Valence Shell Electron Pair Repulsion (VSEPR) Theory

Each type of model is made of a central atom (in blue), ligand (bonding electron pair, in red) and nonbonding electron pair. The red spheres represent the ligands of the molecules and at the same time the vertices of the geometric figures/solids in the arrangements.

The basic molecular shapes are linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral, square antiprismatic, tricapped trigonal prismatic, and icosahedral.

The vertices for the six polyhedra (tetrahedron, trigonal bipyramid, octahedron, square antiprism, tricapped trigonal prism, and icosahedron) were extracted from PolyhedronData within Mathematica.

In 1904, the physicist J. J. Thomson posed the problem of determining the minimum energy configuration of electrons on the surface of a sphere that repel each other with a force given by Coulomb's law.

One generalization of Thomson's problem arises in finding a quantitative approach for the VSEPR theory.

For the trigonal pyramid and the triply capped trigonal prism, the radius of the sphere shown was set to the maximum of the distances of the polyhedron's vertices to the center. For the other figures/solids, a circumsphere exists or can be constructed.

Drag the 3D graphic to rotate it and to emphasize that some or all of the red spheres are on the surface of the sphere.

Use "show 3D example" to show a ball-and-stick structure of a molecule with the same geometry. Chemical formulas for examples with this geometry are listed.

Karl N. Harrison at 3Dchem.com is the source for the ball-and-stick structures.

The integrated data sources for ChemicalData within Mathematica and en.wikipedia.org were very helpful in finding and checking the multiple examples for the various types of VSEPR models.

References

[1] R. Gillespie and P. Popelier, Chemical Bonding And Molecular Geometry, New York: Oxford University Press, 2001.

[2] U. Müller, Inorganic Structural Chemistry, New York: J. Wiley & Sons, 2006.

[3] K. Harrison. Chemistry, Structures & 3D Molecules @ 3Dchem.com. (Feb 2011) www.3dchem.com.