Towards a Systematic Improvement of the Fixed-Node Approximation in Diffusion Monte Carlo for Solids
Résumé
While Diffusion Monte Carlo (DMC) has the potential to be an exact stochastic method for ab initio electronic structure calculations, in practice the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros) must be used. This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wave-functions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method, which iteratively selects the most relevant Slater determinants from the full configuration interaction (FCI) space. By introducing a simple protocol combining both exact and approximate finite-supercell results and a controlled extrapolation procedure to reach the thermodynamic limit, we show accurate DMC energies can be obtained using a manageable number of Slater determinants. This approach is illustrated by computing the cohesive energy of carbon diamond in the thermodynamic limit using Slater-Jastrow trial wavefunctions including up to one million Slater determinants.