Modified Buckingham potential

The most frequently used model potentials are Rigid sphere, point center of repulsion, Sutherland s model, Lennard-Jones potential, modified Buckingham potential, Kihara potential, Morse potential. Their advantages and disadvantages are thoroughly discussed elsewhere [39] [28]. 

Errington, J. R. Panagiotopoulos, A. Z., Phase equilibria of the modified Buckingham exponential-6 potential from Hamiltonian scaling grand canonical Monte Carlo, J. Chem. Phys. 1998,109, 1093-1100... 

At short range, a plot of In V versus r will be a straight line with a slope (equal to a) and an intercept (equal to A) and thus the value of A and a for Buckingham potential can be determined. The point where the potential V becomes zero would fix the value of B (when n = 6 or any other fixed value). The function can be made more flexible by modifying as... 

More complex combining laws have been developed by Mason (M6) for the modified Buckingham (6-exp) potential. 

A Buckingham potential replaces the twelfth power term with an exponential, which is a better theoretical description of the repulsion expected between electron clouds. In both MM2 and MM3, an exponential-6 equation is used. This is a modified Hill equation, which is a particular formulation that contains only two adjustable parameters for the interaction between any two atoms. Equation [9] is for MM3. For MM2 the exponential part was slightly harder, with 12.50 instead of 12.00 in the exponent. 

The exponential form is a better representation of repulsive interactions than the LJ inverse-12 form. The combination of an exponential and a 6th order term has been called the Buckingham potential function, the exponential-6 equation, or the modified Hill equation. 

The pressure dependence of wavenumbers has been investigated theoretically by LD methods on the basis of a Buckingham 6-exp potential. In the studies of Pawley and Mika [140] and Dows [111] the molecules were treated as rigid bodies in order to obtain the external modes as a function of pressure. Kurittu also studied the external and internal modes [141] using his deformable molecule model [116]. The force constants of the intramolecular potential (modified UBFF) were obtained by fitting to the experimental wavenumbers. The results of these studies are in qualitative agreement with the experimental findings. 

---