J. Phys. Chem. 1996, 100, 2993-2997
2993
Hydrogen Bond Energy of the Water Dimer Martin W. Feyereisen* Cray Research, Inc., Eagan, Minnesota 55121
David Feller* EnVironmental Molecular Sciences Laboratory, Pacific Northwest Laboratory, Richland, Washington 99352
David A. Dixon* Du Pont Central Research and DeVelopment, Experimental Station, Wilmington, Delaware 19880-0328 ReceiVed: September 25, 1995; In Final Form: NoVember 7, 1995X
Large scale ab initio molecular orbital calculations on the binding energy of the water dimer have been performed. These calculations extend the previous correlation consistent basis set work to include larger basis sets (up to 574 functions), and core/valence correlation effects have now been included. The present work confirms the earlier estimate of -4.9 kcal/mol as the MP2(FC) basis set limit. Core/valence correlation effects are found to increase the binding energy by ∼0.05 kcal/mol. The best estimate of the electronic binding energy of the water dimer is -5.0 ( 0.1 kcal/mol. Correcting this value for zero-point and temperature effects yields the value ∆H(375) ) -3.2 ( 0.1 kcal/mol. This value is within the error limits of the best experimental estimate of -3.6 ( 0.5 kcal/mol with the calculations favoring the lower end of the experimental energy range. It should be useful to adopt the present estimate in empirical and semiempirical model potentials.
Introduction Hydrogen bonding plays a critical role in a wide range of chemical and biological phenomena. It is also important for describing the behavior of many synthetic materials. The prototypical hydrogen bond, and the one which has received the most theoretical attention, is that found between two water molecules. The small size of the water dimer and the difficulty in obtaining experimental results for this species make it an ideal candidate for ab initio studies. The structure of the water dimer was established by a molecular beam electric resonance experiment1,2 and by a wide range of ab initio electronic structure studies.3-7 However, accurate experimental measurements of the H2O-H2O potential energy surface well depth, ∆E, have proven to be a more elusive goal. There are few measurements of the binding energy of the water dimer. The most recent study was based on measurements of the thermal conductivity of the vapor of H2O and D2O.8 However, this method involves a significant amount of interpretation and the use of theoretical models to analyze the data. This led the authors to estimate errors of (0.5 kcal/mol for the ∆H of binding. The authors were able to measure a binding energy over a specific temperature range, but this alone does not directly yield the well depth, as ∆H includes the effect of thermal corrections as well as zero-point vibrational effects. ∆E is an important component of empirical potentials which are used in molecular dynamics simulations involving water in all of its phases. The available empirical potentials through 1984 have been reviewed by Reimers, Watts, and Klein.9 On the basis of the above discussion of the experimental difficulties, an accurate calculation of ∆E for the water dimer is of interest. Furthermore, a benchmark of the methods needed to calculate an accurate hydrogen bond energy is important in determining how to predict the hydrogen bond energy in larger systems where more accurate calculations may not be possible. There have been a wide range of ab initio molecular orbital X
Abstract published in AdVance ACS Abstracts, January 15, 1996.
0022-3654/96/20100-2993$12.00/0
studies of the well depth. For more details, the reader is referred to the recent review of Scheiner.10 Over the years, a large number of studies have demonstrated the importance of the 1-particle space, i.e. the choice of basis set, in determining the overall quality of the results one could obtain from electronic structure calculations.11 Extensive studies by Dunning and coworkers12-14 and others15-17 have shown that one can use correlation consistent basis sets to approach the complete basis set limit for a given level of the treatment of electron correlation. Several studies of the effect of correlation consistent18 basis sets on the properties of the water dimer have appeared. In his study, Feller19 applied various correlated methods with the ccpVDZ and cc-pVTZ basis sets, as well as their diffuse function augmented counterparts, denoted aug-cc-pVDZ and aug-ccpVTZ. He reported that the effect of correlation corrections beyond second-order Møller-Plesset perturbation theory, MP2,20 was less than 0.1 kcal/mol. All of the calculations in his study utilized the frozen core approximation on oxygen, which will be denoted here by the (FC) suffix. With the larger cc-pVQZ and aug-cc-pVQZ basis sets, which contain up through multiple g functions on oxygen, Feller was unable to go beyond the MP2 level. His calculations clearly showed the need to include diffuse functions in the basis set. Furthermore, the study showed that inclusion of counterpoise corrections21 to account for basis set superposition error (BSSE) was helpful with the cc-pVxZ basis sets but led to poorer agreement with the apparent complete basis set limit with the aug-cc-pVxZ basis sets. Xantheas and Dunning6 explored the potential energy surface of the dimer with various correlation consistent basis sets and various levels of electron correlation. The MP2 binding energies reported by Xantheas and Dunning, ∆E ) -5.34 kcal/mol (aug-cc-pVDZ) and -5.58 kcal/mol (aug-cc-pVTZ), were obtained without the frozen core approximation. These and other previously reported results for the water dimer are listed in Table 1. Exploiting the regularity of the correlation consistent sequence of basis sets, Feller estimated the MP2(FC) binding energy at the complete basis set limit, ∆E∞(MP2) ) -4.95 ( 0.05 kcal/ © 1996 American Chemical Society
2994 J. Phys. Chem., Vol. 100, No. 8, 1996
Feyereisen et al.
TABLE 1: Selected Previous Results for the Water Dimera basis set
no. functs
method
E(H2O dimer)
∆E
∆E(CP)
ref
aug-cc-pVQZb [13s,8p,4d,2f/8s,4p,2d] aug-cc-pVTZ [7s,6p,3d,1f/5s,2p,1d] + {3s,3p,2d,1f} bs’s EZPPPBFD
348 131 184
MP2(FC) MP2 MP2
-152.7118 -152.7903
-5.05 -4.99 -5.58
-4.81 -4.66 -4.65
19 22 6
125
MP2(FC)
-152.6435
-4.62c
22
a
Total energies are given in hartrees. Binding energies are in kcal/mol. b Estimated by assuming the additivity of the effects due to the diffuse g functions on oxygen. c Value obtained at geometry M2 of ref 22. At the optimal MP2 geometry the binding energy was -4.71 kcal/mol.
mol. More recently, a large number of papers have appeared concerning the water dimer. A variety of approaches21 were pursued in an attempt to saturate the 1-particle space, but in the absence of a systematic procedure, such as that which underlies the correlation consistent family of basis sets, this is a very difficult task. In a study which attempted to reach the basis set limit in ∆E to within 0.03 kcal/mol using relatively modest basis sets, Van Duijneveldt et al.22 obtained an MP2(FC) value of -4.71 kcal/mol and estimated the complete basis set full CI value to be -4.73 ( 0.1 kcal/mol. Using a large (spdf) basis, Kim et al.23 reported a CP-corrected MP2 binding energy of -4.66 kcal/mol (-4.99 kcal/mol without the CP correction). Chakravorty and Davidson24 reported MP2 and multireference configuration interaction (CI) binding energies which were similar to the values reported by Van Duijneveldt et al.22 and Kim et al.23 A large basis set nonlocal density functional calculation carried out by Kim and Jordan25 yielded a binding energy of -4.56 kcal/mol. Recent work by Wang et al.26 using a variety of extended basis sets augmented with bond functions produced a counterpoise-corrected value of -4.75 kcal/mol. However, Oliveira and Dykstra27 argued against the use of bond functions, noting that they significantly increase the BSSE, sometimes leading to a BSSE which was larger than the computed well depth. Most of the recent values of ∆E fall outside the error bars quoted by Feller. In order to improve upon his complete basis set MP2(FC) estimate, it is necessary to extend his calculations to larger basis sets in a computationally efficient manner. Since his 1992 study, the resolution of the identity MP2 (RI-MP2)28,29 method has been introduced as a convenient way to obtain results which closely resemble conventional MP2 results, but with far less computational effort. The RI-MP2 method rapidly converges to the conventional MP2 technique as the size of a fitting basis which is used by the new method approaches completeness. This allows one to evaluate MP2-like energies with basis sets as large as the aug-cc-pV5Z basis set in an acceptable period of time. This basis set is a [7s,6p,5d,4f,3g,2h/ 6s,5p,4d,3f,2g] contraction totaling 574 functions for the water dimer. Furthermore, new core/valence correlation consistent basis sets30 have been generated which allow us to evaluate the effect of core/valence correlation on the binding energy. Below we confirm the accuracy of the RI-MP2 method and use it to study the binding energy of the H2O dimer with and without the effect of core/valence correlation. Calculations All calculations were done with the program SUPERMOLECULE31 on Cray supercomputers. Unless otherwise stated, all calculations in the present study used a fixed MP2/6311++G(2d,2p) geometry, as reported by Frisch et al.,5 the same geometry used previously by Feller.19 The effects of ignoring geometry relaxation on ∆E are small. For example, using optimal MP2(FC)/aug-cc-pVQZ geometries7 for the water monomer and dimer increased the magnitude of the binding
energy by only 0.03 kcal/mol compared to the fixed geometry value. The basis sets employed in this study are the correlation consistent basis sets developed by Dunning and co-workers.17 These basis sets are denoted in the usual way as cc-pVxZ, where x ) D, T, Q, or 5. The corresponding basis sets which are augmented with an additional shell of diffuse functions are labeled as aug-cc-pVxZ.32 Core/valence calculations which included the oxygen 1s cores in the correlation treatment were performed with additional Gaussian primitives in the basis set. These primitives were taken from a preliminary version of the new cc-pCVxZ basis sets developed by Woon and Dunning.30 Although the exponents are not identical to the cc-pCVxZ exponents, they are quite similar. For example, the oxygen s exponent which we used has a value of 8.156 compared to the cc-pCVDZ s exponent of 8.215. In order to distinguish these basis sets from the final cc-pCVxZ sets, we shall label them cc-pCVxZ*. Details of the core/valence basis sets are given in the footnotes to Table 2. The calculations were performed with the spherical components of the Cartesian Gaussians, i.e. 5-term d’s; 7-term f’s, etc. The cc-pV5Z basis set is larger than any that has previously been used in calculations on the water dimer. All RI-MP2(FC) calculations in the present work were done with the BV-1B integral approximation described by Vahtras et al.29 These results differ slightly from the RI-MP2 results obtained by Feyereisen et al.,28 which used the integral approximation denoted AB in Vahtras et al.29 The BV-1B approximation has been systematically demonstrated to be superior to the AB approximation and is computationally simpler. The RI-MP2 fitting basis was taken to be the same 1-particle basis set used for expanding the orbitals. Previous results28 indicate that the error in the fitting basis set converges more rapidly than the error in the 1-particle basis. Basis set superposition error was estimated by the full Boys-Bernardi counterpoise correction.20 Results The total energies are shown in Table 2 for the water dimer, the water monomer, and the two water fragments computed in the full dimer basis set, beginning with the cc-pVDZ basis set. As noted before, the size of the fitting set used in the RI-MP2 technique is important. The larger the fitting set, the closer the RI-MP2 results approximate the conventional MP2 results. This effect can be clearly seen in Table 2, where the difference between RI-MP2(FC) and MP2(FC) energies drops from 0.0218 Eh with the cc-pVDZ basis to 0.0003 Eh with the cc-pVQZ basis. Moreover, as shown in Table 3, ∆E converges even faster, having a maximum error of only 0.0004Eh (0.25 kcal/mol). The fidelity with which the RI-MP2 method is able to reproduce conventional MP2 results justifies its use in determining the cc-pV5Z basis binding energy. In these calculations, the size of the fitting basis increases along with the size of the orbital expansion basis.
Hydrogen Bond Energy of the Water Dimer
J. Phys. Chem., Vol. 100, No. 8, 1996 2995
TABLE 2: Total Energies (hartrees) for Water and the Water Dimer method
H2O dimer
acceptora
donorb
H2O
RI-MP2(FC) MP2(FC)c RI-MP2(FC) MP2(FC)c RI-MP2(FC) MP2(FC)c RI-MP2(FC) RI-MP2(FC) MP2(FC)c RI-MP2(FC) MP2(FC)c RI-MP2(FC) MP2(FC) RI-MP2(FC) RI-MP2 MP2 MP4 RI-MP2
-152.490 34 -152.468 50 -152.650 83 -152.646 89 -152.704 26 -152.703 97 -152.725 53 -152.549 40 -152.529 75 -152.669 91 -152.666 05 -152.712 29 -152.711 85 -152.728 59 -152.611 92 -152.610 13 -152.639 55 -152.777 11
-76.239 80 -76.229 05 -76.321 06 -76.319 88 -76.348 09 -76.347 94 -76.358 83 -76.270 86 -76.261 17 -76.331 18 -76.329 27 -76.352 25
-76.243 77 -76.233 18 -76.322 68 -76.320 76 -76.348 71 -76.348 59 -76.359 04 -76.271 27 -76.261 69 -76.331 25 -76.329 39 -76.352 36
-76.306 09 -76.301 34 -76.316 05 -76.384 77
-76.306 53 -76.301 88 -76.316 66 -76.384 83
-76.239 16 -76.228 44 -76.320 57 -76.318 64 -76.347 77 -76.347 64 -76.358 71 -76.270 47 -76.260 76 -76.330 88 -76.328 96 -76.352 09 -76.351 91 -76.360 33 -76.305 64 -76.300 88 -76.315 55 -76.384 50
basis set cc-pVDZ cc-pVTZ cc-pVQZ cc-pV5Z aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z aug-cc-pCVDZ* d aug-cc-pCVTZ* e
a Proton acceptor computed in the full dimer basis set. b Proton donor computed in the full dimer basis set. c Feller, D. ref 18. d Oxygen core/ valence exponents are s ) 8.156 and p ) 27.841. These exponents were taken from a preliminary version of the cc-pCVDZ exponents. e Oxygen core/valence exponents are s ) 17.548 and 6.074, p ) 66.740 and 17.362, and d ) 38.3.
TABLE 3: Interaction Energies (kcal/mol) for the Water Dimer basis set cc-pVDZ cc-PVTZ cc-pVQZ cc-pV5Z aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z aug-cc-pCVDZ*
method
∆E
∆E(CP-corrected)
RI-MP2(FC) MP2(FC) RI-MP2(FC) MP2(FC) RI-MP2(FC) MP2(FC) SCF RI-MP2(FC) RI-MP2(FC) MP2(FC) RI-MP2(FC) MP2(FC) RI-MP2(FC) MP2(FC) RI-MP2(FC) RI-MP2(FC) RI-MP2 MP2 MP4 RI-MP2(FC) RI-MP2
-7.54 -7.29 -6.08 -6.03 -5.47 -5.45 -3.67 -5.09 -5.31 -5.16 -5.18 -5.10 -5.09 -5.03 -4.98 -5.33 -5.42 -5.25 -5.30 -5.04 -5.09
-4.25 -3.94 -4.45 -4.40 -4.68 -4.67 -3.57 -4.80 -4.56 -4.32 -4.69 -4.64 -4.82 -4.79a -4.57 -4.58 -4.34 -4.29 -4.69 -4.72
a Estimated from the CP correction for the aug-cc-pVQZ basis given in ref 18.
Figure 1. Convergence of the MP2(FC) and RI-MP2(FC) electronic binding energies as a function of the size of the basis set, with and without the counterpoise correction. The exponential form used to fit the data is E(x) ) ∆E∞(MP2/FC) + B* exp(-Cx), with x ) 1-4 for DZ through 5Z.
The MP2 and RI-MP2 binding energies are plotted in Figure 1 as a function of the size of the basis set. As noted previously,18 the binding energies computed without the presence of diffuse functions and without the CP correction show the largest dependence on the basis set and approach the limit from below, i.e. overestimate the limiting value. Both CPcorrected sequences (cc-pVxZ and aug-cc-pVxZ) approach the limit from above. The uncorrected binding energies for the basis sets containing diffuse functions show the smallest variation with basis set and approach from slightly below. A simple exponential of the form E(x) ) ∆E∞(MP2/FC) + B* exp(-Cx), with x ) 1-4 for cc-pVDZ through cc-pV5Z, was used to fit the data. ∆E∞ represents our estimate of the complete basis set limit. This empirical form has been used in a number of other studies as a means of extrapolating from limited data to the basis set limit.12-16,33 In selected cases the accuracy of the exponential extrapolation has been compared with fully numerical work on diatomics and with calculations including 1/rij in the wave function by Kutzelnigg and coworkers.34
Simultaneously fitting the cc-pVDZ through cc-pVQZ MP2(FC) binding energies and the cc-pV5Z RI-MP2(FC) value produced a value of ∆E∞(MP2) ) -4.77 kcal/mol (-4.97 kcal/ mol, CP-corrected). If the cc-pVDZ value was dropped, leaving only the three larger basis set values, ∆E∞(MP2/FC) ) -4.53 kcal/mol (-4.92 kcal/mol, CP-corrected). These estimates may be compared to the estimates obtained from the aug-cc-pVxZ sequence of binding energies, where ∆E∞(MP2/FC) ) -4.86 kcal/mol (-4.83 kcal/mol, CP-corrected). Because the raw augcc-pVxZ binding energies vary almost linearly over the four data points, only the three larger basis set values were fit to an exponential. It should be noted that all of the raw aug-cc-pVxZ binding energies are significantly better than the corresponding CP-corrected cc-pVxZ energies. Due to the much larger variation in binding energies being fit, the complete basis set estimate generated from the uncorrected cc-pVxZ energies was considered less reliable than the estimates resulting from the two CP-corrected sequences of points. The three most reliable complete basis set binding energies, as well as the RI-MP2(FC)/aug-cc-pV5Z value, fall in the range
aug-cc-pCVTZ*
2996 J. Phys. Chem., Vol. 100, No. 8, 1996 -5.0 to -4.8 kcal/mol. As noted before, geometry relaxation will increase the magnitude of the binding energy by approximately 0.03 kcal/mol. On the basis of these values we reconfirm the original estimate of the MP2(FC) binding energy limit, although the present analysis suggests that larger (i.e. more conservative) error bars are warranted than the (0.05 kcal/mol ones previously reported.18 Thus, our present best estimate of ∆E∞(MP2/FC) is -4.9 ( 0.1 kcal/mol. As will be discussed, it is likely that the actual binding energy will tend to be slightly higher as opposed to being lower. The enlarged error bars encompass most of the recently published values of ∆E at the low end of the range if you simultaneously assume the high end of the range quoted by other authors. The results of core/valence calculations performed with the aug-cc-pCVDZ* and aug-cc-pCVTZ* basis sets at the MP2, RI-MP2, and MP4 levels are shown in Table 3. Compared to the frozen core findings, the changes in the binding energies are -0.11 (DZ) and -0.05 (TZ) kcal/mol, both tending to increase the magnitude of the bond strength. If the counterpoise correction is added, the effect of core/valence correlation is reduced by a factor of 3-4. It should be noted here that the core/valence extensions to the original correlation consistent basis sets are the appropriate ones to use in correlated calculations without the frozen core restriction. In a recent paper on the water dimer, Kim et al.35 noted that “The correlationconsistent basis sets do not seem to give great energy lowering even at the MP2 level.” It appears from their Table I that the frozen core approximation was not invoked in obtaining their MP2 energies, although we could find no mention of this in the text. Thus, the reason for the relatively poor showing of the cc-pVxZ sets is that they were being used in calculations that correlated all electrons, even though they were only designed to recover valence correlation. By way of contrast, the cc-pCVDZ (28 functions) and cc-pCVTZ (71 functions) sets recover -0.242Eh and -0.318Eh of MP2 correlation energy, respectively. These values are larger than the correlation energies obtained from comparable-sized basis sets listed in Kim’s Table I. Table 3 also shows that, as was found in the earlier frozen core work, calculations beyond the MP2 level are unnecessary for an accurate treatment of the hydrogen bond. The aug-ccpCVDZ* MP4 binding energies differ by only 0.05 kcal/mol from the corresponding MP2 value, exactly matching what was observed with the FC calculations. The difference at the triple zeta-ζ level is even less. We are now able to use the results described above to estimate the binding energy of the water dimer. However, before we do so we consider other possible corrections. As mentioned earlier, the effect of changes in the geometry is small. Geometry relaxation increases the absolute value of the binding energy by 0.03 kcal/mol at the MP2(FC)/aug-cc-pVQZ level. Improvements in the correlation treatment should also play a minor role. We can estimate this effect from the QCISD(T) calculations of Feller at the aug-cc-pVTZ level. Here the correction is to increase the absolute magnitude of the binding energy by 0.06 kcal/mol (0.05 kcal/mol if BSSE is included). Core/valence correlation tends to increase the binding energy by 0.09 kcal/ mol at the best level that we considered. All of these results are in the same direction and would lead to an increase in the binding energy. The corrections would be on the order of 0.10.2 kcal/mol. Thus, our best estimate of the complete basis set electronic binding energy is -5.0 ( 0.1 kcal/mol. The present results can be compared to the findings of Wang et al.26 obtained with bond functions placed at the center of the O-O distance in the dimer. They employed basis sets
Feyereisen et al. comparable in size to the cc-pVTZ basis set of the monomers and then added sets of bond functions up to (3s,3p,2d,1f). The counterpoise correction was applied on the bond functions as well as the atom-centered functions. These authors found convergence to a limit of -4.75 kcal/mol at the MP2(FC) level, similar to but slightly smaller than our best values of -4.80 kcal/mol (cc-pV5Z, CP-corrected) and -5.03 kcal/mol (augcc-pVQZ, without CP correction). Our estimated complete basis set value is also slightly larger in absolute magnitude than their limit. The experimental result determined from the thermal conductivity of the vapor is a binding enthalpy. This is given as -3.59 kcal/mol with an estimated error of (0.5 kcal/mol. In order to compare to the experimental value, the calculated value of the total energy difference has to be corrected by the difference in zero-point energies as well as the thermodynamic correction for the change in temperature from 0 K to the temperature range in which the experimental measurements are made (358-386 K). We chose 375 K as a reasonable average. The calculated vibrational frequencies reported in the literature are harmonic values, and we need to include estimates of the anharmonic correction terms. First, we compared the calculated frequencies6 of the monomer to the experimental values.36 Average scale factors of 0.946 for the stretches and 0.983 for the bend were obtained. These scale factors were used for the monomer modes of the dimer. Initially, we did not vary the six intermolecular modes of the dimer. The value of the change in the zero-point energy is 2.12 kcal/mol, decreasing the magnitude of the binding energy. The temperature correction at this level is in the opposite direction and is -0.29 kcal/mol, leading to ∆H(375) ) -3.17 kcal/mol. This is just inside the experimental error limits. One possibility that must be considered is that the potential between the two monomers is quite anharmonic. In order to estimate the limits of this possibility, we used half the value of the four lowest intermolecular modes. This gave a zero-point correction of 1.67 kcal/mol and a thermodynamic correction of 0.10 kcal/mol. Combining this with the ∆E0 value gives a binding energy of -3.23 kcal/mol. Thus, the effect of anharmonic corrections in this simple statistical model is not large. In order to check the above model, we also calculated the entropy correction37 by using the calculated monomer and dimer geometries used in the energy calculations and the frequencies from ref 6 scaled as described above. The calculated value for S(H2O) at 298 K is 45.06 cal/mol K, and the experimental value for the ideal gas is 45.13 cal/(mol K).38 At 375 K, the calculated ∆S for the dimerization reaction is -19.85 (cal/(mol K) for the reaction forming the dimer from two monomers as compared to the experimental value of -18.59 ( 1.3 cal/(mol K).8 If one uses the alternate set of frequencies given above where the lowest four frequencies are halved, ∆S(375) is -14.41 cal/(mol k), clearly too small a value as compared to experiment.39 Thus, it is likely that there are no large scale anharmonic effects that we are missing in our temperature correction term. On the basis of all of the above results, we can conclude that the dimerization enthalpy for the water dimer near 375 K is -3.2 ( 0.1 kcal/mol. Although this value is within the experimental error limits of -3.6 ( 0.5 kcal/mol, our results suggest that the lower end of the experimental range is more likely than the upper end. Because of the importance of this energy difference as a benchmark, it would be useful to obtain other experimental measurements of the dimerization energy to calibrate the accuracy of the calculations. This becomes more important as one begins to consider possible dynamical effects on the temperature dependence of ∆H. It will be useful to adopt
Hydrogen Bond Energy of the Water Dimer our lower value of the binding energy of 5.0 ( 0.1 kcal/mol in empirical and semiempirical potentials9 to see if the agreement with experiment over a wider range can be improved. Acknowledgment. One of the authors (D.F.) was supported by the U.S. Department of Energy under Contract DE-AC0676RLO 1830 (Division of Chemical Sciences, Office of Basic Energy Sciences). The Pacific Northwest Laboratory is operated by Battelle Memorial Institute. References and Notes (1) Dyke, T. R.; Mack, K. M.; Muenter, J. S. J. Chem. Phys. 1977, 66, 498. (2) Odutola, J. A.; Dyke, T. R. J. Chem. Phys. 1980, 72, 5062. (3) Diercksen, G. H. F.; Kraemer, W. P.; Roos, B. O. Theor. Chim. Acta 1975, 36, 249. (4) Baum, J. O.; Finnery, J. L. Mol. Phys. 1985, 55, 1097. (5) Frisch, M. J.; Del Bene, J. E.; Binkley, J. S.; Schaefer, H. F., III. J. Chem. Phys. 1986, 84, 2279. (6) Xantheas, S. S.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 99, 8774. (7) Feller, D.; Glendening, E. D.; Kendall, R. A.; Peterson, K. A. J. Chem. Phys. 1994, 100, 4981. (8) Curtiss, L. A.; Frurip, D. J.; Blander, M. J. Chem. Phys. 1979, 71, 2703. (9) Reimers, J.; Watts, R.; Klein, M. Chem. Phys. 1982, 64, 95. (10) Scheiner, S. Annu. ReV. Phys. Chem. 1994, 45, 23. (11) Feller, D.; Davidson, E. R. Chem. ReV. 1986, 86, 681. Feller, D.; Davidson, E. R. Basis Sets for Ab Initio Molecular Orbital Calculations and Intermolecular Interactions. In ReViews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH: New York, 1990; pp 1-43. Almlof, J.; Taylor, P. R. AdV. Quantum Chem. 1991, 22, 301. (12) Woon, D. E.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 99, 1914. (13) Peterson, K. A.; Kendall, R. A.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 99, 1930. (14) Peterson, K. A.; Kendall, R. A.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 99, 9790. (15) Bauschlicher, C. W., Jr.; Partridge, H. J. Chem. Phys. 1994, 100, 4329. (16) Feller, D. J. Chem. Phys. 1993, 98, 7059. (17) See for example: Del Bene, J. E. Int. J. Quantum Chem., Symp. 1992, 26, 527. Del Bene, J. E.; Shavitt, I. THEOCHEM 1994, 307, 27.
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