Alternative treatment of relativistic effects in linear augmented plane wave (LAPW) method: application to Ac, Th, ThO2 and UO2

We examine the influence of the relativistic effects within the linear augmented plane wave method (LAPW) for solids and propose a few alternative ways to accurately take them into account: (1) we introduce new radial dependencies for LAPW (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. The proposed radial 6p functions receive more weight from the Dirac p-1/2 solution and, due to this, can on average correctly describe completely filled $6p$ bands even without the additional p-1/2 local atomic function, as is done in the LAPW+p-1/2 method; (2) the canonical LAPW matrix elements for the spherically symmetric component of the potential, assuming non-relativistic radial wave functions, should be corrected; (3) we argue that for a realistic spin-orbit (SO) energy splitting of the semicore 6p-states the spin-orbit interaction constant zeta(p) should be calculated with the 6p-3/2 radial component, because the value of zeta(p) obtained with the canonical mixing of the 6p-1/2 and 6p-3/2 components overestimates the SO splitting. Different ways of taking into account relativistic effects can change the equilibrium lattice constant up to 0.15 A and the elastic modulus up to 26 GPa. We find that in the full treatment of the spin-orbit coupling UO2 has a small gap of forbidden states (0.2-0.4 eV) at the Fermi level, which persists for all k-vectors and, therefore, UO2 should be classified as a semimetal. We also discuss the peculiarities of the electron band structure of actinium, which result in an overestimation of its lattice constant.