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While studying colors of sulfides and searching for the reason why they are black I came across this question:

https://chemistry.stackexchange.com/questions/138309/the-color-of-the-most-sulfides-of-p-and-d-block-elements#:~:text=The%20colours%20tend%20to%20be,of%20the%20transitions%20is%20small.

In it, the top commenter explained the fact that those sulfides are black with the valence band model, because their band gap is so small, they can absorb every visible wavelength of light.

I thought the valence band model only applied to metals, whose atomic orbitals mix with every other atomic orbital in the solid and therefore have an infinite amount of close lying orbitals, thus forming a band. How are ionic solids then able to do the same, when they are composed of different ions? Or does the theory work for all kinds of condensed matter.

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    $\begingroup$ Energy bands in solids apply to all crystals. $\endgroup$
    – Jon Custer
    Oct 17, 2023 at 12:18
  • $\begingroup$ Even to organic frameworks for example?? $\endgroup$
    – Mäßige
    Oct 17, 2023 at 18:38
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    $\begingroup$ Yes, but their conduction band is empty and sits pretty high above. $\endgroup$ Oct 17, 2023 at 18:41
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    $\begingroup$ Broadly speaking, any solid bonded together has overlapping electron wavefunctions with often small energy differences between them. For silicon, the electrons involved with bonding most certainly are delocalized, as are the free carriers (electrons and holes) - the same solid state physics explains insulators, semiconductors, and metals. $\endgroup$
    – Jon Custer
    Oct 17, 2023 at 18:43
  • $\begingroup$ Oh okay that makes sense. But in organic molecules, there are different kind of orbitals; for example consider solid ethylene, so the sigma bonds to the hydrogens form a band and the pi bonds form another or do the sigma and pi bonds form the same band together? $\endgroup$
    – Mäßige
    Oct 17, 2023 at 20:16

2 Answers 2

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As indicated in some comments, all solids, and for that matter all condensed matter, has a band structure. If atoms are packed densely enough, the orbital overlaps that produce "molecular" orbitals become interconnected throughout the volume of the material, and you have bands of energy levels that are filled with closely spaced orbitals. It is true that having discrete molecules, or an ionic structure where the anions tend to hold all the valence electrons, can limit the delocalization of electrons and thus produce narrow bands with wide gaps between them. But the band structure is still there. In the case of water, understanding the band structure, even of a molecular material in the liquid state, is essential to understanding electrochemical reactions commonly carried out in that medium (seehere).

The impact of band structure on color is illustrated in black and white, literally, when we compare magnesium silicide ($\ce{Mg2Si}$) with sodium sulfide ($\ce{Na2S}$). Both have eight valence electrons per formula unit and an antifluorite structure, yet their colors are as shown below. Can you tell which is which (without clicking the attributions) in the pictures below?

enter image description here

Compound A

enter image description here

Compound B

Sodium sulfide, with a large difference in energy between the atomic valence orbitals of the two elements, has its valence electrons largely localized onto the more electronegative sulfur atoms, as in a classically ionic compound; with little delocalization the bands are narrow and the gaps so wide that sodium sulfide can barely absorb visible light. In fact the yellow color seen here actually comes from polysulfides, whose sulfur-sulfur bonding broadens the sulfur-based band and narrows the bandgap somewhat. Pure sodium (mono)sulfide is white.

Not so with magnesium silicide, whose much smaller difference in energy levels between magnesium and silicon atoms facilitates a great amount of electron delocalization and a narrow bandgap. The bandgap of magnesium silicide, like other black semiconductors, is so narrow that it actually falls into the IR range; such materials,including magnesium silicide itself, are candidates for thermoelectric applications.

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  • $\begingroup$ Nice answer and I didn’t even know that band theory also applied to liquids! In university courses, for example ochem, one only looks at MO‘s of single molecules, thats why I was confused. One question though, how can one determine which orbitals are in the bands exactly. For example, there are many different bonds in hydrocarbons (sigma-H bonds, heteroatom bonds, pi bonds), or do those bonds independently form their own bands? $\endgroup$
    – Mäßige
    Oct 18, 2023 at 5:58
  • $\begingroup$ @Mäßige No, their molecular orbitals. $\endgroup$
    – Mithoron
    Oct 18, 2023 at 15:13
  • $\begingroup$ Okay then, their molecular orbitals then. Do those form the bands independently $\endgroup$
    – Mäßige
    Oct 18, 2023 at 17:24
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Metals have a "sea" of electrons at the lowest level, i.e., even at room temperature or close to absolute zero. A potential of even 1 µV will cause a flow of charge in Cu. Metallic conductivity decreases with increasing temperature due to vibration disturbing the regularity of the structure. At operating temperature, a tungsten filament might have ten times its cold resistance.

Semiconductors' electrons need a "boost" to move up and out. In Si diodes, for example, at room temperature, it might take 0.7 V to overcome the barrier between p- and n-type (doped) Si. However, conductivity of semiconductors increases with increasing temperature, as electrons are knocked loose.

It also depends on allotrope, too. For example, in a diamond lattice, undoped C is a nonconductor at room temperature (though doped, it is a semiconductor), but in planar graphite, it's a conductor.

BTW, there are many colored sulfides (and oxides). Cinnabar ($\ce{HgS}$) was used to make vermilion, a bright orange-red. Covellite ($\ce{CuS}$) is blue. Orpiment ($\ce{As2S3}$) is yellow.

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  • $\begingroup$ And this band structure applies to all crystals, be it organic compounds, silicium, carbon etc.? $\endgroup$
    – Mäßige
    Oct 17, 2023 at 18:40
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    $\begingroup$ Graphite is just a conductor, no semi. Also doped diamond can be semiconducting. $\endgroup$
    – Mithoron
    Oct 17, 2023 at 19:40
  • $\begingroup$ @Mithoron, the answer has been edited. The band-gap for diamond is ~5.5 eV, so it has high potential (P.I.) for high temp devices. Interesting to think of oil-well loggers using diamond chips -- rather carbon intensive. $\endgroup$ Oct 17, 2023 at 22:08

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