Convergence peculiarities of lattice summation upon multiple charge spreading generalizing the Bertaut approach

Within investigating the multiple charge spreading generalizing the Bertaut approach, a set of spreading functions with a polynomial behaviour restricted in space, but defined so as to enhance the rate of convergence of Coulomb series even upon a single spreading, is proposed. It is shown that multiple spreading is ultimately effective especially in the case when the spreading functions of neighbouring point charges overlap. In the cases of a simple exponential and a Gaussian spreading functions the effect of multiplicity of spreading on the rate of convergence is discussed along with an additional optimization of the spreading parameter in dependence on the cut-off parameters of lattice summation. All the effects are demonstrated on a simple model NaCl structure.