3d orbital orientation in an Octahedral Crystal Field

In Crystal Field Theory, the central metal ion is treated as positive while the ligands as negative point charges. Graphically though, taking the simple example of TiCl63-, it is more usual to represent this as shown below where the central metal is seen as a grey sphere and the chlorides are green spheres. The orientation of each of the five d orbitals in an octahedral field can be superimposed and related to the faces of a cube.

dx2-y2    dz2
The electron density (i.e., the lobes of the orbitals) lies directly in line with the point charges on the axes.
dxy    dxz    dyz
The electron density lies in between the point charges.

Orbital data calculated with JSmol using routines by Bob Hanson

Copyright © 2006-2015 by Robert John Lancashire, all rights reserved.

Created and maintained by Prof. Robert J. Lancashire,
The Department of Chemistry, University of the West Indies,
Mona Campus, Kingston 7, Jamaica.
Created June 2006. Links checked and/or last modified 14 March 2015.
URL http://wwwchem.uwimona.edu.jm/courses/OctCFT_Orbs.html