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# Langevin thermostat

The Langevin thermostat[1][2][3] maintains the temperature through a modification of Newton's equations of motion

${\displaystyle {\dot {r_{i}}}=p_{i}/m_{i}\qquad {\dot {p_{i}}}=F_{i}-{\gamma }_{i}\,p_{i}+f_{i},}$

where Fi is the force acting on atom i due to the interaction potential, γi is a friction coefficient, and fi is a random force simulating the random kicks by the damping of particles between each other due to friction. The random numbers are chosen from a Gaussian distribution with the following variance

${\displaystyle \sigma _{i}^{2}=2\,m_{i}\,{\gamma }_{i}\,k_{B}\,T/{\Delta }t}$

with Δt being the time-step used in the MD to integrate the equations of motion. Obviously, Langevin dynamics is identical to the classical Hamiltonian in the limit of vanishing γ.

The friction coefficient is set by the LANGEVIN_GAMMA parameter.

As for the NVT ensemble the LANGEVIN_GAMMA parameter has to be set. If the NpT ensemble is used (by setting ISIF=3) additionally the friction coefficient of the lattice LANGEVIN_GAMMA_L has to be provided too.

The Langevin thermostat is selected by MDALGO=3.

## References

1. [ M. P. Allen and D. J. Tildesley, Computer simulation of liquids (Oxford university press: New York, 1991).]
2. W. G. Hoover, A. J. C. Ladd and B. Moran, Phys. Rev. Lett. 48, 1818 (1982).
3. D. J. Evans, J. Chem. Phys. 78, 3297 (1983).