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.Comment: The context of this note is the implementation of TDDFT linear
response for extended molecular system
