Optimized Basis Sets for Electron Correlation in Solids: Energies and 1RDM

Basis incompleteness is a significant source of error in orbital-space electronic structure methods. This problem is particularly acute in solids where readily available bases, e.g. mean-field orbitals and atomic basis sets, can lead to slow and non-linear convergence to the complete basis set (CBS) limit. In this work, we show that optimized Gaussian orbitals can be used to construct fast and smoothly converging correlation-consistent basis sets. CBS energies can be obtained from cc-pVTZ and cc-pVQZ extrapolation in ionic crystals. The same is true in alkaline metals once a single shell of plane waves are added. By analyzing the one-body reduced density matrix in real and reciprocal space, we show that the optimized basis set captures the correct correlation energies for the right reasons: physical charge density and momentum distribution.