Abstract
Existing approximation to the softness kernel, successfully explored in earlier work, has been extended; the normal Gauss distribution function has been used instead of the Dirac delta. The softness kernel becomes continuous functions in space and may be used to calculate the linear response function of the electron density. Three-dimensional visualization of the softness kernel and the linear response function are presented for a nitrogen atom as a working example. By using a single parameter of the spatial Gauss distribution, the novel softness kernel has been adjusted to be consistent with the standard form of the hardness kernel, representing the leading fraction of the electronic interactions in the system.
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