利用电负性和硬度检验密度泛函的普适性
Using Electronegativity and Hardness to Test Density Functional Universality
摘要：
每年有数千篇论文使用密度泛函理论（DFT），但缺乏普适性降低了DFT的预测能力，并且泛函可能会产生能量密度不平衡。绝对电负性（χ）和硬度（η）通过化学势dE/dN直接反映能量密度关系，因此我们假设它们探测普适性。我们研究了原子Z = 1-36的χ和η，使用50个不同的泛函覆盖所有主要类别。很少有泛函能很好地描述χ和η。η受益于误差消除，而χ被来自IP和EA的误差传播破坏;因此几乎所有标准GGA和混合泛函在MAE中对于η在0.2-0.3 eV处显示平台。相比之下，χ的可变性能表明DFT描述化学势存在问题。一个函数的准确度和精确度远不是线性相关的，但对于一个通用的函数，我们期望线性。流行的泛函，如B3 LYP，PBE和revPBE，表现不佳的两个属性。密度敏感性计算表明大的密度衍生的错误，因为占据简并的p-和d-轨道导致“非普遍性”和大的依赖于精确的交换。因此，我们认为，相同系统的χ的性能是通过探测dE/dN的普适性的标志。根据这个指标，B 98、B 97 -1、PW 6 B 95 D3、APFD是最“通用”的测试函数。B 98和B 97 -1对于非常不同的金属-配体键是准确的，支持通过χ和η平衡描述dE/dN和dE 2/dN 2，可能是普适性的第一个简单探针。
英文摘要：
Density functional theory (DFT) is used in thousands of papers each year, yet lack of universality reduces DFT's predictive capacity, and functionals may produce energy-density imbalances. The absolute electronegativity (χ) and hardness (η) directly reflect the energy-density relationship via the chemical potential dE/dN and we thus hypothesized that they probe universality. We studied χand ηfor atoms Z = 1-36 using 50 diverse functionals covering all major classes. Very few functionals describe both χand ηwell. ηbenefits from error cancelation whereas χis marred by error propagation from IP and EA; thus almost all standard GGA and hybrid functionals display a plateau in the MAE at 0.2-0.3 eV for η. In contrast, variable performance for χindicates problems in describing the chemical potential by DFT. The accuracy and precision of a functional is far from linearly related, yet for a universal functional we expect linearity. Popular functionals such as B3LYP, PBE, and revPBE, perform poorly for both properties. Density sensitivity calculations indicate large density-derived errors as occupation of degenerate p- and d-orbitals causes "non-universality" and large dependency on exact exchange. Thus, we argue that performance for χfor the same systems is a hallmark of universality by probing dE/dN. With this metric, B98, B97-1, PW6B95D3, APFD are the most "universal" tested functionals. B98 and B97-1 are accurate for very diverse metal-ligand bonds, supporting that a balanced description of dE/dN and dE2/dN2, via χand η, is probably a first simple probe of universality.
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