One-Center Corrected Two-Electron Integrals in Inner Projection based Integral Evaluation

Cholesky decomposition (CD) of the two-electron integrals and the resolution-of-identity (RI) techniques are established inner projection methods to efficiently evaluate the 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 -- the atomic CD (aCD) and atomic compact CD (acCD) auxiliary basis sets, different to the precomputed auxiliary basis sets -- the Karlsruhe type of auxiliary basis sets. The accuracy of these approximations in the RI approach can be further improved via an explicit correction of the one-centered two-electron integrals, which is the main object of this research. Correcting the one-centered 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 errors as of the uncorrected approach. The benchmarks of the one-center corrections applied to several auxiliary basis set types were investigated in this paper.