Direct summation of dipole-dipole interactions using the Wolf formalism

Abstract

We present an expanded Wolf formalism for direct summation of long-range dipole-dipole interactions and rule-of-thumbs how to choose optimal spherical cutoff (Rc) and damping parameter (α). This is done by comparing liquid radial distribution functions, dipole-dipole orientation correlations, particle energies, and dielectric constants, with Ewald sums and the Reaction field method. The resulting rule states that ασ < 1 and αRc > 3 for reduced densities around ρ(∗) = 1 where σ is the particle size. Being a pair potential, the presented approach scales linearly with system size and is applicable to simulations involving point dipoles such as the Stockmayer fluid and polarizable water models.

Electrostatic pair-potentials based on the Poisson equation

“…Thus optimal parameters for ordered systems seems to imply optimal parameters in unordered systems, yet the reverse does not necessarily hold. For reasonably large values of C (or D) C;D implies that equation (12) can be wellapproximated by equation (16) which is a relatively computationally inexpensive function and shows great resemblance with other short-ranged functions suited for summation of long-ranged electrostatics in thermal systems [4][5][6][8][9][10][11][12][13]. In fact, some of these are special cases of equation (12) with specific values of C or D. For example [9][10][11] using C=D=1, C=D=2, and C=D+1=4, which thus support our conclusions on the optimal parameters.…”

“…We have now seen that Q(q) can be described among others by the complementary error-function. The complementary error-function has been utilized in many previous summation schemes without solid theoretical justification [4][5][6][8][9][10][11][12][13], whereas we here connect this (approximate) Gaussian distribution of the charge directly to requirements of the Poisson equation. However, whereas seemingly all such schemes includes erfc(η q) in their short-ranged functions, where η is some arbitrary parameter, we argue that it should rather be the shifted…”

Fast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. III. Application to crystal structures via the Ewald and direct summation methods

“…The method used for the computation of pairwise electrostatic energies in the crystal may include either a multipole moment approximation (Buckingham, 1967(Buckingham, , 1978Buckingham et al, 1988;Stone, 1996) or a grid-based numerical integration (Gavezzotti, 2002b(Gavezzotti, , 2003(Gavezzotti, , 2005Ma & Politzer, 2004). In addition, very efficient computational methods, for example the Ewald-type summation (Cummins et al, 1976;de Leeuw et al, 1980;Heyes, 1981;Allen & Tildesley, 1987;Williams, 1989;Smith, 1998;Su & Coppens, 1995;Toukmaji & Board, 1996;Challacombe et al, 1997;Abramov et al, 2000;Nymand & Linse, 2000;Frenkel & Smit, 2002;Aguado & Madden, 2003;Sagui et al, 2004;Arnold & Holm, 2005;Stenhammar et al, 2011;Giese et al, 2015) and a clever workaround known as the Wolf formalism (Wolf et al, 1999;Zahn et al, 2002;Fennell & Gezelter, 2006;Lamichhane et al, 2014;Stenqvist et al, 2015), have been developed. Nevertheless, the major drawbacks of these methods are well known: the multipole approximation breaks down for overlapping charge distributions, while a numerical approach is rather computationally demanding and subject to grid limitations.…”

Thermally Induced Wurtzite to h‐BN Structural Transition

“…The cutoff of the LJ potential was set to 10 Å, and the potential was shifted as the energy at the cutoff distance became zero. An adapted Wolf method was employed to calculate the Coulombic interaction with a damping parameter of 0.24 and a cutoff radius of 12.5 Å . Compared with the standard Ewald summation method, this adapted Wolf method is able to achieve similar accuracy for the long‐range Coulombic interaction with a much faster computational speed .…”

“…An adapted Wolf method was employed to calculate the Coulombic interaction with a damping parameter of 0.24 and a cutoff radius of 12.5 Å . Compared with the standard Ewald summation method, this adapted Wolf method is able to achieve similar accuracy for the long‐range Coulombic interaction with a much faster computational speed . DFT calculations were carried out using the Quantum ESPRESSO distribution with the SSSP accuracy pseudopotential library (version 0.7) .…”