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Resolutions of the Coulomb operator

Varganov, S.A.; Gilbert, A.T.B.; Deplazes, E.; Gill, P.M.W.

Journal of Chemical Physics 128(20): 201104

2008

We discuss a generalization of the resolution of the identity by considering one-body resolutions of two-body operators, with particular emphasis on the Coulomb operator. We introduce a set of functions that are orthonormal with respect to 1r(12) and propose that the resulting "resolution of the Coulomb operator," r(12) (-1)=mid R:phi(i)phi(i)mid R:, may be useful for the treatment of large systems due to the separation of two-body interactions. We validate our approach by using it to compute the Coulomb energy of large systems of point charges.

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