Intermolecular pair potential

One consequence of using the pairwise additive approximation is that if a true pair potential is used to calculate the properties of a liquid or solid, there will be an error due to the omission of the nonadditive contributions. Conversely, if the pairwise additive approximation is made in deriving the pair potential U b, the latter will have partially absorbed some form of average over the many-body forces present, producing an error in the calculated properties of the gas phase where only two-body interactions are important. Because the effective pair potential Uab cannot correctly model the orientation and distance dependence of the absorbed nonadditive contributions, there will also be errors in transferring the effective potential to other condensed phases with different arrangements of molecules. 

All the important contributions to the forces between molecules arise ultimately from the electrostatic interactions between the particles that make up the two molecules. Thus our main theoretical insight into the nature of intermolecular forces comes from perturbation theory, using these interactions as the perturbation operator H = Z e, /(4jtSor/y), where is the charge on particle i in one molecule, is the distance between particles i and / in different molecules, and 8q is permittivity of a vacuum. The definitions of the contributions, such as the repulsion, dispersion, and electrostatic terms, which are normally included in model potentials, correspond to different terms in the perturbation series expansion. 

Contribution Additive Sign Comment Form in Model U,y  

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Price S L and Stone A J 1980 Evaluation of anisotropic model intermolecular pair potentials using an ab initio SCF-CI surface Moi. Phys. 40 805... 

In the study of reactivity, Jorgensen and col. have normally used both, the OPLS model and potential functions derived from ab initio calculations. As we have already indicated, when intermolecular pair potentials are applied to the study of a chemical process, the evolution of charges, as well as the Lennard-Jones terms, along the reaction coordinate, has to be considered. For the SN2 reaction in water between chloride anion... 

One of the most important developments in the theory of water is the invention of a realistic effective intermolecular pair potential. Although others had made similar suggestions earlier 59>, it is Stillinger and co-workers 60> who have shown, with the aid of molecular dynamics calculations 3>, how satisfactory such a potential can be. The availability of a water-water potential drastically reduces the scope for parameterization in model based theories, and permits investigation of such concepts as "broken hydrogen bond. We shall frequently have occasion to call upon its properties in the following discussion. 

The virial coefficients B(T), C(T), D(T),... are functions of temperature only. Although these coefficients might be treated simply as empirical fitting parameters, they are actually deeply connected to the theory of intermolecular clustering, as developed by J. E. Mayer (Sidebar 13.5). More specifically, the second virial coefficient B(T) is related to the intermolecular potential for pairs of molecules, the third virial coefficient C(T) to that for triples of molecules, and so forth. For example, knowledge of the intermolecular pair potential V(R) (see Sidebar 2.8) allows B T) to be explicitly evaluated by statistical mechanical methods as... 

The details of the pair potential used in the simulations are given in Table I. This consists of an -trans model of the sec-butyl chloride molecule with six moieties. The intermolecular pair potential is then built up with 36 site-site terms per molecular pair. Each site-site term is compost of two parts Lennard-Jones and charge-charge. In this way, chiral discrimination is built in to the potential in a natural way. The phase-space average R-R (or S-S) potential is different from the equivalent in R-S interactions. The algorithm transforms this into dynamical time-correlation functions. 

E.B. Smith, The intermolecular pair-potential energy functions of the inert gases, Physica, 73 (1974) 211-225. 

Molar or specific internal energy Intermolecular pair-potential function Velocity... 

The intermolecular pair potential U(R, Q) is defined as the difference between the energy of a pair of molecules (at a given separation R and relative orientation Q) and their energy when completely separated that is, U R, Cl) = E(R, Cl) - (co). The pair potential is used to describe the weak interactions between closed-shell molecules, so that the effect of the interaction on the charge distributions of the individual molecules is very small and does not... 

Table 3 Anisotropic Atom—Atom Models for the Intermolecular Pair Potential, Which Can Be Quantified Using Ab Initio Monomer Properties, and Lead References... 

Corresponding States (CS) The principle of CS applies to conformal fluids [Lehmd, T. L., Jr., and P. S. Chappelear, Ind. Eng. Chem., 60 (1968) 15]. Two fluids are conformal if their intermolecu-lar interactions are equivalent when scaled in dimensionless form. For example, the Lennard-Jones (LJ) intermolecular pair potential energy U can be written in dimensionless form as... 

A variety of approaches have been used in the development of models for the interactions between nonspherical molecules, reflecting both the complexity of such interactions and the paucity of truly accurate quantitative information about them that could be used to assess the suitability of different models. Perhaps the most widely studied approach, especially over the last decade or so, is the interaction site formalism, in which the intermolecular pair potential is written as a sum of potentials between interaction sites on each molecule. We have... 

Total intermolecular pair potentials, Mie and Lennard-Jones potentials... 

It is possible to obtain the total intermolecular pair potential by simply summing the attractive and repulsive potentials. In 1903, Mie proposed a semi-empirical interaction pair potential in the form... 

Application of total intermolecular pair potentials in a liquid medium... 

In condensed phases such as liquids, two molecules are not isolated but have many other molecules in their vicinity. If these two molecules are dissolved in another solvent medium then the situation may be very complicated, and only by introducing simplifying assumptions is it possible to construct a simple theory of dense media and a solution using Lennard-Jones or similar total intermolecular pair potentials. Some important facts, which should be taken into account before applying any simplifying assumptions, are given below ... 

Cohesive chemical potential, or cohesive self-energy, ficoh is defined as the free energy of an individual gas or liquid molecule surrounded by the same molecules. This is not an intermolecular pair potential term itself, however it may be calculated from pair potentials by summing this molecule s interactions with all the surrounding molecules. Since we know that the intermolecular forces are not to extend over large distances but only interact with molecules in close proximity for gases, then, similar to the derivation of Equations (19) and (20), the pair potential for a molecule in the gas phase is given as... 

The presence of solvent molecules between solute molecules affects all the interaction energies. We have seen that the presence of solvent molecules changes the molecular polarizabilities of solutes in Section 2.5.3 and decreases the strength of van der Waals interactions (Section 2.6.4) and the total intermolecular pair potential energies (Section 2.7.4). When two molecules interact in a condensed liquid medium, there are many solvent molecules interfering in this interaction. Now, this becomes a many-body interaction and we have to consider some important new effects ... 

A primary aim of theoretical work in this field is to obtain the phenomenological transport coefficients in terms of molecular scale processes and in terms of molecular parameters such as the intermolecular pair potential energy. Most of the work prior to 1946 rested on rather crude pictures of the liquid state, and various arbitrary assumptions were made as to the nature of the molecular scale transport processes taking place. Born and Green 3 20 21 and... 

In the case of interacting molecules with distances short enough for the electronic shells to overlap, Mie (1903) suggested a relationship with an empirical constant and a certain decay law of high power against distance. Later, on the basis of Mie s equation and the van der Waals law h" Lennard-Jones (1936) derived an intermolecular pair potential... 

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