Multiple charge spreading as a generalization of the Bertaut approach to lattice summation of Coulomb series in crystals

Abstract

The Bertaut approach associated with charge spreading so as to enhance the rate of convergence of Coulomb series in crystals is extended to the case of an arbitrary multiple spreading with a given initial spreading function. It is shown that the effect of spreading may in general be treated as a uniform transformation of space, providing that zero mean potential as a universal spatial property is sustained. As a result, electrostatic potentials driven by different orders of multiple spreading can be obtained from the same energy functional in a consistent manner. It is found that the effect of multiple spreading gives rise to more advanced forms described, for example, by simple exponential decrease, but the functional description based on a Gaussian spreading turns out to be invariant. In addition, the effects of a multiple charge spreading based on simple exponential and Gaussian spreading functions are compared as typical of molecular calculations.

Physical meaning of the Ewald sum method

“…In all studies on electrostatic potential and energy of crystals till date, including recent studies [20][21][22], whether based on Ewald method or Fourier method, the emphasis has been on computational issues. No attempt has been made to incorporate the role of thermal vibrations that are universally present in real crystals.…”

Topological quantum correction to an atomic ideal gas law as a dark energy effect

“…On the other hand, in the isotropic case of interest we believe that all the unit-cell parameters increases in the same manner so that they can be described in the form r x = r y = r z = x 0 Q, where Q is a variable dimensionless parameter. Substituting the latter relation into formula (7), where each square brackets gives the same result, we get…”

“…The traditional ambiguity about the bulk electrostatic potentials in crystals is due to the conditional convergence of Coulomb series [1,2]. The classical Ewald approach [3,4] turns out to be the first one resolving this task as consistent with a translational symmetry [5][6][7]. The latter result appears to be directly associated with the thermodynamic limit in crystals [8].…”

“…It is surprising that relation (10) can be addressed to the cosmological problem. Indeed, the expansion of v as a local effect leading to relation (7) can happen in the most natural way on the surface of the Friedman threedimensional hypersphere [10], providing that the radius of that hypersphere increases. In this event the value Q/Q may be associated with the Hubble function [17,18] H 0 dependent on the initial gas density.…”