Visualization of Atomic Orbitals

Hybrid Orbitals

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

The reason is that the geometry of the atomic orbitals must be the same as that of the orbitals with which overlap is to occur. (This notion is embodied in Valence Bond Theory. Molecular Orbital Theory does not require hybridization.)

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 (this atom is not shown), and the various valence-shell orbitals on this atom may be visualized. Surrounding the atom are several (2, 3, or 4) small balls. These balls are used to represent the desired geometry. The balls represent either an atom, which is bonded to the central atom, or a direction along which a long pair of electrons is located. (This geometry is dictated by VSEPR.)

In the virtual reality display, the orbitals on the central atom can be rotated to establish the proper orbital orientation: for each ball, there should be an orbital on the central atom that points directly at the ball. This orbital that points directly at the ball will either be used to form a sigma bond or will hold a nonbonding pair of electrons. The balls can also be rotated, and doing so rotates the entire display.

Perform this exercise by following these steps.

1. Select a geometry: linear (two positions), trigonal planar (three positions), or tetrahedral (four positions).

2. Identify the set of orbitals that is consistent with this geometry.

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 and correctly aligned the orbitals, you will be able to jump from one hybrid orbital to the next, and each hybrid orbital will point directly at one of the balls.

Because the orbitals are relatively large, it may be difficult to clearly identify the direction of each orbital. An arrow that points in the correct direction may be substituted for the orbital isosurface itself.

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 nonbonding orbitals.)

Hybrid Orbitals

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