To sum up, we show in the present paper that magnetic response inNb$_2$O$_2$F$_3$ at the high-temperatures ($T>$90 K) is related to the orbitalselective regime, when part of the electrons form molecular orbitals whileother electrons have local magnetic moments. The charge disproportionation,which occurs at $T\sim$90 K is seen in the GGA calculations, but its degree($\delta n \sim 0.1$ electron) is far from what one would expect from naiveexpectations based on the formal ionic valences. The mechanism of the chargeordering is argued to be related with a sizable kinetic energy gain due toformation of two molecular orbitals in short Nb$^{3+}$-Nb$^{3+}$ dimers causedby a strong nonlinearity of the distance dependence on electron hopping. Wethink that this mechanism of charge ordering, stabilized not by decrease ofinteraction energy, but rather by the gain in kinetic energy, may be operativein many other systems, especially consisting of structural dimers.
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机译：综上所述，我们在本文中表明，在高温下（$ T> $ 90 K），Nb $ _2 $ O $ _2 $ F $ _3 $的磁响应与轨道选择区域有关，此时部分电子形成分子轨道，而其他电子具有局部磁矩。在GGA计算中可以看到发生在$ T \ sim $ 90 K的电荷歧化，但是其程度（$ \ delta n \ sim 0.1 $电子）远不及基于形式离子化合价的天真的预期。电荷排序的机制被认为与较大的动能增益有关，这是由于距离依赖性的强非线性导致短Nb $ ^ {3 +} $-Nb $ ^ {3 +} $二聚体形成两个分子轨道电子跳跃。我们认为，这种电荷有序机制不是通过降低相互作用能而是通过增加动能来稳定的，它可以在许多其他系统中起作用，尤其是由结构二聚体组成的系统。
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