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The series expansion formulae are established for the one- and two-centercharge densities over complete orthonormal sets of exponential type orbitalsintroduced by the author. Three-center overlap integrals of appearing in theserelations are expressed through the two-center overlap integrals between-orbitals. The general formulae obtained for the charge densities are utilizedfor the evaluation of arbitrary multicenter-multielectron integrals occurringwhen the complete orthonormal sets of exponential type orbitals are used asbasis functions in the Hartree-Fock-Roothaan and explicitly correlated methods.The relationships for charge densities and multicenter-multielectron integralsobtained are valid for the arbitrary quantum numbers, screening constants andlocation of orbitals.

Expansion formulae for one- and two-center charge densities over  complete orthonormal sets of exponential type orbitals and their use in  evaluation of multicenter-multielectron integrals