Analytic Energy Gradients for Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Theory

作者：Maradzike Elvis; Gidofalvi Gergely; Turney Justin M; Schaefer Henry F III; DePrince A Eugene III^*

来源：Journal of Chemical Theory and Computation, 2017, 13(9): 4113-4122.

DOI：10.1021/acs.jctc.7b00366

Analytic energy gradients are presented for a variational two electron reduced-density-matrix (2-RDM)-driven complete active space self consistent field (CASSCF) method. The active-space 2-RDM is determined using a semidefinite programing (SDP) algorithm built upon an augmented Lagrangian formalism. Expressions for analytic gradients are simplified by the fact that the Lagrangian is stationary with respect to variations in both the primal and the dual solutions to the SDP problem. Orbital response contributions to the gradient are identical to those that arise in conventional CASSCF methods in which the electronic structure of the active space is described by a full configuration interaction (CI) wave function. We explore the relative performance of variational 2-RDM (v2RDM)- and 'CI-driven CASSCF for the equilibrium geometries of 20 small molecules. When enforcing two-particle N-representability conditions, full-valence v2RDM-CASSCF-optimized bond lengths display a mean unsigned error of 0.0060 angstrom and a maximum unsigned error of 0:0265 angstrom, relative to those obtained from full-valence CI-CASSCF. When enforcing partial three-particle N-representability conditions, the mean and maximum unsigned errors are reduced to only 0.0006 and 0.0054 angstrom, respectively. For these same molecules, full-valence v2RDM-CASSCF bond lengths computed in the ccpVQZ basis set deviate from experimentally determined ones on average by 0.017 and 0.011 angstrom when enforcing two- and three particle conditions, respectively, whereas CI-CASSCF displays an average deviation of 0.010 angstrom. The v2RDM-CASSCF approach with two-particle conditions is also applied to the equilibrium geometry of pentacene; optimized bond lengths deviate from those derived from experiment, on average, by 0.015 angstrom when using a cc-pVDZ basis set and a (22e,22o) active space.

• 出版日期2017-9