Self-interaction-corrected local spin density theory of $5f$ electron localization in actinides

The electronic structures of the actinide elements U, Np, Pu, Am, Cm, and Bk are investigated within the self-interaction-corrected local spin density approximation. This method allows us to describe a dual character of the $5f$ electrons, some of which occupy localized and corelike states, while the remaining $5f$ electrons hybridize and form bands. Based on energetics, the calculations predict delocalization and/or paramagnetism in the early actinides and localization and/or antiferromagnetism in the later actinides. The corresponding calculated equilibrium volumes are in agreement with the experimental values. For Pu and Am, the method wrongly predicts magnetic ordering, but we find that the paramagnetic state gives a better description of cohesive properties. Under compression, in the later actinides, a localization-delocalization transition happens gradually as more and more $f$ electrons become bandlike with decreasing volume. Pu is already at this transition point at ambient conditions. Delocalization sets in for Am and Bk at a compression of $V\sim 0.75V_0$, for Cm at $V\sim 0.60V_0$, where $V_0$ is the equilibrium volume, and the transition is complete for $V\sim (0.4–0.5)V_0$ in these three elements.

Figure 1

(Color online) Total energy of fcc Np as function of volume for several scenarios distinguished by the different numbers of localized $f$ electrons on Np ions. Both nonmagnetic (spheres) and ferromagnetic (squares) configurations are considered.

Figure 2

(Color online) Total energy of paramagnetic fcc Pu as function of volume for several scenarios distinguished by the different numbers of localized $f$ electrons on Pu ions.

Figure 3

Density of states of paramagnetic fcc plutonium in (a) the LSD scenario, (b) the localized $f^4$ scenario, and (c) the localized $f^6$ scenario. The full line is the total density of states, while the dashed line gives the $f$ partial density of states. Units are states per atom and per eV, and the energy is given relative to the Fermi level.

Figure 4

(Color online) Total energy of paramagnetic fcc Am as function of volume. Several paramagnetic configurations of the localized $5f$ subshell are considered, as discussed in text.

Figure 5

Density of states of hcp americium in the paramagnetic state with 6 localized $f$ electrons per Am atom at $V=V_0=200.6\mathrm{a.u.}$ The full line is the total density of states, while the dashed line gives the $f$ partial density of states. Units are as in Fig. 3. Only the itinerant electron states are shown. The localized states by the transition state argument may be estimated to be situated around $-4.0\mathrm{eV}$.

Figure 6

(Color online) Total energy of fcc Cm as function of volume for several scenarios differing with respect to the number of localized $f$ electrons on Cm, notably 6, 7, or 8 localized $f$ electrons. The balls correspond to the ferromagnetic ordering scenario, while the triangles correspond to the nonmagnetic scenario, as discussed in text. In addition, the asterisks correspond to hcp antiferromagnetic arrangement of $f^7$ curium atoms.

Figure 7

(Color online) Total energy of ferromagnetic fcc Bk as function of volume for several scenarios differing with respect to the number of localized $f$ electrons on Bk.

Figure 8

(Color online) Trends in the Wigner-Seitz radius through the actinide series. The (red) circles and (black) squares are calculated (in fcc structure) and experimental Wigner-Seitz radii, respectively. For Pu, the $f^4$ nonmagnetic ground state is taken and compared with the experimental Wigner-Seitz radius of $\delta \text{−}\mathrm{Pu}$. The calculated $\left(f^0\right)$ and experimental $\alpha \text{−}\mathrm{Pu}$ Wigner-Seitz radii are marked with an open circle and an open square, respectively.

Figure 9

(Color online) Trends in the number of band $f$ electrons through the actinide series. For Pu, the $\alpha$ and $\delta$ phases are identified with the $f^0$ and $f^4$ paramagnetic states, respectively.

Figure 10

(Color online) Trends in the ranges of volumes of $f$-electron delocalization in the actinide elements. Onset (completion) of delocalization is marked with balls (squares), for each element with experimental data (blue and full line) to the left and theoretical data (red and dashed line) to the right. Volumes are given relative to the (localized) equilibrium volume at ambient conditions. Experimental ranges are defined by the smallest volumes observed in the high-symmetry (fcc) phase and the largest volumes observed for the low-symmetry ($\alpha -\mathrm{U}$ type or similar) phases in high-pressure experiments (Refs. 11, 60, 64; for Pu, the range is defined by the zero pressure volumes of the $\delta$ and $\alpha$ phases). The theoretical ranges are defined within the fcc structure only.