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Spin gaps and spin-flip energies in density-functional theory

机译：密度泛函理论中的自旋间隙和自旋翻转能量

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摘要

Energy gaps are crucial aspects of the electronic structure of finite and extended systems. Whereas much is known about how to define and calculate charge gaps in density-functional theory (DFT), and about the relation between these gaps and derivative discontinuities of the exchange-correlation functional, much less is known about spin gaps. In this paper we give density-functional definitions of spin-conserving gaps, spin-flip gaps and the spin stiffness in terms of many-body energies and in terms of single-particle (Kohn-Sham) energies. Our definitions are as analogous as possible to those commonly made in the charge case, but important differences between spin and charge gaps emerge already on the single-particle level because unlike the fundamental charge gap spin gaps involve excited-state energies. Kohn-Sham and many-body spin gaps are predicted to differ, and the difference is related to derivative discontinuities that are similar to, but distinct from, those usually considered in the case of charge gaps. Both ensemble DFT and time-dependent DFT (TDDFT) can be used to calculate these spin discontinuities from a suitable functional. We illustrate our findings by evaluating our definitions for the Lithium atom, for which we calculate spin gaps and spin discontinuities by making use of near-exact Kohn-Sham eigenvalues and, independently, from the single-pole approximation to TDDFT. The many-body corrections to the Kohn-Sham spin gaps are found to be negative, I.e., single-particle calculations tend to overestimate spin gaps while they underestimate charge gaps.
机译：能隙是有限和扩展系统的电子结构的关键方面。尽管在密度泛函理论（DFT）中如何定义和计算电荷间隙以及这些间隙与交换相关函数的导数不连续之间的关系知之甚少，但对自旋间隙的知之甚少。在本文中，我们以多体能量和单粒子（Kohn-Sham）能量的形式给出了自旋保持间隙，自旋翻转间隙和自旋刚度的密度泛函定义。我们的定义与电荷情况下的定义尽可能相似，但是自旋和电荷隙之间的重要区别已经出现在单粒子水平上，因为与基本电荷隙不同，自旋间隙涉及激发态能量。预计Kohn-Sham和多体自旋间隙会有所不同，并且这种差异与导数间断有关，后者与电荷间断时通常考虑的导数间断相似但又不同。集成DFT和时间相关DFT（TDDFT）均可用于根据合适的函数计算这些自旋不连续性。我们通过评估我们对锂原子的定义来说明我们的发现，通过使用近似精确的Kohn-Sham特征值以及独立于单极近似到TDDFT，我们可以计算出锂原子的自旋间隙和自旋不连续性。已发现对Kohn-Sham自旋间隙的多体校正为负，即单粒子计算倾向于高估自旋间隙，而低估电荷间隙。

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