  Many body trial wave functions are the key ingredient for accurate Quantum
Monte Carlo estimates of total electronic energies in many electron systems. In
the Coupled Electron-Ion Monte Carlo method, the accuracy of the trial function
must be conjugated with the efficiency of its evaluation. We report recent
progress in trial wave functions for metallic hydrogen implemented in the
Coupled Electron-Ion Monte Carlo method. We describe and characterize several
types of trial functions of increasing complexity in the range of the coupling
parameter $1.0 \leq r_s \leq1.55$. We report wave function comparisons for
disordered protonic configurations and preliminary results for thermal
averages.

Computational Physics