Optimizing the Four-Index Integral Transform Using Data Movement Lower Bounds Analysis

Abstract

The four-index integral transform is a fundamental and computationally demanding calculation used in many computational chemistry suites such as NWChem. It transforms a four-dimensional tensor from one basis to another. This transformation is most efficiently implemented as a sequence of four tensor contractions that each contract a four- dimensional tensor with a two-dimensional transformation matrix. Differing degrees of permutation symmetry in the intermediate and final tensors in the sequence of contractions cause intermediate tensors to be much larger than the final tensor and limit the number of electronic states in the modeled systems.