Deriving Model Intermolecular Potentials

the usual approach to deriving intermolecular potentials from experimental data is to choose a functional form for the model potential, for example, the Lennard-Jones 12-6 potential  

In this multiparameter form, the exponential term is multiplied by a fifth-order polynomial with coefficients A to give a sufficiently accurate representation of the overlap contributions. The sum over / provides the Q, Cg, and Cio terms in the dispersion series. The modification of the dispersion, due to overlap, is absorbed into the approximately exponential short-range repulsion term, with the minor parameter 8 = 0.01 used just to prevent a nonphysical maximum in 

The usual model intermolecular potential for organic molecules is based on the assumption that the interaction between the molecules is the sum of the interactions between their constituent atoms. For example, the interaction energy between molecules M and N can be given by 

Another common approach to reduce the number of parameters is to assume some form of combining rules, so that the hetero-interaction parameters are given by homo-parameters  

Although these model potentials are adequate for many modeling studies, the limitations imposed by their empirical nature, assumptions of transfer-ability, and limited functional form mean that they may be inadequate for some simulations outside the range of interpolation between the data used in their validation. Hence, we need to develop more accurate models, learning from the lessons of small-molecule potentials. 

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Mitchell JBO, Price SL (2000) A systematic nonempirical method of deriving model intermolecular potentials for organic molecules application to amides. J Phys Chem A 104 10958-10971... 

Orowan (1949) suggested a method for estimating the theoretical tensile fracture strength based on a simple model for the intermolecular potential of a solid. These calculations indicate that the theoretical tensile strength of solids is an appreciable fraction of the elastic modulus of the material. Following these ideas, a theoretical spall strength of Bq/ti, where Bq is the bulk modulus of the material, is derived through an application of the Orowan approach based on a sinusoidal representation of the cohesive force (Lawn and Wilshaw, 1975). 

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... 

Hope et al. (116) presented a combined volumetric sorption and theoretical study of the sorption of Kr in silicalite. The theoretical calculation was based on a potential model related to that of Sanders et al. (117), which includes electrostatic terms and a simple bond-bending formalism for the portion of the framework (120 atoms) that is allowed to relax during the simulations. In contrast to the potential developed by Sanders et al., these calculations employed hard, unpolarizable oxygen ions. Polarizability was, however, included in the description of the Kr atoms. Intermolecular potential terms accounting for the interaction of Kr atoms with the zeolite oxygen atoms were derived from fitting experimental results characterizing the interatomic potentials of rare gas mixtures. In contrast to the situation for hydrocarbons, there are few direct empirical data to aid parameterization, but the use of Ne-Kr potentials is reasonable, because Ne is isoelectronic with O2-. 

There are presently two main difficulties which handicap attempts at exact calculation. The first concerns the intermolecular potential, and the hazards of extrapolation from models derived from viscosity measurements have been discussed. Furthermore, such a method is of dubious validity for polyatomic molecules, because the intermolecular repulsive potential will generally appear to become progressively shallower with increasing molecular dimensions if the viscosity data are cast, for example, in the Lennard-Jones form. Energy transfer depends... 

Carbon tetrafluoride. Carbon tetra-fluoride, which undergoes a transition to a plastically crystalline (orientationally disordered) phase, has been investigated by the Parrinello-Rahman molecular dynamics method under constant-pressure conditions (6). A simple intermolecular potential model of the Lennard-Jones form was derived by taking into account the experimen-... 

In atom-atom potentials the anisotropy of the intermolecular potential, i.e., its dependence on the molecular orientations atom-atom potential in the form (15). It has been demonstrated by Sack (1964), Yasuda and Yamamoto (1971), and Downs et al. (1979) that analytic expressions can be derived for the expansion coefficients v rPP ) in (15) for atom-atom potentials (see Section II,A) with fM(rafi) = r dependence and by Briels (1980) that they can be derived for atom-atom interactions with exponential dependence... 

Xantheas and co-workers [159,160] have incorporated polarization in a model scheme and have used that to provide a clear basis for the enhancement of water s dipole in ice. A model potential with polarization has been reported for the formaldehyde dimer [161]. It is an example of a carefully crafted potential, which is system-specific because of its application to pure liquid formaldehyde, but which has terms associated with properties and interaction elements as in the above models. As well, some of the earliest rigid-body DQMC work, which was by Sandler et al. [162] on the nitrogen-water cluster, used a potential expressed in terms of interaction elements derived from ab initio calculations with adjustment (morphing). Stone and co-workers have developed interaction potentials for HF clusters [163], water [164], and the CO dimer [165], which involve monomer electrical properties and terms derived from intermolecular perturbation theory treatment. SAPT has been used for constructing potentials that have enabled simulations of molecules in supercritical carbon dioxide [166]. There are, therefore, quite a number of models being put forth wherein electrical analysis and/or properties of the constituents play an essential role, and some where electrical analysis is used to understand property changes as well as the interaction energetics. 

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