Ewald methods in molecular dynamics for systems of finite extent in one of three dimensions

Rhee, Yuna; Halleý, J. W.; Hautman, Joseph; Rahman, A.

doi:10.1103/physrevb.40.36

Cited by 74 publications

(57 citation statements)

References 12 publications

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“…Partially periodic boundary conditions consist of taking periodic boundary conditions for only one or two dimensions, while the remaining dimensions are considered with their finite extension. For these systems, straightforward applications of the Ewald summations lead to a computational effort that scales as N 2 and not as N 3/2 , because the analytical formulation of the electrostatic energy of this kind of systems is more complicated than for bulk-like systems [9][10][11][12][13][14][15]. To compute coulombic or dipolar energies in these quasi-two (or quasi-one) dimensional systems, several others methods have been proposed [9,[16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Lekner summations and Ewald summations for quasi-two-dimensional systems

Mazars

2005

Molecular Physics

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Using the specific model of a bilayer of classical charged particles (bilayer Wigner crystal), we compare the predictions for energies and pair distribution functions obtained by Monte Carlo simulations using three different methods available to treat the long range Coulomb interactions in systems periodic in two directions but bound in the third one. The three methods compared are: the Ewald method for quasi-two dimensional systems [D.E. Parry, Surf. Sci. 49, 433 (1975); ibid., 54, 195 (1976)], the Hautman-Klein method [J. Hautman and M.L. Klein, Mol. Phys. 75, 379 (1992)] and the Lekner summations method [J. Lekner, Physica A176, 485 (1991)]. All of the three method studied in this paper may be applied to any quasi-two dimensional systems, including those having not the specific symmetry of slab systems. For the particular system used in this work, the Ewald method for quasi-two dimensional systems is exact and may be implemented with efficiency; results obtained with the other two methods are systematically compared to results found with the Ewald method. General recommendations to implement with accuracy, but not always with efficiency, the Lekner summations technique in Monte Carlo algorithms are given.

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Section: Introductionmentioning

confidence: 99%

Lekner summations and Ewald summations for quasi-two-dimensional systems

Mazars

2005

Molecular Physics

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“…The long-ranged contributions to the energies and forces can be determined by a variety of methods. They include transformation to rapidly convergent sums in real space [4], the fast multipole method [5] and various Ewald-type methods [4,[6][7][8][9]. The latter involve summations over the reciprocal lattice of the 2-D lattice.…”

Section: Introductionmentioning

confidence: 99%

Ewald methods for polarizable surfaces with application to hydroxylation and hydrogen bonding on the (012) and (001) surfaces of α-Fe2O3

et al. 1997

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We present a clear and rigorous derivation of the Ewald-like method for calculation of the electrostatic energy of the systems infinitely periodic in two-dimensions and of finite size in the third dimension (slabs). We have generalized this method originally developed by Rhee et al. [Phys. Rev. B 40, 36(1989)] to account for charge-dipole and dipole-dipole interactions and therefore made it suitable for treatment of polarizable systems. This method has the advantage over exact methods of being significantly faster and therefore appropriate for large-scale molecular dynamics simulations. It however involves a Taylor expansion which has to be demonstrated to be of sufficient order. The method was extensively benchmarked against the exact methods by Leckner and Parry. We found it necessary to increase the order of the multipole expansion from 4 (as in original work by Rhee et al.) to 6. In this case the method is adequate for aspect ratios (thickness/shortest side length of the unit cell) ≤ 0.5. Molecular dynamics simulations using the transferable/polarizable model by Rustad et al. were applied to study the surface relaxation of the nonhydroxylated, hydroxylated, and solvated surfaces of α-Fe2O3 (hematite). We find that our nonhydroxylated structures and energies are in good agreement with previous LDA calculations on α-alumina by Manassidis et al. [Surf. Sci. Lett. 285, L517, 1993]. Using the results of molecular dynamics simulations of solvated interfaces, we define end-member hydroxylated-hydrated states for the surfaces which are used in energy minimization calculations. We find that hydration has a small effect on the surface structure, but that hydroxylation has a significant effect. Our calculations, both for gas-phase and solutionphase adsorption, predict a greater amount of hydroxylation for the α-Fe2O3 (012) surface than for the (001) surface. Our simulations also indicate the presence of four-fold coordinated iron ions on the (001) surface.

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“…2 are accepted on the basis of a modified Metropolis criterion involving the probability 19) where the argument of the pseudo Boltzmann factor is given by [35] −β∆ A→A ′ = −β∆U…”

Section: Monte Carlo Methodsmentioning

confidence: 99%

“…Within the last years much work has been done in generalizing and optimizing methods originally designed for three-dimensional Coulombic or dipolar systems, in particular the so-called Ewald summmation methods [11][12][13][14], to "simple" confined geometries such as slits (see e.g., Refs. [15][16][17][18][19][20][21][22]). Up to now most simulations studies for slitlike systems refer to fluids near or in between insulating walls, i.e.…”

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confidence: 99%

Monte-Carlo simulations of strongly interacting dipolar fluids between two conducting walls

Klapp

2006

Molecular Simulation

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Ewald methods in molecular dynamics for systems of finite extent in one of three dimensions

Cited by 74 publications

References 12 publications

Lekner summations and Ewald summations for quasi-two-dimensional systems

Lekner summations and Ewald summations for quasi-two-dimensional systems

Ewald methods for polarizable surfaces with application to hydroxylation and hydrogen bonding on the (012) and (001) surfaces of α-Fe2O3

Monte-Carlo simulations of strongly interacting dipolar fluids between two conducting walls

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