Noncovalent Interaction Energies with Phaseless Auxiliary-Field Quantum Monte Carlo

Noncovalent interactions are ubiquitous in chemistry and play key roles in, e.g., drug-protein interactions, secondary-sphere effects in catalysis, molecular crystals, the structure of biomolecules, and the properties of liquids. However, their description with approximate electronic structure models is a long-standing challenge due to the many-body correlation effects, relatively small energy scales, and potentially large system sizes involved. In this work, we first assess the simplest phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) model, which uses restricted Hartree-Fock trial wave functions, for representative test sets of noncovalent interactions such as hydrogen bonding, electrostatics, and dispersion (S66, A24, S22, and X31). Against CCSD(<i>T</i>) reference values, we find accuracy consistently better than CCSD, and sometimes dramatically better than MP2. In addition, we use the water dimer (with available CCSDTQ reference energies) to demonstrate that noncovalent interaction energies calculated with ph-AFQMC-RHF benefit significantly from error cancellation. In this spirit, we further show how a branching correlated sampling scheme can be used to reduce the computational cost of noncovalent interaction energy calculations, paving the way for more tractable ph-AFQMC studies of larger molecules.