Momentum conservation for ab initio calculations with pseudopotentials via a phase space electronic structure formulation

We demonstrate how to build a robust phase space electronic Hamiltonian $\hat{H}_\text{PS}(\boldsymbol{R},\boldsymbol{P})$ that depends on nuclear position $\boldsymbol{R}$ and nuclear momentum $\boldsymbol{P}$ in the presence of ionic pseudopotentials. In particular, we show that in order to accoun