A representation of the average (squared) distance traveled by an atom or particle during a defined period of time at a specific temperature. In a molecular dynamics simulation, the mean square displacement is used to calculate the diffusion coefficient for a given atomic or molecular species (e.g., interlayer cation or H2O). In an atomic structure determination, the mean square displacement describes the time averaged movement of an atom about its mean equilibrium position at a given temperature. This “movement” involves not only (dynamic) thermal vibrations, but also an apparent movement caused by (static) disorder from the random distribution of atoms over different equilibrium positions at (or near) a site from all the unit cells sampled in the experiment (where perfect periodicity is lacking in a crystal).
Cf., density functional theory, Grand Canonical Monte Carlo simulation, molecular dynamics, Monte Carlo molecular simulation, quantum calculation