Singularity-free algorithm

D. J. Evans and S. Murad, Mol. Phys., 34, 327 (1977). Singularity-Free Algorithm for Molecular Dynamics Simulation of Rigid Polyatomics. 

Molecular Dynamics Simulation ol Methane Using a Singularity-Free Algorithm... 

Among the important recent advances in computing methods for molecular dynamics simulations of condensed matter are the singularity free algorithm for rigid polyatomics, developed by Evans and Murad (, , and the multiple time step (MTS) method, developed by Streett, et al. In the method of Evans and Murad, the equations of rotational motion are expressed in terms of four parameters, x h, C, C, called quaternions, defined by... 

We describe here increases in computing speed and storage requirements associated with adapting a Fortran program for 108 methane CH4) molecules from conventional molecular dynamics to several variations of the MTS method. The program uses the singularity free algorithm of Evans and Murad (2 ), and a site-site potential of the form... 

When A = 0 one recovers the Lennard-Jones potential. When A = 1, the atom is annihilated smoothly and the singularity disappears progressively. The parameter a can be chosen to increase the smoothness of the free energy. A small a results in a near singularity around A = 1 while a large a results in a near singularity around A = 0. See article by Beutler et al. [55] for an algorithm to calculate an appropriate value of a. 

Excel does not provide functions for the factor analysis of matrices. Further, Excel does not support iterative processes. Consequently, there are no Excel examples in Chapter 5, Model-Free Analyses. There are vast numbers of free add-ins available on the internet, e.g. for the Singular Value Decomposition. Alternatively, it is possible to write Visual Basic programs for the task and link them to Excel. We strongly believe that such algorithms are much better written in Matlab and decided not to include such options in our Excel collection. 

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