Potential energy truncation methods

T. Schlick and M. L. Overton. A powerful truncated Newton method for potential energy functions. J. Comp. Chem., 8 1025-1039, 1987. 

A disadvantage of the two-state methods is that modelling of a real potential energy surface (PES) by a TLS cannot always been done. Moreover, this truncated treatment does not cover the high-temperature regime since the truncation scheme does not hold at T> coq. With the assumption that transition is incoherent, similar approximations can be worked out immediately from the nonlocal effective action, as shown in Sethna [1981] and Chakraborty et al. [1988] for T = 0, and in Gillan [1987] for the classical heat bath. 

Figure 2. The electrostatic potential energy for atoms with half charges of opposite signs for the different methods of long range truncation.

T. Schlick and M. Overton, J. Comput. Chem., 8, 1025 (1987). A Powerful Truncated Newton Method for Potential Energy Minimization. 

The second difficulty with the superposition method is obtaining expressions for 0, and Z,. As we noted earlier, the natural starting point is to truncate a Taylor expansion for the potential energy around each minimum at second order giving the harmonic approximation. This truncation... 

If, however, the ab-initio calculation of a specific molecule jdelds the complete potential energy hypersurface (as discussed above) the FG-matrix method (7) can be used. This was done by, e.g. AUavena (52), Hartmann and Gliemann (55) and Menna, Mocda and Randaccio (44). Huff and Ellison (144) present an easier and simpler method which is very favourable for computational purposes it also depends on truncating the potential after the harmonic term the 3 N mass-weighted (mi) Cartesian displacement co-ordinates Axi are called qi, and are given by... 

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