# Configurational bias Monte Carlo

**Configurational bias Monte Carlo** is a Monte Carlo technique used in the simulation of flexible molecules, *i.e.*
molecules that can adopt various configurations. For this reason the configurational bias Monte Carlo method has been widely
applied to simulations of alkanes and polymers.

It is usual that many of the accessible configurations have a small probability and only a few ones are probable. In these cases, the simulation is more efficient if the probabilities of the different configurations are previously considered. With this end, the new position for a unit is randomly chosen between a discrete number of possibilities (the neighboring sites in lattice models or a randomly chosen set of positions in other cases), taking into account their Boltzmann probabilities. In the case of polymers, an entirely new part of a chain up to an end can be generated following a path of easily accessible positions. This introduces a bias which should be compensated by considering a weight factor for each new position chosen (or a product of these factors for a new chain). A similar weight corresponding to reconstructing the old configuration from the new one has also to be calculated. The probability ratios are corrected by introducing the ratio between the new and the old configurational weight factors.

## References[edit]

- Jonathan Harris and Stuart A. Rice "A lattice model of a supported monolayer of amphiphile molecules: Monte Carlo simulations", Journal of Chemical Physics
**88**pp. 1298-1306 (1988) - Jörn Ilja Siepmann and Daan Frenkel "Configurational bias Monte Carlo: a new sampling scheme for flexible chains", Molecular Physics
**75**pp. 59-70 (1992) - D. Frenkel, G. C. A. M. Mooij and B. Smit "Novel scheme to study structural and thermal properties of continuously deformable molecules", Journal of Physics: Condensed Matter
**4**pp. 3053-3076 (1992) - Juan J. de Pablo, Manuel Laso, and Ulrich W. Suter "Simulation of polyethylene above and below the melting point", Journal of Chemical Physics
**96**pp. 2395- (1992)