[论文解读] Density Functional Theory for Electronic Excited States

John M. Herbert|arXiv (Cornell University)|Apr 21, 2022

Advanced Chemical Physics Studies被引用 15

一句话总结

本文全面综述了时间依赖密度泛函理论（TDDFT）在电子激发态中的应用，涵盖线性响应TDDFT、激发态Kohn-Sham理论的ΔSCF方法以及实时TDDFT。结果表明，尽管线性响应TDDFT可实现低成本且精确的激发能（通常在~0.3 eV以内），但在电荷转移和锥形交叉处仍存在挑战，可通过轨道优化SCF方法或实时TDDFT加以缓解，尤其适用于高能和宽带光谱，包括X射线边带。

ABSTRACT

This chapter provides a basic introduction to excited-state extensions of density functional theory (DFT), including time-dependent (TD-)DFT in both its linear-response and its explicitly time-dependent formulations. As applied to the Kohn-Sham DFT ground state, linear-response theory affords an eigenvalue-type problem for the excitation energies in a basis of singly-excited Slater determinants, and is widely known simply as "TDDFT" despite its frequency-domain formulation. This form of TDDFT is the mostly widely-used quantum-chemical method for excited states, due to a favorable combination of low cost and reasonable accuracy. The chapter surveys the accuracy of linear-response TDDFT, which is generally more sensitive to the details of the exchange-correlation functional as compared to ground-state DFT, and also describes some known systemic problems exhibited by this approach. Some of those problems can be corrected on a case-by-case basis using orbital-optimized, excited-state self-consistent field (SCF) calculations, in what is known as excited-state Kohn-Sham theory or a "Delta-SCF" procedure, a class of methods that includes restricted open-shell Kohn-Sham theory. Recent successes of these approaches are highlighted, including double excitations and core-level excitations. Finally, explicitly time-dependent (or "real-time") TDDFT involves propagation of the molecular orbitals in time following an external perturbation, according to the Kohn-Sham analogue of the time-dependent Schroedinger equation. The time-dependent approach has been used to model strong-field electron dynamics, and in the weak-field limit it provides a route to broadband spectra based on the time evolution of the dipole moment function. This is useful for describing high-energy excitations (as in x-ray spectroscopy) and in systems where the density of states is high, as demonstrated by a few examples.

研究动机与目标

• 提供TDDFT在电子激发态中的理论与实践综述，强调其在量子化学中的作用。
• 解决线性响应TDDFT的局限性，特别是对电荷转移和锥形交叉的描述问题。
• 探索替代方法，如ΔSCF和实时TDDFT，以提升复杂情况下的计算精度。
• 展示实时TDDFT在宽带和高能光谱中的实用性，包括X射线吸收边带。
• 提供克服实时模拟中数值伪影的指导，如虚假前边峰和基组噪声。

提出的方法

• 采用线性响应TDDFT，通过基于Kohn-Sham对扰动响应的频率域公式计算激发能。
• 应用绝热近似和Tamm-Dancoff近似以简化响应核并降低计算成本。
• 采用轨道优化SCF（ΔSCF）方法，以获取标准TDDFT难以描述的双激发和核心能级激发。
• 通过数值求解时间依赖Kohn-Sham方程，实现实时TDDFT，模拟在外场扰动下轨道的演化。
• 通过时间依赖偶极矩的傅里叶变换计算吸收光谱，实现宽带和高能光谱分析。
• 对偶极矩矩阵应用滤波技术，以抑制来自未束缚态的虚假前边特征，尤其在核心能级光谱中。

实验结果

研究问题

• RQ1 线性响应TDDFT在垂直激发能上的准确性如何？哪些因素影响其性能？
• RQ2 线性响应TDDFT的系统性失效表现为何？如何通过ΔSCF或实时方法加以纠正？
• RQ3 实时TDDFT能否准确再现高能和宽带光谱，如X射线光谱？
• RQ4 实时TDDFT光谱中虚假前边峰的成因是什么？如何在不牺牲精度的前提下将其去除？
• RQ5 经验寿命参数（iΓ）或矩阵滤波在提升实时TDDFT对电离态或亚稳态的可靠性方面能发挥多大作用？

主要发现

• 线性响应TDDFT在垂直激发能上的统计精度约为~0.3 eV，计算成本仅为基态DFT的几倍。
• 该方法对交换-相关泛函的选择敏感，尤其在电荷转移激发和锥形交叉问题上。
• ΔSCF和轨道优化SCF方法可成功描述双激发和核心能级激发，而标准TDDFT对此类态描述不佳。
• 实时TDDFT可实现宽带吸收光谱，并准确捕捉K边X射线跃迁等高能特征。
• 由有限基组中未束缚态引起的X射线光谱虚假前边峰，可通过仅保留相关核心轨道的偶极矩矩阵滤波予以抑制。
• 对未束缚轨道引入经验寿命参数（iΓ）可减少实时TDDFT光谱中的噪声，提升实验特征的分辨率。