Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants

Abstract

The effective interactions of ions, dipoles and higher-order multipoles under periodic boundary conditions are calculated where the array of periodic replications forms an infinite sphere surrounded by a vacuum. Discrepancies between the results of different methods of calculation are resolved and some shape-dependent effects are discussed briefly. In a simulation under these periodic boundary conditions, the net Hamiltonian contains a positive term proportional to the square of the net dipole moment of the configuration. Surrounding the infinite sphere by a continuum of dielectric constant ε.' changes this positive term, the coefficient being zero as ε' ->∞ . We report on the simulation of a dense fluid of hard spheres with embedded point dipoles; simulations are made for different values of showing how the Kirkwood gr-factor and the long-range part of hA (r) depend on ε' in a finite simulation. We show how this dependence on ε' nonetheless leads to a dielectric constant for the system that is independent of ε . In particular, the Clausius-Mosotti and Kirkwood formulae for the dielectric constant e of the system give consistent ε values.

DL_MULTI—A molecular dynamics program to use distributed multipole electrostatic models to simulate the dynamics of organic crystals

“…As has been noted above, for dipole dipole interactions there is no self interaction term in the spherical harmonic case. The Cartesian direct space sum also contains a first order term in equation (39) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 energy of zero for a unit cell with one particle consisting of a lattice of dipoles all pointing in the same direction, in agreement with [59].…”

Computational methodology for solubility prediction: Application to the sparingly soluble solutes

“…We used real atomic masses. LAMMPS' default PPPM (Particle-Particle-Particle-Mesh) summation 63,64 with tin-foil boundary conditions 65 was used for all long-range electrostatics. Gauss-Legendre quadrature method 66 and the trapezoid rule 67 were used for TI.…”

The (Non-)Local Density of States of Electronic Excitations in Organic Semiconductors

“…In organic semiconductors, the lead-ing multipole moment in the expansion of the charge density originates from the molecular quadrupole. The charge-quadrupole interaction energy scales as r −3 with distance r. Therefore, the energy of a molecular ion embedded in a 3D-infinite bulk environment is conditionally convergent, i.e., can in principle assume any value depending on the surface structure [147]. The situation is mitigated in lower-dimensional systems.…”