Quantum Theory of the Equation of State for Solid Hydrogen

Abstract

A variational calculation of the ground-state energy of molecular crystalline hydrogen has been carried out, including the effect of correlation between the motions of the particles. The principal purpose was to obtain the equation of state for solid hydrogen at absolute-zero temperature over a wide range of densities. We are concerned with energies on a scale appropriate to high-pressure phenomena, and therefore approximated the molecular rotational behavior, so that the very low-temperature phase transitions are not describable in the present model. The variational form of the energy was obtained by truncating the cluster expansion of the ground-state energy. The effect of short-range dynamic correlation is taken into consideration through a Jastrow-type pair-correlation function in the trial wave function. To facilitate the fast convergence of the cluster expansion, a model correlation function with an explicit hard-core exclusion effect was employed. With this pair-correlation function, the truncation approximation was extended into the high-density region where previous functional forms for pair correlation had not been satisfactory. Numerical computations were done for a Lennard-Jones potential, a Buckingham exp-6-type potential, and a nonspherical molecular interaction due to Wang Chang. The results compare favorably with experiment, although there is a systematic difference at high density; either all of the assumed potentials are inadequate or the experimental data are in error.