J . Phys. Chem. 1990, 94, 2306-2312
2306
A Comparatlve Study of Isoelectronic and Isogyrlc Reactions: Molecular Orbital Calculations of Diatomic Hydrides and Halides Carol A. Deakyne,*?’ Ionospheric Physics Division. Geophysics Laboratory, Hanscom AFB, Massachusetts 01 731 -5000
Joel F. Liebman, Department of Chemistry and Biochemistry, University of Maryland, Baltimore County Campus, Baltimore, Maryland 21 228
Gernot Frenking, Fachbereich Chemie, Uniuersitat Marburg, Hans- Meerwein-Strasse, 0 - 3 5 5 0 Marburg, West Germany
and Wolfram Koch IBM Scientific Center, Tiergartenstrasse 15, 0 - 6 9 0 0 Heidelberg, West Germany (Received: June 30, 1989)
MP4/6-31 lG(2df,2pd)//MP2/6-31G** and MPn/6-31G**//CID/6-31G** ( n = 2-4) calculations have been carried out for H e v , N e P , A r P , ArH’, HCI, HCP, ClF, Cl,, HF, H P , F2,Ha, and H2+. Structures, vibrational frequencies, ionization potentials, reaction enthalpies, and triplet vs singlet energies (for H e r , N e P , and ArF+) have been examined. The reactions considered include hydrogenolysis and bond dissociation reactions. Isoelectronic comparisons have been made to assist in the study of reaction enthalpies. It is found that the MP4/6-3 1 IG(2df,2pd) enthalpies of reaction reproduce the experimental enthalpies well for all but nonisogyric reactions. MP4/6-31G** results reproduce the higher level computational results and the experimental results consistently well only for isogyric reactions that involve isoelectronic pairs of reactants and products. There is also considerable disagreement in the ionization potentials and singlet-triplet splittings obtained with the two basis sets. The MP4/6-3 1 1G(2df,2pd) and experimental ionization potentials differ by 1 0 . 3 eV. Calculated vibrational frequencies and bond lengths are in good accord with experiment.
Introduction Since fluorine and its compounds provide so many paradoxes and paradigms, they have long been of interest and importance to both the experimental and theoretical chemistry communities.’ The atomic species F and F were studied2 very early in the development of computational theory. F is a spherical, closed-shell anion and is thus both conceptually and computationally welldefined. The corresponding neutral species F is open shell and so the comparison of F and F provided qualitative and quantitative understanding of electron pairing and correlation effects. In particular, this study documented difficulties in the prediction of electron affinities. Neutral H F was investigateds5 as an archetypal example of a polar, covalent diatomic molecule. Additionally, H F is part of a well-defined series of closed-shell isoelectronic polyhydrides CH4, NH4, and H 2 0 . The computation of the structures and energetics of these species (sometimes including Ne) allowed for systematic variation of nuclear charge, effective nuclear charge, and the number of lone pairs and bond pairs. BF was also “popuIar”6-8 as it was part of an isoelectronic series of strongly bound diatomics: BF, CO, and N2. Indeed, C O and N, are a classic pairg.l0 of isoelectronic species. If experimental knowledge about BF was meager because of its difficulty of preparation and its reactivity, computational theory could unabashedly provide useful data. F2 was likewise actively studied.6J1J2 F2 is a closed-shell, nonpolar, singly bonded diatomic molecule which might suggest that computational theory would find this species easy to describe. However, early molecular orbital theory, even at the so-called Hartree-Fock limit, failed to show that F, could even exist! More precisely, the total energy of molecular F2 exceeded that of the two component atoms and so diatomic fluorine was seemingly unbound relative to the atoms. Berkowitz and Wahl13 chronicle the heroic efforts to match theory and experiment for F2, a situation additionally exacerbated by significant disagreement in the experimental literature at that time +On contract to Geophysics Laborator? from Wentworth Institute of Technology
as to how strongly F2 is in fact bound. Other diatomic fluorides were also studied, although usually by only one set of computational investigators. Such species included the noble gas containing species HeF,I4 NeF,I4 HeF+,15 NeF+,ISand ArF+,16 and most of the remaining nonmetal fluorides and their cations and anion^.'^-^^
(1) See, for example: Fluorine-containing Molecules: Structure, Reactivity. Synthesis and Applications; Liebman, J. F., Greenberg, A., Dolbier, W. R., Jr., Eds.; VCH: New York, 1988. (2) Allen, L. C. J . Chem. Phys. 1961, 34, 1156. (3) Clementi, E. J . Chem. Phys. 1962, 36, 750. (4) Clementi, E. J. Chem. Phys. 1962, 36, 33. (5) Nesbet, R. K.J . Chem. Phys. 1962, 36, 1518. (6) Fraga, S.;Ransil, B. J. J . Chem. Phys. 1962, 36, 1127. (7) Fraga, S.;Ransil, B. J. J . Chem. Phys. 1962, 37. 1112. (8) Nesbet, R. K. J . Chem. Phys. 1964, 40, 3619. (9) Langmuir, I. J . A m . Chem. S o t . 1919, 41, 1543. (IO) Bent, H. A. In Molecular Structure and Energetics: Bonding Models; Liebman, J. F., Greenberg, A,, Eds.; VCH: Deerfield Beach, FL, 1986; p 17. ( 1 1 ) Hijikata, K . J . Chem. Phys. 1961, 34, 221. (12) Wahl, A. C. J . Chem. Phys. 1964, 41, 2600. (13) Berkowitz, J.; Wahl, A. C. Ado. Fluorine Chem. 1973, 7 , 147. (14) Allen, L. C.;Lesk, A. M.; Erdahl, R. M. J . Am. Chem. SOC.1966, 88,615. (15) Liebman, J. F.;Allen, L. C. J . Am. Chem. SOC.1970, 92, 3539. (16) Liebman, J. F.; Allen, L. C. Chem. Commun. 1969, 1355. (17) OF: O’Hare, P. A. G.; Wahl, A. C. J . Chem. Phys. 1970,53,2469. (18) SF, SeF: O’Hare, P. A. G.; Wahl, A. C. J . Chem. Phys. 1970,53, 2834. (19) NF, PF: O’Hare, P. A. G.; Wahl, A . C. J . Chem. Phys. 1971, 54, 4563. (20)CF, SiF: O’Hare, P.A. G.;Wahl, A. C. J . Chem. Phys. 1971, 55, 666. (21) AsF: O’Hare, P.A. G.; Bateman, A,; Wahl, A . C. J . Chem. P h y s . 1973, 59, 6495. (22) Hay, P. J.; Wadt. W. R.; Dunning, T.H., Jr. Annu. Reo. Phys. Chem. 1979, 30, 3 1 1.
0022-3654/90/2094-2306~02.50/0 0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 6 , 1990 2307
Isoelectronic and Isogyric Reactions Qualitative comparison of isoelectronic species provided a useful conceptual framework for the understanding of these species.'e23 Indeed, a recent round of computational studies on noble gas containing cations2e26made heavy use of isoelectronic reasoning,*' both "vertical" (Le., comparison of He-, Ne-, and Ar-containing species) and "horizontal" (i.e., comparison of H and He+, and CI and Ar'). In the current paper we wish to quantitate the use of isoelectronic comparisons in assisting the calculational study of the energetics of some of the above fluorides. We will provide a general conceptual framework, and other studies, in progress, are designed to test the qualitative and quantitative utility of our approach.
The experimental enthalpies of reaction were calculated via eq 3.38.39
AH',,,
= CAHDf(products)- CAHDf(reactants) (3)
Results and Analysis of Results Total energies, basis set superposition errors, and zero-point vibrational energies (ZPEs) at the various basis set levels are tabulated in Table I. Some of these data are from the literat ~ r eand ~ are ~ ,included ~ ~ for completeness. The electronic state of the ion or molecule is also given in the table. Problems with convergence and with the stability of the Hartree-Fock wave function were encountered for CIF+ and CI2+;therefore, these ions and the valence isoelectronic F2+ are not included in this work. Theoretical Details Calculated and experimental reaction enthalpies for a number The calculations were carried out ab initio using the VAX and of gas-phase reactions are listed in Tables 11-V. Reaction energies IBM versions of GAUSSIAN 8228 and GAUSSIAN 86.29 On the basis are also furnished in the tables. The reactions are for ground-state of extensive literature p r e ~ e d e n c efully , ~ ~ optimized geometries NgF+, Ng = He, Ne and Ar. The difference in the stabilities were obtained utilizing the HF/6-31G*, MP2(fu)/6-31G**, and of singlet and triplet HeF', NeF+, and ArF+ are given in Table CID(fu)/6-3 IC** approximations employing analytical graVI. Adiabatic ionization potentials are tabulated in Table VII. d i e n t ~ . ~ 'Bond , ~ ~ lengths were optimized to 0.001 A and bond The data are compared for several basis set levels (this work and angles to 0.1'. The CID/6-31G** and MP2/6-31G** equilibrium ref 24). structures were used to compute single-point energies with fourth Table VI11 presents equilibrium geometries and harmonic vi(MP4SDTQ)-order Mdler-Plesset perturbation t h e ~ r y . ~ ~ .brational ~~ frequencies. The HF/6-3 1G*, MP2/6-31G**, and (MP4SDTQ will be designated as simply MP4.) CID/6-31G** optimum bond lengths are given in the table. The calculated enthalpies of reaction were obtained via eq 1 .35 Table IX lists the expectation values of Szfor the doublets and triplets considered in this work. The data are for the 6-31G** AH298 = AEelec + A F i b 2 9 8 + Ab?"298 AEtranS 298 + A(p1/)Z98 basis set. The expectation value of S2 is 0.75 for a pure doublet (1) and 2.00 for a pure triplet. A . Enthalpies of Reaction. The reactions listed in Tables 11-V The translational and rotational energies were calculated clashave been divided into four categories. The reactions in Table sically. The pressure-volume work term was determined from I1 (category 1) are isogyric and the reactant and product pairs the ideal gas law. Normal-mode vibrational frequencies and are isoelectronic, e.g., Ar', CI and ClF, ArF+ in reaction 4. In standard statistical formulas were utilized to obtain AEVibz98.36 isogyric reactions the number of unpaired electrons is identical The normal-mode vibrational frequencies were computed with the on both sides of the equation. Reactions that are not isogyric will HF/6-3 lG* and MP2/6-31G** equilibrium structures. Following suffer from severe electron correlation effects. The reactions in recommended procedure, the zero-point energies were scaled by category 2 (Table 111) are isogyric and the reactant and product a factor of 0.89 (HF/6-31G*) and 0.93 (MP2/6-31G**).30 mIef pairs are valence isoelectronic, e.g., HC1, H F and F, Cl in reaction is the electronic energy change for the reaction and is given by 2. The reactions in Table IV (category 3) are only isogyric. The eq 2, where E T is the total energy of the species. The basis set reactions in category 4 (Table V) are not euen isogyric. In each table, the reactions have been arranged alphabetically with respect AEelcc= xET(products) - xET(reactants) (2) to the first neutral reactant. 6-3IG** os 6-31IG(ZdJ2pd) Enthalpies of Reaction. Compare superposition errors (BSSE) were estimated via the counterpoise the results for the MP4/6-3 lG**//CID/6-31G** (abbreviated method.37 as MP4/6-31G**) and MP4/6-31 lG(2df,2pd)//MP2/6-31G** (abbreviated as MP4/6-311G(2df,2pd)) enthalpies of reaction for the reactions in category 1, Table 11. Although the data are (23) Liebman. J . F. J. Chem. Educ. 1971. 48. 188 limited, the deviations in the two enthalpies of reaction are gen(24j Frenking, G.; Koch, W.; Deakyne, C. A.; Liebman, J. F.; Bartlett, N. erally small, ranging from about 0.5 to 3 kcal/mol. Even the J . A m . Chem. SOC.1989, 1 1 1 , 31. (25) Frenking, G.; Koch, W.; Cremer, D.; Gauss, J.; Liebman, J. F. J . MP2/6-31G** and MP3/6-31G** values are within 4 kcal/mol Phys. Chem. 1989, 93, 3397. of the MP4/6-311G(2df,2pd) values. Reactions 6 and 8, Table (26) Frenking, G.; Koch, W.; Cremer, D.; Gauss, J.; Liebman, J. F. J. 11, are exceptions for the following reason. Note that for most Phys. Chem. 1989, 93, 3410. reactions in this category the electron correlation contribution is (27) Frenking, G.; Koch, W.; Liebman, J. F. In From Atoms to Polymers: Isoelectronic Analogies Liebman, J. F., Greenberg, A , , Eds.; VCH: New small, which is due to a cancellation of correlation effects between York, 1989; p 169. isoelectronic pairs rather than within isoelectronic pairs. For (28) Binkley, J . S.; Frisch, M . J.; DeFrees, D . J.; Raghavachari, K.; reactions 6 and 8 the correlation contribution from the F, HF+ Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. A . GAUSSIAN 82; and C1, HCI+ isoelectronic pairs is not offset by a contribution Carnegie-Mellon University, Pittsburgh, PA, 1982. (29) Frisch, M . J.; Binkley, J. S.; Schlegel, H. B.; Raghavachari, K.; from the H , H2+ pair. The electron correlation contribution for Melius, C . F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, the latter pair is, of course, zero. More examples are required C. M.; Kahn, L. R.; DeFrees, D. J.; Seeger, R.; Whiteside, R. A,; Fox, D. J.; to test the generality of these results. Fluder, E. M.; Pople, J. A . GAUSSIAN86; Carnegie-Mellon Quantum ChemFor the reactions in categories 2-4 (Tables 111-V), the situation istry Publishing Unit, Pittsburgh, PA, 1984. (30) Hehre, W . J.; Radom, L.; Schleyer, P. v. R.; Pople, J . A . A b Initio is less promising. The deviations in the MPn/6-31G** (n = 2-4) Molecular Orbital Theory; Wiley: New York, 1986. and MP4/6-311G(2df,2pd) enthalpies of reaction are as large as (31) Pulay, P. Mol. Phys. 1969, 17, 197. 1 1 kcal/mol for the valence isoelectronic, isogyric (category 2, (32) Schlegel, H . B.; Wolfe, S.; Bernardi, F. J . Chem. Phys. 1975, 63, Table 111) and isogyric (category 3, Table IV) reactions. Often 3632.
+
(33) Maller, C.; Plesset, M . S. Phys. Reu. 1934, 46, 618. (34) Pople, J . A.; Binkley, J. S.; Seeger, R . Znt. J . Quam. Chem. Symp. 1976, IO, I . (35) Del Bene, J. E. In Molecular Structure and Energetics: Bonding Models; Liebman, J . F., Greenberg, A , , Eds.; VCH: Deerfield Beach, FL, 1986; p 319. (36) Pitzer, K . S. Quantum Chemistry; Prentice Hall: Englewocd Cliffs, NJ, 1961. (37) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553.
(38) Lias, S. G.; Liebman, J. F.; Levin, R . D. J . Phys. Chem. Ref. Data 1984, 13, 695. (39) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W . G. J. Phys. Chem. Ref Data, Suppl. I . 1988, 17, 1 .
(40) Whiteside, R. A,; Frisch, M . J.; Pople, J . A. 'Carnegie-Mellon Quantum Chemistry Archive"; Department of Chemistry, Carnegie-Mellon University, Pittsburgh, PA 15123, 1983.
2308 The Journal of Physical Chemistry, Vol. 94, No. 6, 1990 TABLE I: Total Enereies ( E T )and BSSE and Zero-Point Enereies molecule basis" ETb BSSE ZPE' Ar('S)
HF/6-31G* ' -526.773 74 MP2/6-31G** -526.91 105 MP3/6-3IG**' -526.923 07 MP4/6-31G** -526.92444 MP4/6-31 I G ( 2 d f , 2 ~ d ) ~-527.031 3 HF/6-31G* -526.235 04 MP2/6-31G** -526.347 I 1 MP3/6-31G** -526.362 18 MP4/6-31G** -526.364 56 MP4/6-31 l G ( 2 d f , 2 ~ d ) ~-526.4590 HF/6-31G* -625.583 12 MP2/6-3 1G** -625.900 75 MP3/6-31G** -625.914 13 MP4/6-31G** -625.926 89 MP4/6-31 I G ( 2 d f , 2 ~ d ) ~-626.1402 HF/6-31G* -625.6 13 6 1 MP2/6-31G** -625.863 62 MP3/6-31G** -625.885 35 MP4/6-3 lG** -625.89282 MP4/6-31 I G ( 2 d f , 2 ~ d ) ~-626.095 5 HF/6-31G* -526.900 78 MP2/6-3 1 G** -527.057 51 MP3/6-31G** -527.071 87 MP4/6-31G** -527.074 32 MP4/6-31 IG(2df,2pd) -527.18348 HF/6-3 IC* ' -459.447 96 MP2/6-31G** ' -459.55243 MP3/6-3 IC** -459.567 11 MP4/6-3 IC** -459.56983 MP4/6-3 11G ( 2 d f , 2 ~ d ) ~-459.656 3 HF/6-31G8 -459.01502 MP2/6-3 1G** -459.100 49 M P3/ 6-3 1G * * -459.1 16 27 MP4/6-3 I G * * -459.11951 MP4/6-31 IG(2df,2pd) -459.187 64 HF/6-31G* -558.81952 MP2/6-3 IC** -559.12684 MP3/6-31G** -559.137 41 .MP4/6-31G** -559.150 17 MP4/6-31 I G ( 2 d f . 2 ~ d ) ~-559.353 2 HF/6-31G* -460.059 98 .MP2/6-3 1G * * -460.205 45 MP3/6-31G** -460.220 65 MP4/6-3 1G* * -460.223 93 MP4/6-3 I IG(2df,2pd) -460.323 98 HF/6-3 1 G* -459.633 97 MP2/6-3 IG** -459.753 91 MP3/6-31G** -459.771 77 MP4/6-3IG8* -459.775 02 MP4/6-3 IlG(2df,2pd) -459.859 46 HF/6-31Gr ' -9 18.912 82 %fP2/6-3lG** -919.171 39 MP3/6-3IG** -919.19643 MP4/6-31G** -919.204 38 MP4/6-3 I IG(2df,2pd) -919.397 42 HF/6-31G* -99.36496 MP2/6-31G**' -99.487 27 MP3/6-31G**' -99.495 69 MP4/6-3 IG**' -99.498 65 MP4/6-31 I G ( 2 d f , 2 ~ d ) ~ -99.607 9
1.1
5.7 5.9 6.2 2.8 2.7 2.7 2.9 1.3 2.7 2.8 2.9 2.0
l.ld
0.4 0.6d
3.7 3.8
1.2 7.5 7.8 8.2 1.0
I.ld
4.1
4.2
3.7 3.8
4.8 5.2 5.3 2.4
0.8 0.7
Deakyne et al.
molecule F+('P)
basis" ET^ BSSE HF/6-31G*' -98.192 06 MP2/6-3lG** -98.86963 MP3/6-31G**' -98.879 92 MP4/6-31G** ' -98.882 84 MP4/6-3 1 l G ( 2 d f , 2 ~ d ) ~ -98.978 0 HF/6-31G*' -100.00291 MP2/6-3 1G** -100.194 62 MP3/6-31G** -100.196 40 -100.201 41 MP4/6-3 1G** MP4/6-3 1 I G ( 2 d f , 2 ~ d ) ~-100.327 0 HF/6-31G* -99.489 60 MP2/6-3 1G** -99.626 13 -99.635 31 MP3/6-3 1G** MP4/6-31G** -99.639 40 -99.746 63 MP4/6-311G(2df,2pd) -198.671 16 HF/6-31G*' -199.03458 MP2/6-3 IC** 4.7 -199.033 84 4.1 MP3/6-31G** -199.05043 5.1 MP4/6-3 1G** 3.1 MP4/6-31 IG(2df,2pd) -199.21419 HF/6-31G*' -0.498 23 HF/6-31 I G ( 2 d f , 2 ~ d ) ~ -0.499 8 HF/6-3IG*' -1.126 83 MP2/6-3 1G** -1.15765 -1.163 16 MP3/6-3 I G** -1. I64 57 MP4/6-3 1G** -1.171 67 MP4/6-311G(2df,2pd) -0.58408 HF/6-3 1G* -0.602 I O HF/6-31 lG(2df,2pd) HF/6-3 1G* ' -2.855 16 -2.88064 MP2/6-31G** -2.886 08 MP3/6-31GL* MP4/6-3 IC** -2.887 15 MP4/6-31 I G ( 2 d f , 2 ~ d ) ~ -2.891 2 HF/6-31G* -101.53809 MP2/6-31GL* -101.71223 1.6 MP3/6-31G** -101.72669 1.7 1.7 MP4/6-31G** -101.73560 MP4/6-31 I G ( 2 d f , 2 ~ d ) ~-101.8576 1.1 -101.647 44 HF/6-3 1G* -101.751 53 MP2/6-3 IC** 0.2 -101.16730 0.1 MP3/6-31G** -101.771 39 0.2 MP4/6-3 IC** 0.3 MP4/6-3 I l G ( 2 d f . 2 ~ d ) ~-101.877 9 -1 28.414 41 HF/6-31G*' MP2/6-3 IG** -128.62472 -128.62476 MP3/6-31G**' -128.62921 MP4/6-31Gt*' MP4/6-31 I G ( 2 d f , 2 ~ d ) ~-128.7867 -227.15530 HF/6-31C* -227.455 69 MP2/6-31G** 4.0 -227.458 85 MP3/6-3 1G* * 4.0 -221.485 23 4.2 MP4/6-3 1G** 2.7 MP4/6-31 1G(2df,2pdId -221.737 5 HF/6-31G* -227.211 00 MP2/6-31G** -227.504 34 1.8 MP3/6-31G** -221.51374 1.7 MP4/6-3 IC** -227.523 31 1.9 1.3 MP4/6-31 I G ( 2 d f , 2 ~ d ) ~-227.772 5
ZPE'
5.5 5.6d
4.1 4.2
1.6 1.3
5.9 6.1
2.7 3.2
1.7 2.4d
0.1 0.2d
0.9 1.3d
0.3 0.4d
a HF/6-31Gt//HF/6-31G* calculation. MPn/6-31Ga*/C1D/6-3IG** or MP4/6-31 lG(2df,2pd)//MP2/6-3lG** calculation. bTotal energies (E,) in au. 'Reference 40. dReference 24. 'Basis set superposition error (BSSE) in kcal/mol. (Zero-point energies (ZPE) in kcal/mol. HF/631G* ZPE scaled bq 0.89:47 MP2/6-31G** ZPE scaled by 0.93.48
the MP2/6-31G** or MP3/6-31G** reaction enthalpies and not the MP4/6-31G** reaction enthalpies are closest to the MP4/ 6-31 IG(2df,2pd) values for these reactions. The worst agreement occurs for the nonisogyric reactions (category 4, Table V). The MPn/6-31G** (n = 2-4) enthalpies differ from the MP4/6-311G(2df,2pd) enthalpies by as much as 17 kcal/mol. Clearly for the examples in category 4 (Table V), the MP4/6-3 11G(2df,2pd) data are most closely paralleled by the MP2/6-31G** data, although the discrepancies in the two sets of data are still quite large. This is due to a fortuitous error cancellation of the small basis set and the insufficient description
of electron correlation effects via MP2. Comparison of MPn/6-31 G** Enthalpies of Reaction. For the reactions in categories 1 and 2 (Tables I1 and 111), the MPn/6-31G** (n = 2-4) reaction enthalpies differ from each other by at most 5 kcal/mol and generally the deviation is much smaller. For these cases, the MPn energies are converging or the oscillations between them tend to be small. The oscillations and the differences in the MPn/6-31G** (n = 2-4) reaction enthalpies for the reactions in category 3 (Table IV) tend to be larger than those for the reactions in categories 1 and 2. In fact, they are as large as 8 kcal/mol. Even worse results are obtained for the
Isoelectronic and Isogyric Reactions
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990 2309
TABLE II: Reaction Energies (kcal/mol) for Isoelectronic, Isogyric Reactions
-
reaction" basisb H+ + Ar HF/6-31G* MP2/6-3 IC**' MP3/6-3 IC** MP4/6-31G** MP4/6-31 IG(2df,2pd) 2. Ar + HCI' HF/6-31G* ArH+ + CI MP2/6-31G** MP3/6-31G** MP4/6-31G** MP4/6-31 IG(2df,2pd) 3. Ar + HF+ HF/6-3 IG* ArH' + F MP2/6-3 IC** MP3)6-31G** MP4/6-31G** MP4/6-31 lG(2df,2pd) 4. Cl + ArF' HF/6-31G* Ar' + CIF MP2/6-31G** MP3/6-3 1G** MP4/6-3 lG** MP4/6-31 1G(2df,2pd) 5. CI + ArH+ HF/6-31G* Ar' + HCI MP2/6-31G** MP3/6-31G** MP4/6-31G** MP4/6-311G(2df,2pd) 6. CI + H,+ HF/6-31G* HCI+ + H MP2/6-31G** MP3/6-3 IC** MP4/6-31G** MP4/6-31 IG(2df,2pd) 1. CIF + ArH' -. HF/6-31G* ArF' + HCI MP2/6-3 IC** MP3/6-3 1G** MP4/6-31G** MP4/6-31 1G(2df,2pd) HF/6-31G* 8. F + H2+ HF+ + H MP2/6-3 1G* * MP3/6-3 IC** MP4/6-3 IC** MP4/6-31 lG(2df,2pd) 1. ArH'
-
-
-
-
-
LiE
pa,,'
19.7 89.2 90.6 91.1 93.5 31.0 34.5 35.1 34.1 32.0 -1.5
86.5 81.9 88.4 90.6 31.0 34.5 35.1 34.1 32.0 -1.9
-4.8
-5.2 . _
-6.8 -6.1 -8.4 -14.1 -13.0 -11.5 -11.3 -9.8 33.1 36.0 35.2 34.9 35.6 -62.9 -12.6 -14.6 -14.9 -63.3 48.4 49.0 46.1 46.2 45.5 -24.3 -33.3 -33.1 -34.4 -22.9
71.0
-1.2 -1.1 -8.8 -14.6 -12.9 -11.4 -11.2 -9.8 34.1 36.4 35.6 35.3 36.0 -61.9 -11.6 -13.6 -13.9 -62.7 48.1 49.3 41.0 46.5 45.9 -22.9 -3 1.9 -32.3 -33.0 -21.9
M"upd
88.7
34.1
TABLE III: Reaction Energies (kcal/mol) for Valence Isoelectronic, Isogyric Reactions reaction' basisb AE AHoa~; AH',,: 1. Cl F2HF/6-31G* -36.9 -37.3 -22.0 CIF t F MP2/6-31G** -17.0 -17.4
+
MP3/6-31G** MP4/6-3 IC** MP4/6-31 IG(2df,2pd) 2. HCI F HF/6-31G* CI H F MP2/6-31G** MP3/6-31G** MP4/6-31G** MP4/6-311G(2df,2pd) 3. HCI + F? HF/6-31G* H F Clk MP2/6-3 IC** MP3/6-31G** MP4/6-31G** MP4/6-31 IG(2df,2pd) HF/6-31G* 4. C12 + F MP2/6-31G** CIF + CI MP3/6-3 1G** MP4/6-3 lG** MP4/6-31 1G(2df,2pd) 5. Cl2 H F HF/6-31G* MP2/6-3 lG** HCI CIF MP3/6-3 1G** MP4/6-31G** MP4/6-3 1 IG(2df,2pd) 6. C12 HF+ HF/6-3 lG* HCI + CIF MP2/6-31G** MP3/6-31G** MP4/6-31G** MP4/6-3 1 1G(2df,2pd) HF/6-31G* 7. C12 F2 MP2/6-31G** 2ClF MP3/6-31G** MP4/6-31G** MP4/6-311G(2df,2pd) 8. F ArF+ HF/6-3 1G* Ar+ F2 MP2/6-31G** MP3/6-31G** MP4/6-31G** MP4/6-311G(2df,2pd) 9. F HC1+ HF/6-31G* C1 HF' MP2/6-31G** MP3/6-3 1G** MP4/6-31G** MP4/6-31 1G(2df,2pd) 10. F2 HCI+ HF/6-31G* HF+ + CIF MP2/6-31G** MP3/6-31G** MP4/6-31G** MP4/6-31 1G(2df,2pd)
+
-8.9
+
-
+
+
35.3
-60.1
+ +
-
+
-
+
-11.7
"All reactants and products are gas-phase species. Reaction energies for ground-state NgF+. bHF/6-31G*//HF/6-31G*, MPn/6-3 IG**//CID/631G**, or MP4/6-31 lG(2df,2pd)//MP2/6-31G** calculations. corrected for the zero-point energy, temperature term, and pressurevolume work term differences (see text, eq I ) . dReferences 38 and 39. 'MPn/631G** and MP4/6-31 IG(2df,2pd) energies corrected for BSSE.
reactions in category 4 (Table V). For the nonisogyric reactions the MPn/6-31G** (n = 2-4) enthalpies vary by up to 10 kcal/mol. Calculated us Experimental Enthalpies of Reaction. With the exception of reactions 6 and 8 (see the explanation above), the MPn (n = 3,4) calculations with the 6-31G** basis set and the MP4 calculations with the 6-31 IG(2df,2pd) basis set yield AHoal, values within 2.5 kcal/mol of AHoerp for the reactions in category 1 (Table 11). The error bars on the MP2/6-31G** calculations are slightly larger at f3.5 kcal/mol. Again this looks promising but may be fortuitous since the information is limited. It does, however, fit our intuition which suggests that more errors are likely to cancel out when isogyric reactions involve isoelectronic reactant and product pairs. The MP4/6-311G(2df,2pd) enthalpies of reaction for the reactions in categories 2 and 3 are generally within 3.5 kcal/mol of the experimental enthalpies (Tables 111 and IV). The only exception is reaction 3, Table 111. The MPn/6-31G** (n = 2-4) enthalpies of reaction differ from the experimental values by up to 16 kcal/mol. The disagreement found for reactions involving open-shell species is similar to, and is often smaller than, that found for reactions involving only closed-shell species. The errors in the Hartree-Fock reaction enthalpies (2-26 kcal/mol, categories 1, 2, and 3) are consistently larger than those for the MPn (n = 2-4) enthalpies. The effect of electron correlation on the reaction enthalpies can be quite large, Le., 27.5 kcal/mol for reaction 1 2 (Table IV). The largest deviations in the calculated and experimental Me's are obtained when the reactions are not isogyric (category 4, Table
+
+
+ +
-
-
-
-+
-20.2 -11.9 -18.8 -16.3 -34.1 -29.6 -30.5 -32.3 -53.2 -51.1 -49.7 -48.5 -51.1 6.5 -12.9 -1.8 -10.6 -2.6 22.7 21.2 21.8 19.9 29.6 -32.0 -52.2 -48.6 -51.1 -43.1 -30.4 -29.9 -28.0 -28.6 -21.5 22.1 4.0 8.7 6.6 9.0 38.5 39.3 40.8 40.4 40.4 1.6 22.3 20.6 22.5 21.6
-20.6 -18.3 -19.0 -14.9 -32.1 -28.2 -29.1 -30.9 -52.2 -50.1 -48.7 -41.5 -49.9 6.8 -12.6 -1.5 -10.3 -2.3 21.6 20.1 20.1 18.8 28.5 -32.1 -52.3 -48.1 -51.2 -43.2 -30.4 -29.9 -28.0 -28.6 -21.4 22.6 4.5 9.2 1.1 9.2 38.9 39.1 41.2 40.8 40.8 1.6 22.3 20.6 22.5 21.8
-33.0
-55.0
-2.0
31.0
-45.0
-24.0
43.0
21.0
"dSee Table 11.
V). For these cases the error in the Hartree-Fock AHocalcis as high as 70 kcal/mol and the Hartree-Fock AHoalccan have the wrong sign. The deviations in the experimental and 6-31G** calculated enthalpies of reaction observed in this work are typical for enthalpies associated with bond dissociation reactions, hydrogen-transfer reactions, and proton-transfer reactions computed at this level.30 The results in Table I1 suggest that for reactions of type 1 the 6-3 1G** basis set reproduces both the higher level calculations and the experimental data well. It is not even necessary to go to fourth-order perturbation theory in order to obtain accurate results. In contrast, the 6-31G** basis set is not sufficiently extensive to produce uniformly reliable enthalpy values for the type 2-4 reactions (Tables 111-V). Including electron correlation in the calculations yields data consistently closer to the experimental data. Note that the poorest results are often associated with reactions involving F2. BSSE. The reactions for which basis set superposition errors have been taken into account are noted in Tables 11-V. The BSSE for the 6-31G** basis is often quite substantial, ranging from 0.1 to 8.2 kcal/mol. These values are upper limits to the magnitude
2310 The Journal of Physical Chemistry, Vol. 94, No. 6, 1990
Deakyne et al.
TABLE IV: Reaction Energies (kcal/mol) for Iwgyric Reactions reactionD 1 . HeF+- He + F+
basisb HF/6-31G* MP2/6-3 IG** e MP3/6-31G** MP4/6-31G** MP4/6-31 IG (2df,2pd) 2. NeF' Ne + F+ HF/6-31G* MP2/6-31GttC MP3/6-31G** MP4/6-31G** MP416-311G (2df,2pd) 3. CI + H, HCI + H HF/6-31G* MP2/6-3 IC** MP3/6-3 1G** MP4/6-31G** MP4/6-311G (2df,2pd) 4. CIF + H C1 + H F HF/6-31G* MP2/6-31G** MP3/6-31G** MP4/6-31G** MP4/6-311G (2df32pd) 5. CIF + H F + HCI HF/6-31G* MP2/6-3 IC** MP3/6-31G1* MP4/6-31G** MP4/6-31 IG (2df,2pd) 6. CIF + H2 HCI + H F HF/6-31G* MP2/6-31G** MP3/6-3 1G* * MP4/6-31G** MP4/6-31 IG (2df92pd) 7. CI, + H2 2HCl HF/6-3 lG* MP2/6-31G** MP3/6-31G** MP4/ 6-3 1G * * MP4/6-311G (2df32pd) HF/6-31G* 8. F H2 HF + H MP2/6-31G** MP3/6-31G** MP4/6-31G** MP4/6-311G (2d f, 2pd 1
AE 0.1
0.6 0.7 0.7 1.4
-
-
-
-
-
+
-
AH0,,,( 0.5 1 .O
AHu&
9. F2 + H
reaction' F + HF +
1.1
1.1
1.7 10. F2 + H2
-
2.8 4.2 3.7 4.9 3.6
3.0 4.4 3.9 5.1 3.7
10.4 4.0 7.1 7.7 2.6
8.6 2.2 5.3 5.9 0.7
1.o
-83.5 -76.5 -80.2 -77.1 -81.8
-79.2 -72.2 -75.9 -72.8 -77.3
-16.2
12. H
+ ArF+-
-67.3 -42.5 -50.6 -46.5 -49.5
-64.4 -39.6 -47.7 -43.6 -46.4
-43.2
13. H
+ ArF+-
-73.1' -72.5 -73.1 -69.4 -79.1
-70.5 -69.9 -70.5 -66.8 -76.5
-75.2
14. H + ArF+ ArH+ + F
-50.4' -51.4 -51.3 -49.5 -49.5
-49.0 -50.0 -49.9 -48.1 -48.0
-44.2
15. H2 + Ar+ArH+ + H
-5.9 -30.1 -22.5 -22.9 -29.6
-6.3 -30.5 -22.9 -23.3 -30.1
-32.0
16. HZ
+ FC
2HF
basisb HF/6-31G* MP2/6-31Gt* MP3/6-31G** MP4/6-31Gt* MP4/6-311G (2df,2pd) HF/6-31G* MP2/6-31G** MP3/6-31G** MP4/6-31G** MP4/6-311G
MP2/6-31G** MP3/6-3lG** MP4/6-3lG** MP4/6-311G (2df.2pd) Ar + HF+ HF/6-31G* MP2/6-31G** MP3/6-31G** MP4/6-31G** MP4/6-31 IG (2dfJpd) Ar' + H F HF/6-31G* MP2/6-31G1* MP3/6-31G** MP4/6-3 1G** MP416-311G (2df.2pd) HF/6-31G* MP2/6-31G1* MP3/6-31G** MP4/6-31G** MP4/6-311G (2df,2pd) HF/6-31G* MP2/6-3 lG** MP3/6-3 lG** MP4/6-3 IG** MP4/6-31 IG (2df,2pd) HF+ + H HF/6-31G* MP2/6-31G** MP3/6-31G1* MP4/6-31G** MP4/6-311G (2dfJpd)
-
-
-120.4 -93.5 -100.4 -95.0 -100.6
AHU,l,C -1 16.5 -89.6 -96.5 -91.1 -96.3
-126.2' -123.6 -122.9 -1 17.9 -130.2
-122.7 -120.1 -119.4 -114.4 -126.4
-130.2
-144.7 -126.8 -134.2 -129.5 -123.5
-139.4 -121.5 -128.9 -1 24.2 -1 18.2
-115.9
-114.2 -86.7 -91.6 -87.0 -86.6
-111.2 -83.7 -88.6 -84.0 -83.5
-98.3 -89.6 -91.7 -88.4 -91.6
-93.9 -85.2 -87.3 -84.0 -87.1
-1 15.7
-1 13.1
-91.5 -97.4 -92.8 -95.0
-88.9 -94.8 -90.2 -92.3
-23.3 -32.0 -28.1 -27.2 -33.0
-25.5 -34.2 -30.3 -29.4 -35.3
-34.3
-43.3 -60.9 -56.8 -56.6 -60.7
-45.1 -62.7 -58.6 -58.4 -62.6
-63.1
LE
Muex:
-98.2
"(See Table 11. 'Reference 30.
of the BSSE but should give some indication of the size of the effe~t.~'.~' Triplet us Singlet Energies. The MPn/6-31G** computations simulate the MP4/6-311G(2df,2pd) energy ordering of the lowest singlet vs the lowest triplet states of ArF+, HeF+, and NeF+ correctly (Table VI). In contrast, the HF/6-31G* calculations are incorrect for ArF'. The HF/6-31G* and MPn/6-31G** ( n = 2-4) values of AE(singlet-triplet) are too negative for all three cations compared to the MP4/6-311G(2df,2pd) values. This is additional evidence that 6-31G** computations overestimate the stability of states with higher spin m ~ l t i p l i c i t y .Even ~ ~ the relative magnitudes of the singlet-triplet separations are not reproduced. According to the 6-3 1 lG(2df,2pd) results the ordering of the magnitude of the splitting is ArFC > NeF+ > H e r . The 6-31G** results yield the ordering ArF+ > NeF+ = HeF+. Heat of Formation of ArF+(g). In order to calculate the enthalpy of formation of ArF+(g) with 6-31G** data, we choose reactions which are isogyric and involve isoelectronic reactant and product pairs. The MP4/6-31 G** calculated enthalpy of reaction for ArF+(g) + Cl(g) Ar+(g) + ClF(g) is -1 1.3 kcal/mol (Table 11, reaction 4). Employing this value and experimental heats of formation for the other reactants and product^^^.^^ yields 334 kcal/mol for the enthalpy of formation of ArF+(g). Following the same process for ArH+(g) CIF(g) ArF+(g) HCl(g)
-
+
-
+
(41) Schwenke, D. W.: Truhlar, D. G . J . Chem. Phys. 1985, 82, 2418.
gives AHro(ArF+) = 334 kcal/mol (Table 11, reaction 7). Therefore, our best calculated estimate of AHfo(ArF+)is 334 kcal/mol, which leads to a bond dissociation energy of 48 kcal/mol for ArF+(g). This result is in excellent agreement with the value of 49 f 3 kcal/mol obtained from the MP4/6-31 lG(2df,2pd) calculations (this work and ref 24). The only experimental estimate of the dissociation energy of ArF+(g) is by Berkowitz and Chupka4* who report a lower limit of 38 kcal/mol. The bond dissociation energy of ArF+(g) computed directly from the reaction ArF+(g) Ar+(g) + F(g) is 33.8 and 42.9 kcal/mol from the MP4/6-31G** and MP4/6-311G(2df,2pd) calculations, respectively (Table V, reaction 1). The discrepancy in these values and the value given above is not unexpected since this reaction is not an isogyric reaction. Deviations in calculated and experimental data of 5-15 kcal/mol are typical for nonisogyric reactions when these basis sets are utilized (Table V and ref 30). Ionization Potentials. The errors in the MP4/6-3 1 lG(2df,2pd) adiabatic ionization potentials (IPS) compared to the experimental ionization potentials range from 0 to 0.28 eV (Table VII). The errors in the Hartree-Fock 6-3 l G * and post-Hartree-Fock 631G** computations are considerably larger. The HF/6-31G* values are often over an electronvolt too low. The MPn/6-31G** values are as much as 0.75 eV too low. Little accuracy is gained by carrying the computations out to the higher levels of pertur-
-
(42) Berkowitz, J.; Chupka, W. A. Chem. Phys. Letz. 1970, 7, 447
The Journal of Physical Chemistry, Vola94, No. 6,1990 2311
Isoelectronic and Isogyric Reactions TABLE V: Reaction Energies (kcal/mol) for Nonisogyric Reactions reaction' basisb AE AHo,,,C AH'..? 1. ArF' Art
+ F
-
2. CIF CI F
+
3. C12
-
+
2CI
4. F H2+ H F Ht
5. F,
+
-
6. H2 HF
''See
-
2F
-
+ Ft + H+
HF/6-3 1G* -10.6 MP2/6-3 1G* * 35.9 29.4 MP3/6-31G** 33.8 MP4/6-31G** 43.2 MP4/6-31 IG(2df.2pd) HF/6-3 1G* 4.1 47.2 MP2/6-31G**' 39.0 MP3/6-31G** 43.3 MP4/6-31G** MP4/6-31 IG(2df,2pd) 55.8 10.6 HF/6-3 IG* 36.9 MP2/6-3 IG** 33.8 MP3/6-31G** 35.3 MP4/6-31G** 50.8 MP4/6-3 1 1G(2df,2pd) HF/6-31G* -33.8 -77.4 MP2/6-31G**e -73.2 MP3/6-3 1G** M P4/6- 3 1G * * -74.5 MP4/6-31 IG(2df,2pd) -73.4 -32.8 HF/6-31G* MP2/6-3IG**' 33.0 21.9 MP3/6-31G** MP4/6-31G** 28.2 MP4/6-31 IG(2df,2pd) 33.9 -52.7 HF/6-31G* MP2/6-31G** -105.0 MP3/6-3 1G** -96.2 MP4/6-3 1G** -96.6 MP4/6-31 IG(2df,2pd) -111.3
-10.9 35.6 29.1 33.5 42.9 3.9 47.0 38.8 43.1 55.6 10.6 36.9 33.8 35.3 50.9 -32.0 -75.6 -71.4 -72.7 -71.0 -33.5 32.3 21.2 27.5 33.5 -53.1 -105.4 -96.6 -97.0 -111.8
238.11
CI
58.0
HCI
-74.1
38.0
-120.1
NeF'
ArF'
F
HF
H
H2
TABLE VI: Singlet vs. Triplet Energies (kcal/mol) basis''b HF/6-31G* MP2/6-3 1G** MP3/6-3 1G** MP4/6-31G** MP4/6-31 IG(2df,2pd) HF/6-31G* MP2/6-3 1G** MP3/6-31G** MP4/6-3 1G** MP4/6-3 1 1G(2df,2pd) HF/6-31G* MP2/6-3 IG** MP3/6-31G** MP4/6-31G** MP4/6-31 lG(2df,2pd)
molecule Ar
60.0
Table 11. /Reference 42.
molecule HeFt
TABLE VII: Adiabatic Ionization Potentials (eV)
AEe -68.6 -24.7 -25.5 -22.5 -12.7d -72.6 -30.5 -34.4 -23.9 -22.0d -19.1 23.3 18.1 21.4 28.0d
HF/6-3 IG*//HF/6-3 1G* calculation. MPn/6-31G**/CID/631G** calculation. C Anegative value indicates that the triplet is more stable than the singlet. dMP4/6-31 lG(2df,2pd)//MP2/6-3lG** calculation, ref 24.
bation theory. The MP4/6-3 11G(2df,2pd) calculations order the IPS correctly; the HF/6-31G* and MPn/6-31G** calculations do not. B. Geometries. The largest difference in the MP2/6-31G**24 and CID/6-31G** geometries (Table VIII) is 0.044 8, for NeFt(311); the smallest is 0.001 8, for HCI', HCI, and ArH'. Despite the considerable variation in some of the bond lengths, the MP2/6-31G**//MP2/6-3lG** and MP2/6-31G**// CID/6-31G** total energies vary very little (Table I). The biggest variation in total energy is 0.2 kcal/mol, indicating that the minima in the potential energy surfaces are quite flat for these molecules. The MP2/6-31G** and CID/6-31G** geometries are both in reasonable agreement with the available experimental geomeThe largest differences are 0.025 8,for CI2 (CID) and (43) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Sfrucfure. IV. Constants of Diatomic Molecules; Van Nostrand Reinhold: New York, 1979. (44) Johns, J. W. C. J . Mol. Specfrosc. 1984, 106, 124.
basis' HF/6-31G* MP2/6-3 1 G** MP3/6-3 1G** MP4/6-3 IG** MP4/6-3 1 IG(2df,2pd) HF/6-31G* MP2/6-31G** MP3/6-31G** MP4/6-3 IG** MP4/6-3 1 IG(2df,2pd) HF/6-31G* MP2/6-31G** MP3/6-31G** MP4/6-3 1G** MP4/6-31 IG(2df,2pd) HF/6-31G* MP2/6-31G** MP3/6-31G** MP4/6-31G** MP4/6-311G(2df,2pd) HF/6-3 1G* MP2/6-31G** MP3/6-31G** MP4/6-31G** MP4/6-31 IG(2df,2pd) HF/6-31G* MP2/6-31G** MP3/6-31G** MP4/6-31G1* MP4/6-31 IG(2df,2pd) HF/6-31G* MP2/6-31G** MP3/6-31G** MP4/6-3 I G** MP4/6-31 lG(2df,2pd)
IP,l,b 14.66 15.35 15.26 15.24 15.57 11.78 12.30 12.27 12.25 12.75 11.59 12.29 12.21 12.22 12.64 15.59 16.8 I 16.76 16.76 17.14 13.97 15.47 15.27 15.29 15.79 11.80 13.56 13.56 13.56 13.60 15.61 15.61 15.76 15.80 15.50
IP..d 15.76
12.97
12.75
17.42
16.04
13.60
15.43
'HF/6-31G*//HF/6-3IG*, MPn/6-31G**//CID/6-31G**, or MP4/6-31 lG(2df,2pd)//MP2/6-3 IG** calculations. bThis work and ref 24. Reference 39.
0.027 8, for ClF (MP2); the others are all 0.015 8, or less. There are some large variations in the Hartree-Fock and post-Hartree-Fock geometries. Cases of both longer and shorter optimum Hartree-Fock bond lengths compared to the postHartree-Fock values are found (Table VIII). For example, the Hartree-Fock optimum bond length for HeF+(311) is 0.355 8, longer than the optimum CID bond length, while it is 0.054 8, shorter for F2. When the equilibrium geometries are compared to the experimental bond lengths, the error range is wider for the Hartree-Fock calculations than for the post-Hartree-Fock calculations. It has been shown that structures and energetics of open-shell species computed in the U H F approximation can be affected by the degree to which the states of interest are contaminated by states of higher spin m u l t i p l i ~ i t y . ~The ~ * ~agreement between calculated and experimental geometries and reaction enthalpies increases as the extent of spin contamination decrease^.^^,^^ For example, Hehre et aL30 have correlated the expectation value of S2 with structural data for AH, and ABH, open-shell systems. The values of ( S 2 )given in Table IX indicate that the degree of spin contamination is small for these radicals. It is therefore unlikely that the disparities in experimental and theoretical structures and energetics found in this work can be attributed primarily to spin contamination. C. Vibrational Frequencies. The nonequivalent equilibrium geometries account for most of the discrepancy in the HF/6-3 1G* (45) Baiocchi, F. A,; Dixon, T. A,; Klemperer, W. J . Chem. Phys. 1982, 77, 1632. (46) Baker, J.; Nobes, R. H.; Radom, L. J . Compuf. Chem. 1986, 7,349. (47) Pople, J . A,; Schlegel, H. B.; Krishnan, R.; DeFrees, D. J.; Binkley, J. S.;Frisch, M . J.; Whiteside, R. A,; Hout, R. F., Jr.; Hehre, W. J. I n f . J . Quantum Chem. Symp. 1981, 15, 269. (48) Hout, R. F., Jr.; Levi, B. A.; Hehre, W. J. J . Compuf.Chem. 1982, 3, 234.
2312
The Journal of Physical Chemistry, Vol. 94, No. 6,1990
TABLE VIII: Tbeoretical and Experimental Bond Lengths ( R , and Harmonic Vibrational Frequencies (w, em-')
A)
I
molecule basisa R,(calc)b R,(exp)c w,(calc) w,(exp)c ArF+('Z+) HF/6-31G* 1.609 736 CID/6-31G** 1.635 MP2/6-31G** 1.6378 8069 ArFC('II) HF/6-31G* 2.226 263 ClD/6-31G** 2.136 MP2/6-3 lG** 2.1208 4208 ArHt('Zt) HF/6-31G* 1.267 1.280d 2873 2711d CID/6-31G** 1.266 MP2/6-31G** 1.267 2885 CIF('Z') HF/6-31G* 1.613' 1.632' 914 786 CID/6-31G** 1.647 MP2/6-3IG** 1.6598 8049 HCI('Zt) HF/6-31G* 1.266 1.275 3189 2991 CID/6-31G** 1.269 MP2/6-31G** 1.268 3128 HC1+(211) HF/6-31G* 1.293 1.315 2942 2674 CID/6-31G** 1.302 MP2/6-31G** 1.301 2857 C12('ZsC) HF/6-31G* 1.996 1.987 600 560 CID/6-31G** 2.01 3 MP2/6-3 lG** 2.01 5 546 HF('ZC) HF/6-31G* 0.9111 0.917 435V 4138 CID/6-31G** 0.917 MP2/6-31G** 0.9219 42038 HF"('n) HF/6-31G* 1.006 1.001 3158 3090 ClD/6-31G** 1.003 MP2/6-31G** 1.006 3122 F2('Z.B+) HF/6-31Gt 1.345' 1.412 1245' 917 CID/6-31G** 1.399 MP2/6-3lG** 1.421 1008 HZ('Z,+) HF/6-31G* 0.736 0.741 4646 4401 CID/6-31G** 0.738 MP2/6-31G** 0.734' 4612f H2+(2Z8t) HF/6-31G* 1.041 1.052 2151 2321 HF/6-31G** 1.031 2422 HeF+('Z+) HF/6-31G* 1.093 1307 CID/6-31G** 1.045 MP2/6-31G** 1.024 1781 HeF+(311) HF/6-31G* 2.450 85 ClD/6-3 IC** 2.095 MP2/6-31G** 2,123 174 NeF+('Z+) HF/6-31G* 1.515 686 CID/6-31G** 1.470 MP2/6-31G** 1.456 942 NeFt('II) HF/6-31G* 2.187 194 CID/6-31G** 2.004 MP2/6-31G** 1.9608 2868 "The CID/6-31G** and MP2/6-31G** calculations include all electrons. bThis work unless otherwise specified. cReference 43 unless otherwise specified. Reference 44. Reference 45. IReference 30. 8 Reference 24.
and MP2/6-3 1G** harmonic vibrational frequencies (Table VIII). When the HF/6-31G* equilibrium bond lengths are a good representation of the CID/6-31G** or MP2/6-31G** equilibrium bond lengths. the HF/6-3 1G* harmonic vibrational frequencies
Deakyne et al. TABLE I X Expectation Values of S2for Radicalsa.b species Ar+(2P) ArF+(311) CI(2P) CI+(3P) HCl+('II) CIF+('II)
(S2)
0.755 2.015 0.755 2.006 0.757 0.759
species U2P) F+('P) HF+(211) HeF+('II) Ne+(2P) NeFt('II)
(S*) 0.753 2.004 0.754 2.004 0.752 2.005
" ( S 2 )is 0.75 for a pure doublet and 2.00 for a pure triplet. b631G** basis set.
are a good representation of the MP2/6-31G** frequencies. When the Hartree-Fock bond length is shorter (longer) than the MP2 bond length, the Hartree-Fock vibrational frequency is higher (lower) than the MP2 frequency. The only exception to this is ArFf ( '2'). The MP2 and H F harmonic vibrational frequencies are larger than the experimental freq~encies!~.~The greatest overestimation is 322 cm-I for F,; the others are all within 250 cm-I. These results are typical for calculations carried out at these basis set levels.30 For the diatomic molecules examined in this work, the agreement between the HF/6-31G* and MP2/6-31G** zero-point energies is excellent (Table I). A difference in vibrational frequency of -500 cm-l (Table VIII, HeFY(lX+)) yields a difference in ZPE of 0.7 kcal/mol (Table I).
Conclusions The following conclusions were drawn from this work: (1) The MP4/6-31 1G(2df,2pd) reaction enthalpies are in good accord with the experimental values for all but nonisogyric reactions. (2) The MPn/6-31G** ( n = 2-4) reaction enthalpies are a good representation of the MP4/6-3 11G(2df,2pd) and the experimental enthalpies for those reactions which are isogyric and involve isoelectronic reactant and product pairs. (3) The MP4/6-311G(2df,2pd) ionization potentials are within 0.3 eV of the experimental values; the MPn/6-31G** IPS are much less accurate. (4) The MPn/6-31G** ( n = 2-4) computations reproduce the MP4/6-3 1 lG(2df,2pd) predicted ground states of HeF+, NeF+, and ArF' correctly but predict the magnitudes of the singlettriplet splittings incorrectly. (5) The CID/6-31G** and MP2/6-31G** optimum bond lengths are in reasonable agreement with each other and with the experimental bond lengths. (6) The MP2/6-3 1G** harmonic vibrational frequencies are too large but are within 10% of the experimental harmonic frequencies. (7) Including electron correlation in the calculations improves both structures and energetics. Acknowledgment. The support of the Air Force Geophysics Laboratory Information Resources Center is gratefully acknowledged.
