Tensor HyperContraction: A Physically Motivated Compression of the Electron Repulsion Integral

Robert Parrish, Georgia Institute of Technology

The Electron Repulsion Integral (ERI) is an order-four tensor encapsulating the two-body Coulomb interaction between electrons in molecular electronic structure theory. Operations involving generation, manipulation and storage of this tensor are a major hurdle in the tractability of electronic structure methods. Recently, we have shown that a physically motivated order-two tensor compression scheme exists for the ERI. This Tensor HyperContraction (THC) representation allows for substantial memory compression and formal scaling reductions in electronic structure. Additionally, we have shown that, for particular but widely used basis sets, the compression is lossless, regardless of the local potential operator used. The latter finding has significant application in nuclear structure. Overall, THC shows significant promise for increasing the tractability limits of many-body quantum computations.

Abstract Author(s): Robert M. Parrish, C. David Sherrill, Edward G. Hohenstein, and Todd J. Martínez