title: Madelung energy of Yukawa lattices.
abstract: We propose a method to obtain an approximate closed form expression for the Madelung energy (ME) of Yukawa lattices. Such a method is applied for lattices of different topologies and dimensions. The obtained Madelung energies have a satisfactory accuracy for all ranges of the screening parameter κ of the Yukawa potential, and it becomes exact in the asymptotic limits κ→0 and κ→+∞. For instance, for the triangular lattice, the maximum relative error of the ME given by the method is about 0.0047. Also, satisfactory results are obtained for the one-component plasma limit. The Madelung constants of the two-dimensional hexagonal BN and square NaCl and the three-dimensional cubic NaCl crystals are estimated with a relative error of 0.004, 0.006, and 0.03, respectively. Finally, different ways to improve the method are presented and discussed.
authors.affiliation: Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, Brazil. pcnp@df.ufpe.br
authors.forename: P C N
authors.initials: PC
authors.lastname: Pereira
authors.forename: S W S
authors.initials: SW
authors.lastname: Apolinario