Computational methods in coupled electron-ion Monte Carlo simulations

In the last few years, we have been developing a Monte, Carlo simulation method to cope with systems of many electrons and ions in the born-Oppenheimer approximation the coupled electron-ion Monte Carlo method (CEIMC). Electronic properties in CEIMC are computed by quantum Monte Carlo rather than by density functional theory (DFT) based techniques CEMC can, in principle, overcome some of the limitations of the present DFT based a initio dynamical methods. The new method has recently been applied to high-pressure metallic hydrogen. Herein we present a new sampling algorithm that we have developed in the framework of the reputation quantum Monte Carlo method chosen to sample the electronic degrees of freedom, thereby improving its efficiency. Moreover we show herein that, at least for the case of metallic hydrogen, variational estimates of the electronic energies lead to an accurate sampling of the proton degrees of freedom.