Sundstrom, Eric J. | Search NASA

DOE OSTI2015

A simple way to test for collinearity in spin symmetry broken wave functions: General theory and application to generalized Hartree Fock

We introduce a necessary and sufficient condition for an arbitrary wavefunction to be collinear, i.e., its spin is quantized along some axis. It may be used to obtain a cheap and simple computational procedure to test for collinearity in electronic structure theory calculations. We adapt the procedure for Generalized Hartree Fock (GHF), and use it to study two dissociation pathways in CO{sub 2}. For these dissociation processes, the GHF wave functions transform from low-spin Unrestricted Hartree Fock (UHF) type states to noncollinear GHF states and on to high-spin UHF type states, phenomena that are succinctly illustrated by the constituents of the collinearity test. This complements earlier GHF work on this molecule.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Wavefunction stability analysis without analytical electronic Hessians: application to orbital-optimised second-order Møller–Plesset theory and VV10-containing density functionals

Wavefunction stability analysis is commonly applied to converged self-consistent field (SCF) solutions to verify whether the electronic energy is a local minimum with respect to second-order variations in the orbitals. By iterative diagonalisation, the procedure calculates the lowest eigenvalue of the stability matrix or electronic Hessian. However, analytical expressions for the electronic Hessian are unavailable for most advanced post-Hartree-Fock (HF) wave function methods and even some Kohn-Sham (KS) density functionals. To address such cases, here we formulate the Hessian-vector product within the iterative diagonalisation procedure as a finite difference of the electronic gradient with respect to orbital perturbations in the direction of the vector. As a model application, following the lowest eigenvalue of the orbital-optimised second-order Møller-Plesset perturbation theory (OOMP2) Hessian during H 2 dissociation reveals the surprising stability of the spin-restricted solution at all separations, with a second independent unrestricted solution. We show that a single stable solution can be recovered by using the regularised OOMP2 method (δ-OOMP2), which contains a level shift. Internal and external stability analyses are also performed for SCF solutions of a recently developed range-separated hybrid density functional, ωB97X-V, for which the analytical Hessian is not yet available due to the complexity of its long-range non-local VV10 correlation functional.

Brueckner orbitals↗