基于精确因式分解的电子和原子核密度泛函理论
Exact factorization-based density functional theory of electrons and nuclei
摘要：
证明了电子-核系统的基态能量是条件电子密度$n_R(\mathbf{r})$、核波函数$χ(R)$以及由条件电子波函数$Φ_R(r)$导出的诱导矢量势$A_μ(R)$和量子几何张量$\mathcal{T}_{μν}(R)$在核组态空间上的变分泛函，其中$r=\mathbf{r}_1,\mathbf{r}_2,\ldots$为电子坐标，$R=\mathbf{R}_1,\mathbf{R}_2,\ldots$为核坐标.基态$(n_R,χ,A_μ,\mathcal{T}_{μν})$可以通过自洽求解（i）包含有效势$v_{\rm s}(\mathbf{r})$的条件Kohn-Sham方程，该有效势参数依赖于$R$，（ii）$χ(R)$的薛定谔方程和（iii）确定$\mathcal{T}_{μν}$的欧拉-拉格朗日方程来计算。将该理论应用于$E\otimes e$ Jahn-Teller模型。
英文摘要：
The ground state energy of a system of electrons and nuclei is proven to be a variational functional of the conditional electronic density $n_R(\mathbf{r})$, the nuclear wavefunction $χ(R)$ and an induced vector potential $A_μ(R)$ and quantum geometric tensor $\mathcal{T}_{μν}(R)$ derived from the conditional electronic wavefunction $Φ_R(r)$ over nuclear configuration space, where $r=\mathbf{r}_1,\mathbf{r}_2,\ldots$ are electronic coordinates and $R=\mathbf{R}_1,\mathbf{R}_2,\ldots$ are nuclear coordinates. The ground state $(n_R,χ,A_μ,\mathcal{T}_{μν})$ can be calculated by solving self-consistently (i) conditional Kohn-Sham equations containing an effective potential $v_{\rm s}(\mathbf{r})$ that depends parametrically on $R$, (ii) the Schrödinger equation for $χ(R)$ and (iii) Euler-Lagrange equations that determine $\mathcal{T}_{μν}$. The theory is applied to the $E\otimes e$ Jahn-Teller model.
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