Properties of solid and gaseous hydrogen, based upon anisotropic pair interactions

Abstract

Properties of ${\mathrm{H}}_2$ are investigated using an analytic anisotropic potential which has been deduced from recent atomic orbital and perturbation calculations. The low-pressure solid results are based upon a spherical average of the anisotropic potential. The calculated ground-state energy is $E_0=-88.76\mathrm{}\pm 2$ K. The pressure-volume curve agrees with experiment to within 10% over the range $9\le V\le 22.65$ ${\mathrm{cm}}^3$/mole ${\mathrm{H}}_2$. The high-pressure solid properties are calculated using the anisotropic potential for particular frozen orientations, as well as the spherically averaged potential. The structures investigated are the $P_{a}3$ and $\frac{P{4}_2}{\mathrm{mnm}}$ orientations. The $\frac{P{4}_2}{\mathrm{mnm}}$ orientation yields energies and pressures 10-20% lower than either the spherical average or the $P_{a}3$ arrangement. Agreement with experimental shock-wave data is tolerable. The metal-insulator phase-transition pressure is predicted to be between 1.61 × ${10}^6$ and 3.76 × ${10}^6$ atm, depending on the metallic equation of state used. Second virial coefficients $B\left(T\right)\mathrm{}$ are calculated for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ over the range $60 \mathrm{K}\le T\le 523 \mathrm{K}$, using a formalism which fully accounts for the potential anisotropies and the discrete rotational spectrum. The results are in excellent agreement with experiment except at high temperatures, where the discrepancy is nearly 10%. A comparison of the results with those obtained using the spherically averaged potential indicates that the effect of anisotropies on $B\left(T\right)\mathrm{}$ is small. This coupled with the results from solid calculations implies that anisotropies are generally not very important except at extremely high pressures. The difference in $B\left(T\right)\mathrm{}$ between ortho and para ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ is also calculated.