Water three-body potentials

So far, this method has been successfully applied to the development of effective potentials for a series of cations in water [129-132]. In this case, the radius of the spherical cavity that encloses the cation has been fixed so that the three-body potential for the complex cation-two water molecules given by the PCM, can be decomposed into the sum of two-body potentials, also obtained with the PCM... 

At the same time, the first empirical trimer potentials fitted to spectroscopic data were developed by Ernesti and Hutson [29,30]. Einally, recently it was possible to develop a three-body potential for the water [34]. Some of this work will be discussed in more detail later on. 

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]. 

Attempts to represent the three-body interactions for water in terms of an analytic function fitted to ab initio results date back to the work of dementi and Corongiu [191] and Niesar et al. [67]. These authors used about 200 three-body energies computed at the Hartree-Fock level and fitted them to parametrize a simple polarization model in which induced dipoles were generated on each molecule by the electrostatic field of other molecules. Thus, the induction effects were distorted in order to describe the exchange effects. The three-body potentials obtained in this way and their many-body polarization extensions have been used in simulations of liquid water. We know now that the two-body potentials used in that work were insufficiently accurate for a meaningful evaluation of the role of three-body effects. 

The three-body potential computed earlier on a grid of 568 geometries, at the same level as the data used in the fit discussed above, was utilized in Ref. [31] in a three-dimensional calculation of the vibrational spectmm of the water trimer. Here again,... 

In our simulations we used the empirical force fields for the interaction among ions of HAP reported earlier [90, 91]. Two-body ionic short-range interaction potential of the Buckingham type and Coulombic interaction term were adopted. A Morse potential was adopted for both O-H and P-O bond interactions. The harmmiic three-body potential was used to describe the tetrahedral configuration of oxygen ions around phosphorus. The force fields describe the structures and the mechanical properties of HAP reasonably well, and show excellent agreement with the experimental data. For the interactions between water molecides and ions of HAP, we adopted the same approach as in the previous study [92]. 

In a truly remarkable application on water, Bukowski et al. (2006) derived a SAPT(DFT) two-body potential, together with a three-body potential from SAPT (Mas et al. 2003a, b)... 

E. M. Mas, R. Bukowski, and K. Szalewicz, Ab initio three body interactions for water. I. Potential and structure of water trimer. J. Chem. Phys. 118, 4386 4403 (2003). 

Water Potentials. The ST2 (23), MCY (24), and CF (2J5) potentials are computationally tractable and accurate models for two-body water-water interaction potentials. The ST2, MCY and CF models have five, four, and three interaction sites and have four, three and three charge centers, respectively. Neither the ST2 nor the MCY potentials allow OH or HH distances to vary, whereas bond lengths are flexible with the CF model. While both the ST2 and CF potentials are empirical models, the MCY potential is derived from ab initio configuration interaction molecular orbital methods (24) using many geometrical arrangements of water dimers. The MCY+CC+DC water-water potential (28) is a recent modification of the MCY potential which allows four body interactions to be evaluated. In comparison to the two-body potentials described above, the MCY+CC+DC potential requires a supercomputer or array processor in order to be computationally feasible. Therefore, the ST2, MCY and CF potentials are generally more economical to use than the MCY+CC+DC potential. 

If two-body potentials and the three-body contribution of Li+(H20)2 are taken into account the optimum coordination number for a static Li+(H20)n complex turns out to be 4. For the most stable conformation of Li+(H20)6 they found that two water molecules are bound in a second, outer hydration layer. 

In this section we present some results obtained with the SAPT code for three-body interactions, SAPT3 371. Routine applications of SAPT to three-body interactions are relatively scarce. Here we concentrate on the water clusters with a special emphasis on the simulations of the liquid water properties starting from ab initio SAPT potentials for pair and three-body interactions and on clusters of water with hydrogen chloride in the context of protolytic dissociation of HC1 in small water clusters. Other applications of SAPT to, e.g. Ar2-HF trimer can be found in Ref. (313). 

Simulations of the liquid water properties have been the subject of many papers, see Ref. (374) for a review. Recently a two-body potential for the water dimer was computed by SAPT(DFT)375. Its accuracy was checked375 by comparison with the experimental second virial coefficients at various temperatures. As shown on Figure 1-16, the agreement between the theory and experiment is excellent. Given an accurate pair potential, and three-body terms computed by SAPT376, simulations of the radial 0-0, 0-H, and H-H distribution functions could be... 

Yoon BJ, Morokuma K, Davidson ER (1985) Structure of ice Ih. Ab-initio two and three-body water-water potentials and geometry optimization. J Chem Phys 83 1223-1231... 

Realistic three-dimensional computer models for water were proposed already more than 30 years ago (16). However, even relatively simple effective water model potentials based on point charges and Leimard-Jones interactions are still very expensive computationally. Significant progress with respect to the models ability to describe water s thermodynamic, structural, and dynamic features accurately has been achieved recently (101-103). However, early studies have shown that water models essentially capture the effects of hydrophobic hydration and interaction on a near quantitative level (81, 82, 104). Recent simulations suggest that the exact size of the solvation entropy of hydrophobic particles is related to the ability of the water models to account for water s thermodynamic anomalous behavior (105-108). Because the hydrophobic interaction is inherently a multibody interaction (105), it has been suggested to compute pair- and higher-order contributions from realistic computer simulations. However, currently it is inconclusive whether three-body effects are cooperative or anticooperative (109). 

Most of the potential energy surfaces reviewed so far have been based on effective pair potentials. It is assumed that the parameterization is such as to account for nonadditive interactions, but in a nonexplicit way. A simple example is the use of a charge distribution with a dipole moment of 2.ID in the ST2 model. However, it is well known that there are significant non-pairwise additive interactions in liquid water and several attempts have been made to include them explicitly in simulations. Nonadditivity can arise in several ways. We have already discussed induced dipole interactions, which are a consequence of the permanent diple moment and polarizability of the molecules. A second type of nonadditive interaction arises from the deformation of the molecules in a condensed phase. Some contributions from such terms are implicitly included in calculations based on flexible molecule potentials. Other contributions arises from electron correlation, exchange, and similar effects. A good example is the Axilrod-Teller three-body dispersion interaction ... 

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