非经验含时密度泛函理论框架用于非局域交换关联势

中文摘要 AI 辅助

先进的、依赖轨道的交换关联（XC）泛函可以显著改善电子结构性质的描述，但在标准线性响应含时密度泛函理论框架内计算的光谱性质却会大幅恶化。这并非底层Kohn-Sham态失效，而是由于在完整非对角密度矩阵层面上未一致地考虑XC势的非局域性时，对动态密度响应的处理存在形式上的不一致性。为避免这些复杂性，我们提出一种非经验的加性修正 $\Delta f_\textnormal{xc}(\mathbf{q},\omega)$ 作用于动态XC核，该修正重新强制了TDDFT内非局域KS哈密顿量的精确f求和规则。将我们的新结果与一组代表性的精确实验测量（环境条件下的铝、硅和碳，以及加热和压缩的铝）进行比较，在所有情况下均显示出显著改善，且无需额外计算成本。相应的扩展到开源GPAW代码已免费在线提供。我们进一步研究了非局域赝势的影响，并表明非局域性具有重要的、物理上合理的作用，对于在无需全电子模拟的情况下捕捉正确的等离激元色散是必不可少的。除了对估计大量动态和光谱性质具有重要意义外，我们的工作还朝着通用XC泛函迈出了重要一步，该泛函可用于高精度地估计各种可观测量。最后，我们概述了我们的框架在开发先进非局域XC泛函方面的潜在用途，并提出了一种新方法，通过集体激发的实验测量来严格验证非局域赝势。

英文摘要

Advanced, orbital-dependent exchange--correlation (XC) functionals can significantly improve the description of electronic structural properties, but they substantially worsen spectral properties that are computed within standard linear-response time-dependent density functional theory frameworks. This is not a failure of the underlying Kohn-Sham states, but due to a formal inconsistency in the treatment of the dynamic density response when the non-locality of the XC potential is not taken into account consistently on the level of the full off-diagonal density matrix. To avoid these complexities, we present a non-empirical additive correction $Δf_\textnormal{xc}(\mathbf{q},ω)$ to the dynamic XC kernel that re-enforces the exact f-sum rule of the non-local KS Hamiltonian within TDDFT. Comparing our new results against a representative set of accurate experimental measurements (ambient aluminum, silicon and carbon, as well as heated and compressed aluminum) reveals a dramatic improvement in all cases without any additional computational cost. The corresponding extension to the open-source GPAW code is made freely available online. We further investigate the implications of non-local pseudopotentials and show that the non-locality has an important, physically motivated effect that is indispensable to capture the correct plasmon dispersion in lieu of full all-electron simulations. In addition to being important for the estimation of a plethora of dynamic and spectral properties, our work constitutes an important step towards a universal XC functional that can be used to estimate all kinds of observables with high accuracy. Finally, we outline the potential utility of our framework for the development of advanced non-local XC functionals, and suggest a new way to rigorously verify non-local pseudopotentials against experimental measurements of collective excitations.

发表机构

• Helmholtz-Zentrum Dresden-Rossendorf (HZDR)（德累斯顿-罗斯多夫亥姆霍兹中心）
• Rutgers University（罗格斯大学）

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