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The Bertaut approach associated with charge spreading so as to enhance therate of convergence of Coulomb series in crystals is extended to the case of anarbitrary multiple spreading with a given initial spreading function. It isshown that the effect of spreading may in general be treated as a uniformtransformation of space, providing that zero mean potential as a universalspatial property is sustained. As a result, electrostatic potentials driven bydifferent orders of multiple spreading can be obtained from the same energyfunctional in a consistent manner. It is found that the effect of multiplespreading gives rise to more advanced forms described, for example, by simpleexponential decrease, but the functional description based on a Gaussianspreading turns out to be invariant. In addition, the effects of a multiplecharge spreading based on simple exponential and Gaussian spreading functionsare compared as typical of molecular calculations.

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