Non-orthogonal multi-Slater determinant expansions in auxiliary field quantum Monte Carlo

Abstract

We investigate the use of non-orthogonal multi-Slater determinant (NOMSD) expansions as trial wavefunctions in auxiliary field quantum Monte Carlo simulations of molecular systems. We show that NOMSD trial wavefunctions with as few as twenty determinants are sufficient in order to achieve chemical accuracy across most of the G1 molecular test set. We also show that NOMSD trial wavefunctions are useful for more challenging strongly correlated systems by computing relative energies along the isomerization path of the [Cu2O2]2+ molecule. Our results for [Cu2O2]2+ compare favorably with other accurate quantum many-body methods, including density matrix renormalization group and completely renormalized coupled cluster methods.

An auxiliary-Field quantum Monte Carlo perspective on the ground state of the dense uniform electron gas: An investigation with Hartree-Fock trial wavefunctions

“…The statistical variance in the estimator should not be confused with the wavefunction variance in variational MC. Therefore, it is possible to observe some improvement in the statistical error bar while the energy estimator does not improve noticeably as observed before 32 . This long tail in the convergence of the ph-AFQMC energy is indicative that the system is strongly correlated.…”

“…AFQMC has been successfully applied in recent years to a number of challenging problems in both quantum chemistry [29][30][31][32][33] and solid state physics [34][35][36] . However, the broad applicability of the method is not as well under-stood as more traditional quantum chemistry approaches which have seen decades worth of sustained development and benchmarking.…”

“…Singledeterminant trial wavefunctions from Hartree-Fock (HF) or density functional theory calculations have shown remarkable accuracy for a broad range of applications including the two-dimensional Hubbard model 37 , dipolebound anions 38 and solid state applications [39][40][41][42] , with total energies often approaching the accuracy of coupled cluster singles and doubles with perturbative triples CCSD(T) 22 . However, for more strongly correlated systems such as transition metal containing complexes single determinant trial wavefunctions are not sufficiently accurate and multi determinant trial wavefunctions become necessary 32,33,[43][44][45][46] .…”

“…Often short determinantal expansions from complete active space self-consistent field (CASSCF) wavefunctions 31,33 or non-orthogonal multi-Slater deteraminant trial wavefunction 32 can help to restore the accuracy of the method. However, since multideterminant wavefunctions scale exponentially with system size, this approach to improving the trial wavefunction is ultimately limited, particularly for large scale applications.…”

In silico prediction of annihilators for triplet–triplet annihilation upconversion via auxiliary-field quantum Monte Carlo

“…The use of unrestricted single determinant trials has been shown to yield sub-kcal mol −1 accuracy for the triplet energies of polyacenes with closed-shell ground-states, and many biradicaloid molecules with open-shell singlet states that can be qualitatively described by two determinants. 53,68 However, some highly multi-reference systems such as transition metal compounds require the use of non-orthogonal determinant expansions 69 or truncated CASSCF trial wavefunctions 55,70,71 to yield high accuracy. In this work, all AFQMC calculations implement unrestricted single-determinant trial wavefunctions selected according to the AFQMC/U protocol, 53 except for those on the BTD and BSeD derivatives, which were found to exhibit signs of strong correlation ( vide infra ) and thus required truncated CASSCF trials.…”