Augmented-Plane-Wave Hartree-Fock First-Principles Calculation of the Fermi Surfaces of Li, Na, and K

The Fermi-surface distortions are used as a criterion to test the relative importance of the various contributions which have to be taken into account for the construction of a crystal potential for the alkali metals. The Fermi energy, thermal mass, and several excited one-electron states are also calculated for a first-principles nonlocal potential, using the augmented-plane-wave (APW) Hartree-Fock (HF) method with non-muffin-tin corrections. The ionic part of the metal HF potential is a superposition of $V_{\mathrm{ion}}^{\mathrm{HF}}$, the ionic contribution to the HF potential of the isolated atom. The nonlocal exchange operator is treated without any approximation. The core-valence correlations are crudely described by means of a dipolar adiabatic polarization potential due to Callaway and doubly screened (in the Thomas-Fermi approximation) by the conduction electrons. The conduction-electrons contribution to the exchange-and-correlation potential is given by the linearized effective local potential of the $N$-body-problem formulation due to Kohn and Sham. The thermal masses obtained in this work are in good agreement with the semiempirical values of Ham. No agreement with Ham's calculation for the Fermi-surface distortions is obtained except for Li. The agreement with experiment is not significant for Li, and good for Na, with a considerable improvement over APW Hartree-Fock-Slater calculation with reasonable exchange coefficients. On the other hand, the calculated distortions are too large for potassium, where the effect of the screened polarization potential is quite significant: The dipolar adiabatic approximation used here for the polarization optical potential is not accurate enough.