Spin symmetry breaking in electronic structure theory

Abstract

In this thesis, two electronic structure methods are proposed that leverage symmetry breaking and restoration at the mean-field Hartree-Fock (HF) level to address the electron correlation problem in molecular systems.

A new application of the Generator Coordinate Method (GCM) is presented as an electronic structure method for strong electron correlation in molecular systems. We identify spin fluctuations as an important generator coordinate responsible for strong static electron correlation that is associated with bond-breaking processes. The continuous manifold of basis states for the Hill-Wheeler equations is constructed from spin-constrained Unrestricted HF (c-UHF) states, which is converted into a non-orthogonal configuration interaction (NOCI) expansion. The method was tested on two-electron systems that are dominated by static and/or dynamic correlations.

The spin-projected constrained-unrestricted-Hartree-Fock (SPcUHF) method is also introduced. This approach restores the broken spin symmetry inherent in c-UHF determinants by projecting possible configurations derived from a Clebsch-Gordon recoupling scheme in the spin space and including them in a NOCI basis. Our proposed SPcUHF method recovers missing static correlation and significantly reduces computational costs of full projection without compromising accuracy. When combined with a NOCI-PT2 correction, SPcUHF effectively captures both static and dynamic correlations, offering a robust solution for a wide range of molecular systems.