In this section we provide a brief overview of the ph-AFQMC method (detailed treatments can be found in, e.g., Ref.s 73, 74, and 6). We start with the non-relativistic Born-Oppenheimer molecular Hamiltonian in second-quantized notation (where W is the oneelectron "core" Hamiltonian matrix, V is the 2-electron repulsion tensor and the summation indices pqrs run over an orthonormal single-particle orbital space):