  Fragmentation methods applied to multireference wave functions constitute a
road towards 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
the energy obeys a variational principle; i.e., that 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 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.
