On an "interaction by moments" property of four center integrals
Abstract
Description
The four center integrals needed in the Hartree Fock approximation and in TDDFT linear response are known to be difficult to calculate for orbitals of the Slater type or of finite range. We show that the interaction of pairs of products that do not mutually intersect may be replaced by the interaction of their moments, of which there are O(N). Only quadruplets of orbitals 'close' to one another need an explicit calculation and the total calculational effort therefore scales as O(N). We provide a new and concise proof of this "interaction by moments" property.
The context of this note is the implementation of TDDFT linear response for extended molecular systems
The context of this note is the implementation of TDDFT linear response for extended molecular systems