Pfaffian pairing and backflow wavefunctions for electronic structure quantum Monte Carlo methods

We investigate pfaffian trial wavefunctions with singlet and triplet pair orbitals by quantum Monte Carlo methods. We present mathematical identities and the key algebraic properties necessary for efficient evaluation of pfaffians. Following upon our previous study [Bajdich et al., Phys. Rev. Lett. 96, 130201 (2006)], we explore the possibilities of expanding the wavefunction in linear combinations of pfaffians. We observe that molecular systems require much larger expansions than atomic systems and linear combinations of a few pfaffians lead to rather small gains in correlation energy. We also test the wavefunction based on fully anti-symmetrized product of independent pair orbitals. Despite its seemingly large variational potential, we do not observe additional gains in correlation energy. We find that pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wavefunctions and exhibit the minimal number of two nodal domains in agreement with recent results on fermion nodes topology. We analyze the nodal structure differences of Hartree-Fock, pfaffian, and essentially exact large-scale configuration interaction wavefunctions. Finally, we combine the recently proposed form of backflow correlations [Drummond et al., J. Phys. Chem. 124, 22401 (2006); Rios et al., Phys. Rev. E. 74, 066701 (2006)] with both determinantal and pfaffian based wavefunctions.