Integral evaluation algorithms and their implementation

Abstract Three different algorithms for the calculation of many center electron‐repulsion integrals are discussed, all of which are considered to be economic in terms of the number of arithmetic operations. The common features of the algorithms are as follows: Cartesian Gaussian functions are used, integrals are calculated by blocks (a block being defined as the set of integrals obtainable from four given exponents on four given centers), and functions may be adopted to R (3). Adaption to molecular point group symmetry is not considered. Tables are given showing the minimum number of operations for a selection of block types allowing one to identify the theoretically most economic, and the corresponding salient features. Comments concerning the computer implementations are also given both on sealar and vector processors. In particular, the Cyber 205 is considered, a vector processor on which we have implemented what we believe to be the most efficient algorithm.