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 ∂E/∂N and we thus hypothesized that they probe universality. We studied χ and η for atoms Z = 1–36 using 50 diverse functionals covering all major classes. Very few functionals describe both χ and η well. η benefits from error cancellation, whereas χ is 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 eV–0.3 eV for η. In contrast, variable performance for χ indicates 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 χ for the same systems is a hallmark of an important aspect of universality by probing ∂E/∂N. With this metric, B98, B97-1, PW6B95D3, MN-15, rev-TPSS, HSE06, and APFD are the most “universal” among the tested functionals. B98 and B97-1 are accurate for very diverse metal–ligand bonds, supporting that a balanced description of ∂E/∂N and ∂E²/∂N², via χ and η, is probably a first simple probe of universality.

中文翻译：

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使用电负性和硬度测试密度泛函。

每年，成千上万的论文使用密度泛函理论（DFT），但是缺乏通用性会降低DFT的预测能力，并且泛函可能会导致能量密度失衡。的绝对电负性（χ）和硬度（η）直接反映通过化学势的能量密度关系∂ E / ∂N，因此我们假设他们探讨了普遍性。我们使用涵盖所有主要类别的50种多样的函数研究了Z = 1–36的原子的χ和η。很少有函数能够很好地描述χ和η。η受益于错误消除，而χ受IP和EA的错误传播所损害；因此，几乎所有的标准GGA和混合功能在MAE中的η均处于0.2 eV–0.3 eV的平稳状态。相反，对于χ的可变性能表明在用DFT描述化学势时存在问题。函数的准确性和精确度远非线性相关，但对于通用函数，我们期望线性。流行的功能（例如B3LYP，PBE和revPBE）对于这两个属性均表现不佳。密度敏感性计算表明，由于退化的p轨道和d轨道的占用会导致“非通用性”并严重依赖于精确交换，因此存在较大的密度衍生误差。因此，我们认为对于相同系统的χ的性能是普遍性重要方面的标志，这是通过探索∂ E / ∂ N.有了这个指标，B98，B97-1，PW6B95D3，MN-15，REV-TPSS，HSE06和APFD是测试函中最“普及”。B98和B97-1是准确非常多样的金属-配体键，支持该均衡描述∂ E / ∂ N和∂ ë ² / ∂ Ñ ²，通过χ，η，大概是普遍性的第一简单探针。