J . Phys. Chem. 1987, 91, 6148-6151
6148
in the experimental work. Thanks are also due to the Information Processing Center, Hiroshima University, and the Computer Center, Institute for Molecular Science, Okazaki National Research Institutes, for the use of their HITAC M-200H computers. The present work was partially supported by a Grant-in-Aid for Scientific Research No. 60540289 from the Ministry of Education, Science, and Culture, Japan. Registry NO. 112-25-4; C6E2, 112-59-4; CgE1, 10020-43-6; CgE2, 19327-37-8; CsE,, 19327-38-9; CgE4, 19327-39-0; CIoEI, 2323840-6; CIOE2, 23238-41-7; CloEJ, 4669-23-2; CloE4, 5703-94-6; CloE,, 5168-89-8; CloEs, 24233-81-6; C12E1, 4536-30-5; C12E2, 3055-93-4; Cl2E3, 3055-94-5; C12E4, 5274-68-0; Cl2E5, 3055-95-6; Cl2E6, 3055-96-7; CI2E7, 3055-97-8; C12Eg, 3055-98-9; ClJEo, 112-70-9; CIdEo, 112-72-1; CisEo, 629-76-5; Cl6E4, 5274-63-5; C1&6, 5168-91-2; C16Eg15698-39-5.
helical conformation as in poly(oxyethy1ene) and the end alkyl blocks are in an extended zigzag conformation. This molecular conformation resembles the p form that we have found for the C,E, compounds. The helical conformation of the oxyethylene chain in these triblock compounds is expected from the conformational competition between the oxyethylene and alkyl chains, the oxyethylene chain in the central block being long enough to stabilize the helical structure. The tilting of the alkyl chains has also been established for the n-alkyl-oligo(oxyethy1ene)-n-alkyl compounds,4649 in conformity with the requirement by their molecular conformation.
Acknowledgment. We express our thanks to Dr. Keiichi Ohno for his helpful discussion and Mr. Toru Oyama for his assistance
Theoretical Determination of the Ground State of N,*+ Peter R. Taylor* ELORET Institute,t Sunnyvale, California 94087
and Harry Partridge N A S A Ames Research Center, Moffett Field, California 94035 (Received: April 13, 1987)
-
The dication Nz2+is shown to have a IZ ground state, with a 311uexcited state less than 0.1 eV higher in energy. The lowest 3Z; state lies more than 0.5 eV a%ove the ground state. The computed T, for the DIE,+ X'Zg+ transition is in excellent agreement with experiment. The largest calculations performed include g-type basis functions and employ second-order CI expansions of up to 2 756 000 CSFs: the effect of selecting reference CSFs for the CI is also discussed. +
Introduction The dication N?+ is important in energetic processes involving molecular nitrogen, such as reactions in the ionosphere and in bow shock waves ahead of reentry vehicles. The available experimental results have been comprehensively reviewed and compared with theoretical calculations in a recent paper by Wetmore and Boyd.' The most accurately characterized data are derived from emission 'Z +) band ~ y s t e m . ~ , ~ spectroscopy of the Carroll-Hurley ('Z,+ While some theoretical studies have identified dZg+as the ground state of N22+,e6 including those of Wetmore and Boyd, suggest that the ground state is 311u. Earlier CASSCF studies by TaylorS accounted for near-degeneracy effects, but not dynamical correlation, and predicted a lZg+ground state. Wetmore and Boyd' employ a multireference CI treatment, which includes dynamical correlation, but use SCF M O s , which in the light of the CASSCF results5 may compromise the description of neardegeneracy effects. It is somewhat surprising that the calculations of Wetmore and Boyd predict a 311, ground state, as singlet states are generally lowered more by dynamical correlation than triplet states, and it is unusual to see a CASSCF singlet ground-state prediction reversed by inclusion of dynamical correlation. Few calculations on NzZ+have used extended 1-particle basis sets. The basis of Wetmore and Boyd' is very restricted (a [3s 2p Id] contracted Gaussian basis), and the basis set used by TaylorS is only slightly larger ([5s 3p Id]). Cossart and coworkers6 have used a Slater-type basis in a small C I calculation (yielding a IZg.+ ground state), and Cobb et a1.* have used more flexible Gaussian basis sets in S C F calculations, but the latter are very unreliable for N22+because of the severe near-degeneracy effects. It certainly seems desirable to perform CI calculations on N?+ in larger 1-particle basis sets than have been used to date. In the present work, we investigate the low-lying IZg+, 311u,and
-
'Mailing address: NASA Ames Research Center, Moffett Field, CA 94035.
0022-3654/87/209 1-6148$01 .SO10
3Z,- states in the immediate region of the minima in their respective potential curves. As the results of high-resolution optical spectroscopy on N?+ are limited to the lZu+ IZ,+transition, we have also computed spectroscopic constants for the '2,' state for comparison with experiment. The aim of this work is not only to establish the ground state of Nz2+,but also to calibrate approaches for computing the entire potential curves of many states of Nz2+.
-
Computational Methods Several different atomic basis sets have been used in this work. The smallest is a [Ss 3p Id] set given by Dunning's segmented contractiong of Huzinaga's (9s 5p) primitive setlo for N, augmented with a single d function with exponent 0.9. This is the basis used in earlier CASSCF studiesSand is similar to that used by Wetmore and Boyd,' but more flexibly contracted. The two larger basis sets are derived from the (13s 8p) primitive set of van Duijneveldt," augmented with a (6d 4f 2g) polarization set. The polarization functions are taken as even-tempered sequences with an internal ratio of 2.5. The geometric mean of the d exponents is 1.0,l2while the f and g sets are based on scaling of the mean d exponent by 1.2 and 1.44, respectively. This primitive (1) Wetmore, R. W.; Boyd, R. K. J. Phys. Chem. 1986, 90, 5540. (2) Carroll, P. K. Can. J . Phys. 1958, 36, 1585. Carroll, P. K.; Hurley, A. C. J. Chem. Phys. 1961, 35, 2247. (3) Hurley, A. C. J. Mol. Specirosc. 1962, 9, 18. (4) Thulstrup, E. W.; Andersen, A. J. Phys. B 1975, 44, 285. (5) Taylor, P. R. Mol. Phys. 1983, 49, 1297. (6) Cassart, D.; Launay, F.; Robbe, J. M.; Gandara, G. J . Mol. Spectrosc. 1985, 113, 142. (7) Stalherm, D.; Cliff, B.; Hillig, H.; Mehlhorn, W. Z . Naturforsch., A. 1969, 24, 1728. ( 8 ) Cobb, M.; Moran, T. F.; Borkman, R. F.; Childs, R. J . Chem. Phys. 1980, 72, 4463. (9) Dunning, T. H. J. Chem. Phys. 1970, 53, 2823. (10) Huzinaga, S. J. Chem. Phys. 1965, 42, 1293. (1 1 ) van Duijneveldt, F. B. ZBM Res. Rep. 1971, RJ 945. (12) Ahlrichs, R.; Taylor, P. R. J . Chim. Phys. 1981, 78, 1413.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 24, 1987 6149
The Ground State of N22+ TABLE I: CI Results for States of N2*’
‘E,+
’n”
re
“e
re
CASSCF SOCI SOCI + Q
1.139 1.146 1.146
2004 1959 1953
1.252 1.257 1.258
CASSCF SOCI SOCI + Q
1.135 1.137 1.138
1995 1962 1954
1.134 1.133 1.134 1.129
calculation
I 2,+
Te
re
“e
1460 1432 1428
0.579 0.044 0.001
1.140 1.151 1.153
1951 1897 1887
9.077 8.102 8.023
1.249 1.247 1.248
1511 1498 1493
0.574 0.054 -0.002
1.136 1.142 1.145
1934 1894 1880
9.071 7.971 7.864
1991 1961 1953 1966
1.248 1.243 1.245
1507 1498 1493
0.585 0.078 0.020
1.136 1.137 1.140 1.133
1931 1900 1885 1894
9.047 7.919 7.809 7.802c
1.16
1760
1.25
1500
1.17
1903
1.161
1780
1.23
1521
1.14
2034
“e
Te
re
We
Te
1.374 1.374 1.376
1041 1030 1025
1.475 0.777 0.696
8.247
1.38
1350
0.252
8.544
1.34
1372
0.072
[5s 3p Id] basisb
[4s 3p 2d l f l A N 0 basisc
[5s 4p 3d 2f l g ] AN0 basis”
CASSCF SOCI SOCI + Q experiment Wetmore and Boyd SOCIZ
Cossart et al.k CI‘
-0.091 0.256
“rein h;, we in cm-I, Te in eV. b l X : total energies (EH)at r = 2.15a0: CASSCF, -107.653429; SOCI, -107.763 196; SOCI + Q,-107.766 182. ‘‘Eg+total energies (EH)at r = 2.15ao: CASSCF, -107.670 125; SOCI, -107.811 587; SOCI + Q, -107.816204. dlEg+ total energies (EH)at r = 2.1500: CASSCF, -107.676189; SOCI, -107.830228; SOCI + Q,-107.835275. ‘Based on experimental To(7.799 eV) and [5s 4p 3d 2f lg] harmonic frequencies. /Reference 1 . gperturbation extrapolation treatment. The results given were derived as described in the text. * Reference 6.
‘Selected configuration variation/perturbation treatment.
set is contracted to [5s 4p 3d 2f lg] by using a general contraction based on natural orbitals from an atomic C I calculation, as described by Almlof and Tay10r.I~ Such atomic natural orbital (ANO) basis sets allow the use of extended primitive sets but avoid the contracted set becoming unmanageable in size; previous workI3 has demonstrated that there is little resulting contraction error at either the S C F or correlated level. A smaller [4s 3p 2d lfl set was obtained by deleting the g-type A N 0 and the spdf ANO’s with the smallest occupation number. The 3s, 4p, 5s, and 5d components of Cartesian d, f, and g functions were deleted in all calculations. Most of the multireference C I (MRCI) wave functions used in this work are of second-order C I type (SOCI), that is, they comprise all single and double excitations out of a CASSCF reference wave function. For the [4s 3p 2d lfl basis, selection of reference configurations was studied by using selection thresholds, as described below. The results of a multireference analogue of Davidson’s correctionI4 (denoted +Q and defined as hE( l-XRcR2), where AE is the MRCI correlation energy and CR is the MRCI coefficient of reference C S F R ) are also given. The CASSCF active space included the eight valence MO’s (2ug, ; derived from the 2aU,3ug, 3u,, 1sU, Is,, lap, 1 ~ ~the) MO’s N 1s orbitals were not correlated in the C I calculations. Equilibrium geometries and spectroscopic constants for all calculations have been derived from a fit in the variable 1/r to three points about the respective minima. A grid spacing of 0.05 a. was used. Of course, none of the states of N>+ are true bound states, and ultimately the potential curves must display a 1/r dissociative behavior, but the barriers to dissociation of all the states considered here are so high that for the purpose of identifying and characterizing the ground state it is perfectly acceptable to use a simple fit to points near equilibrium. Calculations were performed on the Ames CRAY X-MP and N A S Facility CRAY 2 computer systems, using the MOLECULE-SWEDEN c o d e ~ . ~ ~ J ~
Results and Discussion The spectroscopic constants for four electronic states of N22+ obtained by using SOCI wave functions and various atomic basis ~
~~
(1 3) Almlof, J.; Taylor, P. R. J . Chem. Phys. 1987, 86, 4070. (14) Langhoff, S. R.; Davidson, E.R. Inr. J. Quanrum Chem. 1974, 8, 61. Blomberg, M. R. A.; Siegbahn, P. E. M. J . Chem. Phys. 1983, 78, 5682. (15) MOLECULE is a vectorized Gaussian integral program written by
Almlof, J. (16) SWEDEN is a vectorized SCF-MCSCF-direct CI-conventional CICPF-MCPF program, written by Siegbahn, P. E. M.; Bauschlicher, C. W. Jr.; Roos, B.; Taylor, P.R.; Heiberg, A.; Almlof, J.; Langhoff, S. R.; Chong, D. P.
sets are listed in Table I. The re and we values show only a slight dependence on basis set size, with both the [5s 4p 3d 2f lg] and [4s 3p 2d lfl A N 0 basis sets yielding results close to the experimental values. The re values are hardly affected by the inlZg+ clusion of dynamical correlation. The computed I&+ transition energy (T,) for the [5s 4p 3d 2f lg] basis is in excellent agreement with experiment: this is especially noteworthy as previous theoretical values’sH for this transition have been in error by 0.5 eV or more. This transition energy shows a considerable basis set dependence at the SOCI level, but the results here are evidently converging toward the experimental value. It is clear from Table I that the most sophisticated treatments (SOCI or SOCI + Q in a [5s 4p 3d 2f lg] basis) predict a lZg+ ground state for N22+.Relativistic effects, estimated by using first-order perturbation theory,” decrease Te (Q,) by 0.01 eV, which does not alter the prediction of a IZg+ground state, although the resulting T, is only 0.01 eV at the SOCI Q level. However, considerable support for preferring the SOCI results over SOCI + Q is furnished by a recent study of the 8-valence-electron systems C2, Si2, and Sic (all valence isoelectronic with N22+)by Bauschlicher and Langhoff.18 These authors compared full C I results (in split-valence plus polarization A N 0 basis sets) with results from SOCI and MRCI wave functions, and showed that for these systems the SOCI (and MRCI) results agree much better with the full CI than do results which include the +Q correction. As a consequence, it seems very likely that the SOCI results for N22+would be in better agreement with the full CI than SOCI + Q. Noting that convergence of Tefor 311u-12,’with increasing basis set size is rather slow, it is likely that the [5s 4p 3d 2f lg] SOCI result of 0.078 eV is an underestimate of the (nonrelativistic) separation, and even if a relativistic contribution of -0.01 eV is included it is still likely that the true Te is larger than 0.08 eV. While it seems incontrovertible that the ground state of N?+ is indeed IZg+, it is pertinent to examine why the CASSCF T , of 0.585 eV is so much larger than the SOCI result of 0.078 eV. As stated in the Introduction, singlet states generally have greater correlation energies than triplet states, and therefore the expectation is that CASSCF will favor a triplet state. A clue to the CASSCF behavior can be obtained from examining the lZg+wave function. The CSF
-
+
2 4 2 4 17r: is the most important CSF in both the CASSCF and SOCI (17) Cowan, R. D.; Griffin, D. C. J . Opr. SOC.Am. 1976, 66, 1010. Martin, R. L. J . Phys. Chem. 1983, 87, 750. ( 1 8 ) Bauschlicher, C. W.; Langhoff, S.R. J . Chem. Phys. 1987,87, 2919.
6150 The Journal of Physical Chemistry, Vol. 91, No. 24, 1987
Taylor and Partridge
TABLE 11: Multireference CI Results in 14s 30 2d lfl Basis for States of N,*+'
3n"
IZg+ calculation selection threshold 0.05b MRCI MRCI
lZY+
re
'"e
re
4
TC
re
+Q
1.132 1.138
2005 1960
1.244 1.250
1514 1484
-0.007 -0.015
1.138 1.148
1922 1852
7.984 7.844
+Q
1.136 1.138
1974 1953
1.245 1.249
1511 1488
0.071 0.001
+Q
1.137 1.138
1968 1952
1.247 1.248
1500 1491
0.056 0.002
1.137 1,138
1962 1954
1.247 1.248
1498 1493
0.054 -0.002
1.142 1.145
1894 1880
7.971 7.864
'"e
TC
selection threshold 0.025' MRCI MRCI
selection threshold 0.0Id MRCI MRCI
no selection SOCI SOCI + Q
at
+
' r e in A, o, in cm-', T. in eV. blZ: total energies ( E H )at r = 2.1500: MRCI, -107.805424; MRCI Q, -107.816419. clZ: total energies (EH) Q,-107.816 164. d'L',+ total energies (EH)at r = 2.15ao: MRCI, -107.810987; MRCI Q , r = 2.1500: MRCI, -107.809937; MRCI
+
+
-107.816 143.
expansions. However, its importance is considerably underestimated at the CASSCF level, while the importance of the C S F is overestimated. As CSF(2) is more strongly binding than CSF( l), the CASSCF overestimates the stability of the IZgf state, compared to the SOCI. Exactly the same effect is seen in Cz,I8 where (relative to the SOCI) CASSCF overestimates the '8,' ground state De and the separation between the ground and various excited states. This redistribution of importance of the various valence CSFs should perhaps be regarded as a nondynamical correlation effect, because it occurs within the valence CSF space, but it is only observed when dynamical correlation is also included. The results obtained by Wetmore and Boyd' and by Cossart et a1.6 are also included in Table I. The Wetmore and Boyd results were published as a tabulation of vibrational energy levels: we have used the lowest few levels for each state to define oevalues, which have in turn been used to obtain Te values. A notable feature of the earlier calculations is the relatively poor T, values obtained for the excited '2,' state. This is related to the complicated correlation effects in the lZU+state, which has one electron ionized from the N 2s orbitals5 In general, the results of Wetmore and Boyd and of Cossart et al. are in only fair agreement with the present calculations, especially compared to the A N 0 basis set results. Basis set incompleteness favors the 311ustate relative to 'Zg+, owing to the larger dynamical correlation contribution in singlet states. Further, the use of SCF M O s favors those states which are best described by a single configuration. Of the four states treated here, the 'Xi state is approximated best by a single c~nfiguration,~ followed by 'nu.The 'Eg+and 'ZU+ states are both described very poorly by a single configuration: clearly, this will again cause the triplet states to be favored relative to the singlets. While both Wetmore and Boyd and Cossart et al. include all valence CSFs (as defined in this work) in their CI expansions, it is likely that some bias from the use of S C F MO's remains. Finally, only in the present work is the full second-order CI problem solved exactly. In other studies1g6the C I expansion is drastically truncated, with the effect of the deleted CSFs being estimated by perturbation theory. It is difficult to make any estimate of the effect on the computed spectroscopic constants. Given the above observations, the differences between the results of Wetmore and Boyd' or Cossart et aL6 and the present work can be understood. Wetmore and Boyd employ a small basis set, which favors the triplet relative to the singlets, and use IZg+ S C F MO's for all states. While this might be expected to favor the 'Zg+state, the S C F configuration used is CSF( 1) above, which tends to lower the stability of the lZgf state. It is therefore reasonable that, relative to our best SOCI calculations, Wetmore and Boyd predict 311uand '2; too low and find re too large and we too small for IZg+ (and '8,'). The total correlation energy state is recovered is rather small, and therefore T, for the overestimated. Cossart et al. employ a large Slater basis but truncate the MO space very severely, so that their final orbital
space for the CI calculations is similar in size to that of Wetmore and Boyd. Again, this favors the triplet states. However, Cossart et al. use S C F MO's optimized separately for each state, and as E,', which as shown above overestimates they use CSF(2) for ' the stability of this state, they find 'Eg+too far below 311u.This approach favors the '2; state, because it is best represented by a single CSF, and indeed they predict this state to lie too low. These workers also observe6 an avoided crossing in the 'Z,' state curve at relatively low energies (about 0.04 eV above the minimum). No such avoided crossing was observed by Wetmore and Boydl or T a y l ~ rand , ~ it is possible that this is an artifact introduced by using S C F MO's defined by CSF(2), which is not the C S F with the largest weight in the C I wave function. The present results for Nzz+involve very extensive atomic basis sets and SOCI wave functions which, for the [5s 4p 3d 2f lg] basis, include more than 1 600000 CSFs for the 'Eg+ and '2,' states and more than 2 750 000 CSFs for the 'II, state, in DZhsymmetry. Even in the [4s 3p 2d lfl basis the SOCI expansion for 311u numbers more than 600000 CSFs. C I calculations with such expansions are very expensive computationally, and the cost of investigating a large number of states and a large range of r values would become prohibitive. Hence we have investigated reference CSF selection as a means of reducing the length of the C I expansion. Those orbital occupations which give rise to at least one C S F whose coefficient in the CASSCF wave function exceeds a given threshold are used as reference occupations, and the reference CSF set is taken as all CSFs that can be generated from these reference occupations. Selection thresholds of 0.05, 0.025, and 0.01 were used. Studies on CZ1*suggest that 0.05 as a selection threshold does not give satisfactory agreement with SOCI Te results, but that 0.01 is not necessarily superior to 0.025 in this regard, so convergence to the SOCI result is not always monotonic. The results obtained with reference CSF selection are displayed in Table 11. The [4s 3p 2d If] basis was used throughout, so that the same basis set is used for all calculations; for convenience the SOCI results are also given in the table. The MRCI results converge rather smoothly on the SOCI results, and for this case, at least, it seems that reduction of the selection threshold gives a monotonic convergence of improvement in the results, unlike C,.'* Interestingly, a threshold of 0.05 hardly affects T, for the l.2"' state, although the other spectroscopic constants differ perceptibly from the SOCI values. The MRCI + Q results converge less regularly than MRCI, but the inclusion of the Davidson correction leads to much smaller differences between the various MRCI Q (and the SOCI + Q) results, and therefore the effect of selection threshold is less important. However, in view of the conclusion that the SOCI results shculd be more reliable than SOCI + Q, it seems necessary to use a threshold of no more than 0.025 if MRCI results similar in accuracy to SOCI are required, and 0.01 would be preferable. The latter threshold reduces the length of the C I expansion by some 45%. Finally, while many of the differences between entries in Table I1 are smaller than those in Table I, so that the effect of ccn-
+
J . Phys. Chem. 1987, 91, 6151-6158 figuration selection is less severe than that of basis set truncation, it is clear that only the smaller truncation thresholds provide acceptable agreement with the SOCI results. Based on these findings it seems that rather accurate results for N?+ can be obtained by using a [4s 3p 2d 1f3 basis set and MRCI with a selection threshold of 0.025 or less. The very large near-degeneracy observed for many states argues strongly for a multiconfigurational treatment from the outset: when CASSCF calculations are used to define the M O space for the C I calculation the ordering of states is generally close to the SOCI or MRCI ordering, which is not the case for S C F wave functions.s It should be possible to obtain high accuracy by performing a single CASSCF calculation on an average of states of the same spin and symmetry type, followed by a single MRCI calculation for all desired states of this type. Such an approach has been shown to agree very well with full C I results for excitation and ionization energies,l9
6151
Conclusions The spectroscopic constants of low-lying states of N22f have been computed by using extended basis sets and SOCI wave functions. The ground state is definitively shown to be ]Eg+, while the computed T, for the lZu+-lEg+ transition, which should be labeled D X, agrees with high-resolution optical measurements to within about 0.1 eV. Selection of reference CSFs is shown to give agreement with the SOCI results only when small selection thresholds are used.
-
Acknowledgment. We acknowledge the support provided by the NAS Facility. Helpful discussions with C. W. Bauschlicher and S. R. Langhoff are gratefully acknowledged. Registry No. N?',
12192-19-7.
(19) Bauschlicher, C. W.; Taylor, P. R. J . Chem. Phys. 1987, 86, 2844.
Ab Initio Studies of the Structure and Energetics of the H-(H,) Complex Grzegorz Cbalasiiiski, Department of Chemistry, University of Utah, Salt Lake City, Utah 84112, and Department of Chemistry, University of Warsaw, 02-093 Warsaw, Poland
Rick A. Kendall, and Jack Simons* Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 (Received: April 21, 1987)
The H-(H2) complex is examined by using various levels of Merller-Plesset perturbation theory (MPPT). Ab initio interaction energies are calculated through fourth-order MPPT (MP4) by using large and flexible basis sets. Our best atomic orbital basis yields an attractive interaction energy, relative to Hz and H-, of 1.2 kcal/mol at the MP4 level, but proper accounting of zero-point vibrational energies shows that H-(H2) is thermodynamically unstable. The importance of correcting for basis set superposition error is demonstrated. Analytically optimized geometries at the SCF and MP2 levels and pointwise geometry optimizations with basis set superposition corrections are reported. The weak vibrational stretching mode of the H- in the complex is also investigated. The potential energy surface along this mode supports six vibrational levels. SCF harmonic frequencies are reported for all vibrational modes. The correspondingstretching modes of the isotopically substituted complexes H-(HD) and D-(H2) are also analyzed. The potential energy surface crossings between H-(H2) and the neutral H3at pertinent geometries are shown, and their relevance to electron detachment in H2+ H- collisions is discussed.
-
I. Introduction There has been an interest in the study of hydrogen ion clusters. However, only positive clusters, Hn+, where n = 3, 5, 7, ..., have been discovered1 and successfully analyzed by means of both experimental* and a b initio theoretical methods (cf. Hirao and Yamabe3 and references cited therein). Substantially weaker H; complexes, where n = 3, 5, 7, ..., have so far eluded experimental determination. Yet, it has been argued that the extreme conditions in gaseous nebulae may be suitable for weakly bound negative ion clusters to e x i ~ t . ~It. ~is, in fact, possible that some diffuse interstellar absorption lines are due to vibrational structure in the electronic transitions of. Hn-. So far, theoretical calculations have predicted the stabilization of H;, in particular of H-(H2), to be less than 1 kcal/m01,~3~ which may not be strong enough to support a vibrational leveL3 In addition, as a very weak van der Waals complex, H-(H2) proves to be quite challenging to ab initio calculations. In earlier theoretical studies, the problem of dealing with a large basis set superposition error (BSSE) turned out to be serious even at the S C F level due to the diffuse character of the H- electron charge c10ud.~To make matters worse, BSSE is usually much worse at the correlated Finally, the CI-SD method used in the previous calculations is size-inconsistent, and the size-consistency 'Permanent address.
0022-3654/87/2091-6151$01.50/0
Davidson corrections turned out to be very ~ignificant.~ The aim of this paper is to provide advanced calculations on the ground electronic state of the H-(H2) complex, the simplest of the H-, n = 3, 5, ... sequence. An inherently size-consistent method, Moller-Plesset perturbation theory (MPPT)9 through the fourth order (MP4), was used to allow for electron correlation effects. Optimization of geometry at the S C F and MP2 levels was carried out with and without BSSE corrections. Several fairly large basis sets were used, and our best results are only slightly affected by BSSE. The results with smaller basis sets are also shown to be reliable but only when the CP methodlo is used to (1) Clampitt, R.; Gowland, L. Nalure (London) 1969, 223, 815. (2) Hiraoka, K.; Kebarle, P. J . Chem. Phys. 1975, 62, 2267. (3) Hirao, K.; Yamabe, S. Chem. Phys. 1983,80, 237. (4) Sapse, A. M.; Rayez-Meaume, M. T.; Rayez, J . C.; Massa, L. J . Nature (London) 1979, 278, 332. (5) Rayez, J. C.; Rayez-Meaume, M. T.; Massa, L. J. J. Chem. Phys. 1981, 75, 5393. (6) Van Lenthe, J. H.; van Dam, T.; van Duijneveldt, F. B.; Kroon-Batenburg, L. M. J. Faraday Symp. Chem. SOC.1984, 19, 125. (7) Gutowski, M.; van Lenthe, J. H.; Verbeek, J.; van Duijneveldt, F. B.; Chalasifiski, G. Chem. Phys. Lett. 1986, 124, 370. (8) Davidson, E. R. In The World of Quantum Chemistry; Daudel, R.; Pullman, B., Eds.; Reidel: Dordrecht, 1974; p 17. (9) Binkley, J. S.; Pople, J. A. Int. J . Quantum Chem. 1975, 9, 229. Krishnan, R.; Frisch, M. J.; Pople, J. A. J . Chem. Phys. 1980, 72, 4244.
0 1987 American Chemical Society
