Potential nonadditivity

The intermolecular potential in gases is usually assumed to be additive. It has been pointed out, however, that the effect of potential nonadditivity on the equation of state of gases does not seem to be negligible (Kihara9). The simplest system for which the nonadditivity of the intermolecular potential plays a role is the system composed of three spherically symmetric atoms, which will be treated in Sectiqn I. The aim of Sections I. A and I. B is to investigate quantum-mechanically the van der Waals interaction between three distant atoms. By use of the results, a model of nonadditive potential is introduced in Section I. C, which model will be applied, in Part II, to the equation of state of gases. 

As regards the classical third cluster integral, 3(0) given by Eq. 11.19, let us expand it into a series in v, the measure of the potential nonadditivity,... 

A nitrogen molecule has an electric quadrupole Q = 1.29 x 10 26 e.s.u. which contributes —0.30 kcal/mol to the interaction energy. The sum of the zero-point energy and the effect of potential nonadditivity is about 0.6 kcal/mol.)... 

The intennolecular forces between water molecules are strongly non-additive. It is not realistic to expect any pair potential to reproduce the properties of both the water dimer and the larger clusters, let alone liquid water. There has therefore been a great deal of work on developing potential models with explicit pairwise-additive and nonadditive parts [44, 50, 51]. It appears that, when this is done, the energy of the larger clusters and ice has a nonadditive contribution of about 30%. 

Caldwell J, Dang LX, Kollman PA (1990) Implementation of nonadditive intermolecular potentials by use of molecular-dynamics - development of a water water potential and water ion cluster interactions. J Am Chem Soc 112(25) 9144—9147... 

Saint-Martin H, Medina-Llanos C, Ortega-Blake I (1990) Nonadditivity in an analytical intermolec-ular potential - the water-water interaction. J Chem Phys 93(9) 6448-6452... 

Valdez-Gonzales M, Sanit-Martin H, Hernandez-Cobos J, Ayala R, Sanchez-Marcos E, Ortega-Blake I (2007) Liquid methanol Monte Carlo simulations with a refined potential which includes polarizability, nonadditivity, and intramolecular relaxation. J Chem Phys 127(22) 224507... 

Patel S, Brooks CL (2006) Revisiting the hexane-water interface via molecular dynamics simulations using nonadditive alkane-water potentials. J Chem Phys 124(20) 204706... 

Calculations of forces may be improved in several ways. One is to pursue efforts towards the development of accurate classical, atomic-level force fields. A promising extension along these lines is to add nonadditive polarization effects to the usual pairwise additive description of interatomic interactions. This has been attempted in the past [35-39], but has not brought the expected and long-awaited improvements. This is not so much because polarization effects are not important, or pairwise additive models can account for them accurately in an average sense in all, even highly anisotropic environments. Instead, it seems more likely that the previously developed nonadditive potentials were not sufficiently accurate to offer an enhanced description of those systems in which induction phenomena play a crucial role. 

As it will be explained in section 6, the usual way to evaluate the potential energy of a system simulated by Monte Carlo techniques, makes use of the pair potential approximation (although, as it will also be reviewed, several works have already appeared where nonadditivity corrections to the interaction potential have been included). In the pair potential approximation only two body interactions are taken into account. We will briefly explain here how to apply this approximation for the calculation of the potential energy, to the periodic system just described. The interaction potential energy under the pair potential approximation can be written as ... 

Role of electron correlation in nonadditive forces and ab initio model potentials for small metal clusters... 

Abstract. The physical nature of nonadditivity in many-particle systems and the methods of calculations of many-body forces are discussed. The special attention is devoted to the electron correlation contributions to many-body forces and their role in the Be r and Li r cluster formation. The procedure is described for founding a model potential for metal clusters with parameters fitted to ab initio energetic surfaces. The proposed potential comprises two-body, three-body, and four body interation energies each one consisting of exchange and dispersion terms. Such kind of ab initio model potentials can be used in the molecular dynamics simulation studies and in the cinalysis of binding in small metal clusters. 

There are many empirical and semi-empirical pair potentials which describe quite satisfactorily the properties of liquids and solids, see chapter 5 in book The parameters in these potentials are not real parameters of a true two-body interaction, their values depend upon properties of a medium. So these effective two-body potentials include nonadditive interactions through their parameters. The latter can not be directly related to the definite physical... 

Studies of larger species are more complex and the difficulty in the evaluation of their potential surfaces increases with their size. Up to now accurate potentials have been obtained by inversion of spectroscopic data or through high level ab initio calculations " for several triatomic vdW systems. Thus, the interactions for such clusters are available with satisfactory accuracy, which permits the testing of various models of nonadditivity for their ability to reproduce a number of experimental observations. These facts made complexes composed of two rare-gas atoms and a dihalogen molecule especially attractive targets for the study of nonadditive forces. The first attempt to extract information on nonadditive interactions from... 

In the field of intermolecular forces a book has been published by Kaplan241 which provides a coverage of the theory from long-range forces (including retardation effects) to short-range forces and nonadditivity. The determination of molecular potentials from experimental data is also considered in one chapter of this book. 

Dang, L.X., Development of nonadditive intermolecular potentials using molecular-dynamics -solvation ofLi+ and F- ions in polarizable water. J. Chem.Phys. (1992) 96 6970-6977. 

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