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arXiv:1801.10307 · The Journal of Chemical Physics

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

Edgar Josué Landinez Borda, John A. Gomez, Miguel A. Morales

Published Feb 20, 2019• 3 citations
arXivHTMLPDF

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.

DOI
10.1063/1.5049143

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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.
We investigate here 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.
For optimal accuracy, auxiliary-field quantum Monte Carlo (AFQMC) requires trial states consisting of multiple Slater determinants. We develop an efficient algorithm to select the determinants from an AFQMC random walk eliminating the need for other methods. When determinants contribute significantly to the non-orthogonal configuration interaction energy, we include them in the trial state. These refined trial wave functions significantly reduce the phaseless bias and sampling variance of the local energy estimator. With 100 to 200 determinants, we lower the error of AFQMC by up to a factor of 10 for second row elements that are not accurately described with a Hartree-Fock trial wave function. For the HEAT set, we improve the average error to within the chemical accuracy. For benzene, the largest studied system, we reduce AFQMC error by 80% with 214 Slater determinants and find a 10-fold increase of the time to solution. We show that the remaining error of the method prevails in systems with static correlation or strong spin contamination.
For optimal accuracy, auxiliary-field quantum Monte Carlo (AFQMC) requires trial states consisting of multiple Slater determinants. We develop an efficient algorithm to select the determinants from an AFQMC random walk eliminating the need for other methods. When determinants contribute significantly to the nonorthogonal configuration interaction energy, we include them in the trial state. These refined trial wave functions significantly reduce the phaseless bias and sampling variance of the local energy estimator. With 100 to 200 determinants, we lower the error of AFQMC by up to a factor of 10 for second-row elements that are not accurately described with a Hartree-Fock trial wave function. For the HEAT set, we improve the average error to within chemical accuracy. For benzene, the largest studied system, we reduce AFQMC error by 80% with 214 Slater determinants and find a 10-fold increase of the time to solution. We show that phaseless errors prevail in systems with static correlation or strong spin contamination. For such systems, improved trial states enable stable free-projection AFQMC calculations, achieving chemical accuracy even in the strongly correlated regime.
We explore different ways of incorporating accurate trial wave functions into free projection auxiliary field quantum Monte Carlo (fp-AFQMC). Trial states employed include coupled cluster singles and doubles, multi-Slater, and symmetry projected mean-field wave functions. We adapt a recently proposed fast multi-Slater local energy evaluation algorithm for fp-AFQMC, making the use of long expansions from selected configuration interaction methods feasible. We demonstrate how these trial wave functions serve to mitigate the sign problem and accelerate convergence in quantum chemical problems, allowing the application of fp-AFQMC to systems of substantial sizes. Our calculations on the widely studied Cu2O22+\text{Cu}_2\text{O}_2^{2+}Cu2​O22+​ model system show that many previously reported isomerization energies differ substantially from the near-exact fp-AFQMC value.
We explore different ways of incorporating accurate trial wave functions into free projection auxiliary-field quantum Monte Carlo (fp-AFQMC). States employed include coupled-cluster singles and doubles, multi-Slater, and symmetry-projected mean-field wave functions. We adapt a recently proposed fast multi-Slater local energy evaluation algorithm for fp-AFQMC, making the use of long expansions from selected configuration interaction methods feasible. We demonstrate how these wave functions serve to mitigate the sign problem and accelerate convergence in quantum chemical problems, allowing the application of fp-AFQMC to systems of substantial sizes. Our calculations on the widely studied model Cu 2 O 2 2+ system show that many previously reported isomerization energies differ substantially from the near-exact fp-AFQMC value.
In this work, we test a recently developed method to enhance classical auxiliary-field quantum Monte Carlo (AFQMC) calculations with quantum computers against examples from chemistry and material science, representative of classes of industry-relevant systems. As molecular test cases, we calculate the energy curve of H4 and the relative energies of ozone and singlet molecular oxygen with respect to triplet molecular oxygen, which is industrially relevant in organic oxidation reactions. We find that trial wave functions beyond single Slater determinants improve the performance of AFQMC and allow it to generate energies close to chemical accuracy compared to full configuration interaction or experimental results. In the field of material science, we study the electronic structure properties of cuprates through the quasi-1D Fermi-Hubbard model derived from CuBr2, where we find that trial wave functions with both significantly larger fidelities and lower energies over a mean-field solution do not necessarily lead to AFQMC results closer to the exact ground state energy.