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

We present accurate electronic densities for several prototypical solids, including the ionic crystal NaCl, covalent-bond semiconductor Si, and metalic Cu. These results are obtained using ab initio auxiliary-field quantum Monte Carlo (AFQMC) method¹ working in a plane-wave basis with multiple-projector, norm-conserving pseudopotentials. AFQMC has been shown to be an excellent many-body total energy method. Computation of observables and correlation functions other than the ground-state energy requires back-propagation², which we have implemented in this work in the plane-wave basis AFQMC framework. Our (near-exact) results are used to benchmark several density functionals, which can be useful in constructing improved density functionals. Besides density, we have also implemented the calculation of atomic forces, which paves the way for geometry optimization in solids.

[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)