No 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.

A simple polarizable water model is developed and optimized for molecular dynamics simulations of the liquid phase under ambient conditions. The permanent charge distribution of the water molecule is represented by three point charges: two hydrogen sites and one additional M site positioned along the HOH bisector. Electronic induction is represented by introducing a classical charged Drude particle attached to the oxygen by a harmonic spring. The oxygen site carries an equal and opposite charge, and is the center of an intermolecular Lennard-Jones interaction. The HOH gas-phase experimental geometry is maintained rigidly and the dipole of the isolated molecule is 1.85 D, in accord with experiment. The model is simulated by considering the dynamics of an extended Lagrangian in which a small mass is attributed to the Drude particles. It is parametrized to reproduce the salient properties of liquid water under ambient conditions. The optimal model, refered to as SWM4-DP for “simple water model with four sites and Drude polarizability,” yields a vaporization enthalpy of 10.52 kcal/mol, a molecular volume of 29.93 Å3, a static dielectric constant of 79±5, a self-diffusion constant of (2.30±0.04)×10−5 cm2/s, and an air/water surface tension of 66.9±0.9 dyn/cm, all in excellent accord with experiments. The energy of the water dimer is −5.18 kcal/mol, in good accord with estimates from experiments and high level ab initio calculations. The polarizability of the optimal model is 1.04 Å3, which is smaller than the experimental value of 1.44 Å3 in the gas phase. It is likely that such a reduced molecular polarizability, which is essential to reproduce the properties of the liquid, arises from the energy cost of overlapping electronic clouds in the condensed phase due to Pauli’s exclusion principle opposing induction.

An accurate representation of ion solvation in aqueous solution is critical for meaningful computer simulations of a broad range of physical and biological processes. Polarizable models based on classical Drude oscillators are introduced and parametrized for a large set of monoatomic ions including cations of the alkali metals (Li + , Na + , K + , Rb + and Cs + ) and alkaline earth elements (Mg 2+ , Ca 2+ , Sr 2+ and Ba 2+ ) along with Zn 2+ and halide anions (F − , Cl − , Br − and I − ). The models are parameterized, in conjunction with the polarizable SWM4-NDP water model [Lamoureux et al., Chem. Phys. Lett. 418, 245 (2006)], to be consistent with a wide assortment of experimentally measured aqueous bulk thermodynamic properties and the energetics of small ion-water clusters. Structural and dynamic properties of the resulting ion models in aqueous solutions at infinite dilution are presented.