The large-$Z$ asymptotic expansion of atomic energies has been useful in determining exact conditions for corrections to the local density approximation in density functional theory. The correction for exchange is fit well with a leading $Z\ln Z$ term, and we find its coefficient numerically. The gradient expansion approximation also has such a term, but with a smaller coefficient. Analytic results in the limit of vanishing interaction with hydrogenic orbitals (a Bohr atom) lead to the conjecture that the coefficients are precisely 2.7 times larger than their gradient expansion counterparts, yielding an analytic expression for the exchange-energy correction which is accurate to $\sim 5\%$ for all $Z$.

中文翻译：

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大型 ZAtoms 交换局部密度近似的领先修正

大号——$Z$原子能量的渐近膨胀在确定对密度泛函理论中的局部密度近似进行校正的精确条件方面非常有用。交换的修正非常适合领先$Z\ln Z$项，我们在数值上找到它的系数。梯度展开近似也有这样的项，但系数较小。分析结果与氢轨道（玻尔原子）的相互作用消失的极限导致了系数恰好是其梯度扩展对应物的 2.7 倍的猜想，从而产生了交换能量校正的解析表达式，该表达式精确到$～5\%$对所有人$Z$.