Cartesian stochastic method

The most commonly used stochastic methods are the torsional Monte Carlo method11101 and the cartesian stochastic (or random kick) method11111. The two methods differ in the coordinate system in which they operate. The torsional Monte Carlo method uses internal coordinates, while the random kick method uses cartesian coordinates. The advantage of using internal coordinates is that the molecular degrees of freedom are reduced. The reason for choosing torsional angles as the vari-... 

Conformational isomers represent minima on an energy surface, and all structures and the corresponding strain energies can be obtained by a careful analysis. This can be performed manually (such as in Sections 17.3 and 17.4) or automatically. An automatic procedure may involve a systematic search (grid search methods), a stochastic search (e.g., torsional Monte Carlo or cartesian stochastic, i.e., the random kick method) or molecular dynamics (see Chapter 5 and Section 16.5). Implemented in MOMEC is a random kick stochastic search module, and this has been shown to lead to excellent results, not only for conformational equilibria, but also for distributions of configurational isomers[37]. 

The method we describe is analogous to the one used by us [52] in order to study dielectric relaxation of polar fluids in the presence of a DC electric field using the Langevin equation. Our calculations are carried out by interpreting the Cartesian components of Gilbert s equation as a set of stochastic nonlinear differential equations of Stratonovich type [12]. 

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