Coding of Anisotropic Potentials

The interaction between the two dipole moments will produce a force at the site 2 on molecule B 

Note that there are torques on each molecule from the interaction, even if the interaction sites are the centers of mass a = b = 0). The sum of the torques is usually not zero. Rather, it is the total torque on the system, arising from all the torques and forces that must sum to zero [i.e., + (A x F ) + (B x F ) = 0 

Equations [22]-[24] illustrate why the derivation and programming of the forces and torques, and second derivatives for all the terms up to R in the atom-atom multipole expansion of the electrostatic energy is a nontrivial exercise in classical mechanics. It has been described in detail by Popelier and Stone,and, with the additional derivatives required for modeling molecular crystal structures, by Willock et al.  

Calculations on the gas phase interactions of most pairs (or small clusters) of molecules have been possible using ORIENT for some time. This program is available on request from the author s web site (http //fandango.ch.cam.ac.uk/). The latest version ORIENT3 not only can determine the minimum energy structures of van der Waals clusters, their transition states, and other stationary points, it also can calculate their vibrational modes, and it has the ability to use anisotropic repulsion, dispersion, and induction energy models. 

There have been some molecular dynamics simulations with anisotropic atom-atom potentials, the earliest being simulations with chlorine poten-tials. Those simulations demonstrated that the computer time requirements were quite reasonable, and the results were effective compared with the inclusion of additional isotropic sites. The technique has also been extended to butane by means of a four-site anisotropic carbon model. A general DMA based potential model is being implemented into the new CCP5 molecular simulation program DL POLY. Monte Carlo simulations can use anisotropic atom-atom potentials readily, since the calculations require the evaluation of only the energy. 

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