Modeling induced polarization with classical Drude oscillators: Theory and molecular dynamics simulation algorithm

Abstract

A simple treatment for incorporating induced polarization in computer simulations is formulated on the basis of the classical Drude oscillator model. In this model, electronic induction is represented by the displacement of a charge-carrying massless particle attached to a polarizable atom under the influence of the local electric field. The traditional self-consistent field (SCF) regime of induced polarization is reproduced if these auxiliary particles are allowed to relax instantaneously to their local energy minima for any given fixed configuration of the atoms in the system. In practice, such treatment is computationally prohibitive for generating molecular dynamics trajectories because the electric field must be recalculated several times iteratively to satisfy the SCF condition, and it is important to seek a more efficient way to simulate the classical Drude oscillator model. It is demonstrated that a close approximation to the SCF regime can be simulated efficiently by considering the dynamics of an extended Lagrangian in which a small mass is attributed to the auxiliary particles, and the amplitude of their oscillations away from the local energy minimum is controlled with a low-temperature thermostat. A simulation algorithm in this modified two-temperature isobaric–isothermal ensemble is developed. The algorithm is tested and illustrated using a rigid three-site water model with one additional Drude particle attached to the oxygen which is closely related to the polarizable SPC model of Ahlström et al. [Mol. Phys. 68, 563 (1989)]. The tests with the extended Lagrangian show that stable and accurate molecular dynamics trajectories for large integration time steps (1 or 2 fs) can be generated and that liquid properties equivalent to SCF molecular dynamics can be reproduced at a fraction of the computational cost.