Large-Scale Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Methods

A large-scale implementation of the complete active space self-consistent field (CASSCF) method is presented. The active space is described using the variational two-electron reduced-density-matrix (v2RDM) approach, and the algorithm is applicable to much larger active spaces than can be treated using configuration-interaction-driven methods. Density fitting or Cholesky decomposition approximations to the electron repulsion integral tensor allow for the simultaneous optimization of large numbers of external orbitals. We have tested the implementation by evaluating singlet–triplet energy gaps in the linear polyacene series and two dinitrene biradical compounds. For the acene series, we report computations that involve active spaces consisting of as many as 50 electrons in 50 orbitals and the simultaneous optimization of 1892 orbitals. For the dinitrene compounds, we find that the singlet–triplet gaps obtained from v2RDM-driven CASSCF with partial three-electron <i>N</i>-representability conditions agree with those obtained from configuration-interaction-driven approaches to within one-third of 1 kcal mol^–1. When enforcing only the two-electron <i>N</i>-representability conditions, v2RDM-driven CASSCF yields less accurate singlet–triplet energy gaps in these systems, but the quality of the results is still far superior to those obtained from standard single-reference approaches