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Overlap of Atomic Orbitals to form Molecular Orbitals

Concepts

If two atoms are sufficiently close together, an orbital from one atom can overlap with an orbital from the other atom. Within the framework of Molecular Orbital Theory, this overlap can produce one of two results:

1. The two orbitals have correct symmetry to interact or "mix".
2. The two orbitals do not have correct symmetry to interact or "mix".

In the event the two orbitals do not interact, there is no bonding interaction, one atomic orbitals is unaffected by the presence of the other atomic orbital, and the atomic orbitals are regarded as nonbonding (n). Orbitals do not interact when the degree of constructive interaction (areas of overlap where both wave functions have the same sign) is exactly offset by the degree of destructive interaction (areas of overlap where the wave functions have opposite signs).

In the event the two orbitals do interact, the two atomic orbitals are transformed into two molecular orbitals. One molecular orbital results from constructive interaction (overlap occurs in areas where both wave functions have the same sign) between the two orbitals, and the resulting molecular orbital is a bonding orbital. The other molecular orbital results from destructive interaction where the wave functions have opposite signs) between the two orbitals, and the resulting molecular orbital is an antibonding orbital. The two molecular orbitals result from "adding" and "subtracting" the two wave functions for the atomic orbitals.

The bonding and antibonding orbitals can be placed into one of three categories, depending upon where the constructive/destructive interaction occurs.

sigma (σ): The interaction occurs along the line connecting the two nuclei.
pi (π): The interaction occurs in two regions, one directly above and the other directly below the line connecting the two nuclei.
delta (δ): The interaction occurs in four regions: above, below, to the left, and to the right of the line connecting the two nuclei.


Example 1: Sigma Bonding and AntiBonding Orbitals

In the interactive display below, the 3s orbitals on two atoms are shown. Use the controls to move the orbitals close to each other and carefully observe the overlap of the two orbitals.


                    Adjust Atom Separation :                    


Notice that there is only one region where overlap occurs, thus there must be a net interaction.

If both wave functions have the same sign, as is the case in this example, there is net constructive interaction and the two orbitals interact ("mix") to form a new molecular orbital that is a bonding orbital.

If the two wave functions have the opposite sign, there is net destructive interaction and the two orbitals interact ("mix") to form a new molecular orbital that is an antibonding orbital. This case would occur if one orbital in the overlap region was green (positive wave function sign) and the other orbital was red (negative wave function sign).

In this case the region of interaction occurs along the line connecting the two orbitals. Thus the molecular orbitals formed (bonding and antibonding) are of the sigma (σ) type.



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