### Computational study of the hydrogen equation of state using the Coupled Electron-Ion Monte Carlo method

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** Miguel Morales,
University of Illinois, Urbana-Champaign **

We study the equation of state of liquid hydrogen at Mbar pressures, in the regime of pressure dissociation/ionization, using the Coupled Electron-Ion Monte Carlo (CEIMC) method. Our aim is to accurately describe the crossover from the molecular to the atomic regime. The CEIMC method is based on the Born-Oppenheimer approximation and consists of a Monte Carlo simulation of the ionic degrees of freedom (either with path integrals or classical Metropolis) using a potential energy surface obtained from a zero temperature Quantum Monte Carlo (QMC) method [1]. The electronic calculation is done using either Variational Monte Carlo or the more accurate Reptation Quantum Monte Carlo. A Slater-Jastrow wavefunction is used, with an analytical random-phase approximation (RPA) Jastrow term and one-body orbitals obtained from a fast band structure calculation [2,3]. Recently, we incorporated backﬂow corrections to the orbitals obtained from Density Functional Theory (DFT). This results in a much improved wavefunction over the entire crossover regime. We report preliminary results using this new wavefunction. We also compare our results with recent calculations obtained using Born-Oppenheimer Molecular Dynamics.

[1] C. Pierleoni and D. M. Ceperley, physics/0510254 (2005).

[2] K. Delaney, C. Pierleoni, D. M. Ceperley, cond-mat/0603750.

[3] M. Holzmann, D. M. Ceperley, C. Pierleoni and K. Esler, Phys. Rev. E 68, 046707 (2003).

**Abstract Author(s):** Miguel A. Morales, Kris Delaney, David M. Ceperley and Carlo Pierleoni