analogues, have a planar singlet ground state. On the contrary, trans-HGeSH is found to be consistentlymore stable than cis-HGeSH at all levels of theory examined while trans-
+
HGeOH fallsenergetically below cis-HGeOH only when electron correlation is taken into consideration. When evaluated at the MP3 and MP4SDTQ levels for the SCF or MP2 geometries, the energies of the various [Ge,H2,S]specieshave the following order of relative magnitude: 2 < 1 < 3 < 7 < 4 < 5 < 8b < 8a < 9. In addition, correlation-induced changes in geometry yield only minor lowering (up to 0.00050 au) in the total energies of the species except 8a and 8b. Nevertheless, correlation effects on energies are larger for the [Ge,H2,0] ~pecies.~ At the vibrationally corrected MP4SDTQ/3-21 G(*)//MP2/ 3-21G(*)level of theory, H2GeS lies 0.88 kcal mol-' above cisHGeSH which is in turn less stable than the ground state transHGeSH by 2.32 kcal mol-I. The singlet-triplet (triplet being higher) energy separation is 35.4 kcal mol-I for H2GeS and 37.6 kcal mol-I for trans-HGeSH. The corresponding energy separations between the [Ge,H2,0] isomers' are much larger except that between cis-HGeOH and trans-HGeOH, namely 9.3,0.52, 47.4, and 43.0 kcal mol-I. This suggests that germanium does not prefer to form doubly bonded structures whenever an alternative exists and is less reluctant to form double bonds with sulfur than with oxygen. A similar conclusion has also been reached' for H2SiX (X = 0, S) whose corresponding singlettriplet energy separations (at the MP3/6-31GS*//HF/6-31G* level) are respectively 53.3 and 40.4 kcal mol-' and are much smaller than that (70.6 kcal mol-') for H2C0. The least-motion removal of H2 from HzGeS, while retaining C2"symmetry,is forbidden from orbital symmetry considerations. The true transition structure 9 in fact has been found to distort to C, symmetry. This hydrogen elimination reaction 2G is predicted here to be exothermic with a reaction energy (the MP4SDTQ energy at MP2 geometry is -1.14707 au for H2and -2461.47476 au for GeS) of -16.0 kcal mol-1 and a barrier (or activation energy) of 66.1 kcal mol-' (or -18.5 and 63.7 kcal mol-I after zero-point energy correction, respectively). This energy has not been measured experimentally. The rearrangement reaction 3G of H2GeS to trans-HGeSH via the transition state 8b (see above) has, on the other hand, a barrier or 52.8 kcal mol-l (or 50.5 kcal mol-' after corrected for zero-point energy). Hence, the destruction of H2GeS by the 1,l-elimination route to H2 and GeS is much less favored energetically than that by rearrangement to trans-HGeSH. For the corresponding [Ge,H2,0] species, the hydrogen-elimination reaction 2G was predicted3 to have a vibrationally corrected MP4SDTQ reaction energy of -34.5 kcal mol-', and an activation energy of 66.6 kcal mol-', and the activation energy for the rearrangement reaction 3Gis, however, muchlower,namely 34.2 kcal mol-I. Accordingly, H2GeS is kinetically more stable than H2GeO toward destruction through the rearrangement reaction 3G. In addition, a lower activation energy for the hydrogen elimination reaction 2G and smaller GeH2 stretching frequencies predicted for H2GeS both reflect that the GeH bonds of H2GeS are weaker than those in H2Ge0. The vibrationally corrected MP4SDTQ barrier for the transto-cis conversion reaction 4G through internal rotation has been computed to be 17.3 kcal mol-I. This barrier probably arises from the fact that the closing-up of the internal rotational angle from 180' (for trans-HGeS) to 95.1' (for transition state 7) decreases the sulfur-lone-pair germanium-p, A 0 stabilizing conjugation. This idea can bevisualized from the Mullikenatomic charge distributionsand overlap populations (at MP2 geometries) as listed in Table VII. The correspondinginternal rotation barrier for HGeOH3 is 11.4 kcal mol-I. It is seen from Table I that the trans-to-cis isomerization reaction 4G proceedsviainternal rotation but not inversion. During the isomerization process, the GeS bond (MP2) of HGeSH increases by about 0.085 A at the transition state but the GeO bond of HGeOH shortens slightly by about 0.021 A instead.3 Similar findings have been reported for HSiXH (X = 0, S).'
-
4646 The Journal of Physical Chemistry, Vol. 97, No. 18, 1993
so
TABLE I V Vibrational Frequencies (cm-1) of Isotopic Singlet Thiogermylenes' H, 32S
H, 34S
D, 32S
D, 34S
vibration*
mode
cis
trans
cis
trans
cis
trans
cis
trans
V I(a")
torsion def GeS str def GeH str S H str
46 1 632 365 760 1804 2573
528 591 370 834 1820 2564
46 1 632 358 759 1804 2571
528 591 362 833 1820 2561
331 449 363 555 1285 1848
379 424 364 608 1296 1841
33 1 448 356 553 1285 1845
378 423 358 606 1296 1838
~(a') vda') v4(a') vda') v6(a')
*
a Frequencies have been uniformly scaled by a factor of 0.89. Species with mixed hydrogen isotopes are not considered. Vibrations are numbered in such a way that they represent the same vibrational modes for both HGeOH and HGeSH.
TABLE V: Vibrational Frequencies (cm-I) of Isotopic Singlet Germathiones'
TABLE VII: Mulliken Charge Distributions and Overlap Po~ulationsof HGeSH
mode
H,32S
H,34S
D,32S
D, 34S
GeH2 rock GeH2 wag GeH2 scis GeS str GeH2 s-str GeH2 a-str
520(525)< 558 (802) 869 (874) 533 (522) 1977 (1968) 1985 (2006)
520 558 869 522 1977 1985
382 407 620 530 1410 1410
38 1 407 620 519 1410 1410
See footnote a of Table IV. Vibrations are numbered in such a way that they represent the same vibrational modes for both H2GeO and H2GeS. Calculated frequencies fronm ref 4 scaled by 0.89 are in parentheses.
TABLE VI: Vibrational Frequencies (cm-*) and Zero-Point Enereies (kcal mo1-I)' Calculated at SCF Geometries ~~~
~~
species 1 2 3 4 5 6 7
8b 9
GeS H2 HjGeOH H3GeSH
frequencies
zero-point energies
365,461,632,760, 1804,2573 370,528,591,834, 1820,2563 520,533,558,869, 1977,1985 301,372,559,730, 1878,2553 373,462,612,796, 1911,1939 494,643,672,792, 1899, 1932 5321,329,564,686, 1791,2521 14471 424,528,674,1628,1857 17341,415,501,523, 1345,1949 556 4144 164,603,627,698,807,838,848, 872,1957,1970,2006,3480 155,378,492,549,771,815,845, 861,1980, 1986, 1999,2560
9.43 9.59 9.21 9.14 8.71 9.19 8.42 7.31 6.77 0.79 5.92 21.3 19.1
Frequencies have been uniformly scaled by a factor of 0.89 and imaginary frequencies neglected in calculating zero-point energies.
This suggests that the germanium-sulfur *-bonding is stronger than the germanium4xygen *-bonding and/or HGeSH has more double bond character than HGeOH. This conclusion is also in line with the above result that HGeSH has a larger barrier to internal rotation than HGeOH. Toassess the relativestabilitiesof theGe=S and G e 4 d o u b l e bonds of H2GeS and H2Ge0, the energies released upon the addition of hydrogen (i.e. hydrogenation energies) to these molecules to form H3GeSH and H3GeOH have been calculated. At the MP4SDTQ/3-2lG(*)//MP2/3-21 G(*)level, the hydrogenation energies of H2GeS and H2Ge0 are 24.8 and 33.2 kcal mol-' (the state energies of staggered H3GeSH and H3GeOH are -2463.78293 and -2142.54580au) or 12.4 and 19.2 kcal mol-' after being corrected for zero-point energy, respectively. The
trans-HGeSH Ge H(W
S H Ge-H Ge-S S-H
cis-HGeSH
ts-HGeSH (7)
Charge Distribution +0.229 +0.246 -0.054 -0.043 -0.313 -0.333 +0.127 +0.141
+0.326 -0.056 -0,387 +0.117
Overlap Population 0.683 0.691 0.51 1 0.469 0.571 0.581
0.648 0.344 0.553
hydrogenation energy of H2GeS being smaller indicates that the Ge=S bond is thermodynamically more stable than the G e 4 bond in agreement with the above conclusion that germanium is more reluctant to form double bonds with oxygen than with sulfur. Acknowledgment. I thank Mr. David Choi of the Chinese University Computer Services Centre for his assistance in implementing the GAUSSIAN 90 package on our IBM RS/ 6000 workstation. References and Notes (1) (a) Kudo, T.; Nagase, S. J . Phys. Chem. 1984,88,2833. (b) Kudo, T.; Nagase, S.Organometallics 1986, 5, 1207. (2) Withnall, R.; Andrews, L. J . Phys. Chem. 1990, 94, 2351. (3) So, S.P. J. Phys. Chem. 1991, 95, 10658. (4) Trinquier, G.; Pelissier, M.; Saint-Roch, B.; Lavayssiere, H. J . Organomef. Chem. 1981, 214, 169. ( 5 ) 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, Reuision F; Gaussian, Inc.: Pittsburgh, PA, 1990. (6) Dobbs, K. D.; Hehre, W. J. J . Comput. Chem. 1986, 7, 359. (7) Merller, C.; Plesset, P. S.Phys. Rev. 1934, 46, 618. (8) Krishnan, R.; Pople, J. A. Int. J . Quantum Chem. 1978, 14, 91. (9) Trinquier, G.; Barthelat, J. C.; Satge, J. J . Am. Chem. SOC.1982, 104, 5931. (10) Druand, Ph.; Barthelat, J. C. Theor. Chim. Acta 1975, 38, 283. (1 1) McDouall, J. J. W.; Schlegel, H. B. J . Chem. Phys. 1989, 90,2363, and references cited therein. (12) Huber, K. P.; Herzberg, G. Constants of Diatomic Molecules; Van Nostrand, Reinhold Co.: New York, 1979. (13) Harding, L. B.; Schlegel, H. B.; Krishnan, R.; Pople, J. A. J . Phys. Chem. 1980,84, 3394. (14) Nguyen, M. T.; Ha, T. K. Chem. Phys. Lett. 1989, 158, 135.
