Molecular Dynamics

Molecular Dynamics Molecular Dynamics Molecular dynamics (MD) 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.

In the most common version, the trajectories of molecules and atoms are determined by numerically solving the Newton's equations of motion for a system of interacting particles, where forces between the particles and potential energy are defined by molecular mechanics force fields.

The method was originally conceived within theoretical physics in the late 1950s and early 1960s ,[2] but is applied today mostly in materials science and the modeling of biomolecules.

Because molecular systems consist of a vast number of particles, it is impossible to find the properties of such complex systems analytically; MD simulation circumvents this problem by using numerical methods.

However, long MD simulations are mathematically ill-conditioned, generating cumulative errors in numerical integration that can be minimized with proper selection of algorithms and parameters, but not eliminated entirely.

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The results of molecular dynamics simulations may be used to determine macroscopic thermodynamic properties of the system based on the ergodic hypothesis: the statistical ensemble averages are equal to time averages of the system. MD has also been termed "statistical mechanics by numbers" and "Laplace's vision of Newtonian mechanics" of predicting the future by animating nature's forces and allowing insight into molecular motion on an atomic scale.

Design constraints Design of a molecular dynamics simulation is constrained by the availability of computational power. Simulation size (n=number of particles), time step and total time duration are selected, so that the calculations can be finished within a reasonable period of time.

The time allocated to the simulations should be in close harmony to the actual time of completion of the natural process, i.e., for the conclusions to be valid the time span should match the kinetics of the natural process. To obtain these simulations, several days to years are needed. Parallel algorithms could be used for load distribution among the CPU's.

Another factor that impacts total CPU time required by a simulation is the size of the time-step of integration. This is the time period between subsequent evaluations of the potential.

The time step should be small enough to avoid discretization errors (i.e. smaller than the fastest vibration frequency in the system). Typical time-steps are in the order of 10-15s. This value may be extended by using algorithms, e.g., SHAKE, which fixes the vibrations of the fastest atoms (for e.g. hydrogen) into place.

Classical molecular dynamic simulation Classical molecular dynamic simulation methods can be divided into equilibrium molecular dynamics and non equilibrium molecular dynamics. Most of the work on molecular dynamic was based on equilibrium molecular dynamics and non equilibrium molecular dynamics has not been treated thoroughly.

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However, because it can handle calculation of transport coefficient easily, non equilibrium molecular dynamics will receive increasing attention in the future.

Non classical molecular dynamic simulation Any phenomena that involve electrons or photons cannot be treated easily by classical molecular dynamics simulation unless empirical equations can be obtained to describe dynamics of these particles. Usually interactions among electrons and photons have the quantum mechanical nature and must be obtained by solving the Schrodinger equation.

However limited by computational capacity quantum molecular dynamics can simulate a system with only about 100 molecules. Attracted by the fact that classical molecular dynamics can treat a relatively large number of molecules researchers attempted to combine quantum molecular dynamics and classical molecular dynamics in one simulation and such a technique has been successfully applied in simulating the chemical reactions.

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