Intermolecular potential, effect 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. 

The discrepancy between the calculated and observed values (in Table X) may be partly due to the zero-point energy and partly due to nonadditivity of the intermolecular potential. In fact, according to calculations by Kihara and Koba, the zero-point energy is about 0.48 kcal/mol and the effect of nonadditivity is about 0.23 kcal/mol. These two effects slightly increase the nearest-neighbor distance d. 

The second and third virial coefficients in the equation of state of rare gases calculated by the use of Eq. (49) with s = 12 agree with observed values when the nonadditivity of the intermolecular potential is taken into account. If we assume additivity, on the other hand, then we must use an effective intermolecular potential with a wider bowl in order to explain the temperature dependence of the third virial coefficient.In other words, the influence of nonadditivity of the intermolecular potential can, to some extent, be eliminated by using an effective (additive) intermolecular potential with a wider bowl. An appropriate choice seems to be not far from Eq. (50) with a = 8.675, for which the two structures of close packing have exactly equal cohesive energies. 

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. 

Strictly taken, a prerequisite for the discussion of cooperativity or nonadditivity requires the definition of the additive or noncooperative case [50]. Generally, in the field of intermolecular interaction, the additive model is a model based on the concept of pairwise additive interactions. For atomic clusters per definition, but also for molecular clusters, the use of pairwise additive interactions is almost always used in combination with the assumption of structurally frozen interaction partners. Even in cases of much stronger intermolecular interactions the concept of pair potentials modified to that of effective pair potentials is often used. Most of the molecular dynamics calculations of liquids and molecular solids take advantage of this concept. 

The assumption of a strict, vapor-phase derived pair potential appears acceptable only in those cases where a weak intermolecular interaction does not cause appreciable structural relaxations in the monomers. In the case of hydrogen-bonded systems, the use of the frozen monomer assumption precludes, however, almost always the investigation of all the observable structural and spectroscopic features of the A—H moiety. Therefore, the reference system for the discussion of cooperative, nonadditive effects is exclusively the structurally fully optimized hydrogen-bonded dimer with a single isolated hydrogen bond and with all the properties derivable from the global 3N-6 dimensional potential energy surface of the dimer. 

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