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Mathematical & Computational Physics

Molecular Dynamics

A computer simulation method for analyzing the physical movements of atoms and molecules by numerically integrating Newton's equations of motion.

Governing formula m_i d²r_i/dt² = F_i = -∇_i V(r₁, r₂, ..., r_N)
SI unit Atomic Trajectory Simulation

In depth

Interatomic forces are derived from empirical potentials or quantum ab-initio calculations. Time integration algorithms (like Verlet or leapfrog) update positions and velocities at femtosecond time steps.

Examples in the real world

Simulating protein folding, lipid membrane dynamics, and nanomaterial fracture mechanics.