The fundamental ERI , which is the basis of all ERI algorithms, is usually represented asGill:1994a
which can be reduced to a one-dimensional integral of the form
and can be efficiently computed using a modified Chebyshev interpolation scheme.Gill:1991a Equation (B.4) can also be adapted for the general case integrals required for most calculations. Following the fundamental ERI, building up to the full bra-ket ERI (or intermediary matrix elements, see later) are the problems of angular momentum and contraction.
Note: Square brackets denote primitive integrals and parentheses denote fully-contracted integrals.