First-principle computations on structural and electronic properties of cubic rare-earth $$\hbox {ErX}_{{3}}$$ ($$\hbox {X}= \hbox {Ga}$$, In and Sn) intermetallic compounds have been accomplished using the full-potential linearised augmented plane wave (FP-LAPW) method within the framework of density functional theory (DFT). For the exchange correlation, we used local spin density approximation (LSDA) plus Hubbard parameter $$U~(\hbox {LSDA}{+}U)$$ approach because of the strong on-site Coulomb repulsion between the localised RE-4f states. Calculated ground-state properties such as lattice constant $$(a_{\mathrm{0}})$$ and other parameters with exchange correlation functional are found compatible with the experimental results. The electronic properties have been determined in terms of band structures, total and partial density of states (DOSs) and Fermi surfaces, which demonstrate the metallic behaviour of all the compounds. Also, the effect of Hubbard potential on this is discussed in detail. The bonding descriptions of these compounds have also been evaluated from charge density difference plots, which display the presence of metallic and mixed covalent–ionic bonding. The determined magnetic moments explain the ferromagnetic behaviour of these compounds.

中文翻译：

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ErX$$_{3}$$ ($$\hbox {X} = \hbox {Ga}$$, In and Sn)金属间化合物的结构和电子性质稳定性研究

立方稀土结构和电子性质的第一性原理计算$$\hbox {ErX}_{{3}}$$ ($$\hbox {X}= \hbox {Ga}$$, In and Sn)在密度泛函理论 (DFT) 的框架内，已经使用全电位线性化增强平面波 (FP-LAPW) 方法完成了金属间化合物。对于交换相关性，我们使用局部自旋密度近似 (LSDA) 加哈伯德参数 $$U~(\hbox {LSDA}{+}U)$$ 方法，因为局部 RE-4f 之间存在强大的现场库仑排斥力状态。计算出的基态属性如晶格常数 $$(a_{\mathrm{0}})$$ 和其他具有交换相关函数的参数与实验结果相一致。电子特性已根据能带结构确定，总态密度和部分态密度 (DOS) 和费米面，展示了所有化合物的金属行为。此外，还详细讨论了哈伯德势对此的影响。这些化合物的键合描述也已通过电荷密度差异图进行评估，显示存在金属和混合共价离子键。确定的磁矩解释了这些化合物的铁磁行为。