Assessing Relativistic Effects and Electron Correlation in the Actinide Metals Th to Pu

Abstract

Density functional theory (DFT) calculations are employed to explore and assess the effects of the relativistic spin-orbit interaction and electron correlations in the actinide elements. Specifically, we address electron correlations in terms of an intra-atomic Coulomb interaction with a Hubbard U parameter (DFT + U). Contrary to recent beliefs, we show that for the ground-state properties of the light actinide elements Th to Pu, the DFT + U makes its best predictions for U = 0. Actually, our modeling suggests that the most popular DFT + U formulation leads to the wrong ground-state phase for plutonium. Instead, extending DFT and the generalized gradient approximation (GGA) with orbital-orbital interaction (orbital polarization; OP) is the most accurate approach. We believe the confusion in the literature on the subject mostly originates from incorrectly accounting for the spin-orbit (SO) interaction for the p 1/2 state, which is not treated in any of the widely used pseudopotential plane-wave codes. Here, we show that for the actinides it suffices to simply discard the SO coupling for the p states for excellent accuracy. We thus describe a formalism within the projector-augmented-wave (PAW) scheme that allows for spin-orbit coupling, orbital polarization, and non-collinear magnetism, while retaining an efficient calculation of Hellmann-Feynman forces. We present results of the ground-state phases of all the light actinide metals (Th to Pu). Furthermore, we conclude that the contribution from OP is generally small, but substantial in plutonium.

Phase Stability in U-6Nb Alloy Doped with Ti from the First Principles Theory

“…For niobium, the solids-biased gradient approximation PBEsol [45] is better, but since we are focusing on the uranium-rich side of the U-Nb phase diagram we adopt the GGA either in its original [42] or similar but simplified form [43]. There are discussions in the literature on applying an intra-atomic Coulomb interaction with a Hubbard U parameter (DFT + U) for metallic uranium fuels [46], but we have previously proved that this ad hoc interaction does not improve the accuracy of the model, but rather worsens it [47][48][49].…”

“…The number of k points that are included in the calculations depends on the crystal structure, but we apply~1000 k points for the simpler structures and fewer for the multi-atom phases. It should be mentioned that this method has been validated and proven accurate on actinide systems numerous times dating back to the early 1990 s up until very recently [37,38,[47][48][49][52][53][54].…”

Thermodynamics of Uranium Tri-Iodide from Density-Functional Theory

“…This theory is in principle exact, but it relies on practical simplifications and the foundational one is that for the electron interactions. For the actinides [16,17] the most robust formulation is the so-called generalized gradient approximation (GGA) [18].…”

“…There is a need to determine the MT sphere radius (r MT ) and here it is selected so that r MT~0 .7r WS , where r WS is the Wigner-Seitz (atomic-sphere) radius. The radial part of the basis functions inside the MT spheres is calculated from a wave equation for the l = 0 component of the potential that includes all relativistic corrections, including spin-orbit coupling for d and f states but not for the p states, as explained in [17].…”

“…The orbital-orbital interaction (orbital polarization (OP)) is only operating on the uranium f states [21]. This interaction is not explicit in conventional density-functional theory but has been shown to be important for some f-electron systems, particularly plutonium [17,22].…”