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The accuracy and efficiency of ab-initio quantum Monte Carlo (QMC) algorithmsbenefits greatly from compact variational trial wave functions that accuratelyreproduce ground state properties of a system. We investigate the possibilityof using multi-Slater-Jastrow trial wave functions with non-orthogonaldeterminants by optimizing identical single particle orbitals independently inseparate determinants. As a test case, we compute variational and fixed-nodediffusion Monte Carlo (FN-DMC) energies of a C$_2$ molecule. For a givenmulti-determinant expansion, we find that this non-orthogonal orbitaloptimization results in a consistent improvement in the variational energy andthe FN-DMC energy on the order of a few tenths of an eV. Our calculationsindicate that trial wave functions with non-orthogonal determinants can improvecomputed energies in a QMC calculation when compared to their orthogonalcounterparts.

Non-orthogonal determinants in multi-Slater-Jastrow trial wave functions for fixed-node diffusion Monte Carlo