A new, fast, semi-direct implementation of linear scaling local coupled cluster theory

Abstract

A new way to compute the external exchange matrices in the local coupled cluster (LCC) theory is presented, which eliminates the most important bottleneck of our previous linear scaling LCC methods. It is based on a decomposition of the transformed two-electron integral set involving four external indices into blocks belonging to quadruples of atoms. A new additional transformation module was developed, which generates this very compact 4-external integral set before the LCC iteration loop is entered. The length of this integral set and the computational cost for producing it scale linearly with molecular size. Using these precomputed integrals, their contraction with the amplitudes, i.e. the assembly of the external exchange matrices occurring in each LCC iteration now is performed directly in the (external) space of the projected AOs (AOs, atomic orbitals) rather than in AO basis as previously, and proceeds exceedingly fast (3 min compared to 15 h with our previous algorithm, for the largest test-molecule considered in this paper).