J . Phys. Chem. 1994,98, 7819-7822
7819
Ab Initio Calculations of the Hydrogen Peroxide-Hydrogen Halide Complexes (HOOH-*XH, X =
F, CI) J. A. Dobado and Jose Molina Molina' Grupo de Modelizacibn y Disefio Molecular, Departamento de Quimica Orgbnica, Facultad de Ciencias, Universidad de Granada, Granada 18071, Spain Received: February 24, 1994; In Final Form: May 27, 1994"
A b initio molecular orbital calculations have been performed in the study of the hydrogen-bonded complexes between hydrogen peroxide and hydrogen halide (XH, X = F, Cl). Five stationary points are characterized (structures 1-5); using different basis sets (6-31G** and 6-31 lG(3d,2p)), with and without adding diffuse functions, and employing different levels of theory (HF, MP2, MP4(SDTQ)). The nature of the studied structures has been analyzed; structures 1,3, and 5 are true minima, and structures 2, and 4 are transition states. The binding energies of these complexes have been determined and corrected for the basis set superposition error (BSSE).
Introduction
In previous papers, we have reported ab initio theoretical calculations of the hydrogen peroxide (HP) interactions with hydrogen-bonded agents, which yielded hydrogen bonds of different strength. We have described the study of hydrogen peroxide dimer' (HPD) and the hydrogen peroxidewater complex2 (HPW), includinga basis set superpositionerror (BSSE) estimation at different levels of theory. Hence, in the study of the water dimer, the nature of the so-called bifurcated structure has been considered for years.3-8 However, Marsden et ala9 concluded that the bifurcated structure is a saddle point on the self-consistentfield (SCF) potential energy surface (PES). The BSSEIO is one of the major factors limiting the accuracy of ab initiointermolecularcomplexescalculations.~1-13 The most widely used scheme to correct for the BSSE is the full function counterpoise method (FCP) proposed by Boys and Bernardi.14 Neither experimental nor theoretical results of hydrogen peroxidehydrogen halide (HPX) complexes have been reported to date. But, some efforts have been devoted to the very similar systems of water-hydrogen halide complexes. Both theoretical and experimental studies show the minima on the PES as a nonlinear structure with pyramidal oxygen, showing always the water oxygen as electron donor in the hydrogen bond.1sJ6 In this paper we present theoretical calculations of hydrogen peroxidehydrogen halide complexes (HOOH-XH) (X = F, Cl), at the Hartree-Fock (HF) and M~rller-Plesset(MP) levels of theory. So, for the analyzed complexes the BSSE will be estimated, as well as the nature of different stationary points. Computational Methods Ab initio SCF calculations have been carried out with the GAUSSIAN92l' and SPARTAN1*series of programs on SGI 4D/320GTXb, Convex C240, and Convex C3820 computers. The 6-31G** l9 and 6-311G(3d,2~)~O basis sets were used, augmented by diffuse functions. The notation used throughout this work was described previous1y.lJ Full geometry optimization was performed in all the calculations. Electron correlation correction was taken into account at the MP2 and MP4(SDTQ) levels, including all the electrons in the calculations. Symmetry restrictions (Cz) were imposed for structures 2 and 4. Geometry optimizationhave been done with the Berny gradient optimization algorithm.21 Analytically calculated second derivatives of the energy with respect to the Cartesian coordinates22 at the H F
* To whom correspondence should be addressed. *Abstract published in Advance ACS Absrrucfs,July 15, 1994. 0022-3654/94/2098-7819$04.50/0
level, and numerically calculated second derivativesof the energy using analytically calculated first derivatives at the MP2 level, were compared to test the nature of the stationary points. The BSSE was estimated using the counterpoise method of Boys and Bemardi,14employing the MASSAGE keyword into the GAUSSIAN92 program.
Results Ab initio calculations, at the H F and MP2 levels with different sets, predict three stationary points on the PES for the HOOH-FH, structures 1-3, and two for the HOOH-ClH complex, structures 4 and 5 (see Figure 1). The energies for the HOOH, FH, and ClH monomers are depicted in Table 1 for comparison. Tables 2 and 3 show the energies of the studied systems at the H F and MP2 levels respectively for structures 1-5. Numerical values of the optimized geometrical parameters for structures 1-5, at different levels of theory, are available as supplementary material (see paragraph at the end of this paper). Structures 1 and 3 for the HOOH-.FH, and structure 5 for the HOOH.-ClH complexes were obtained as true minima, and structure2for HOOH-mFH and structure4 for the HOOH--ClH complexes, as saddle points. Structures 2 and 4 are threemembered two-hydrogen-bondedcyclicones with the Cz symmetry and with oxygens of the H P acting as electron donor. Both structures have only one imaginary frequency (transition state). Structures 3 and 5 are linear, without symmetry (Cl), where the H P is the electron donor. However, structure 1 is found to be a five-memberedcyclic hydrogen-bondedone of Cl symmetry, containingboth the 0Hs-F and the FH-0 interactions (see later). The minimum energy structure on the HOOH-C1H PES is structure 5, both at the H F and MP2 levels (see Tables 2 and 3). Nevertheless, structures 1 and 3 have similar energies at the different levels. In Tables 2 and 3 the BSSE, zero point vibrational energy (ZPVE), and the binding energy A E b C P (counterpoise corrected) are also collected. Vibrational frequencies were calculated for structures 1-5at the HF/6-31G**//HF/6-31G** level, and the results are available as supplementary material.
Discussion
(a) Molecular Structures. The fully optimized geometrical parameters for structures 1-5 are summarized in Figure 1. In all the structures, the bond lengths and angles of the H P are only slightly perturbed from their values at the monomer geometry. Thereis an 0-Hinvolved in the hydrogen bonding only in structure 1, and this bond increases in length around 0.005 A, compared 0 1994 American Chemical Society
Dobado and Molina
7820 The Journal of Physical Chemistry, Vol. 98, No. 32, 1994
3
L
163.4. (160.4
4
5
Figure 1. Geometry of structures 1-5 obtained for the hydrogen peroxidehydrogen halide complexes (HOOH-XH) at the HF/6-31 l+G(3d,Zp)/ /HF/6-31+G(3d,2p) level(va1uesinparenthesesat theMP2/6-31 lG(3d,2p)//MP2/6-31 lG(3d,2p) level). Forstructures 1-3X = F,andforstructures 4 and 5 X = CI.
TABLE 1: Total Energy (au) for the Hydrogen Fluorine, Hydrogen Chloride, and Hydrogen Peroxide Optimized Monomers method 6-31G** 6-31+G** 6-31 1G(3d92p) 6-31 1+G(3d,2p) 6-31G** 6-31+G** 6-311G(3d,2p) 6-3 1 1+G(3d,2p) 6-31G** 6-31+G** 6-31 1G(3d,2p) 6-31 1+G(3d,2p)
EHF FH -100.01 1 690 8 -100.024 306 8 -100.050 680 7 -100.056 266 8 CIH -460.066 214 3 -460.067 363 9 -460.098 057 8 -460.098 691 0 HOOH -150.776 965 4 -150.783 917 0 -150.828 338 1 -150.833 210 5
EMPZ -100.196 -100.218 -100.320 -100.330
700 4 108 5 488 3 235 4"
-460.215 621 3 -460.218 360 9 460.362 516 6 460.363 750 1" -151.157 -151.173 -151.323 -151.330
089 3 167 7 161 8 206 6'
Calculated at the MP2/6-31 l+G(3d,2p)//HF/6-31 l+G(3d,2p) level of theory.
with the corresponding HP monomer value at both the H F and MP2 levels. On the other hand, the X H bonds involved in hydrogen bonding undergo the expected length increase. In the same way, the FH and ClH bond lengths involved in hydrogen bonding increase compared to the HF and ClH itself. The increasing is larger than in the OH one, and the values are around 0.01 and 0.008 A for the FH and ClH, respectively, both a t the HF and MP2 levels. The geometrical parameters obtained depend on both sets and levels used. In general, bond lengths decrease with larger sets, but increase when both diffuse functions are electron correlation are taken into account. The largest differences occur when electron correlation is included, yielding larger AH (A = 0, F, C1) bond lengths around 0.025 A, when passing from the HF to the MP2 calculations. The bond angles are less sensitive to the change in the basis sets but decrease around 5' when electron correlation is included. Structure 1 contains a cyclic five-membered ring, and it is evident from the dihedral angles that although the ring containing the hydrogen bonds is puckered, the deviations from planarity
are not great. Structure 1 resembles a ring disposition with two hydrogen bonds acting in both the FH and HP as electron donor and acceptor; however, we are going to discuss the existence of both hydrogen bonds. The hydrogen bond formed by H2 and Os seems to be a strong one, with the Hz-05 distance and the LFI-H2.-05 angle being compatible with a normal hydrogen bond. Moreover, the values for the Hy-05 bond are around 1.9 8, at the HF and less than 1.8 A a t the MP2 level, with the L F , - H ~ O ~angle being larger than 140°, for both HF and MP2 levels with different sets. The geometrical parameters for the H3 and F1 hydrogen bond correspond to a weaker one, with the F1***H3 distance going from 2.0 to 2.5 8,and the LFI-HyOs angle going from 120' to 130°, depending on the level and set; in fact no bond critical point of the charge density was found between FI and H3 atoms, showing that structure 1 is linear. Structures 3 and 5 are also linear ones, where the geometrical parameter values are compatiblewith the formation of a hydrogen bond; hence, the Hz-04 distance is between 1.7 and 1.9 A and the LF1-Hy-04 angle is between 169 and 175' for structure 3; and the H y O s distance is between 1.8 and 2.1 A and the LCll-Hz.-04 angle is between 174 and 178' for structure 5. Hydrogen bonds in structures 3 and 5 are thus stronger than in the HPW complex.* Structure 3 could evolve to structure 1 by the HO-OH bond rotation and subsequent reorganizations by the interactions between the F1 and Hb atoms. Structures 2 and 4 are transition states, resembling in some way the bifurcated structure postulated for the water dimer, both having the Cz symmetry. In both structures the geometrical parameters of the hydrogen bonds are compatible with weak ones (hydrogen-bond distances around 2.1 and 2.2 A, for structures 2 and 4, respectively); however, the existence of two equivalent hydrogen bonds in each structure leads to a neat stabilization of both transition states (1.4 and 0.3 kcal/mol larger in energy than the most stable complex for HOOH-.FH and HOOH-ClH, respectively, a t the MP2/6-31 l+G(3d,2p)//HF/6-311+G(3d,2p) level). (b) BSSE and Binding Energy. The estimation of the BSSE for the HP-XH (X = F, Cl) complexes presented in this paper (structures 1-5) has been performed by the FCPI4 method, at both the HF and MP2 levels. The results are presented in Tables
The Journal of Physical Chemistry, Vol. 98, No. 32, 1994 7821
Hydrogen Peroxide-Hydrogen Halide Complexes
TABLE 2 Total Energy Efoslpkx, Monomer Energies at the Com lex Geometry (EHwH..., Em-), Monomer Energies at the Complex Geometry with Ghost Functions Added (EHOOH-G, Em.&!, Basis Set Superposition Error W E , ZPVE, and Binding Energy A&ep (Counterpoise Corrected) for Structures 1-5, with Different Basis Sets at the HF Level Efomplcx (au) E H O O H(au) ~ EXH-G(au) EHOOH(au) EXH-(au) ZPVE (kcal/mol) BSSE (kcal/mol) hEb* (kcal/mol) HF/6-3lG**//HF/6-31GSS 1 -250.801 291 8 -150.777 871 5 -100.014 870 7 -150.776 935 2 -100.011 602 2
2 -250.797 538 8 3 -250.799 314 4 4 -610.849 409 7 5 -610.850 158 0
-150.777 -150.777 -150.777 -150.777
638 7 803 3 633 5 651 4
1 -250.817 659 9 2 -250.816 592 7 3 -250.818 639 6 4 -610.856 974 3 5 -610.857 662 0
-150.784 -150.784 -150.784 -150.784 -150.784
525 1 386 6 547 7 150 2 225 8
1 2 3 4 5
168 3 375 1 216 2 815 4 569 0
-150.829 -150.829 -150.829 -150.829 -150.829
448 8 290 1 433 9 280 1 420 4
1 -250.898 379 5 2 -250.897 033 6 3 -250.898 925 5 4 -610.936 598 0 5 -610.937 101 8
-150.833 -150.833 -150.833 -150.833 -150.833
649 2 735 5 566 5 486 1 465 7
-250.890 -250.887 -250.889 -610.931 -610.932
27.4 -150.776 941 8 -100.01 1 677 2 26.2 -150.776 938 5 -100.011 632 2 26.9 24.1 -150.776 949 5 -460.066 206 4 24.5 -150.776 950 5 -460.066 179 7 HF/6-3 l+G**//HF/6-3 1+G** -100.024 600 2 -150.783 877 3 -100.024 217 1 -100.024 592 5 -150.783 891 3 -100.024 286 3 -100.024 503 4 -150.783 888 1 -100.024 218 6 -460.067 875 5 -150.783 896 6 -460.067 356 2 -460.067 955 4 -150.783 897 8 -460.067 335 1 HF/6-3 1lG(3d,Zp)//HF/6-311G(3d,2~) -100.052 530 4 -150.828 313 8 -100.050 584 1 -100.051 197 1 -150.828 291 5 -100.050 668 5 -100.051 107 7 -150.828 312 5 -100.050 620 5 -460.098 219 8 -150.828 322 9 -460.098 048 1 -460.098 209 4 -150.828 326 7 -460.098 025 4 HF/6-311+G(3d,2p)//HF/6-31 1+G(3d,2p) -100.056 544 7 -150.833 178 3 -100.056 164 8 -100.056 592 5 -150.833 168 5 -100.056 249 6 -100.056 575 3 -150.833 182 5 -100.056 186 3 -460.099 081 7 -150.833 198 8 -460.098 683 4 -460.099 091 8 -150.833 202 0 -460.098 668 1
-100.012 055 0 -100.012 008 8 -460.066 541 6 -460.066 606 8
2.6 0.7 0.8 0.6 0.7
-5.3 -4.9 -5.9 -3.3 -3.7
0.6 0.5 0.6 0.5 0.6
-5.3 -4.7 -5.9 -3.1 -3.4
1.9 0.9 1.o 0.7 0.8
-5.1 -4.3 -5.4 -2.7 -3.1
0.5 0.6 0.5 0.4 0.4
-5.0 -4.2 -5.4 -2.5 -2.8
TABLE 3: Total Energy Efomptex, Monomer Energies at the Complex Geometry (EHwH-., Em-), Monomer Energies at the Complex Geometry with Ghost Functions Added (&WH-C, ExH-G),Basis Set Superposition Error BSSE, and Binding Energy A&eP (Counterpoise Corrected) for Structures 1-5, with Different Basis Sets at the MP2 Level BSSE (kcal/mol) hEb* (kcal/mol) EXH-G (au) EHOOH(au) EXH-( a 4
1 2
3 4
5
-251.371 898 1 -251.365 418 7 -251.367 085 8 -611.381 668 0 -611.382 594 7
-151.159 -151.158 -151.159 -151.158 -151.159
720 9 998 6 454 7 943 1 179 6
-251.403 671 7 -25 1.402 003 8 -251.404 220 2 -611.400 180 7 -61 1.400 739 4
-151.174 928 5 -151.174 535 6 -151.1749800 -151.174 206 6 -151.174445 0
-251.661 068 7 -251.655 639 8 -251.657 646 6 -61 1.695 676 8 -611.6968092
-151.326 -151.325 -151.326 -151.325 -151.326
189 5 726 1 240 5 865 4 165 3
-25 1.672 668 5 -251.670 291 4 -251.672 735 9 -611.701 181 8 -611.701 869 3
-151.331 -151.331 -151.331 -151.330 -151.330
472 0 407 3 377 0 851 1 831 1
MP2/6-31G**//MP2/6-31G** -100.196 422 2 -100.202 444 3 -151.157 025 5 -100.196 679 0 -100.197 654 7 -151.157 025 4 -100.197 533 1 -151.157 064 9 -100.196 597 6 -460.216 311 3 -151.157 063 4 -460.215 600 5 -151.157 071 4 -460.215 527 2 -460.216 314 3 MP2/6-3 1+G**//MP2/6-31 +G** -100.217 856 7 -100.219 002 6 -151.173 107 4 -100.218 072 6 -100.218 972 6 -151.173 132 1 -100.217 926 8 -100.218 840 8 -151.173 142 6 -460.220 213 3 -151.173 140 6 -460.218 343 6 -460.218 293 7 -460.220 1467 -151.173 151 1 MP2/6-3 1lG(3d,2p)//MP2/6-3 11G(3d,2p) -100.320 144 2 -100.324 126 2 -151.323 105 7 -100.320 458 0 -100.321 582 4 -151.322 965 7 -100.321 489 4 -151.323 096 6 -100.320 350 3 -460.363 282 4 -151.323 037 7 -460.362 537 9 -151.323 088 0 -460.362 397 0 -460.363 206 6 MP2/6-3 1 l+G(3d,Zp)//HF/6-3 1 l+G(3d,2p) -151.330 273 8 -100.330 562 9 -100.331 426 8 -100.331 1640 -151.330 347 6 -100.330 393 3 -100.331 460 1 -151.330 168 6 -100.330 535 9 -460.363 767 0 -460.364 576 3 -151.330 291 8 -460.363 770 3 -460.364 611 8 -151.330 204 8
2 and 3 together with the obtained energy for the different studied systems. From this table we remark that the BSSE becomes very small withlarge sets, when diffuse functions are added a t the HF level. For example, the BSSE goes from 1 kcal/mol at 6-3 11G(3d,2p) to around 0.5 kcal/mol when diffuse functions are added to the heavy atoms. The above is also true at the MP2 level, the BSSE decreases in a large amount when diffuse functions are added, but in this case the values remain large enough even with the largest sets. In general, the MP2 BSSE values are at least double the HF ones. In the present paper we have characterized different stationary points on the PES for the HPe-XH complexes. When X = F, there are two minima (structures 1 and 3), and when the X = C1, there is only one minimum (structure 5). At this point, we are going to study the binding energy for these minima, but before doing so, it is interesting to discuss the nature
5.5 1.8 2.1 1.6 1.8
-5.9 -5.4 -6.3 -4.0 -4.4
1.9 1.4 1.7 1.8 2.0
-5.9 -5.3 -6.4 -3.6 -3.8
4.4 2.4 2.7 2.2 2.4
-6.5 -5.1 -6.1 -4.0 -4.5
1.3 1.1 1.3 0.8 0.9
-6.4 -5.0 -6.4 -3.7 -4.0
of structures 1 and 3; both are minima (no imaginary frequency present) with similar energy. At the HF level, structure 3 is the most stable one with different sets (AE between them approximately 0.5 kcal/mol), but at the MP2 level with larger sets both structures present the same energy after the BSSEcorrection, although they remain with different geometries. So we are going to discuss the binding energy for structure 1 (which is the most stable one at the MP4 single point calculation; see Table 4) in the HP-FH complex and for structure 5 in the HP-C1H one. The largest basis set chosen is 6-3 1l+G(3d,2p), which should give a binding energy not far from the HF limit for these systems, as pointed out elsewhere.192 Our best binding energies for the HP-XH complexes arecalculated at the HF/6-31 l+G(3d,2p)/ /HF/6-311+G(3d,2p) level, givingvalues of -5.4 and -2.8 kcal/
7822 The Journal of Physical Chemistry, Vol. 98, No. 32, 1994 TABLE 4 Totat Energy Erm**r, B and e4,and Correlation Energy A&#
Dobado and Molina
Energy AJ&w (Countecpolse Corrected), Contributions to Correlation Energy e2, e3,
( oliaterpbise Corrected) for Structures 1-5
MP4(SDTQ)/6-3 1 l+G(3d,2p)//HF/6-3 1 1+G(3d,2p) structurcs 1 2 3 4
5
Eonnplax -251.708 236 9 -251.705 829 0 -251.708 237 5 -611.747 881 4 -611.748 498 9
BSSE (kcal/mol) 1.4 1.2 1.4 0.9 1 .o
hEbq
(kcal/mol) -6.4 -5.0 -6.3 -3.5 -3.8
mol when X = F and C1, respectively (counterpoisecorrected and exclusive of vibrational zero point considerations). The correlation energy has been calculated at the MP level performing single point MP4(SDTQ) energy calculations at the HF/6-311+G(3d,2p) geometry; the results are summarized in Table 4, for structures 1-5. As can be seen, the MP3 and MP4 contributions to the correlation energy (e2 and e4) tend to cancel each other, when the basis set is of enough quality. From Table 4, the MP correlation energy estimations of 1.32 and 1.OO kcal/ mol are extracted from structures 1 and 5, respectively. From all of the above discussion,we proposed as our best binding energy estimations -6.4 kcal/mol for the HP-mFH complex and -3.8 kcal/mol for the HP-ClH complex (both values exclusive of ZPVE considerations and CP corrected). The binding energy values obtained should be an underestimation of the real ones, taking into account that the correlation energy recovered for the MP method could be 60-7076 of the total correlation energy.
Concluding Remarks On the basis of our calculated results we draw the following conclusions: The stationary points on the potential energy surface for the HPW complexesare described at different levels of theory, yielding two minima and a transition state for the HOOH-FH complex and one minimum and a transition state for the HOOH.-ClH complex. Thus, the two transition states are cyclic structures, and the three minima are linear ones. In all the structures the HP acts as an electron donor. Moreover, our best estimation of the binding energy for HPX is -6.4 kcal/mol for the HOOH-FH complex and -3.8 kcal/mol for the HOOH-C1H complex (both values exclusive of ZPVE considerations and CP corrected). However, correction for the BSSE in necessary, at least when the diffuse functions are not added, and the MP2 calculations are performed.
Acknowledgment. We thank J. L6pez-Pelhez Casellas and Maria Rodrfguez Espinosa for correction of the original English manuscript. We are grateful to the Laboratorio de Modelizaci6n y DiseRo Molecular of the Universidad de Granada supported by FEDER funds, to the CICA Centro Informhtico Cientffico de Andalucla, and to the Centrode Supercomputacibndel Pais Vasco for the computer time.
e2 (kcal/mol)
e3 (kcal/mol)
4 (kcal/mol)
-1.32 -0.86 -0.93 -1.16 -1.21
0.14 0.1 1 0.12 0.32 0.34
-0.14 -0.1 1 -0.07 -0.15 -0.13
hEq ,
(kcal/mol) -1.32 -0.86 -0.88 -0.99 -1.00
Supplementary Material Available: Tables listing the geometrical parameters for structures 1-5 at different levels of theory (Table 5 ) and showing vibrational frequencies calculated at the HF/6-31G**//HF/6-31GS* level for all structures (Table 6) (2 pages). Ordering information is given on any current masthead page. References and Notes (1) Dobado, J. A.; Moliia, J. J. Phys. Chem. 1993,97,7499-7504. (2) Dobado, J. A.; Molina, J. J . Phys. Chem. 1994, 98, 1819-1825. (3) Frisch, M. J.; Pople, J. A.; Del Bene, J. E. J. Phys. Chem. 1985,89, 3664-3669. (4) Amos, R. D. Chem. Phys. 1986, 104, 145-151. (5) Vos, R. J.; Hendricb, R.; Van Duijneveldt, F. B. J . Comput. Chem. 1990, 11, 1-18. (6) Smith, B. J.; Swanton, D. J.; Pople, J. A.; Schaefer, H. F., 111. J . Chem. Phys. 1990,92, 1240-1247. (7) Muguet, F. F.; Robinson, G. W.; Bassez-Muguet, M. P. Inf. J . Quantum Chem. 1991,39,449-454. (8) Dunning.T. H.;Hay, P. J. InMethodso~ElecfronicSfrucfure Theory; Schaefer, H. F., III., Ed.;Plenum: New York, 1977. (9) Maden,C. L.;Smith,B.J.;Pople, J.A.;Schaefer,H. F., III;Radom, L. J . Chem. Phys. 1991,95, 1825-1828. (10) Kestner, N. R. J . Chem. Phys. 1968,48, 252-257. (11) Hobza, P.; Zahradnk, R. Chem. Rev. 1988,88,871-897. (12) Yang, S.; Kestner, N. R. J . Phys. Chem. 1991, 95, 9214-9220. (13) Yang, S.; Kwtner, N. R. J . Phys. Chem. 1991, 95,9221-9230. (14) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553-566. (15) Szczesniak, M. M.; Scheiner, S.; Bouteiller, Y. J. Chem.Phys. 1984, 81, 5024-5030, and references cited therein. (16) Hannachi,Y.; Silvi, B.; Bouteiller, Y. J . Chem.Phys. 1991,94,29152922, and references cited therein. (17) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley,
J.S.;Gonzalcz,C.;Martin,R.L.;Fox,D.J.;Defrees,D.J.;Baker,J.;Stewart,
J. J. P.; Pople, J. A. Gaussian 92 Revision E Gaussian, Inc.: Pittsburgh, PA, 1992. (18) SPARTAN Version 2.0; Wavefunction, Inc.: Irvine, CA. (19) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J . Chem. Phys. 1972, 56, 2257-2261. (20) Krishnan, R.; Binkley, J. S.;Seeger, R. and Pople, J. A. J. Chem. Phys. 1980, 72,650-654. (21) Schlegel, H. B. J . Compuf. Chem. 1982, 3, 214-218. (22) Pople, J. A.; Krishnan, R. A.; Schlegel, H. B.; Binkely, J. S.Inf. J. Quantum Chem. Symp. 1979,13, 225-241.
