Energy vs. density on paths toward more exact density functionals†,Physical Chemistry Chemical Physics

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Energy vs. density on paths toward more exact density functionals†
Physical Chemistry Chemical Physics ( IF 2.9 ) Pub Date : 2018-02-23 00:00:00 , DOI: 10.1039/c7cp07730k
Kasper P. Kepp _{1,

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Affiliation

Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a “path”. Here I use the Hohenberg–Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness and “straying” from the “path” by separating errors in ρ and E[ρ]. A consistent path toward exactness involves minimizing both errors. Second, a suitably diverse test set of trial densities ρ′ can be used to estimate the significance of errors in ρ without knowing the exact densities which are often inaccessible. To illustrate this, the systems previously studied by Medvedev et al., the first ionization energies of atoms with Z = 1 to 10, the ionization energy of water, and the bond dissociation energies of five diatomic molecules were investigated using CCSD(T)/aug-cc-pV5Z as benchmark at chemical accuracy. Four functionals of distinct designs was used: B3LYP, PBE, M06, and S-VWN. For atomic cations regardless of charge and compactness up to Z = 10, the energy effects of the different ρ are <4 kJ mol⁻¹ (chemical accuracy) defined here as “normal”, even though these four functionals ranked very differently in the previous test. Thus, the “off-path” behavior for such cations is energy-wise insignificant. An interesting oscillating behavior in the density sensitivity is observed vs. Z, explained by orbital occupation effects. Finally, it is shown that even large “normal” problems such as the Co–C bond energy of cobalamins can use simpler (e.g. PBE) trial densities to drastically speed up computation by loss of a few kJ mol⁻¹ in accuracy. The proposed method of using a test set of trial densities to estimate the sensitivity and significance of density errors of functionals may be useful for testing and designing new balanced functionals with more systematic improvement of densities and energies.

中文翻译：

朝着更精确的密度函数前进的道路上的能量与密度的关系†

最近，人们对更精确的密度泛函理论的发展提出了质疑，这意味着需要更正式的方法来系统地衡量进展，即“路径”。在这里，我使用Hohenberg–Kohn定理和Burke等人的正态性定义。通过分离ρ和E [ ρ ]中的误差来定义一条通往精确性和从“路径”“偏离”的路径。通往精确性的一致途径包括最小化两个误差。其次，可以使用适当不同的试验密度测试集ρ '来估计ρ中误差的重要性。不知道通常无法获得的确切密度。为了说明这一点，以前由Medvedev等人研究的系统。，以CCSD（T）/ aug-cc-pV5Z为基准，研究了Z = 1至10的原子的第一电离能，水的电离能以及五个双原子分子的键解离能。使用了不同设计的四个功能：B3LYP，PBE，M06和S-VWN。对于原子阳离子，无论电荷和紧密度如何（最高Z = 10），不同ρ的能量效应均小于4 kJ mol ^-1（化学准确性）在这里定义为“正常”，即使这四个功能在先前的测试中排名差别很大。因此，此类阳离子的“偏离路径”行为在能量方面微不足道。观察到了密度敏感度与Z值之间有趣的振荡行为，这可以通过轨道占据效应来解释。最后，结果表明，即使是较大的“常规”问题，例如钴胺素的Co–C键能，也可以使用更简单的试验密度（例如PBE），通过损失几kJ mol ^-1来极大地加快计算速度。在准确性上。所提出的使用试验密度测试集估算官能度密度误差的敏感性和重要性的方法，可能对于测试和设计密度和能量得到更系统的改进的新型平衡官能度很有用。

更新日期：2018-02-23

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