J. Phys. Chem. 1994, 98, 13489-13497
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Structures and Energetics of F-(HzO)~,n = 1-3, Clusters from ab Initio Calculations Sotiris S. Xantheas" and Thom H. Dunning, Jr. Theory, Modeling and Simulation, Environmental Molecular Sciences Laboratory, Pacific Northwest Laboratory, Richland, Washington 99352 Received: June 14, 1994; In Final Form: September 27, 1994@ We have computed the optimal structures and harmonic vibrational frequencies of the F-(H20),, n = 1-3, clusters at the MP2 level of theory. For the n = 2 and 3 cases, the minimum-energy configurations correspond to asymmetric structures where the ion sits outside the water cluster. The electronic energy difference between these configurations and the symmetric ones, in which the ion is completely surrounded by water molecules is, however, very small (0.5- 1.5 kcaymol). When zero-point vibrational energy corrections are included, the energy difference becomes negligible and, in the n = 3 case, it is reversed making the symmetric structure favorable by 0.1 kcal/mol. It is therefore concluded that the dynamical effects in addition to the static features of the potential energy surface are important in determining the most probable orientation of the water molecules around the ion. The energy differences between the critical points were analyzed in terms of the relative magnitudes of the second- and higher-order interaction energy terms. We have found that electron correlation is very important in the computation of accurate energy differences and many-body interaction energy terms, especially for the n = 2 and 3 cases.
fluoride ion is bonded to water via one of its end hydrogens. Clementi and co-workers4 and Janoschek9 have computed An understanding of the water-water and ion-water interacextensive regions of the potential energy surface corresponding tion at the molecular level is the cornerstone in the development to the interaction between F- and water at the HF level of and parametrization of interaction potentials for modeling ionic theory. The optimal structure of the n = 2 cluster has been solvation processes. Although energetic trends for the succesreported, to date, only at the HF level of theory.2J2 Ab initio sive addition of water molecules to halide negative ions have results on larger clusters have been reported either at symmetry been measured the structures of these clusters restricted configurations at the HF level of theory with minimal can only, to date, be modeled via ab initio or molecular basis sets" or at fixed geometries using semiempirical methdynamics simulations based on interaction potentials. The ods.1° Clementi and co-worker$ have used HF based two-body former provides information about the static properties of the ion-water and water-water pairwise additive interaction potential energy surface (PES), while the latter explores its dynamical features. The static features of the PES consist of potentials to optimize the structures for the F-(H20),, n = 1-10 the various stationary points such as local and global minima, clusters. They found that symmetrical configurations were the transition states, and maxima. The actual orientation of the lowest in energy for the n 55 clusters, whereas for larger values water molecules around an ion at some finite temperature is, of n some of the water molecules tend to form a second shell however, statistically determined by dynamically sampling the of solvated water around the ion. The use of a pairwise additive PES around the various minima. The area over which the potential neglects nonadditive effects arising, to fist order, from sampling occurs is determined by the features of the PES: the the interaction of the ion with two water molecules as well as flatter the surface, the more extended the sampling away from between three water molecules. Kollman6 reported F-(H20)2 the minimum. Nevertheless, the theoretical predictions of the nonadditivities to be large, although nearly independent of the optimal structures and vibrational frequencies of the ion-water 0-F-0 angle at the HF level of theory. The neglect of clusters are of particular importance as they provide a measure nonadditivities due to water-water-water interaction is exof the various intermolecular interactions and cooperative effects pected to introduce an even smaller error. We have recently which have their maximum magnitudes for the first few cluster estimated" an upper limit for this effect at 20% of the total configurations. Furthermore, theoretical prediction of the interaction energy for the cyclic water trimer geometry at the vibrational spectra of these species is of particular importance, MP4 level of theory. since the application of standard experimental techniques, such The optimal geometry of the n = 2 cluster has been reported as infrared spectroscopy, is difficult for these systems due to the very low ion densities of ionic clusters that can currently at the HF level of theory with the 4-3 1G (ref 11) and the 6-3 lG, be ~ b t a i n e d . ~ 6-31G*, and 6-31G** basis sets (ref 12). In a previous study1* The interaction between F- and water has been previously we have reported the optimal structures of the H-(H20),, (n = studied by using both experimenta11q2and ab initio4-16 tech1-3) clusters. These results suggested a substantial degree of niques. The structure and binding energy of the n = 1 cluster hydrogen bonding between the water molecules which cluster have been reported at the Hartree-Fock (HF),2,4,6-9,11,13,14,16 on one side of the ion. We have subsequently explored the complete active space (CASSCF),15 singles and doubles contheoretical requirements needed to describe hydrogen bonding figuration interaction (CISD),l5 and second-order perturbation in cyclic water clusters up to the h e ~ a m e rand ~ ~analyzed , ~ ~ the theory (MP2)12 levels of theory. All previous calculations and magtrends in the structure^,^^ vibrational frequen~ies,'~ suggested a non-linear hydrogen-bonded structure in which the nitudes of the many-body energy terms17 with cluster size for these cyclic geometries. Our results indicated that HF severely * Author to whom correspondence should be addressed. underestimates binding energies and produces larger nearestAbstract published in Advance ACS Abstracrs, November 15, 1994.
I. Introduction
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0022-365419412098- 13489$04.50/0
0 1994 American Chemical Society
13490 J. Phys. Chem., Vol. 98, No. 51, 1994 neighbor 0-0 separations for cyclic water clusters. It was therefore suggested that electron correlation is necessary in order to describe the essential structural and energetic features of hydrogen-bonded water clusters. We first reported the unusual asymmetric structures for the F-(H20), (n = 1-3) clusters at the MP2 level of theory in ref 21. In this study we will present the optimal structures, vibrational frequencies, and stationary points of interest on the ground-state potential energy surfaces of the F-(H20), (n = 1-3) clusters. In section 11 we will outline the computational details as regards methods and basis sets. In section I11 we will present the optimized geometries, energetics, and vibrational frequencies of the minima and transition states for the n = 1-3 clusters and outline the structural and energetic trends with cluster size. Final conclusions will be drawn in section IV.
Xantheas and Dunning F H2
Ob H2b
n=l
n=2 F
F
11. Methods and Basis Sets
We used the augmented correlation-consistent polarized valence basis sets22of double-(aug-cc-pVDZ) and triple-5 (augcc-pVTZ) quality. Only the spherical components of the polarization functions were used (five component d's, seven component f's). The total number of basis functions are 23 and 46 for F and 41 and 92 per water molecule for the augmented double- and triple-5 basis sets, respectively. The aug-cc-pVDZ basis set was chosen as a compromise between feasibility and accuracy in earlier benchmark studies of water cluster^.^^^^^,^^ It has been shown to produce accurate results for the structure, vibrational frequencies, dipole moment, and polarizability of the water monomer as well as results of comparable accuracy for the structure, harmonic vibrational frequencies, and binding energy of the water dimer at the MP2 level of theory.20 Furthermore the water dimer MWaug-ccpVDZ optimal geometry with the experimental anharmonic corrections for the 0-0 bond yielded rotational constant^'^ for the mixed isotopic species DxH4-x02 to within
