How polarizabilities and $C_6$ coefficients actually vary with atomic volume

Abstract

In this work we investigate how atomic $C_6$ coefficients and static dipole polarizabilities $\alpha$ 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 $\alpha /{\alpha }^R\approx (V/V^R{)}^{p_Z^{\prime }}$ (for volume $V=\int dr\frac{4\pi }{3}{r}^{3}n(r)$) where $C_6^R$, ${\alpha }^R$ and $V^R$ are the reference values and effective volume of the free atom. The scaling exponents $p_Z$ and $p_Z^{\prime }$ vary substantially as a function of element number $Z=N$, in contrast to the standard "rule of thumb" that $p_Z=2$ and $p_Z^{\prime }=1$. Remarkably, We find that the polarizability and $C_6$ exponents $p^{\prime }$ and $p$ are related by $p^{\prime }\approx p-0.615$ rather than the expected $p^{\prime }\approx p/2$. 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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Cited by in corpus (6)

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• The Static Dipole Polarizability of Palladium from Relativistic Coupled Cluster Theory
• Relativistic and Electron Correlation Effects in Static Dipole Polarizabilities for Main-Group Elements
• Relativistic and electron-correlation effects in static dipole polarizabilities for group 12 elements
• Relativistic and electron-correlation effects in static dipole polarizabilities for group 11 elements