Hellgren Maria, von Barth Ulf
Department of Mathematical Physics, Institute of Physics, Lund University, S-22362 Lund, Sweden.
J Chem Phys. 2009 Jul 28;131(4):044110. doi: 10.1063/1.3179756.
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.
在这项工作中，我们在含时密度泛函理论（TDDFT）的精确交换（EXX）近似下计算了铍（Be）和氖（Ne）的激发能和光电离截面。主要关注点在于EXX核的频率依赖性，以及与相应绝热近似相比，它如何影响光谱。我们表明，对于某些离散激发能，频率依赖性对于重现含时Hartree-Fock理论的结果至关重要。不幸的是，我们发现EXX近似在较高能量下完全失效，产生具有错误解析结构的响应函数，并使内壳层激发从计算光谱中消失。我们将这种失效归因于Kohn-Sham非相互作用响应函数存在零本征值。基于绝热TDDFT形式，我们提出了一种推导自电离共振的Fano参数的新方法。
