Monte Carlo molecular modeling
Encyclopedia
Monte Carlo molecular modeling is the application of Monte Carlo method
s to molecular problems. These problems can also be modeled by the molecular dynamics
method. The difference is that this approach relies on statistical mechanics
rather than molecular dynamics. Instead of trying to reproduce the dynamics of a system, it generates states according to appropriate Boltzmann probabilities. 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
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 equilibrium be properly described, but detailed balance
, a stronger condition,
is usually imposed when designing new algorithms. An additional advantage is that some systems, such as the Ising model
, 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
for optimization, in which a fictitious temperature is introduced and then gradually lowered.
Monte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...
s to molecular problems. These problems can also be modeled by the molecular dynamics
Molecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...
method. The difference is that this approach relies on statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
rather than molecular dynamics. Instead of trying to reproduce the dynamics of a system, it generates states according to appropriate Boltzmann probabilities. 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
Monte Carlo method in statistical physics
Monte Carlo in statistical physics refers to the application of the Monte Carlo method to problems in statistical physics, or statistical mechanics.-Overview:...
.
It employs a Markov chain
Markov chain
A Markov chain, named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized as memoryless: the next state depends only on the current state and not on the...
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 equilibrium be properly described, but detailed balance
Detailed balance
The principle of detailed balance is formulated for kinetic systems which are decomposed into elementary processes : At equilibrium, each elementary process should be equilibrated by its reverse process....
, a stronger condition,
is usually imposed when designing new algorithms. An additional advantage is that some systems, such as the Ising model
Ising model
The Ising model is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables called spins that can be in one of two states . The spins are arranged in a graph , and each spin interacts with its nearest neighbors...
, 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
Simulated annealing is a generic probabilistic metaheuristic for the global optimization problem of locating a good approximation to the global optimum of a given function in a large search space. It is often used when the search space is discrete...
for optimization, in which a fictitious temperature is introduced and then gradually lowered.
See also
- Quantum Monte CarloQuantum Monte CarloQuantum Monte Carlo is a large class of computer algorithms that simulate quantum systems with the idea of solving the quantum many-body problem. They use, in one way or another, the Monte Carlo method to handle the many-dimensional integrals that arise...
- Monte Carlo method in statistical physicsMonte Carlo method in statistical physicsMonte Carlo in statistical physics refers to the application of the Monte Carlo method to problems in statistical physics, or statistical mechanics.-Overview:...
- List of software for Monte Carlo molecular modeling
- Software for molecular mechanics modeling
- Bond fluctuation modelBond fluctuation modelThe BFM is a lattice model for simulating the conformation and dynamics of polymer systems. There are two versions of the BFM used: The earlier version was first introduced by Carmesin and Kremer in 1988, and the later version by Shaffer in 1994...