A fifth-order method for two-electron integral derivative transformation

A new method for transforming first derivatives of two-electron integrals with respect to nuclear positions from the atomic orbital basis to the molecular orbital basis is presented. It has a floating point operation count proportional to the fifth power of molecular size, unlike conventional sixth-order algorithms. Additionally far less data transfer is required. This development reduces a major step in obtaining analytical force constants at the second-order Moller—Plesset level of theory, and is generally useful in evaluating correlated force constants. An implementation of the method is described, and illustrative calculations are reported.