Correcting Approximated Two-electron Integrals

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 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 accuracy as of the uncorrected approach.