The orbital ordering (OO) resulting from the partial occupancy of the subshell of the transition metals in KBF (B = Sc, Ti, Ffe, Co) perovskites, and the many possible patterns arising from the coupling between the B sites, have been investigated at the quantum mechanical level ( Gaussian type basis set, B3LYP hybrid functional) in a 40 atoms supercell. The numerous patterns are distributed into 162 classes of equivalent configurations. For each fluoroperovskite, one representative per class has been calculated. The four compounds behave similarly: an identical dependence of the energy and volume (or cell parameters) on the OO pattern; the spanned energy interval is small (1 to 2 mE per formula unit), suggesting that most of the configurations are occupied at room and even at low temperature. A linear model, taking into account the relative orbital order in contiguous sites, reproduces the energy order in the full set for each compound, suggesting that it could be used for studying OO in larger supercells.

中文翻译：

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KBF3（B = Sc、Ti、Fe、Co）钙钛矿中的 t2g d 轨道排序模式

由于部分占据而产生的轨道排序（OO）$t_{2G}$ $d$KBF 中过渡金属的亚壳层${}_3$(B = Sc、Ti、Ffe、Co) 钙钛矿以及 B 位点之间耦合产生的许多可能模式，已在量子力学水平上进行了研究（$\text{全电子}$40 个原子超晶胞中的高斯型基组，B3LYP 混合泛函）。众多的模式被分为 162 类等效配置。对于每种氟钙钛矿，计算出每类的一个代表。这四种化合物的行为相似：能量和体积（或细胞参数）对 OO 模式的依赖性相同；跨越的能量间隔很小（1到2 mE${}_H$每个配方单元），表明大多数构型是在室温甚至低温下占据的。线性模型考虑了相邻位点的相对轨道顺序，重现了每种化合物的全套能量顺序，表明它可用于研究较大超级细胞中的 OO。