In this work we investigate how atomic $C_6$ coefficients and static dipolepolarizabilities $\alpha$ scale with effective volume. We show, using confinedatoms covering rows 1-5 of the periodic table, that $C_6/C_6^R\approx(V/V^R)^{p_Z}$ and $\alpha/\alpha^R\approx (V/V^R)^{p'_Z}$ (for volume $V=\intdr \frac{4\pi}{3}r^3 n(r)$) where $C_6^R$, $\alpha^R$ and $V^R$ are thereference values and effective volume of the free atom. The scaling exponents$p_Z$ and $p'_Z$ vary substantially as a function of element number $Z=N$, incontrast 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 arelargely independent of the form of the confining potential (harmonic, cubic andquartic potentials are considered) and kernel approximation, justifying thisanalysis.
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机译:在这项工作中,我们研究原子的$ C_6 $系数和静态偶极极化率$ \ alpha $如何与有效体积成比例。我们使用覆盖元素周期表第1-5行的约束原子来显示$ C_6 / C_6 ^ R \ approx(V / V ^ R)^ {p_Z} $和$ \ alpha / \ alpha ^ R \ approx(V / V ^ R)^ {p'_Z} $(卷$ V = \ intdr \ frac {4 \ pi} {3} r ^ 3 n(r)$)其中$ C_6 ^ R $,$ \ alpha ^ R $和$ V ^ R $是游离原子的参考值和有效体积。缩放指数$ p_Z $和$ p'_Z $作为元素编号$ Z = N $的函数有很大变化,这与$ p_Z = 2 $和$ p'_Z = 1 $的标准“经验法则”相反。值得注意的是,我们发现极化率和$ C_6 $指数$ p'$和$ p $与$ p'\大约p-0.615 $而不是预期的$ p'\大约p / 2 $相关。结果在很大程度上与约束势的形式(考虑谐波,三次和四次势)和核近似无关,从而证明了这一分析的正确性。
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