单键解离的良态与劣态密度泛函：拉伸H $_2$的成功与失败泛函的分离
Well-behaved versus ill-behaved density functionals for single bond dissociation: Separating success from disaster functional by functional for stretched H$_2$
摘要：
非限制性DFT方法通常被期望以定性的准确性描述中性物种中非极性单键的均裂解离，由于缺乏显著的离域误差。然而，我们发现，许多广泛使用的密度泛函近似不能描述功能沿解离曲线的简单H $_2$分子。这不是DFT的普遍失败，因为许多经典泛函如PBE和B3 LYP给出了非常合理的结果，一些更现代的方法如MS 2也是如此。然而，其他一些广泛使用的泛函，如B 97-D（经验拟合）和TPSS（非经验约束）预测定性错误的静态极化率，力常数，有些甚至引入了一个人工障碍，对独立的H原子的缔合形成H $_2$。的极化率和力常数预测失败似乎源于不完整的自旋本地化到个别H原子超出Coulson-Fisher点，导致在“分数键合”物种的离子的贡献斯莱特行列式不完全消除，不像不受限制的Hartree-Fock的情况下。因此，这些错误似乎是有问题的功能差的自洽密度预测的结果。同样的原因可能导致对H原子缔合的虚假障碍，间接地也导致不正确的力。这些非物理性表明，在\textit{ab initio}动力学计算中使用有问题的泛函可能是不明智的，特别是如果强静电相互作用是可能的。
英文摘要：
Unrestricted DFT methods are typically expected to describe the homolytic dissociation of nonpolar single bonds in neutral species with qualitative accuracy, due to the lack of significant delocalization error. We however find that many widely used density functional approximations fail to describe features along the dissociation curve of the simple H$_2$ molecule. This is not an universal failure of DFT in the sense that many classic functionals like PBE and B3LYP give very reasonable results, as do some more modern methods like MS2. However, some other widely used functionals like B97-D (empirically fitted) and TPSS (non-empirically constrained) predict qualitatively wrong static polarizabilities, force constants and some even introduce an artificial barrier against association of independent H atoms to form H$_2$. The polarizability and force constant prediction failures appear to stem from incomplete spin localization into individual H atoms beyond the Coulson-Fisher point, resulting in `fractionally bonded' species where the ionic contributions to the Slater determinant are not completely eliminated, unlike the case of unrestricted Hartree-Fock. These errors therefore appear to be a consequence of poor self-consistent density prediction by the problematic functional. The same reasons could potentially lead to spurious barriers towards H atom association, indirectly also leading to incorrect forces. These unphysicalities suggest that the use of problematic functionals is probably unwise in \textit{ab initio} dynamics calculations, especially if strong electrostatic interactions are possible.
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