Improved Treatment of Relativistic Effects in the Linear Augmented Plane Wave Method
Nikolaev A.V., Kurelchuk U.N., Tkalya E.V.

Received: March 25, 2026

DOI: 10.31857/S0044451026070022

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We critically review the methodology for relativistic effects in the linear augmented plane wave method (LAPW) for solids and offer a few ways to account them more accurately. (1) We introduce new radial (Bloch-type) basis functions, based on two actual radial solutions of the Dirac equation for j=l-1/2 and j=l+1/2 states. This treatment differs from the canonical one, where for the basis function an effective differential equation is used. For the 6p semicore states of actinides the new basis function gets weight of the 6p_1/2 component and can describe the 6p density adequately even without the p_1/2 local function. (2) We find that canonical matrix element expressions for the spherically symmetric potential are implicitly based on non-relativistic radial wave functions, which should be corrected. (3) In the canonical treatment the full spin-orbit (SO) energy splitting (in doubled basis set) of two 6p subbands is always overestimated. To reduce this value we suggest using the SO coupling constants ζ (p), \dot ζ (p), \ddot ζ (p), calculated with the 6p_3/2 radial component. We apply the new treatment to solid Ac, Th, ThO₂, and UO₂, and discuss how new treatment affects the equilibrium lattice constants and bulk modulus. In the full treatment of SO coupling, UO₂ turns out to be a semimetal. For actinium a considerable overestimation of its lattice constant is observed. Keywords: ab initio band structure calculations, relativistic effects, LAPW, spin-orbit coupling, thorium, actinium, ThO₂, UO₂