Types of Bonds

The separation between the anti-bonding and bonding molecular orbitals formed will be a direct result of overlap of the atomic orbitals used to form them. The overlap taht can occur depends on the type of orbital that went into making the molecular orbital. The different types of bonds are shown below. It will be assumed that the orbitals contributing to the bonds in the following images originate form homonuclear species so that energy differences between atomic orbitals due to differences in electronegativity of the originating atoms can be ignored.

As we can see, the best overlap betwen orbitals occur when two p orbitals are connected lobe to lobe. This results in a maxiumum overlap because the p-orbitals can reach out to meet each other. In the second sigma bonding case, the p orbital can reach out to the s orbital, but the overlap is smaller because the s orbital cannot reach out to the p orbital. In the sigma bond between the 2 s orbials, the overlap is the smallest because neither can reach out to each other. The pi bond has less overlap because the lobes of the p-orbitals do not touch, but interaciton does occur between them. In the delta bond, there is little interaction of the orbitals that form them since they just face each other and interactions occur over a large distance. Hence they have the smallest overlap of all of the bonds. An image showing a comparison of the overlaps between a sigma, pi and delta bond is shown below.

Anti-bonding molecular orbitals contribute to ripping apart the molecule and come in varying degrees(i.e. the higher in energy, the more antibonding the orbital becomes). These are shown as a phase change that occurs between the orbitals involved. For example, look at the linear triatomic hydrogen molecule. We see that the phases do not match up for a bond in an antibonding orbital, while the phases match up in the bonding orbital.

Now another point to observe is the number of nodes that can happen in a molecular orbital. A node is a point at which the wavefunction passes thgrough 0. It is observed that the number of nodes increases as the molecular orbital increases in energy. Therefore, it is expected that the highest energy molecular orbital would have the most nodes for a linear molecule. This is demonstrated in the image below.

As can be seen in the representation of the pi orbitals from a linear chain of 5 atoms, we get nodes appearing both in between the orbitals and right on an orbital. Now if we set the fully bonding orbital as N=1, we will see there are N - 1 nodes for a particular orbital. For example, in the fully antibonding orbital, N = 5, therefore the number of nodes should be 4, which there is. There is also one more type of molecular orbital, the non-bonding type, and plays no role in bonding. One further note on nodes. These are generally illustrated as a change in phase of the orbitals between one orbital and the next.

There is but a few things left to speak about now. This concerns certain quantitites left to define that are found throughout molecular orbital theory. The first one is B: the overlap integral. This is a measure of the overlap that can occur between two atomic orbitals that make up the molecular orbitals. The larger B is, the better the overlap and the greater the separation between the bonding and anti-bonding orbitals. The other parameter is alpha. This is the measure in energy where the orbital is at without overlap included. It is generally found that the best overlap that can occur is 2B below and 2B above alpha. Therefore, that is why in bands we see a 4B separtaion between the bonding and antibonding orbitals. To be exact, the energy of the bonding orbital is alpha + 2B, and the antibonding orbital is alpha - 2B, alpha can arbitrarily be 0 and B a negative quantity. Therefore, the bonding orbital is said to be at a negative energy. The non-bonding orbital is found at alpha.

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Author:Steve Kornic email

Department of Chemistry and Biochemistry, University of Guelph

Last updated: 97/03/27