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Monte Carlo or Molecular Dynamics

The choice between Monte Carlo and molecular dynamics is largely determined by the phenomenon under investigation. For a simulation of a gas or other low density systems, Monte Carlo simulations are preferable [125]. There can be large energy barriers (often several $k_B T$) to torsional rotations in molecules which can lead to molecules being trapped in a few low energy conformations in a MD simulation, leading to poor conformational sampling. In contrast, the random moves in a MC simulation can easily lead to barrier crossings. For a liquid simulation MD becomes favourable. Here molecular collisions exchange energy between molecules, enabling barrier crossings, improving the ability of MD to sample conformations. For a MC simulation, there is a large probability of selecting random moves for which two or more molecules overlap (especially for rotations near the centre of molecules with long tails such as liquid crystals), leading to large number of rejected moves and a decrease in efficiency of sampling. However, the ability of MC to make unphysical moves, for example to flip a molecule around, can in some cases compensate for this. MD also handles collective motions better than MC. However, recently methods such as Configurational Bias Monte Carlo and Hybrid Monte Carlo have been developed to improve the performance of MC simulations [126]. There are some situations where only one method is appropriate. Determination of transport properties such as viscosity coefficients, is largely only possible using MD, as MC lacks an objective definition of time (except in some special cases such as the bond fluctuation model for polymers). On the other hand MC can be used for simulations with varying particle numbers (Grand Canonical Monte Carlo) by adding moves for the creation and destruction of particles.
next up previous contents
Next: Practicalities Up: Simulation Methods Previous: Constant Pressure () Molecular   Contents
Dr S J Clark
2003-01-30