ct7b00366_si_001.pdf (166.56 kB)
Analytic Energy Gradients for Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Theory
journal contribution
posted on 2017-07-21, 00:00 authored by Elvis Maradzike, Gergely Gidofalvi, Justin M. Turney, Henry F. Schaefer, A. Eugene DePrinceAnalytic 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 Å and a
maximum unsigned error of 0.0265 Å, 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 Å, respectively.
For these same molecules, full-valence v2RDM-CASSCF bond lengths computed
in the cc-pVQZ basis set deviate from experimentally determined ones
on average by 0.017 and 0.011 Å when enforcing two- and three-particle
conditions, respectively, whereas CI-CASSCF displays an average deviation
of 0.010 Å. 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 Å when using a cc-pVDZ basis set and a (22e,22o) active
space.
History
Usage metrics
Categories
Keywords
v 2RDM approachfull-valence v 2RDM bond lengths displayvariational 2- RDMequilibriumtwo-particlemethodthree-particleActive Space Self-Consistent Field Theory Analytic energy gradientsfull-valence v 2RDM bond lengthsCI-CASSCFCASSCFLagrangianÅ.basisCIrepresentability conditionsVariational Two-Electron Reduced-Density-Matrix-Drivenactive-space 2- RDMoptimized bond lengthsOrbital response contributionsAnalytic Energy GradientsmoleculeSDP
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC