The previously developed particle mesh Ewald method is reformulated in terms of efficient B-spline interpolation of the structure factors. This reformulation allows a natural extension of the method to potentials of the form 1/r p with pу1. Furthermore, efficient calculation of the virial tensor follows. Use of B-splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy. We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N). For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 Å or less.

We propose a modification in the three-dimensional Ewald summation technique for calculations of long-range Coulombic forces for systems with a slab geometry that are periodic in two dimensions and have a finite length in the third dimension. The proposed method adds a correction term to the standard Ewald summation formula. To test the current method, molecular dynamics simulations on water between Pt(111) walls have been carried out. For a more direct test, the calculation of the pair forces between two point charges has been also performed. An excellent agreement with the results from simulations using the rigorous two dimensional Ewald summation technique were obtained. We observed that a significant reduction in computing time can be achieved when the proposed modification is used.

An all-atom 5 nanosecond molecular dynamics simulation of a water-solvated micelle containing 60 sodium dodecyl sulfate monomers was performed. Structural properties such as the radius of gyration, eccentricity, micellar size, accessible surface area, dihedral angle distribution, carbon atom distribution, and the orientation of the monomers toward the micelle center of mass were evaluated. The results indicate a stable micellar system over the duration of the simulation. Evaluation of the structure and motion of the sodium counterions show (1) a long equilibration time (1 nanosecond) is required to achieve a stable distribution of counterions and (2) approximately 25% of the sodium ions are located in the first shell and 50% are located in the first two shells of the micelle during the course of the simulation. The structure of the micelle oxygen-sodium ion radial distribution function reveals two distinct peaks which divide the counterions into those close to the micelle (first shell) those far from the micelle (bulk) and those between (second shell). Finally, values of the diffusion coefficient for sodium ions followed a decreasing trend for ions in the bulk of the micellar system (D ) 1.9 × 10 -5 cm 2 /s), ions in the second shell of the micelle (D ) 1.4 × 10 -5 cm 2 /s), and those in the first shell of the micelle (D ) 1.0 × 10 -5 cm 2 /s).

Molecular dynamics simulations are performed on two hydrated dipalmitoylphosphatidylcholine bilayer systems: one with pure water and one with added NaCl. Due to the rugged nature of the membrane/electrolyte interface, ion binding to the membrane surface is characterized by the loss of ion hydration. Using this structural characterization, binding of Na(+) and Cl(-) ions to the membrane is observed, although the binding of Cl(-) is seen to be slightly weaker than that of Na(+). Dehydration is seen to occur to a different extent for each type of ion. In addition, the excess binding of Na(+) gives rise to a net positive surface charge density just outside the bilayer. The positive density produces a positive electrostatic potential in this region, whereas the system without salt shows an electrostatic potential of zero.

To study the effect of the interface on the properties of an anionic surfactant molecule, sodium dodecyl sulfate (SDS), we performed two molecular dynamics computer simulations. In one simulation, the behavior of SDS at the water−vapor interface was examined. In parallel, we performed a simulation with the molecule embedded at the water−CCl4 interface. A substantial difference in the configurational properties of the amphiphile was observed. At the water−vapor interface, the solute in its most probable configuration was bent, giving rise to two domains within the molecule:  the first, containing the head group and several methyl groups, was solvated in water; the second, containing the rest of the molecule, lay down on the water surface. In contrast to these results, the molecule at the water−CCl4 interface was straight on average, with a inclination of approximately 40° from the surface normal.