Buckingham nonbonding potential functions

A typical set of nonbonded potential functions (Scott and Scheraga, 1966c Ooi et al., 1967) obtained by the procedure described above is given in Table 16. Those of Brant and Flory (1965c) and of Brant et al. (1967), obtained by essentially the same procedure, differ somewhat from these because of the different values selected for the parameters of Table 15. Liquori (1966) has used a combination of Lennard-Jones and Buckingham functions, based primarily on work of Mason and Kreevoy (1955). 

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). 

A method for calculating the barriers to internal rotation has recently been proposed (Scott and Scheraga, 1965). It is based on the concept that the barrier arises from two effects, exchange interactions of electrons in bonds adjacent to the bond about which internal rotation occurs, and nonbonded or van der Waals interactions. The exchange interactions are represented by a periodic function, and the nonbonded interactions either by a Buckingham 6-exp or Lennard-Jones 6-12 potential function, the parameters of which are determined semi-empirically. (The parameters of the nonbonded potential energy functions are discussed in Section VB.)... 

In Section 4.2 we describe how nonbonded potentials are derived for polymer systems, but for now we list some of the isotropic functions used for their representation. Of these, two common forms are the Buckingham potential... 

Lennard-Jones potential As two atoms approach one another there is the attraction due to London dispersion forces and eventually a van der Waals repulsion as the interatomic distance r gets smaller than the equilibrium distance. A well-known potential energy function to describe this behavior is the Lennard-Jones (6-12) potential (LJ). The LJ (6-12) potential represents the attractive part as r-6-dependent whereas the repulsive part is represented by an r n term. Another often used nonbonded interaction potential is the Buckingham potential which uses a similar distance dependence for the attractive part as the LJ (6-12) potential but where the repulsive part is represented by an exponential function. 

In other nonbond pairwise potentials, the repulsive portion of the interaction is modeled with an exponential term, which is in better agreement with the functional form of the repulsive term determined from quantum mechanics. One example of such a potential is the Buckingham potential (Buckingham 1938) ... 

The results of calculations for n-alkanes, which are applicable to the PM chain as well, provide an illustrative example. In Figure 1, an energy contour map calculated for two consecutive internal C-C bonds is shown at intervals of 1 kcalmol (4.2kJmor ). In these calculations, an intrinsic threefold potential with barrier height of 2.8 kcalmol" (11.7 kJmol" ) was assigned to rotation about the C-C bond, and Buckingham s 6-exp energy functions were employed for the evaluation of nonbonded interatomic interactions... 

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