Multi-component symmetry-projected approach for molecular ground state correlations

The symmetry-projected Hartree--Fock ansatz for the electronic structure problem can efficiently account for static correlation in molecules, yet it is often unable to describe dynamic correlation in a balanced manner. Here, we consider a multi-component, systematically-improvable approach, that accounts for all ground state correlations. Our approach is based on linear combinations of symmetry-projected configurations built out of a set of non-orthogonal, variationally optimized determinants. The resulting wavefunction preserves the symmetries of the original Hamiltonian even though it is written as a superposition of deformed (broken-symmetry) determinants. We show how short expansions of this kind can provide a very accurate description of the electronic structure of simple chemical systems such as the nitrogen and the water molecules, along the entire dissociation profile. In addition, we apply this multi-component symmetry-projected approach to provide an accurate interconversion profile among the peroxo and bis($\mu$-oxo) forms of [Cu$_2$O$_2$]$^{2+}$, comparable to other state-of-the-art quantum chemical methods.