^{1,a)}, Per Linse

^{1}and Gunnar Karlström

^{2}

### Abstract

Long-range solvation properties of strongly coupled dipolar systems simulated using the Ewald and reaction field methods are assessed by using electric fluctuation formulas for a dielectric medium. Some components of the fluctuating electric multipole moments are suppressed, whereas other components are favored as the boundary of the simulation box is approached. An analysis of electrostatic interactions in a periodic cubic system suggests that these structural effects are due to the periodicity embedded in the Ewald method. Furthermore, the results obtained using the reaction field method are very similar to those obtained using the Ewald method, an effect which we attribute to the use of toroidal boundary conditions in the former case. Thus, the long-range solvation properties of polar liquids simulated using either of the two methods are nondielectric in their character.

Financial support by the Swedish Research Council (VR) through the Linnaeus grant for the Organizing Molecular Matter (OMM) center of excellence and generous computer time at LUNARC as well as the National Supercomputer Center (NSC) are gratefully acknowledged.

I. INTRODUCTION

II. THEORY

A. Electric fluctuations in dielectric media

B. Electrostatic self-interactions in a primitive cubic lattice

III. MODEL AND METHODS

A. Model

B. Simulation aspects

C. Fluctuating multipole moment analyses

D. Evaluation of lattice self-interaction energies

IV. RESULTS AND DISCUSSION

A. Qualitative behavior of probability distributions

B. Ewald summation

C. Reaction field

V. CONCLUSIONS AND OUTLOOK

### Key Topics

- Dielectrics
- 16.0
- Boundary value problems
- 12.0
- Electrostatics
- 12.0
- Electric dipole moments
- 10.0
- Dielectric properties
- 8.0

## Figures

Illustration of two nonoverlapping charge distributions and .

Illustration of two nonoverlapping charge distributions and .

Probability distributions for three components of the quadrupole moment obtained from simulations using (a) Ewald summation (curves) and the RF method (symbols) and (b) the MI convention using particles and .

Probability distributions for three components of the quadrupole moment obtained from simulations using (a) Ewald summation (curves) and the RF method (symbols) and (b) the MI convention using particles and .

Reduced mean-squared multipole moment as a function of the radius of the sampling volume for obtained using Ewald summation with vacuum boundaries for a system with particles. The error bars represent one standard deviation.

Reduced mean-squared multipole moment as a function of the radius of the sampling volume for obtained using Ewald summation with vacuum boundaries for a system with particles. The error bars represent one standard deviation.

Reduced mean-squared multipole moment as a function of the radius of the sampling volume for obtained using Ewald summation with tin-foil boundaries for a system with particles. The error bars represent one standard deviation.

Reduced mean-squared multipole moment as a function of the radius of the sampling volume for obtained using Ewald summation with tin-foil boundaries for a system with particles. The error bars represent one standard deviation.

Reduced mean-squared quadrupole moment as a function of the reduced radius of the sampling volume obtained using Ewald summation with tin-foil boundaries at the indicated system sizes. The color labeling is the same as in Fig. 4(b). The error bars represent one standard deviation.

Reduced mean-squared quadrupole moment as a function of the reduced radius of the sampling volume obtained using Ewald summation with tin-foil boundaries at the indicated system sizes. The color labeling is the same as in Fig. 4(b). The error bars represent one standard deviation.

Reduced mean-squared quadrupole moment as a function of the radius of the sampling volume obtained using Ewald summation with tin-foil boundaries at the indicated system sizes. The color labeling is the same as in Fig. 4(b). The error bars represent one standard deviation.

Reduced mean-squared quadrupole moment as a function of the radius of the sampling volume obtained using Ewald summation with tin-foil boundaries at the indicated system sizes. The color labeling is the same as in Fig. 4(b). The error bars represent one standard deviation.

Reduced multipole moment as a function of the radius of the sampling volume for obtained using the RF approach for a system with particles. The error bars represent one standard deviation.

Reduced multipole moment as a function of the radius of the sampling volume for obtained using the RF approach for a system with particles. The error bars represent one standard deviation.

Illustration of a possible mechanism behind the suppression of fluctuations in the RF method: dipole 1 in the central box interacts repulsively with the nearest image of dipole 2 (labeled with a star), leading to the suppression of the depicted quadrupole moment of the central box. A rotation of the depicted structure by 45° would instead lead to an attractive interaction, which would favor the corresponding fluctuation mode.

Illustration of a possible mechanism behind the suppression of fluctuations in the RF method: dipole 1 in the central box interacts repulsively with the nearest image of dipole 2 (labeled with a star), leading to the suppression of the depicted quadrupole moment of the central box. A rotation of the depicted structure by 45° would instead lead to an attractive interaction, which would favor the corresponding fluctuation mode.

## Tables

Self-energies of the independent components of the multipole moments and according to Eq. (13). The values used for and are described in Sec. III D, and the simulated values were obtained from an Ewald simulation with vacuum boundaries and .

Self-energies of the independent components of the multipole moments and according to Eq. (13). The values used for and are described in Sec. III D, and the simulated values were obtained from an Ewald simulation with vacuum boundaries and .

and calculated from the simulated values of for systems of three different sizes. The attractive and repulsive values are mean values of the three attractive (, , and ) and two repulsive ( and ) modes, respectively.

and calculated from the simulated values of for systems of three different sizes. The attractive and repulsive values are mean values of the three attractive (, , and ) and two repulsive ( and ) modes, respectively.

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