密度泛函共振理论：复密度函数，收敛，轨道能量和泛函
Density Functional Resonance Theory: complex density functions, convergence, orbital energies, and functionals
摘要：
密度泛函共振理论（DFRT）的方面[物理评论快报。\textbf{107}，163002（2011）]，一个最近发展的基态密度泛函理论的复标度版本，进行了详细的研究。复密度函数的渐近行为与复共振能和系统的阈值能有关，而复密度函数的局域振荡行为则与电子衰减的优先方向有关。实现的理论的实际考虑，包括复杂的缩放参数，$θ$的敏感性。在Kohn-Sham DFRT中，它表明，几乎所有的$θ$依赖于计算的能量和寿命可以通过使用适当的基组或细网格熄灭。最高占据的Kohn-Sham轨道能量和寿命与一个物理亲和力和宽度有关，并且Kohn-Sham系统的阈值能量被证明等于相互作用系统的阈值能量被一个定义明确的泛函移动。最后，通过适当的标度因子和一个非厄米耦合常数系统，导出了将基态DFT的泛函与DFRT的泛函联系起来的各种复标度条件。
英文摘要：
Aspects of Density Functional Resonance Theory (DFRT) [Phys. Rev. Lett. \textbf{107}, 163002 (2011)], a recently developed complex-scaled version of ground-state Density Functional Theory (DFT), are studied in detail. The asymptotic behavior of the complex density function is related to the complex resonance energy and system's threshold energy, and the function's local oscillatory behavior is connected with preferential directions of electron decay. Practical considerations for implementation of the theory are addressed including sensitivity to the complex-scaling parameter, $θ$. In Kohn-Sham DFRT, it is shown that almost all $θ$-dependence in the calculated energies and lifetimes can be extinguished via use of a proper basis set or fine grid. The highest occupied Kohn-Sham orbital energy and lifetime are related to a physical affinity and width, and the threshold energy of the Kohn-Sham system is shown to be equal to the threshold energy of the interacting system shifted by a well-defined functional. Finally, various complex-scaling conditions are derived which relate the functionals of ground-state DFT to those of DFRT via proper scaling factors and a non-Hermitian coupling constant system.
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