Fast evaluation of polarizable forces.

Polarizability is considered to be the single most significant development in the next generation of force fields for biomolecular simulations. However, the self-consistent computation of induced atomic dipoles in a polarizable force field is expensive due to the cost of solving a large dense linear system at each step of a simulation. This article introduces methods that reduce the cost of computing the electrostatic energy and force of a polarizable model from about 7.5 times the cost of computing those of a nonpolarizable model to less than twice the cost. This is probably sufficient for the routine use of polarizable forces in biomolecular simulations. The reduction in computing time is achieved by an efficient implementation of the particle-mesh Ewald method, an accurate and robust predictor based on least-squares fitting, and non-stationary iterative methods whose fast convergence is accelerated by a simple preconditioner. Furthermore, with these methods, the self-consistent approach with a larger timestep is shown to be faster than the extended Lagrangian approach. The use of dipole moments from previous timesteps to calculate an accurate initial guess for iterative methods leads to an energy drift, which can be made acceptably small. The use of a zero initial guess does not lead to perceptible energy drift if a reasonably strict convergence criterion for the iteration is imposed.