As quantum chemistry calculations deal with molecular systems of increasing size, the memory requirement to store electron-repulsion integrals (ERIs) greatly outpaces the physical memory available in computing hardware. The Cholesky decomposition of ERIs provides a convenient yet accurate technique to reduce the storage requirement of integrals. Recent developments of a two-step algorithm have drastically reduced the memory operation (MOP) count, leaving the floating operation (FLOP) count as the last frontier of cost reduction in the Cholesky ERI algorithm. In this report, we introduce a dynamic integral tracking, reusing, and compression/elimination protocol embedded in the two-step Cholesky ERI method. Benchmark studies suggest that this technique becomes particularly advantageous when the basis set consists of many computationally expensive high-angular-momentum basis functions. With this dynamic ERI improvement, the Cholesky ERI approach proves to be a highly efficient algorithm with minimal FLOP and MOP count.<br/>Besides, we also extend the method to approximate spin-orbit two-electron integrals in four-component quantum chemistry computations. In this way, Dirac-Coulomb and Gaunt interactions are simulated in dramatically reduced time and memory requirements, which flatten the pathway to accurate computational chemistry study of heavy elements.

Efficient Cholesky decomposition of electron repulsion integrals and applications in relativistic quantum chemistry computation

ACS Fall 2021

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