  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.
