If you like us, please share us on social media.
The latest UCD Hyperlibrary newsletter is now complete, check it out.

ChemWiki: The Dynamic Chemistry E-textbook > Inorganic Chemistry > Crystal Field Theory > Virtual: Electronic Structure > Crystal Field Theory

Copyright (c) 2006-2014 MindTouch Inc.

This file and accompanying files are licensed under the MindTouch Master Subscription Agreement (MSA).

At any time, you shall not, directly or indirectly: (i) sublicense, resell, rent, lease, distribute, market, commercialize or otherwise transfer rights or usage to: (a) the Software, (b) any modified version or derivative work of the Software created by you or for you, or (c) MindTouch Open Source (which includes all non-supported versions of MindTouch-developed software), for any purpose including timesharing or service bureau purposes; (ii) remove or alter any copyright, trademark or proprietary notice in the Software; (iii) transfer, use or export the Software in violation of any applicable laws or regulations of any government or governmental agency; (iv) use or run on any of your hardware, or have deployed for use, any production version of MindTouch Open Source; (v) use any of the Support Services, Error corrections, Updates or Upgrades, for the MindTouch Open Source software or for any Server for which Support Services are not then purchased as provided hereunder; or (vi) reverse engineer, decompile or modify any encrypted or encoded portion of the Software.

A complete copy of the MSA is available at http://www.mindtouch.com/msa

Crystal Field Theory

Table of Contents


Why is a ruby red?

The mineral corundum is a crystalline form of alumina: Al2O3. A pure crystal of corundum is colorless. However, if just 1% of the Al3+ ions are replaced with Cr3+ ions, the mineral becomes deep red in color and is known as ruby (Al2O3:Cr3+). Why does replacing Al3+ with Cr3+ in the corundum structure produce a red color?

Ruby is an allochromatic mineral, which means its color arises from trace impurities. The color of an idiochromatic mineral arises from the essential components of the mineral. In some minerals the color arises from defects in the crystal structure. Such defects are called color centers.

Corundum, from Eheliyagoda, near Ratnapura, Sri Lanka (3.9 x 2.5 x 1.4 cm). ©Rob Lavinsky (irocks.com), used by permission.
Ruby on white marble, from Jegdalik, Sorobi District, Afghanistan (2.1 x 1.4 x 1.3 cm), ©Rob Lavinsky (irocks.com), used by permission.



The mineral beryl is a crystalline beryllium aluminosilicate with the chemical formula Be3Al2Si6O18. A pure crystal of beryl is colorless. However, if just 1% of the Al3+ ions are replaced with Cr3+ ions, the mineral becomes green in color and is known as emerald (Be3Al2Si6O18:Cr3+).

Why does replacing Al3+ with Cr3+ in corundum produce a red mineral (ruby) while replacing Al3+ with Cr3+ in beryl produces a green mineral (emerald)?

Beryl on albite, from Shigar Valley, Pakistan (4.9 x 3.7 x 3.2 cm). ©Rob Lavinsky (irocks.com), used by permission.
Emerald on white marble, from Panjshir Valley, Afghanistan (2.1 x 1.7 x 1.1 cm). ©Rob Lavinsky (irocks.com), used by permission.


Crystal Field Theory was developed in 1929 by Hans Bethe to describe the electronic and magnetic structure of crystalline solids. The theory was further developed through the 1930's by John Hasbrouck van Vleck. Crystal Field Theory describes the interaction between a central metal ion that is surrounded by anions. A quantum mechanical description of the metal ion is employed, with attention focused on the valence shell d, s, and p orbitals. The surrounding anions are typically treated as point charges.

The essential insight of Crystal Field Theory is that the geometry of the negatively charged point charges influences the energy levels of the central metal ion. Consider the 3d orbitals of a first-row transition metal. A spherical distribution of negative charge surrounding the metal ion affects each of the five 3d orbitals in the same way and consequently all five 3d orbitals have the same energy. But what happens if the negative charge is not distributed spherically?


This exercise depicts the various 3d orbitals for a first-row transition metal. A set of negative charges (white spheres) are positioned around the metal center using one of four geometries: linear, square planar, tetrahedral, and octahedral. (Obviously other geometries are possible, but these four geometries are the most common.) The diagram at the right shows the absolute energy of the individual orbitals (E) or the energy difference from the average (spherical field) energy (ΔE). When the negative charges are infinitely far away (approximated by the maximum displacement in this exercise), all 3d orbitals have the same energy (ΔE = 0 and E = 0).

Use the controls to vary the distance between the metal center and the negative charges. Carefully observe how the energies of the orbitals change as the distance becomes smaller and smaller. Answer the questions below and explain the observed behavior. Bear in mind that an orbital represents the distribution of electron density.

  1. How does the orbital energy change as the negative charges get closer to the metal center?
  2. For the linear geometry, why is the 3dz2 orbital more strongly affected by the surrounding negative charge than the 3dxy orbital?
  3. For the square planar geometry, why is the 3dx2-y2 orbital more strongly affected by the surrounding negative charge than the 3dxy orbital?
  4. For which of the four geometries is the change in E greatest when the negative charge is close to the metal center? Why?
  5. For each geometry a specific splitting pattern is observed in the ?E plot. Explain each pattern.
  6. Compare the splitting patterns (ΔE plot) for the tetrahedral and octahedral complexes. Is the splitting in the ?E plot greater for the tetrahedral or octahedral geometry? Explain the observed behavior.


Geometry:     Linear     Square Planar     Tetrahedral     Octahedral           View:        

Orbitals:       none     3dxy     3dxz     3dyz     3dx2-y2     3dz2                     Adjust Distance:  

You must to post a comment.
Last modified
18:17, 1 Oct 2013



(not set)
(not set)

Creative Commons License Unless otherwise noted, content in the UC Davis ChemWiki is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License. Permissions beyond the scope of this license may be available at copyright@ucdavis.edu. Questions and concerns can be directed toward Prof. Delmar Larsen (dlarsen@ucdavis.edu), Founder and Director. Terms of Use