  Quantum Monte Carlo (QMC) methods such as Variational Monte Carlo, Diffusion
Monte Carlo or Path Integral Monte Carlo are the most accurate and general
methods for computing total electronic energies. We will review methods we have
developed to perform QMC for the electrons coupled to a classical Monte Carlo
simulation of the ions. In this method, one estimates the Born-Oppenheimer
energy E(Z) where Z represents the ionic degrees of freedom. That estimate of
the energy is used in a Metropolis simulation of the ionic degrees of freedom.
Important aspects of this method are how to deal with the noise, which QMC
method and which trial function to use, how to deal with generalized boundary
conditions on the wave function so as to reduce the finite size effects. We
discuss some advantages of the CEIMC method concerning how the quantum effects
of the ionic degrees of freedom can be included and how the boundary conditions
can be integrated over. Using these methods, we have performed simulations of
liquid H2 and metallic H on a parallel computer.
