Plutonium (Pu), in which the $5f$ valence electrons always wander the boundary between localized and itinerant states, exhibits quite complex crystal structures and unprecedentedly anomalous properties with respect to temperature and alloying. Understanding its chemical and physical properties, especially its $5f$ electronic structure is one of the central and unsolved topics in condensed matter theory. In the present work, the electronic structures of the six allotropes of Pu (including its $\alpha , \beta , \gamma , \delta , {\delta }^{\prime }$, and $\epsilon$ phases) at ambient pressure are studied comprehensively by means of the density functional theory in combination with the single-site dynamical mean-field theory. The band structures, total and partial density of states, valence state histograms, $5f$ orbital occupancies, x-ray branching ratios, and self-energy functions are carefully studied. It is suggested that the $\alpha , \beta$, and $\gamma$ phases of Pu are typical Racah metals in which the atomic multiple effect dominates near the Fermi level. The calculated results reveal that not only the $\delta$ phase, but also all the six allotropes are archetypal mixed-valence metals with remarkable atomic eigenstate fluctuation. As a consequence, the $5f$ occupancy $n_{5f}$ is around 5.1–5.4, which varies with respect to the atomic volume and electronic correlation strength of Pu. The $5f$ electronic correlation in Pu is moderately orbital-dependent. Moreover, the $5f$ electrons in the ${\delta }^{\prime }$ phase are the most correlated and localized.

中文翻译：

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f电子结构的性质

（Pu），其中 $5F$价电子总是在局部态和流动态之间徘徊，显示出非常复杂的晶体结构，并且在温度和合金化方面表现出前所未有的异常性质。了解其化学和物理性质，尤其是其$5F$电子结构是凝聚态理论中尚未解决的中心问题之一。在目前的工作中，Pu的六个同素异形体的电子结构（包括其$\alpha ， \beta ， \gamma ， \delta ， {\delta }^{\prime }$和 $\epsilon$结合密度泛函理论和单点动力学平均场理论，对环境压力下的相进行了综合研究。能带结构，状态的总和部分密度，价态直方图，$5F$仔细研究了轨道占有率，X射线分支比和自能函数。建议$\alpha ， \beta$和 $\gamma$Pu的相是典型的Racah金属，其中原子多重效应在费米能级附近占主导地位。计算结果表明，不仅$\delta$相，但所有六个同素异形体都是具有明显本征态波动的原型混合价金属。结果，$5F$ 占用 ${ñ}_{5F}$大约在5.1–5.4之间，随Pu的原子量和电子相关强度而变化。的$5F$Pu中的电子相关性是中等轨道依赖性的。而且，$5F$ 中的电子 ${\delta }^{\prime }$ 相是最相关和本地化的。