Buckingham-type potential functions

From electronic structure theory it is known that the repulsion is due to overlap of the electronic wave functions, and furthermore that the electron density falls off approximately exponentially with the distance from the nucleus (the exact wave function for the hydrogen atom is an exponential function). There is therefore some justification for choosing the repulsive part as an exponential function. The general form of the Exponential - R Ey w function, also known as a ""Buckingham " or ""Hill" type potential is... 

The first three terms, stretch, bend and torsion, are common to most force fields although their explicit form may vary. The nonbonded terms may be further divided into contributions from Van der Waals (VdW), electrostatic and hydrogen-bond interactions. Most force fields include potential functions for the first two interaction types (Lennard-Jones type or Buckingham type functions for VdW interactions and charge-charge or dipole-dipole terms for the electrostatic interactions). Explicit hydrogen-bond functions are less common and such interactions are often modeled by the VdW expression with special parameters for the atoms which participate in the hydrogen bond (see below). 

In the development of the set of intermolecular potentials for the nitramine crystals Sorescu, Rice, and Thompson [112-115] have considered as the starting point the general principles of atom-atom potentials, proven to be successful in modeling a large number of organic crystals [120,123]. Particularly, it was assumed that intermolecular interactions can be separated into dispersive-repulsive interactions of van der Waals and electrostatic interactions. An additional simplification has been made by assuming that the intermolecular interactions depend only on the interatomic distances and that the same type of van der Waals potential parameters can be used for the same type of atoms, independent of their valence state. The non-electric interactions between molecules have been represented by Buckingham exp-6 functions,... 

For the description of the elastic forces within molecular crystals and between atoms of the same molecule which are not directly connected by a chemical bond but which are approaching each other (as in biomolecules), intermolecular force constants are necessary (see Secs. 5.2). These may be calculated using atom-atom potential functions. Kitaigorodsky (1973) introduced a universal potential of the Buckingham type (in kcal /mol) ... 

A potential limction consists of one or more parameter sets that fit the equation and atom types to experimental data. Each of these functions usually contains a small number of adjustable parameters that can be used to optimize the simulations. There are live main potential functions the hard sphere (HS) potential, the soft sphere (SS) potential, Sutherland (S) potential, the Lennard-Jones potential, and the Buckingham (B) potential (2). This section provides a brief review of the most frequently used potential function [Lennard-Jones (LJ) potential] and its application for molecular modeling. 

Rare gas dimers are prototypical systems to examine van der Waals interaction function forms [88, 92, 98-100]. It should be noted that such examinations on the vdW potentials generally employ the assumption that the total interactions between two rare gas atoms are all from the vdW interactions. A seminal work by Halgren [88] found that neither the Lennard-Jones type potentials (Lennard-Jones 12-6 or Lennard-Jones 9-6) nor the Buckingham exp-6 potentials was able to well replicate the high quality reference data, while a buffered 14-7 potential was found to yield much better performance. It should be noted that in the calculation of van der Waals reference energies by Halgren [88], the charge penetration effects have not been separated out. It is well known that there... 

Kitaigorodsky gives non-bonded interaction parameters for use with Buckingham functions on aromatic systems. He also gives a rather special potential energy function of the Buckingham type for peptide work, a "universal potential with just one para-meter for each Interaction type. This set has been... 

The intermolecular interactions are usually assumed to be pair-additive functions such as the Lennard-Jones 12-6 or 9-6 potentials or the Buckingham expontential-6 type of potentials and are parameterized using methods similar to those described in the previous paragraph to reproduce the crystallographic structure and the lattice energy. For the case of liquid systems the parameterization of non-bonded interactions can be done to reproduce the liquid densities and the heats of vaporization. 

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