Monte Carlo molecular modelling is the application of

Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deter ...

s to molecular problems. These problems can also be modelled by the

molecular dynamics Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of th ...

method. The difference is that this approach relies on equilibrium statistical mechanics rather than molecular dynamics. Instead of trying to reproduce the dynamics of a system, it generates states according to appropriate

Boltzmann distribution In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution or probability measure that gives the probability ...

. Thus, it is the application of the Metropolis Monte Carlo simulation to molecular systems. It is therefore also a particular subset of the more general Monte Carlo method in statistical physics. It employs a

Markov chain A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happen ...

procedure in order to determine a new state for a system from a previous one. According to its stochastic nature, this new state is accepted at random. Each trial usually counts as a move. The avoidance of dynamics restricts the method to studies of static quantities only, but the freedom to choose moves makes the method very flexible. These moves must only satisfy a basic condition of balance in order for the equilibrium to be properly described, but

detailed balance The principle of detailed balance can be used in kinetic systems which are decomposed into elementary processes (collisions, or steps, or elementary reactions). It states that at equilibrium, each elementary process is in equilibrium with its reve ...

, a stronger condition, is usually imposed when designing new algorithms. An additional advantage is that some systems, such as the

Ising model The Ising model () (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent ...

, lack a dynamical description and are only defined by an energy prescription; for these the Monte Carlo approach is the only one feasible. The great success of this method in statistical mechanics has led to various generalizations such as the method of

simulated annealing Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. ...

for optimization, in which a fictitious temperature is introduced and then gradually lowered. A range of software packages have been developed specifically for the use of the Metropolis Monte Carlo method on molecular simulations. These include: * BOSS *

CP2K CP2K is a freely available ( GPL) quantum chemistry and solid state physics program package, written in Fortran 2008, to perform atomistic simulations of solid state, liquid, molecular, periodic, material, crystal, and biological systems. It prov ...

* MCPro * Sire * ProtoMS * Faunus

External links

* http://cmm.cit.nih.gov/intro_simulation/node25.html

References

* * * {{cite book , author1=Binder, K. , author2=Heermann, D.W. , name-list-style=amp , title=Monte Carlo Simulation in Statistical Physics. An Introduction (4th edition) , publisher= Springer , year=2002 , isbn=3-540-43221-3 Molecular modelling Theoretical chemistry Monte Carlo methods Stochastic models

See also

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References