论文标题
对原子和原子离子的交换和相关能的简单氢估计，对密度功能理论的影响
Simple hydrogenic estimates for the exchange and correlation energies of atoms and atomic ions, with implications for density functional theory
论文作者
论文摘要
交换和相关能量的确切密度函数在用于多电子系统的地面电子结构的实际计算中近似。构建近似值的一个重要确切约束是要恢复正确的非相关大$ z $扩展，以相应的中性原子的相应能量具有原子数量$ z $和电子$ n = z $，这对于领先订单是正确的（$ -0.221 z^{5/3} $ and $ -0.021 z $ lotimity complentime y s $ soptimity y s $ sopentime complentime）我们发现氢密度导致$ e_x（n，z）\约-0.354 n^{2/3} z $（以前仅以$ z \ gg n \ gg 1 $而闻名）和$ e_c \ of -0.02 n \ ln n n $。这些渐近估计值对于具有大$ n $和$ z \ gg n $的原子离子是最正确的，但是我们发现它们即使对于小$ n $，对于$ n $，对于$ n \ y \ of z $也是质量和半优量的。能量的大$ n $渐近行为是在小$ n $原子和原子离子中预先构造的，支持以下论点：应广泛预测性的近似密度函数旨在恢复正确的渐近学。结果表明，确切的kohn-sham相关能量是根据纯态波函数计算的，对于任何固定的$ n $，在$ z \至\ infty $限制中的贡献不应与$ z $成正比。
Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. An important exact constraint for the construction of approximations is to recover the correct non-relativistic large-$Z$ expansions for the corresponding energies of neutral atoms with atomic number $Z$ and electron number $N=Z$, which are correct to leading order ($-0.221 Z^{5/3}$ and $-0.021 Z \ln Z$ respectively) even in the lowest-rung or local density approximation. We find that hydrogenic densities lead to $E_x(N,Z) \approx -0.354 N^{2/3} Z$ (as known before only for $Z \gg N \gg 1$) and $E_c \approx -0.02 N \ln N$. These asymptotic estimates are most correct for atomic ions with large $N$ and $Z \gg N$, but we find that they are qualitatively and semi-quantitatively correct even for small $N$ and for $N \approx Z$. The large-$N$ asymptotic behavior of the energy is pre-figured in small-$N$ atoms and atomic ions, supporting the argument that widely-predictive approximate density functionals should be designed to recover the correct asymptotics. It is shown that the exact Kohn-Sham correlation energy, when calculated from the pure ground-state wavefunction, should have no contribution proportional to $Z$ in the $Z\to \infty$ limit for any fixed $N$.
