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Overlap of Atomic Orbitals to form Molecular Orbitals

Exercise

Objectives:

1. For any pair of atomic orbitals on two atoms, determine whether there is no interaction or a net interaction between the two orbitals.
2. For orbitals where a net interaction occurs, determine whether the interaction produces sigma, pi, or delta bonding/antibonding orbitals.

Use the controls on the left to select the orbitals on the two atoms. Then use the controls to move the atoms close together so that orbital overlap occurs. Carefully examine the overlap and determine whether the two orbitals interact (bonding/antibonding orbitals are formed) or do not interact (orbitals are nonbonding).

The green color represents an area where the wave function has a positive sign; the red color represents an area where the wave function has a negative sign. The sign of the wave function is important in determining the nature of the overlap.

Bonding Interaction

A bonding interaction occurs when two green (+) regions overlap or when two red (-) regions overlap. Such overlap increases electron density in the overlap region, which lowers the energy of the system. The two atoms stay close to each other to preserve the favorable overlap and lower energy.

Antibonding Interaction

An antibonding interaction occurs when a green (+) region overlaps with a red (-) region. Such overlap decreases electron density in the overlap region, which increases the energy of the system. The two atoms will prefer to move away from each other to eliminate the unfavorable overlap and decrease the energy.

No Interaction

If the overlap of two orbitals produces multiple regions of overlap with some overlap being constructive (green-green or red-red overlap) and some being destructive (green-red overlap), the two effects will offset each other and the energy of the system will be unchanged. In such circumstances there is no net interaction between the orbitals.

NOTE: In this exercise, the two atoms approach each other along the z-axis. In other molecules, especially molecules containing more than two atoms, atoms may approach from other directions, and consequently the orbitals that interact will differ from those in this example. For this reason, do not attempt to memorize orbital combinations; it is necessary to examine the overlap behavior for each molecule individually.

Part 1

Display the 3py orbital on the left atom, and systematically examine the overlap of this orbital with all possible orbitals on the right atom (there are nine orbitals). For each pair of orbitals, indicate whether there is no net interaction or pi bonding/antibonding (π/π*) interactions.

Where a net interaction exists, vary the sign of the wave function on the atom at the right. Identify the sign that leads to a bonding interaction (σ or π). The opposite sign produces the corresponding antibonding interaction (σ* or π*).

Part 2

Although there are 81 combinations of orbitals in this exercise, many combinations are redundant. For the purposes of this exercise, it is only necessary to examine the following combinations:

  1. 3s and 3pz
  2. 3s and 3py
  3. 3px and 3py
  4. 3s and 3dz2
  5. 3py and 3dyz
  6. 3py and 3dxy
  7. 3dyz and 3dyz
  8. 3dxy and 3dxy
  9. 3s and 3dyz
  10. 3dx2-y2 and 3dx2-y2



Left Orbital



Right Orbital










Adjust Atom
Separation





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