Coulomb potentials in two and three dimensions under periodic boundary conditions

Details Coulomb potentials in two and three dimensions under periodic boundary conditions Coulomb potentials in two and three dimensions under periodic boundary conditions

2004-07-28

arxiv.org/abs/cond-mat/0407736v3

Physics

Condensed Matter

Soft Condensed Matter

Generalization of the work done in cond-mat/0405574. To appear in J. Chem. Physics. A few typos have been corrected

Scientific paper

10.1063/1.1824031

A method to sum over logarithmic potential in 2D and Coulomb potential in 3D with periodic boundary conditions in all directions is given. We consider the most general form of unit cells, the rhombic cell in 2D and the triclinic cell in 3D. For the 3D case, this paper presents a generalization of Sperb's work [R. Sperb, Mol. Simulation, \textbf{22}, 199-212(1999)]. The expressions derived in this work converge extremely fast in all region of the simulation cell. We also obtain results for slab geometry. Furthermore, self-energies for both 2D as well as 3D cases are derived. Our general formulas can be employed to obtain Madelung constants for periodic structures.

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