Variational Localized Active Space Self-Consistent Field Method

Fragmentation methods applied to multireference wave functions constitute a road toward the application of highly accurate ab initio wave function calculations to large molecules and solids. However, it is important for reproducibility and transferability that a fragmentation scheme be well defined with minimal dependence on initial orbital guesses or user-designed ad hoc fragmentation schemes. One way to improve this sort of robustness is to ensure that the energy obeys a variational principle; that is, the active orbitals and active space wave functions minimize the electronic energy in a certain ansatz for the molecular wave function. We extended the theory of the localized active space self-consistent field, LASSCF, method (JCTC 2019, 15, 972) to fully minimize the energy with respect to all orbital rotations, rendering it truly variational. The new method, called vLASSCF, substantially improves the robustness and reproducibility of the LAS wave function compared to LASSCF. We analyze the storage and operation cost scaling of vLASSCF compared to orbital optimization using a standard complete active space self-consistent field (CASSCF) approach, and we show results of vLASSCF calculations on some simple test systems. We show that vLASSCF is energetically equivalent to CASSCF in the limit of one active subspace and that vLASSCF significantly improves upon the reliability of LASSCF energy differences, allowing for more meaningful and subtle analysis of potential energy curves of dissociating molecules. We also show that all forms of LASSCF have a lower operation cost scaling than the orbital optimization part of CASSCF.