Revealing correlation mechanisms through nonorthogonal multiconfiguration self-consistent field calculations

The presence of spin and spatial symmetry breaking upon variational optimization of mean-field wavefunctions is known to be an indicator of nondynamical electron correlation. However, a single mean-field wavefunction may not have sufficient flexibility to flag the correlated orbital space where there are multiple correlation mechanisms present. In such situations, there are multiple nearly degenerate self-consistent field solutions that describe different correlation mechanisms, but it is often not possible to know a priori when such situations will occur or if sufficient solutions have been obtained. In this work, we examine the role of spin and spatial symmetries of nonorthogonal multiconfigurational self-consistent field (NOMCSCF) calculations in revealing correlation mechanisms. We provide details of the theory for optimization of NOMCSCF wavefunctions with desired symmetries, establish which types of symmetries recover the most correlation energy when the symmetry constraints are relaxed, and discuss how the different-orbitals for different-configuration wavefunctions reveal the different correlation mechanisms present.