极化率
四次方程
缩放比例
体积热力学
偶极子
原子物理学
物理
Atom(片上系统)
化学
数学
量子力学
几何学
分子
计算机科学
纯数学
嵌入式系统
摘要
In this work, we investigate how atomic C6 coefficients and static dipole polarizabilities α scale with effective volume. We show, using confined atoms covering rows 1-5 of the periodic table, that C6/C6R≈(V/VR)pZ and α/αR≈(V/VR)pZ′ (for volume V=∫dr4π3r3n(r)), where C6R, αR, and VR are the reference values and effective volume of the free atom. The scaling exponents pZ and pZ′ vary substantially as a function of element number Z = N, in contrast to the standard “rule of thumb” that pZ = 2 and pZ′=1. Remarkably, we find that the polarizability and C6 exponents p′ and p are related by p′ ≈ p − 0.615 rather than the expected p′ ≈ 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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