Symmetry-adapted integrals over many-electron basis functions and operators

Abstract.

We consider integrals over symmetry-adapted basis functions that involve the coordinates of more than one electron. We focus on basis functions that can be written as products of one-electron functions and (say) a two-electron function. We show first that the two-electron parts of the basis functions can be absorbed into the operator, resulting in an integral over only one-electron basis functions, but a more complicated many-electron operator. We then prove a general formula for expressing such integrals in terms of symmetry-distinct integrals only.