Visualization of Hybrid Orbitals

Geometry of Hybrid Orbitals

Why employ orbital hybridization instead of using the basic s, p_x, p_y, and p_z orbitals?

Hybrid orbitals are a construct used in Valence Bond Theory to create a localized bonding orbital. The key consideration is that the bonding orbital is mathematically formulated from an atomic orbital from each atom. In order to concentrate electron density between the nuclei of the two atoms bonded to each other, the atomic orbitals should point at each other. That is, the atomic orbitals need to be directional and need to have the same geometry as the molecule itself.

This exercise illustrates the role of geometry in choosing the appropriate hybrid orbitals. The virtual reality display contains an atom at the center of the display (the position of the nucleus is marked by the tiny yellow sphere). The various valence-shell orbitals for this atom may be visualized with isosurfaces. Surrounding the atom are several (2, 3, or 4) white spheres. These white spheres are used to represent the desired geometry. A white sphere represents either an atom, which is bonded to the central atom, or a direction along which a lone electron pair is located. (This geometry is predicted by the Valence-Shell Electron-Pair Repulsion Model.)

In Valence Bond Theory, for each white sphere there should be an orbital on the central atom (tiny yellow sphere) that points directly at a white sphere. The orbital that points directly at the white sphere will either be used to form a sigma bond or will accommodate a nonbonding pair of electrons.

Perform this exercise by following these steps.

1. Select a geometry

Linear : Two white spheres are shown, lying on a line (the z axis) passing through the central atom.
Trigonal Planar : Three white spheres lie at the corners of an equilateral triangle in the xy plane.
Tetrahedral : Four white spheres lie at the corners of a tetrahedron.

2. Identify the set of orbitals that is consistent with this geometry. (This is the hybridization scheme.)

Set 1 is the unhybridized atomic orbitals.
Set 2 is two sp hybrid orbitals plus two unhybridized p orbitals.
Set 3 is three sp² hybrid orbitals and one unhybridized p orbital.
Set 4 is four sp³ hybrid orbitals.

When you have chosen the correct set of orbitals, you will be able to jump from one hybrid orbital to the next and have each hybrid orbital point directly at one of the spheres.

Answer the following questions:

Which hybrid orbitals provide the correct geometry for a linear system?
Which hybrid orbitals provide the correct geometry for a trigonal planar system?
Which hybrid orbitals provide the correct geometry for a tetrahedral system?
For a system that employs sp or sp² hybrid orbitals, what role do the unhybridized p orbitals play? (Hint: Think about the environments for electrons other than sigma bonds and lone-pairs.)