**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 the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton’s equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanics force fields. The method is applied mostly in chemical physics, materials science, and biophysics.

Because molecular systems typically consist of a vast number of particles, it is impossible to determine 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.

For systems that obey the ergodic hypothesis, the evolution of one molecular dynamics simulation may be used to determine macroscopic thermodynamic properties of the system: the time averages of an ergodic system correspond to microcanonical ensemble averages. 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.

————————————————————————-

**Molecular mechanics** uses classical mechanics to model molecular systems. The Born–Oppenheimer approximation is assumed valid and the potential energy of all systems is calculated as a function of the nuclear coordinates using force fields. Molecular mechanics can be used to study molecule systems ranging in size and complexity from small to large biological systems or material assemblies with many thousands to millions of atoms.

All-atomistic molecular mechanics methods have the following properties:

- Each atom is simulated as one particle
- Each particle is assigned a radius (typically the van der Waals radius), polarizability, and a constant net charge (generally derived from quantum calculations and/or experiment)
- Bonded interactions are treated as
*springs*with an equilibrium distance equal to the experimental or calculated bond length

Variants on this theme are possible. For example, many simulations have historically used a *united-atom* representation in which each terminal methyl group or intermediate methylene unit was considered one particle, and large protein systems are commonly simulated using a *bead* model that assigns two to four particles per amino acid.