Miskowiec Andrew
Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.
Phys Chem Chem Phys. 2018 Apr 18;20(15):10384-10395. doi: 10.1039/c7cp07970b.
The DFT+U approach, where U is the Hubbard-like on-site Coulomb interaction, has successfully been used to improve the description of transition metal oxides and other highly correlated systems, including actinides. The secret of the DFT+U approach is the breaking of d or f shell orbital degeneracy and adding an additional energetic penalty to non-integer occupation of orbitals. A prototypical test case, UO2, benefits from the +U approach whereby the bare LDA method predicts UO2 to be a ferromagnetic metal, whereas LDA+U correctly predicts UO2 to be insulating. However, the concavity of the energetic penalty in the DFT+U approach can lead to a number of convergent "metastable" electronic configurations residing above the ground state. Uranium tetrafluoride (UF4) represents a more complex analogy to UO2 in that the crystal field has lower symmetry and the unit cell contains two symmetrically distinct U atoms. We explore the metastable states in UF4 using several different methods of selecting initial orbital occupations. Two methods, a "pre-relaxation" method wherein an initial set of orbital eigenvectors is selected via the self-consistency procedure and a crystal rotation method wherein the x, y, z axes are brought into alignment with the crystal field, are explored. We show that in the case of UF4, which has non-collinearity between its crystal axes and the U atoms' crystal field potentials, the orbital occupation matrices are much more complex and should be analyzed using a novel approach. In addition to demonstrating a complex landscape of metastable electronic states, UF4 also shows significant hybridization in U-F bonding, which involves non-trivial contributions from s, p, d, and f orbitals.
DFT+U方法中，U是类哈伯德在位库仑相互作用，该方法已成功用于改进对过渡金属氧化物和其他高度相关体系（包括锕系元素）的描述。DFT+U方法的秘诀在于打破d或f壳层轨道简并，并对轨道的非整数占据添加额外的能量惩罚。一个典型的测试案例是UO₂，+U方法使其受益，即裸LDA方法预测UO₂是铁磁金属，而LDA+U正确预测UO₂是绝缘的。然而，DFT+U方法中能量惩罚的凹性会导致一些收敛的“亚稳态”电子构型存在于基态之上。四氟化铀（UF₄）与UO₂有更复杂的类比关系，因为其晶体场对称性较低，且晶胞包含两个对称不同的U原子。我们使用几种不同的选择初始轨道占据的方法来探索UF₄中的亚稳态。探索了两种方法，一种是“预弛豫”方法，其中通过自洽程序选择一组初始轨道本征向量，另一种是晶体旋转方法，其中x、y、z轴与晶体场对齐。我们表明，在UF₄的情况下，其晶轴与U原子的晶体场势之间存在非共线性，轨道占据矩阵要复杂得多，应该使用一种新颖的方法进行分析。除了展示亚稳态电子态的复杂图景外，UF₄在U-F键中还表现出显著的杂化，这涉及s、p、d和f轨道的非平凡贡献。
