Extended Lagrangian formalism applied to temperature control and electronic polarization effects in molecular dynamics simulations

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This paper describes the implementation of the extended Lagrangian method to control the temperature, and to compute electronic polarization effects in molecular dynamics simulations of complex systems. Temperature control is achieved by introducing an extra variable coupled to the velocities, whereas induced dipoles are represented as Drude oscillators that respond to the electric field produced by the surrounding particles. Computing the contribution from the induced dipoles therefore requires no iteration or matrix inversion procedures and is as fast as evaluating classical non-bonded interactions. It is shown how a judicious choice of the integration algorithm makes the implementation of both procedures straightforward. The application in a molecular dynamics procedure, which integrates both methods, is illustrated in the constant-temperature simulations of pure water and methane-water mixtures, in which the solvent is represented by the mean-field SPC or by the polarizable PSPC water models.