Ewald methods for inverse power-law interactions in tridimensional and quasi-two-dimensional systems

In this paper, we derive the Ewald method for inverse power-law interactions in quasi-two-dimensional systems. The derivation is done by using two different analytical methods. The first uses Parry's limit that considers the Ewald methods for quasi-two-dimensional systems as a limit of the Ewald methods for tridimensional systems; the second uses Poisson-Jacobi identities for lattice sums. Taking into account the equivalence of both derivations, we obtain a new analytical Fourier transform integral involving an incomplete gamma function. Energies of the generalized restrictive primitive model of electrolytes (η-RPM) and of the generalized one-component plasma model (η-OCP) are given for the tridimensional, quasi-two-dimensional and monolayers systems. Few numerical results, using Monte Carlo simulations, for η-RPM and η-OCP monolayer systems are reported.