Size-extensive auxiliary-field quantum Monte Carlo with perturbative coupled cluster trial wavefunctions

In this work, we develop a size-extensive Auxiliary-Field Quantum Monte Carlo (AFQMC) approach that scales as O(N5) for local energy evaluation by perturbatively treating the Coupled Cluster Singles and Doubles (CCSD) trial wavefunctions. Comprehensive numerical examinations, spanning from main-group molecules to 3d transition metal complexes, demonstrate that this perturbative treatment introduces negligible bias. For small systems, our method achieves an accuracy and level of noise comparable to AFQMC with configuration interaction singles and doubles trial wavefunctions while outperforming CCSD(T). This size extensivity offers a decisive advantage for large systems, as suggested by the ground state energies of non-interacting monomers and one-dimensional atomic chains. Finally, the numerical simulations of the uniform electron gas provide evidence that, unlike the CCSD(T) method, our new approach does not suffer from infrared divergence in the thermodynamic limit.