In physics, Langevin dynamics is an approach to the mathematical modeling of the dynamics of molecular systems using the Langevin equation.
It was originally developed by French physicist Paul Langevin.
The approach is characterized by the use of simplified models while accounting for omitted degrees of freedom by the use of stochastic differential equations.
[1] A real world molecular system is unlikely to be present in vacuum.
Jostling of solvent or air molecules causes friction, and the occasional high velocity collision will perturb the system.
Also, Langevin dynamics allows temperature to be controlled as with a thermostat, thus approximating the canonical ensemble.
Langevin dynamics mimics the viscous aspect of a solvent.
It does not fully model an implicit solvent; specifically, the model does not account for the electrostatic screening and also not for the hydrophobic effect.
For denser solvents, hydrodynamic interactions are not captured via Langevin dynamics.
that constitute a time-dependent random variable, the resulting Langevin equation is[2][3]
is the force calculated from the particle interaction potentials; the dot is a time derivative such that
is the damping constant (units of reciprocal time), also known as the collision frequency;
is a delta-correlated stationary Gaussian process with zero-mean, satisfying
If the main objective is to control temperature, care should be exercised to use a small damping constant
grows, it spans from the inertial all the way to the diffusive (Brownian) regime.
Brownian dynamics can be considered as overdamped Langevin dynamics, i.e. Langevin dynamics where no average acceleration takes place.
The Langevin equation can be reformulated as a Fokker–Planck equation that governs the probability distribution of the random variable X.
[4] The Langevin equation can be generalized to rotational dynamics of molecules, Brownian particles, etc.
A standard (according to NIST[5]) way to do it is to leverage a quaternion-based description of the stochastic rotational motion.