Structure and screening in molecular and metallic hydrogen at high pressure

A variational wave function proposed by Abrikosov is used to express the (spin-restricted) Hartree-Fock energy as reciprocal-lattice sums for static-lattice fcc monatomic hydrogen and diatomic $\mathrm{Pa}3\mathrm{}$ molecular hydrogen. In the monatomic phase the hydrogenic orbital range is found to closely parallel the inverse Thomas-Fermi wave vector; the corresponding energy $E$ has a minimum of -0.929 Ry/electron at $r_s=1.67\mathrm{}$. For the diatomic phase $E\left(r_s\right)$ is similar, but the constituent energies, screening, and bond length all reflect a qualitative change in the nature of the solid at $r_s=2.8\mathrm{}$. This change is interpreted in terms of a transition from protons as structural units (at high density) to weakly interacting molecules (at low density). Insensitivity of the total energy to a rapid fall in the bond length suggests association with the rotational transition, where the rigid molecular orientations characteristic of high pressures disappear and the molecules rotate freely at low pressure. The importance of phonons (neglected here) in a correct treatment of the total energy is emphasized, and the possible connection between the rotational transition and metallization of the diatomic phase is discussed. It is concluded that methods which sphericalize the Wigner-Seitz cell may overlook important structural properties (to which the total energy is relatively insensitive) for the diatomic phase.