Shape of Orbitals in Periodic Crystals: Hybridization and Energy Bands

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SUMMARY

The discussion centers on the shape of orbitals in periodic crystals, specifically using NaCl as an example. It highlights the energy-band model, which describes how discrete energy levels in a crystal can appear continuous. The conversation also questions the existence of macroscopic hybrid orbitals in crystals, akin to those in molecules like H2, and whether these orbitals share the same shape across the energy bands. The inquiry suggests a need for computational studies on the orbital shapes in periodic crystal structures.

PREREQUISITES
  • Understanding of energy-band theory in solid-state physics
  • Familiarity with hybridization concepts in molecular chemistry
  • Knowledge of periodic crystal structures, specifically NaCl
  • Basic principles of quantum mechanics related to atomic orbitals
NEXT STEPS
  • Research the energy-band model in solid-state physics
  • Explore the concept of hybrid orbitals in more complex molecules
  • Investigate computational methods for modeling orbital shapes in periodic crystals
  • Learn about the symmetry properties of crystal lattices and their impact on energy levels
USEFUL FOR

Physicists, chemists, materials scientists, and anyone interested in the quantum mechanical properties of solids and the behavior of electrons in periodic structures.

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I asked myself how the orbitals in a solid look like.
Assume a crystal with a periodic structure, e.g. NaCl. The electrons in the crystal have energys according to the energy-band-model. Every band consists of that much discrete energy-levels that you might nearly call it continous. I know that molecules have hybrid orbitals. For example the H2-molecule has two spatially separated s-orbitals (bonding and anti-bonding), right? Does a crystal also have "hybrid orbitals", i.e. macroscopic orbitals which are as large as the crystal itself? Have the horribly much orbitals, which together build a band, the same shape? Has someone ever computed it for a periodic crystal-structure? I guess not...

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Just thougt of a different picture:

Every nucleous in the solid has its own orbitals i.e. every nucleous contributes one energy-level to every band. But why, in a periodic structure, there are different energy-levels? In NaCl for example every nucleous "sees" the same "environment". Because of symmetry every Na should have the same energy-levels. So no continuous bands...
 
Hey why thread closed??
 

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