Ab initio potentials for water

The number of potentials developed for the water dimer is probably larger than for any other system. However, most of these potentials are effective pair potentials fitted in simulations of liquid water or ice such that the results of these simulations match bulk measurements for the investigated systems. Thus, these potentials are of no help in investigations of nonadditive effects. There was a number of ab initio potentials for water published, the best known are those by dementi and coworkers [67,182]. More recently the ASP potentials of Millot et al. [183] have been very popular. However, only in the last few years it has become possible to develop interaction potentials accurate enough for investigations of nonadditive effects. 

Figure 3 Comparison of empirical and ab initio potentials for water trimer. SAPT 2B is pairwise additive SAPT potential while SAPT 2B + 3B includes the three-body nonadditivity. The remaining curves represent potentials from Refs. 173, 175, and 178...

The use of Wigner type correlation correction to Hartree-Fock energies [78] and/or the inclusion of dispersion forces [79] and/or the use of Cl energies [80] to define different potentials in Monte Carlo simulations of liquid water, underscores the problem on the reliability of ab initio potentials for force fields. Note that at the time the force fields were obtained only semi-empirically, but I was championing the ab initio banner. 

As mentioned above, we must start by calibrating the ion interaction parameters versus the free energy of hydration (see [20] for details). Without the calibration of these parameters in water, it would not be possible to make meaningful comparisons to experimental data. If one were to use, for example, ab initio potentials for the ion inter-actions without verifying that these reproduce the observed hydration energies, attempts to make quantitative comparisons to kinetic data would involve significant uncertainties. 

An ab initio potential for the methane-water bimolecular system has been developed for use in modeling methane hydrates and in order to evaluate currently used statistical thermodynamic models. In this paper, an introduction to gas hydrates is first given, and the problem with the Lennard-Jones and Devonshire (LJD) approximation, typically used for modeling hydrates, is described. Second, the methodologies for generating the ab initio potential energy surface are described and results discussed. Third,... 

Clementi, E., F. Cavallone, and R. Scordamaglia. 1977. Analytic Potentials from ab Initio Computations for the Interaction Between Biomolecules. 1. Water with Amino Acids. J. Am. Chem. Soc. 99, 5531-5545. 

Ragazzi, M., D. R. Ferro, and E. Clementi. 1979. Analytical Potentials from Ab Initio Computations for the Interaction Between Biomolecules. V. Formyl-triglycyl Amide and Water. J. Chem. Phys. 70, 1040-1050. 

In Table I we report the results on water trimer and in Fig. (6) the geometry adopted (dementi at al., 1980). A more complete work on this system will be presented later. The method has been applied to compute non additive effects, AR..JJ, for a variety of conformations of the trimer. The results have been used to generate a new ab-initio potential where many body effects were incorporated (Raimondi et al., 1997). 

As a second model potential we shall briefly discuss the PES for the water dimer. Analytical potentials developed from ab initio calculations have been available since the mid seventies, when Clementi and collaborators proposed their MCY potential [49], More recent calculations by dementi s group led to the development of the NCC surface, which also included many-body induction effects (see below) [50]. Both potentials were fitted to the total energy and therefore their individual energy components are not faithfully represented. For the purposes of the present discussion we will focus on another ab initio potential, which was designed primarily with the interaction energy components in mind by Millot and Stone [51]. This PES was obtained by applying the same philosophy as in the case of ArCC>2, i.e., both the template and calibration originate from the quantum chemical calculations, and are rooted in the perturbation theory of intermolecular forces. 

To exploit this ability of the perturbative approach, some ab initio potential have been constructed by a separate fit of the various terms, as in the NEMO [75,107,108] potentials for water, partly based on Morokuma [25] decomposition of the supermolecular interaction energy, or the ASP-Wn potentials [45,109,110]. 

Beside the empirical or semiempirical models described above, the need for inclusion of many-body effects, polarizability at least, in water-water potentials has also been recognized in the development of more recent ab initio potentials [45,75,103-108]. 

All ion-water potentials adopted in the simulations mentioned above are empirical or semi-empirical. In fact, the parameters of the non Coulomb interactions have been fixed either using formation enthalpy data of small clusters in gas phase [118,121,188] or ab initio calculations for the complex geometry [118,188,189] and the position of the first peak of the ion-oxygen 8(r). 

T. Komatsuzaki and I. Ohmine, Energetics of proton transfer in liquid water. I. Ab initio study for origin of many-body interactions and potential energy surfaces, Chem. Phys., 180 (1994) 239-269. 

Next, intermolecular potential functions are developed to describe the interactions between the reacting system and a solvent molecule. For aqueous solutions, the potential functions are based on numerous ab initio calculations for complexes of the substrate and a water molecule. The potentials vary with Tj and are represented in our work through Coulomb and Lennard-Jones interactions between sites normally coincident with the atoms. 

SAPT avoids the subtraction of large energy values that is necessarily part of a supermolecule ab initio calculation. A supermolecule calculation obtains the interaction energy of monomers A and B, AVab, as Tab - Va - Vb. whereas SAPT finds AVab directly. The interaction evaluated in SAPT is defined so as to be free of BSSE however, the other requirements on basis-set quality and for correlation effects still hold. SAPT has yielded highly accurate interaction data, first for rare gas atoms interacting with small molecules [72 74] and more recently with molecule molecule clusters such as the CO2 dimer [75]. Further examples are the very accurate results achieved for Ne HCN [76] and a parr potential for water [77]. Another example study of perturbative treatment of the interaction potential has been a study of rare gas HCN clusters [78] which included vibrational analysis. 

Whereas the equilibrium structure itself is pretty much agreed on for the water dimer, there are a number of other geometries that one might suppose should be comparable in energy. For example, the notion of a cyclic structure has been advanced over the years as have various types of bifurcated geometries. Smith et al. recently completed the most comprehensive survey of the ab initio potential energy surface of the water dimer to date. They examined the question of a number of possible minima on the surface and potential transition states that connect them. 

The leading nonadditive term in the many-body expansion of a potential is the three-body interaction. Similarly like dimers, trimers (and larger clusters) can be selectively studied by molecular beam spectroscopy. A number of such trimers have been the subjects of investigations. Among them are the Rg2-diatom trimers mentioned above, with the most extensive data available for Ar2-HF [64]. Both empirical [29,30] and ab initio [33] nonadditive potentials have been obtained for this system. A large number of spectral data are available also for the water trimer [65,66]. An accurate three-body potential for water has recently been developed [34]. 

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