含时密度泛函理论的精确交换核：原子的频率依赖性和光吸收谱
Exact-exchange kernel of time-dependent density functional theory: Frequency dependence and photoabsorption spectra of atoms
摘要：
在含时密度泛函理论（TDDFT）的精确交换（ECX）近似下，计算了Be和Ne的激发能和光电离截面。主要的焦点一直在频率依赖性的EXX内核和它如何影响的频谱相比，相应的绝热近似。我们表明，对于某些离散的激发能的频率依赖性是必不可少的再现的结果的含时Hartree-Fock理论。不幸的是，我们已经发现，EXX近似完全打破了在较高的能量，产生一个响应函数与错误的分析结构，使内壳层激发从计算的光谱消失。我们将这种失败追溯到Kohn-Sham非相互作用响应函数的消失特征值的存在。基于绝热TDDFT理论，我们提出了一种新的计算自电离共振Fano参数的方法。
英文摘要：
In this work we have calculated excitation energies and photoionization cross sections of Be and Ne in the exact-exchange (EXX) approximation of time-dependent density functional theory (TDDFT). The main focus has been on the frequency dependence of the EXX kernel and on how it affects the spectrum as compared to the corresponding adiabatic approximation. We show that for some discrete excitation energies the frequency dependence is essential to reproduce the results of time-dependent Hartree-Fock theory. Unfortunately, we have found that the EXX approximation breaks down completely at higher energies, producing a response function with the wrong analytic structure and making inner-shell excitations disappear from the calculated spectra. We have traced this failure to the existence of vanishing eigenvalues of the Kohn-Sham non-interacting response function. Based on the adiabatic TDDFT formalism we propose a new way of deriving the Fano parameters of autoionizing resonances.
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