On the energy per particle in three- and two-dimensional Wigner lattices

Nijboer, B.R.A.; Ruijgrok, Th.W.

doi:10.1007/bf01011562

Cited by 72 publications

(89 citation statements)

References 10 publications

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“…(2.6) of Ref. [17] (a one-dimensional integral presentation of the electrostatic potential) looks quite different from our result in Eq. (6).…”

Section: Discussioncontrasting

confidence: 79%

“…After researching the literature, we became aware of only one previously published work that adopts a similar strategy. This work [17] deals with the energy per particle in an infinite Wigner lattice of electrons in a uniform compensating background. In the process, the authors obtain an expression for the electrostatic potential of the uniformly charged cube as a one-dimensional integral and then proceed to calculate the resulting one-dimensional integral numerically.…”

Section: Discussionmentioning

confidence: 99%

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Concise presentation of the Coulomb electrostatic potential of a uniformly charged cube

Ciftja

2015

Journal of Electrostatics

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a b s t r a c tWe use a novel method to calculate in closed form the Coulomb electrostatic potential created by a uniformly charged cube at an arbitrary point in space. We apply a suitable transformation of variables that allows us to obtain a simple presentation of the electrostatic potential in one-dimensional integral form. The final concise closed form expression of the Coulomb electrostatic potential of the uniformly charged cube is obtained after completing the calculation of the resulting one-dimensional integrals. Such integrals consist of combinations of products of error functions and power functions that can be solved exactly despite their intimidating appearance. The exact analytic formula for the Coulomb electrostatic potential that we derive reflects the symmetry of the cube and is easy to implement. We illustrate its use by calculating the exact values of the electrostatic potential at some points of symmetry such as the center of cube, center of face of cube, center of edge of cube and corner of cube.

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“…(2.6) of Ref. [17] (a one-dimensional integral presentation of the electrostatic potential) looks quite different from our result in Eq. (6).…”

Section: Discussioncontrasting

confidence: 79%

Section: Discussionmentioning

confidence: 99%

Concise presentation of the Coulomb electrostatic potential of a uniformly charged cube

Ciftja

2015

Journal of Electrostatics

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“…Numerical techniques for such integrals have been mentioned above in the context of DFT calculations. In the special case of uniform distribution in a cube some analytic solutions are also known [25,26]. For the energy of distribution of charges, which are represented by six-dimensional integrals of type (1) or (2), save the above-mentioned references, there is a notable lack of specific techniques available.…”

Section: Energy Calculations For Crystalsmentioning

confidence: 99%

On Numerical Approximation of Electrostatic Energy in 3D

Finocchiaro¹,

Pellegrini²,

Bientinesi³

1998

Journal of Computational Physics

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“…In conclusion, expression (A3) shows explicitly that the electrostatic energy of a periodic charged system includes the Madelung self-energies Q 2 ζ/2 of the ions 17,18 . The fact that the Ewald interaction between a pair of particles averages to zero when one particle explores the whole simulation box is also noteworthy aspect of Ewald potential 22 .…”

Section: Discussionmentioning

confidence: 99%

The optimal P3M algorithm for computing electrostatic energies in periodic systems

Ballenegger

Cerda

Lenz

et al. 2008

The Journal of Chemical Physics

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We optimize Hockney and Eastwood's Particle-Particle Particle-Mesh (P3M) algorithm to achieve maximal accuracy in the electrostatic energies (instead of forces) in 3D periodic charged systems. To this end we construct an optimal influence function that minimizes the RMS errors in the energies. As a by-product we derive a new real-space cut-off correction term, give a transparent derivation of the systematic errors in terms of Madelung energies, and provide an accurate analytical estimate for the RMS error of the energies. This error estimate is a useful indicator of the accuracy of the computed energies, and allows an easy and precise determination of the optimal values of the various parameters in the algorithm (Ewald splitting parameter, mesh size and charge assignment order).

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On the energy per particle in three- and two-dimensional Wigner lattices

Cited by 72 publications

References 10 publications

Concise presentation of the Coulomb electrostatic potential of a uniformly charged cube

Concise presentation of the Coulomb electrostatic potential of a uniformly charged cube

On Numerical Approximation of Electrostatic Energy in 3D

The optimal P3M algorithm for computing electrostatic energies in periodic systems

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