An N ·log(N) method for evaluating electrostatic energies and forces of large periodic systems is presented. The method is based on interpolation of the reciprocal space Ewald sums and evaluation of the resulting convolutions using fast Fourier transforms. Timings and accuracies are presented for three large crystalline ionic systems.

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. In addition, the CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This paper provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM paper in 1983.

The development of a smooth solvation potential from which analytic derivatives can be derived is important for molecular applications that require geometry optimization and conformational sampling. Derivatives in conventional boundary element solvation methods are typically treated approximately, and contain singularities that arise from discontinuities in the potential. We present a simple smooth solvation potential that is based on the conductor-like screening model proposed by Klamt and Schüürmann (Klamt, A.; Schüürmann, G. J. Chem. Soc., Perkin. Trans. 2, 1993, 799). The model uses a simple solvent accessible surface with an atomic sphere discretization based on high-order angular quadrature schemes for spherical harmonics. Surface elements are modeled by spherical Gaussian functions with exponents calibrated to obtain the exact Born ion energy and uniform surface charge density and to avoid Coulomb singularities present in conventional point-charge surface element models. The set of linear equations are modified to produce a rigorously smooth solvation potential by allowing the effect of new surface elements to be turned on or off over a finite switching region around each atom. Numerical tests of the method are provided, in addition to discussions of rotational variance, generalization to arbitrary internal dielectric, use of constraints, and extension to a smooth surface area model.

Simulations of the HIV-l protease unit cell using a 9 A cutoff, 9/18 A "twin-range" cutoff, and full Ewald sums have been carried out to 300 ps. The results indicate that long-range electrostatic interactions are essential for proper representation of the HIV-1 protease crystal structure. The 9 A simulation did not converge in 300 ps. Inclusion of a 9/18 A "twin-range" cutoff showed significant improvement. Simulation using the Ewald summation convention gave the best overall agreement with x-ray crystallographic data, and showed the least internal differences in the time average structures of the asymmetric units. The Ewald simulation represents an efficient implementation of the Particle Mesh Ewald method [Darden et aI., J. Chern. Phys. 98, 10 089 (1993)], and illustrates the importance of including long-range electrostatic forces in large macromolecular systems.