Electronic density and atomic forces in solids by plane-wave auxiliary-field quantum Monte Carlo*

We present accurate electronic densities and ionic forces in solids. These results are obtained using the plane-wave basis auxiliary-field quantum Monte Carlo (PW-AFQMC) method [1] with norm-conserving pseudopotentials. AFQMC has been shown to be an excellent many-body total energy method. Computation of observables other than the ground-state energy requires back-propagation [2], which we implement in the PW-AFQMC framework. The (near-exact) electronic densities we obtained in Si, NaCl, and Cu in the thermodynamic limit are used to benchmark several density functionals, potentially providing a reference in constructing better density functionals. Accurate ionic forces can be applied to an improved steepest-descent method [3] for geometry optimization in solids, which we demonstrate in the silicon beta-tin structure. We also discuss the prospect for phonon calculations, and ab initio many-body computation of thermodynamic properties.

[1] S. Zhang and H. Krakauer, Phys. Rev. Lett. 90, 136401 (2003); M. Suewattana et al., Phys. Rev. B 75, 245123 (2007)
[2] S. Zhang, J. Carlson, and J. E. Gubernatis, Phys. Rev. B 55, 7464 (1997); M. Motta and S. Zhang, J. Chem. Theory Comput. 13, 5367 (2017)
[3] M. Motta and S. Zhang, J. Chem. Phys. 148, 181101 (2018)