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In this work, we present an overview of the phaseless auxiliary-field quantumMonte Carlo (ph- AFQMC) approach from a computational quantum chemistryperspective, and present a numerical assessment of its performance on maingroup chemistry and bond-breaking problems with a total of 1004 relativeenergies. While our benchmark study is somewhat limited, we makerecommendations for the use of ph-AFQMC for general main-group chemistryapplications. For systems where single determinant wave functions arequalitatively accurate, we expect the accuracy of ph-AFQMC in conjunction witha single determinant trial wave function to be between that of coupled-clusterwith singles and doubles (CCSD) and CCSD with perturbative triples (CCSD(T)).For these applications, ph-AFQMC should be a method of choice when canonicalCCSD(T) is too expensive to run. For systems where multi-reference (MR) wavefunctions are needed for qualitative accuracy, ph-AFQMC is far more accuratethan MR perturbation theory methods and competitive with MR configurationinteraction (MRCI) methods. Due to the computational efficiency of ph-AFQMCcompared to MRCI, we recommended ph-AFQMC as a method of choice for handlingdynamic correlation in MR problems. We conclude with a discussion of importantdirections for future development of the ph-AFQMC approach.

Twenty Years of Auxiliary-Field Quantum Monte Carlo in Quantum Chemistry: An Overview and Assessment on Main Group Chemistry and Bond-Breaking