Limitations of Intermolecular Potential Theory

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 

In general, the position of a nonlinear rigid polyatomic molecule relative to a global axis system (fixed in space) can be defined by six coordinates three to define the position of the center of mass and three (usually the Euler angles a, p, y) to define the orientation of its local or molecule-fixed axis system relative to the global axis system. The local axis system is defined by the bonds within the molecule and should be chosen to reflect any symmetry because this simplifies the model potential. For example, a water molecule with C21, symme- 

Unless there is a macroscopic feature, such as an external electric field, defining the global axis system, the coordinate system is just an abstract frame of reference, and U(R, Q.) cannot depend on the relative orientation of the two 

In many applications, it is more computationally convenient to express the S functions in terms of the scalar products between the unit local axis vectors (xj, yi, and X2, ya, i) and the unit intermolecular vector R. This set of variables is highly redundant, but easily calculated from the local axis vector information in most simulations. As an illustration. Table 1 gives the S functions that are important in describing the anisotropy of the atom-atom repulsion between an N atom in pyridine and a hydrogen-bonding proton of methanol. 

Molecule-Centered Expansions Versus Atom-Atom Models 

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Introduction.—Most theoretical v> ork on the relation between intermolecular forces and the thermodynamic properties of liquids and liquid mixtures has been limited to potential fields which are independent of the orientation of the particles. This condition, however, is only strictly satisfied by monoatomic substances. For a great many molecular substances directional intermolecular forces are likely to be important and will have a significant effect on the thermodynamic properties of liquids both because of the additional cohesive energy and because of the loss of entropy associated with hindrance to free rotation. Although many of the observed properties of liquids have been attributed to directional forces in a qualitative manner, there has been little in the way of general quantitative theory. 

On the other hand, the analysis of experimental shockwave data for water has shown (Ree 1982) that at the limit of high temperatures and pressures intermolecular interactions of water become simpler. In this case, it becomes even possible to use a spherically-symmetric model potential for the calculations of water properties either from computer simulations (Belonoshko and Saxena 1991, 1992) or from thermodynamic perturbation theory in a way similar to simple liquids (Hansen and McDonald 1986). However, such simplifications exclude the possibility of understanding many important and complex phenomena in aqueous fluids on a true molecular level, which is, actually, the strongest advantage and the main objective of molecular computer simulations. 

Now the expression (19) is an uncoupled formulation of the polarizability. We can replace it by a polarizability derived from coupled Hartree-Fock perturbation theory, which is more accurate, because it takes account of the reorganisation of the electron distribution in a self-consistent manner. Better still would be to evaluate the monomer polarizability by a method that takes account of electron correlation as well . But whatever the level of calculation, we can once again perform a much better calculation of the monomer property than is possible for the dimer. In this way we arrive at a description of the induction energy that is far more accurate than we can obtain through either intermolecular perturbation theory, where the perturbation is treated in an uncoupled fashion, or from a supermolecule calculation, where the size of the basis is limited by the need to perform calculations at a large number of points on the potential energy surface. 

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