Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks
We present a general formulation of analytic nuclear gradients for the coupled-cluster with single and double substitutions (CCSD) and equation-of-motion (EOM) CCSD energies computed using Cholesky decomposition (CD) representations of the electron repulsion integrals (ERIs). By rewriting the correlated energy and response equations such that the storage of the largest four-index intermediates is eliminated, CD leads to a significant reduction in disk storage requirements, reduced I/O penalties, and an improved parallel performance. CD thus extends the scope of the systems that can be treated by (EOM-)CCSD methods, though analytic gradients in the framework of CD are needed to extend the applicability of (EOM-)CCSD methods in the context of geometry optimizations. The paper presents a formulation of analytic (EOM-)CCSD gradient within the CD framework and reports on the salient details of the corresponding implementation. The accuracy and the capabilities of analytic CD based (EOM-)CCSD gradients are illustrated by benchmark calculations and several illustrative examples.