One-centre corrected two-electron integrals in inner projection-based integral evaluations

Cholesky decomposition (CD) of the two-electron integrals and the resolution-of-identity (RI) techniques are established inner projection methods to efficiently evaluate two-electron integrals. Both approaches share the notion of an auxiliary basis set as a mean to reduce the scaling. In the past years, the close relationship between the two approaches has fostered developments on how to systematically derive unbiased auxiliary basis sets – atomic CD (aCD) and atomic compact CD (acCD) auxiliary basis sets, different to the precomputed auxiliary basis sets. The accuracy of these approximations in the RI approach can be further improved via an explicit correction of the one-centred two-electron integrals, which is the main object of this research. Correcting the one-centred two-electron integrals directly, which scales linear with system size, is expected to provide a new degree of freedom to the design of auxiliary basis sets. This can either be used to gain faster convergence towards the conventional treatment of the two-electron integrals or as a mean to design lighter auxiliary basis sets while maintaining the same accuracy as of the uncorrected approach. The benchmarks of the one-centre corrections applied to several auxiliary basis set types were investigated in this paper.