A fresh look at dense hydrogen under pressure. III. Two competing effects and the resulting intra-molecular H-H separation in solid hydrogen under pressure

A preliminary discussion of the general problem of localization of wave functions, and the way it is approached in theoretical condensed matter physics (Wannier functions) and theoretical chemistry (localized or fragment orbitals) is followed by an application of the ideas of Paper II in this series to the structures of hydrogen as they evolve under increasing pressure. The idea that emerges is that of simultaneously operative physical (reduction of available space by an increasingly stiff wall of neighboring molecules) and chemical (depopulation of the σ(g) bonding molecular orbital of H(2), and population of the antibonding σ(u)∗ MO) factors. The two effects work in the same direction of reducing the intermolecular separation as the pressure increases, but compete, working in opposite directions, in their effect on the intramolecular (nearest neighbor, intra-pair) distance. We examine the population of σ(g) and σ(u)∗ MOs in our numerical laboratory, as well as the total electron transfer (small), and polarization (moderate, where allowed by symmetry) of the component H(2) molecules. From a molecular model of two interacting H(2) molecules we find a linear relationship between the electron transfer from σ(g) to σ(u)∗ of a hydrogen molecular fragment and the intramolecular H-H separation, and that, in turn, allows us to estimate the expected bond lengths in H(2) under pressure if the first effect (that of simple confinement) was absent. In essence, the intramolecular H-H separations under pressure are much shorter than they would be, were there no physical/confinement effect. We then use this knowledge to understand how the separate E and PV terms contribute to hydrogen phase changes with increasing pressure.