Accuracy of Localized Resolution of the Identity in Periodic Hybrid Functional Calculations with Numerical Atomic Orbitals.

We present an implementation of hybrid density functional approximations for periodic systems within a pseudopotential-based, numerical atomic orbital (NAO) framework. The two-electron Coulomb repulsion integrals (ERIs) are evaluated using the localized resolution-of-the-identity (LRI) approximation. The accuracy of the LRI approximation is benchmarked unambiguously against independent reference results obtained via a computational scheme whereby the ERIs are accurately evaluated by expanding the products of NAOs in terms of plane waves. An alternative strategy for constructing auxiliary basis sets is proposed, and its accuracy is assessed and compared to the previously used procedure. Finally, the reliability of our algorithm and implementation is benchmarked against other established implementations within different numerical frameworks in terms of the calculated band gap values of a set of semiconductors and insulators.