Coulomb potentials in two and three dimensions under periodic boundary conditions
arXiv:cond-mat/0407736 · doi:10.1063/1.1824031
Abstract
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.
Generalization of the work done in cond-mat/0405574. To appear in J. Chem. Physics. A few typos have been corrected
References in corpus (2)
Cited by in corpus (4)
- Damped reaction field method and the accelerated convergence of the real space Ewald summation
- Rapid evaluation of the periodic Green's function in d dimensions
- Logarithmic interaction under periodic boundary conditions: Closed form formulas for energy and forces
- Evaluation of Coulomb potential in a triclinic cell with periodic boundary conditions