In Situ Pseudopotentials: Calculating pseudopotentials using all-electron theory for solid*

We present a general method of constructing in situ pseodopotentials from first-principles, all-electron, and full-potential electronic structure calculations of a solid. The method is applied to bcc Na, at low-temperature equilibrium volume. The essential steps of the method involve (i) calculating an all-electron Kohn-Sham eigenstate, (ii) replacing the oscillating part of the wave function (inside the muffin-tin spheres) of this state with a smooth function, (iii) representing the smooth wave function in a Fourier series, and (iv) inverting the Kohn−Sham equation, to extract the pseudopotential that produces the state generated in steps (i)−(iii). It is shown that an in situ pseudopotential can reproduce an all-electron full-potential eigenvalue up to the sixth significant digit. A comparison of the all-electron theory, in situ pseudopotential theory, and the standard nonlocal pseudopotential theory demonstrates good agreement, e.g., in the energy dispersion of the 3s band state.