Real space electrostatics for multipoles. II. Comparisons with the Ewald sum

Abstract

We report on tests of the shifted potential (SP), gradient shifted force (GSF), and Taylor shifted force (TSF) real-space methods for multipole interactions developed in Paper I of this series, using the multipolar Ewald sum as a reference method. The tests were carried out in a variety of condensed-phase environments designed to test up to quadrupole-quadrupole interactions. Comparisons of the energy differences between configurations, molecular forces, and torques were used to analyze how well the real-space models perform relative to the more computationally expensive Ewald treatment. We have also investigated the energy conservation, structural, and dynamical properties of the new methods in molecular dynamics simulations. The SP method shows excellent agreement with configurational energy differences, forces, and torques, and would be suitable for use in Monte Carlo calculations. Of the two new shifted-force methods, the GSF approach shows the best agreement with Ewald-derived energies, forces, and torques and also exhibits energy conservation properties that make it an excellent choice for efficient computation of electrostatic interactions in molecular dynamics simulations. Both SP and GSF are able to reproduce structural and dynamical properties in the liquid models with excellent fidelity.

Real space electrostatics for multipoles. III. Dielectric properties

“…One of the findings of the second paper in this series is that the moderately damped GSF and SP methods were most suitable for molecular dynamics and Monte Carlo simulations, respectively. 12 Our current results show that dielectic properties like ε and G K (r) are sensitive probes of local treatment of electrostatic damping for the new real space methods, as well as for the Ewald sum.…”

“…11 The second paper in this series evaluated the fidelity with which the three new methods reproduced Ewald-based results for a number of model systems. 12 One of the major findings was that moderately-damped GSF simulations produced nearly identical behavior with Ewald-based simulations, but the real-space methods scale linearly with system size.…”

“…where the functions v 21 (r) and v 22 (r) depend on the level of the approximation. 11,12 Although the Taylor-shifted (TSF) and gradient-shifted (GSF) models produce to the same v(r) function for point charges, they have distinct forms for the dipole-dipole interaction.…”

Long-range electrostatic corrections in multipolar/polarizable QM/MM simulations

“…While the higher-order moments are neglected in most of this discussion, these long-range methods can readily be extended to include the full multipole–multipole and polarizable interactions [28, 29]. …”

“…The LREC approach uses a combination of a smoothing function and the minimum image convention to scale the electrostatic interactions such that the potential and forces smoothly decrease to zero at a finite cutoff radius. While energy and force shifting approaches also smoothly truncate the potential at a finite radius [16, 28, 29, 35, 36, 44, 49], LREC has an exceptionally simple implementation in the QM/MM Hamiltonian. In the LREC approach, the external MM monopoles are scaled based on their distance from the QM region, which does not require modifications to the matrix elements or post-SCF corrections.…”