Revealing correlation mechanism through nonorthogonal multiconfiguration self consistent field with spin angular momentum and stability analysis

Through examining the role of spin and spatial symmetries of nonorthogonal multiconfiguration self-consistent field calculations in revealing correlation mechanisms. We provide details of 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 wavefunction reveal the different correlation mechanisms present which also would be analyzed through NOMCSCF electronic hessian eigenvalues and eigenvectors. In addition, different orbital in different configuration which has different spin angular momentum, 2>, through applying resolution of identity and linear combination to obtain non-collinear NOMCSCF solution which is neither wavefunction of 2> nor z>. It also disclosed correlation between different spin state in different configuration and exhibited molecular magnetic properties through magnetization.