One-Electron Theory of the Bulk Properties of Crystalline Ar, Kr, and Xe

The cohesive energy as a function of lattice constant and the $P-V$ relation for Ar, Kr, and Xe have been calculated at $T=0\mathrm{}$ K in the static-lattice limit. The calculation employed the self-consistent augmented-plane-wave statistical-exchange (APW-$X\alpha$) method, which, except for our own preliminary work, has not heretofore been applied to the study of the bulk properties of a van der Waals crystal. The agreement with experiment is at least semiquantitative with respect to the cohesive energies. The comparison with extant $P V$ data is acceptable. By use of a static-lattice sum of a pair-potential function with undetermined parameters, an effective pair potential is determined, with fairly realistic parameter values as a result. Comparison with other energy-band calculations shows that the occupied one-electron energies found in this calculation are in good agreement with those found by other workers. The conduction-band energies are not a result that is usual in $X\alpha$ calculations. The over-all trends found in this calculation are related to those found by Averill in a recent APW-$X\alpha$ calculation on the alkali metals.