Relativistic Effects for Copper and Gold

[jeanpinto844]

TL;DR

Relativistic effects on the quantum states of electrons in Copper and Gold

Summary: Relativistic effects on the quantum states of electrons in Copper and Gold

Hello. I am a new member.

I have read that the explanation for the colors of copper(red) and gold(yellow) compared to other metals being silver or grey in color is due to relativistic effects on the valence electrons in those metals. Is this explanation enough? Silver is within the same group as Cu and Au but silver has no characteristic color. How are copper and gold affected by relativity and not silver? I have also read that mercury is a liquid also due to relativistic effects. How is Hg affected but not Zinc or Cadmium? One would perhaps expect the metals on the lower half of the periodic table such as Pb or Bi to also be affected by relativity and have certain characteristics that their neighbors do not. Are relativistic effects just a simple answer/explanation to what is a much more complicated answer?

From a chemist's perspective, the electronic configurations for Cu Ag and Au are 4s1 3d10, 5s2 4d10, and 6s2 4f14 5d10, respectively so one would infer that relativistic effects should take place for all three metals considering they have the exact same configurations. The same can be said for Zn, Cd, and Hg which all end in the same configurations.

 

[TeethWhitener]

Relativistic effects get stronger for heavier atoms. Here's a powerpoint with band structures for copper, silver, and gold:
http://lampx.tugraz.at/~hadley/ss1/lectures16/jun9.pdf
As you can see, the d bands for copper kick in at around 2 eV (~620 nm) below the Fermi level, meaning that most incident light is absorbed above 2 eV, leaving mainly reddish light (>620nm) to be reflected. For silver, the d bands come at around 4 eV (~310 nm) below the Fermi level, well into the UV, meaning most visible light is reflected. For gold, if the periodic trend were to hold, you'd expect the d bands to appear at greater than 4 eV below the Fermi level. Instead, you see the d bands pop up at somewhat less than 2 eV (with another important peak in the blue wavelengths), and the band structure is such that yellow light mainly gets reflected. The breaking of the periodic trend occurs notably in gold, changing the relative spatial extents of the d and s orbitals (and therefore changing the excitation energy/density of states). The relativistic effect for silver is less than in gold, and much less (nearly negligible) in copper.