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arXiv 2403.04604physics.chem-phcond-mat.other
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密度泛函理论中ΔSCF方法的理论基础

Foundation for the ΔSCF Approach in Density Functional Theory

Weitao Yang, Paul W. Ayers

AI总结:

本研究将基态密度泛函理论推广至激发态,通过三组等价的非相互作用参考系统变量构建激发态理论,推导激发态Kohn-Sham方程,证明泛函驻点对应激发态性质,为ΔSCF方法提供理论基础。

摘要:

我们将基态密度泛函理论推广到激发态,为广泛用于计算激发态能量和密度的ΔSCF方法提供了理论表述。由于仅电子密度不足以表征激发态,我们采用非相互作用参考系统的定义变量构建激发态理论,即:(1)激发量子数nₛ和势wₛ(r)(激发态势泛函理论,nPFT);(2)非相互作用波函数Φ(Φ泛函理论,ΦFT);(3)非相互作用单电子约化密度矩阵γₛ(r,r')(密度矩阵泛函理论,γₛFT)。我们证明了这三组变量及其对应的能量泛函具有等价性。重要的是,无论选择(nₛ,wₛ(r))、Φ还是γₛ(r,r')作为系统的基本描述符,基态和激发态的交换关联能都使用相同的普适泛函。我们推导了激发态(广义)Kohn-Sham方程。所有三个泛函的最小值对应基态能量,且对于基态,它们均等价于Hohenberg-Kohn-Sham方法。泛函的其他驻点给出激发态能量和电子密度,为ΔSCF方法奠定了基础。

英文摘要:

We extend ground-state density-functional theory to excited states and provide the theoretical formulation for the widely used $ΔSCF$ method for calculating excited-state energies and densities. As the electron density alone is insufficient to characterize excited states, we formulate excited-state theory using the defining variables of a noninteracting reference system, namely (1) the excitation quantum number $n_{s}$ and the potential $w_{s}(\mathbf{r})$ (excited-state potential-functional theory, $n$PFT), (2) the noninteracting wavefunction $Φ$ ($Φ$-functional theory, $Φ$FT), or (3) the noninteracting one-electron reduced density matrix $γ_{s}(\mathbf{r},\mathbf{r}')$ (density-matrix-functional theory, $γ_{s}$FT). We show the equivalence of these three sets of variables and their corresponding energy functionals. Importantly, the ground and excited-state exchange-correlation energy use the \textit{same} universal functional, regardless of whether $\left(n_{s},w_{s}(\boldsymbol{r})\right)$, $Φ$, or $γ_{s}(\mathbf{r},\mathbf{r}')$ is selected as the fundamental descriptor of the system. We derive the excited-state (generalized) Kohn-Sham equations. The minimum of all three functionals is the ground-state energy and, for ground states, they are all equivalent to the Hohenberg-Kohn-Sham method. The other stationary points of the functionals provide the excited-state energies and electron densities, establishing the foundation for the $ΔSCF$ method.

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