极化率和$C_6$系数实际上如何随原子体积变化
How polarizabilities and $C_6$ coefficients actually vary with atomic volume
摘要：
在这项工作中，我们研究如何原子$C_6$系数和静态偶极极化率$α$规模与有效体积。我们表明，使用受限的原子覆盖周期表的1-5行，即$C_6/C_6^R\approx (V/V^R)^{p_Z}$和$α/α^R\approx (V/V^R)^{p'_Z}$（体积$V=\int dr \frac{4π}{3}r^3 n(r)$），其中$C_6^R$，$α^R$和$V^R$的参考值和有效体积的自由原子。与$p_Z=2$和$p'_Z=1$的标准“经验法则”相反，标度指数$p_Z$和$p'_Z$基本上作为元素编号$Z=N$的函数而变化。值得注意的是，我们发现极化率和$C_6$指数$p'$和$p$是由$p'\approx p-0.615$，而不是预期的$p'\approx p/2$。结果在很大程度上是独立的形式的限制潜力（谐波，三次和四次潜力被认为是）和内核近似，证明这种分析。
英文摘要：
In this work we investigate how atomic $C_6$ coefficients and static dipole polarizabilities $α$ scale with effective volume. We show, using confined atoms covering rows 1-5 of the periodic table, that $C_6/C_6^R\approx (V/V^R)^{p_Z}$ and $α/α^R\approx (V/V^R)^{p'_Z}$ (for volume $V=\int dr \frac{4π}{3}r^3 n(r)$) where $C_6^R$, $α^R$ and $V^R$ are the reference values and effective volume of the free atom. The scaling exponents $p_Z$ and $p'_Z$ vary substantially as a function of element number $Z=N$, in contrast to the standard "rule of thumb" that $p_Z=2$ and $p'_Z=1$. Remarkably, We find that the polarizability and $C_6$ exponents $p'$ and $p$ are related by $p'\approx p-0.615$ rather than the expected $p'\approx p/2$. Results are largely independent of the form of the confining potential (harmonic, cubic and quartic potentials are considered) and kernel approximation, justifying this analysis.
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