title: Analytical gradients of complete active space self-consistent field energies using Cholesky decomposition: geometry optimization and spin-state energetics of a ruthenium nitrosyl complex.
abstract: We present a formulation of analytical energy gradients at the complete active space self-consistent field (CASSCF) level of theory employing density fitting (DF) techniques to enable efficient geometry optimizations of large systems. As an example, the ground and lowest triplet state geometries of a ruthenium nitrosyl complex are computed at the DF-CASSCF level of theory and compared with structures obtained from density functional theory (DFT) using the B3LYP, BP86, and M06L functionals. The average deviation of all bond lengths compared to the crystal structure is 0.042 Å at the DF-CASSCF level of theory, which is slightly larger but still comparable with the deviations obtained by the tested DFT functionals, e.g., 0.032 Å with M06L. Specifically, the root-mean-square deviation between the DF-CASSCF and best DFT coordinates, delivered by BP86, is only 0.08 Å for S0 and 0.11 Å for T1, indicating that the geometries are very similar. While keeping the mean energy gradient errors below 0.25%, the DF technique results in a 13-fold speedup compared to the conventional CASSCF geometry optimization algorithm. Additionally, we assess the singlet-triplet energy vertical and adiabatic differences with multiconfigurational second-order perturbation theory (CASPT2) using the DF-CASSCF and DFT optimized geometries. It is found that the vertical CASPT2 energies are relatively similar regardless of the geometry employed whereas the adiabatic singlet-triplet gaps are more sensitive to the chosen triplet geometry.
authors.affiliation: Department of Chemistry - Ångström, The Theoretical Chemistry Programme, Uppsala University, Box 518, 751 20 Uppsala, Sweden.
authors.forename: Mickaël G
authors.initials: MG
authors.lastname: Delcey
authors.affiliation: Institut für Theoretische Chemie, Universität Wien, Währinger Straße 17, 1090 Vienna, Austria.
authors.forename: Leon
authors.initials: L
authors.lastname: Freitag
authors.affiliation: Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo, Norway.
authors.forename: Thomas Bondo
authors.initials: TB
authors.lastname: Pedersen
authors.affiliation: Department of Chemistry - Ångström, The Theoretical Chemistry Programme, Uppsala University, Box 518, 751 20 Uppsala, Sweden.
authors.forename: Francesco
authors.initials: F
authors.lastname: Aquilante
authors.affiliation: Department of Chemistry - Ångström, The Theoretical Chemistry Programme, Uppsala University, Box 518, 751 20 Uppsala, Sweden.
authors.forename: Roland
authors.initials: R
authors.lastname: Lindh
authors.affiliation: Institut für Theoretische Chemie, Universität Wien, Währinger Straße 17, 1090 Vienna, Austria.
authors.forename: Leticia
authors.initials: L
authors.lastname: González