  The Auxiliary-Field Quantum Monte Carlo (AFQMC) algorithm is a powerful
quantum many-body method that can be used successfully as an alternative to
standard quantum chemistry approaches to compute the ground state of many body
systems, such as molecules and solids, with high accuracy. In this article we
use AFQMC with trial wave-functions built from non-orthogonal multi Slater
determinant expansions to study the energetics of molecular systems, including
the 55 molecules of the G1 test set and the isomerization path of the
$[Cu_{2}O_{2}]^{2+}$ molecule. The main goal of this study is to show the
ability of non-orthogonal multi Slater determinant expansions to produce
high-quality, compact trial wave-functions for quantum Monte Carlo methods. We
obtain systematically improvable results as the number of determinants is
increased, with high accuracy typically obtained with tens of determinants.
Great reduction in the average error and traditional statistical indicators are
observed in the total and absorption energies of the molecules in the G1 test
set with as few as 10-20 determinants. In the case of the relative energies
along the isomerization path of the $[Cu_{2}O_{2}]^{2+}$, our results compare
favorably with other advanced quantum many-body methods, including DMRG and
complete-renormalized CCSD(T). Discrepancies in previous studies for this
molecular problem are identified and attributed to the differences in the
number of electrons and active spaces considered in such calculations.
