Intermolecular potential force center

Fig. 2-1 Models of intermolecular potentials, (a) Forceless mass points (b) elastic hard spheres (c) elastic hard spheres with superposed central attractive forces (d) molecules with central finite repulsive and attractive forces (e) square-well model (f) point centers of inverse-power repulsion or attraction.

The reason that atom-atom potentials are so popular, especially in the study of condensed phases [34] and more complex Van der Waals molecules [35], is that they contain few parameters and can be cheaply calculated, while they still describe (implicitly) the anisotropy of the intermolecular potential and they even model its dependence on the internal molecular coordinates. Moreover, they are often believed to be transferable, which implies that the same atom-atom interaction parameters in Eq. (6) can be used for the same types of atoms in different molecules. One should realize, however, that the accuracy of atom-atom potentials is limited by Eq. (5). Further inaccuracies are introduced when the atom-atom interaction parameters in Eq. (6) are transferred from one molecular environment to another. Furthermore, Eq. (6) does not include a term which represents the induction interactions and there is the intrinsic problem that these interactions are inherently not pairwise additive (see Sect. 1.4). Numerical experimentation on the C2H4-C2H4 and N2-N2 potentials, for example, has taught us [31, 33] that even when sufficient ab initio data are available, so that the terms in Eq. (6) can be fitted individually to the corresponding ab initio contributions and, moreover, the positions of the force centers for each term can be optimized, the average error in the best fit of each contribution still remains about 10%. Since the different contributions to the potential partly cancel each other... 

TABLE 10.2 Contributions from attractive forces to the total intermolecular potential energy of selected molecules, calculated at the equilibrium center of mass separation. 

If the molecules are not small and spherical, the force field around them is not spherical either and, consequently, the distance between the centers of the molecules is not sufficient to describe the intermolecular potential. A third, at least, parameter - such as the acentric factor - is required for this purpose. 

Other flexible molecular models of nitromethane were developed by Politzer et al. [131,132]. In these, parameters for classical force fields that describe intramolecular and intermolecular motion are adjusted at intervals during a condensed phase molecular dynamics simulation until experimental properties are reproduced. In their first study, these authors used quantum-mechanically calculated force constants for an isolated nitromethane molecule for the intramolecular interaction terms. Coulombic interactions were treated using partial charges centered on the nuclei of the atoms, and determined from fitting to the quantum mechanical electrostatic potential surrounding the molecule. After an equilibration trajectory in which the final temperature had been scaled to the desired value (300 K), a cluster of nine molecules was selected for a density function calculation from which... 

A ternary collision may be conveniently pictured as a very rapid succession of two binary collisions one to form the unstable product, and the second, occurring within a period of about 10 sec or less, to stabilize the product. It is immediately obvious that it is not possible to use the elastic-hard-sphere molecular model to represent ternary collisions since two such spheres would be in collision contact for zero time, the probability of a third molecule making contact with the colliding pair would be strictly zero. It is therefore necessary to assume a potential model involving forces which are exerted over an extended range. One such model is that of point centers having either inverse-power repulsive or inverse-power attractive central forces. This potential, shown in Fig. 2-If, is represented by U r) = K/r. For the sake of convenience, we shall make several additional assumptions first, at the interaction distances of interest the intermolecular forces are weak, that is, U(r) < kT second, when the reactants A and B approach each other, they form an unstable product molecule A B when their internuclear separations are in the range b third, the unstable product is in essential... 

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