Pictures of the Day

The sigma bonding molecular orbitals is shown for the H2 molecule. You can tell this is a sigma bond in that there is cylindrical symmetry around the bond axis. In the case of H2 the sigma bonding interaction results from overlap of the 1s orbitals on each H atom. Recall that a sigma bond is a bond in which the majority of the electron density is between the two nuclei. A sigma bond also results from the overlap of an sp3, sp2 or sp hybrid orbital and any s, sp3, sp2 or sp hybrid orbital. Because rotating a sigma bond does not decrease the overlap of the orbitals involved (sigma bonds have cylindrical symmetry), a sigma bond can rotate freely about the bond axis.

Above is the structure of ethylene, acetylene and ethane, including the representations of the pi bonds. The two carbons of ethylene are joined by a double bond and share four electrons. Two electrons are located in the sigma bond fromed from the overlap to two sp2 hybrid orbitals and the electron density is located between the two carbons. The remaining two electrons exist in the pi bond that is formed from the overlap of the 2p orbitals on each sp2 hybidized carbon atom. For acetylene, the two carbons of acetylene share 6 electrons and are joined by a triple bond. Two electrons are located in the sigma bond formed from the overlap of sp hybrid orbitals and the electron density is located between the two carbons. The remaining four electrons exist in the two orthogonal pi bonds that are formed from the overlap of the 2p orbitals on each sp hybidized carbon atom. Ethane on the bottom has two carbons joined by a single bond and share 2 electrons. The two electrons on located in the sigma bond formed by overlap of two sp3 hybrid orbitals.

Pictured above are the atomic orbitals most interesting to an organic chemist. In particular, the 2s, and three 2p orbitals are displayed. These are interesting because they hold the valence electrons for atoms such as C, N, O and F. Here, the red and blue correspond to areas of positive and negative amplitude of the wave function. THE SIGN OF THE AMPLITUDE OF THE WAVE FUNCTION HAS NOTHING TO DO WITH CHARGE. You are just as likely to find electron density in a lobe with positive amplitude (+) as it is to find it in a similar lobe with negative amplitude (-). Recall that the wave function is the particular solution to the Schrodinger equation that describes each orbital.

BOTTOM LINE: READ THIS IF ORBITALS FRIGHTEN YOU:

This material is very complex, yet what you should know at this point is rather simple:
1. Electrons have properties of waves (you should know what those properties are)
2. The wave functions help us understand the location of electron density around an atom.

The sigma bonding (below) and antibonding (above) molecular orbitals are shown for the H2 molecule. You can tell this is a sigma bond in that there is cylindrical symmetry around the bond axis. In the case of H2 the sigma bonding interaction results from overlap of the 1s orbitals on each H atom. In the case of the antibonding orbital shown above, the red and blue correspond to areas of positive and negative amplitude of the wave function. Recall that a sigma bond is a bond in which the majority of the electron density is between the two nuclei. A sigma bond can result from the overlap between an s orbital and any other type of atomic orbital. A sigma bond also results from the overlap of an sp3, sp2 or sp hybrid orbital and any s, sp3, sp2 or sp hybrid orbital. Because rotating a sigma bond does not decrease the overlap of the orbitals involved (sigma bonds have cylindrical symmetry), a sigma bond can rotate freely about the bond axis. Note that the sigma antibonding orbital is not filled with any electron density under normal circumstances. Thus, the main take home message from this graphic is what a sigma bond looks like, namely the bonding molecular orbital shown on the bottom.

Above is the structure of ethylene, including the representations of the pi bonds. The two carbons of ethylene are joined by a double bond and share four electrons. Two electrons are located in the sigma bond and the electron density is located between the two carbons. The remaining two electrons exist in the pi bond that is formed from the overlap of the 2p orbitals on each sp2 hybidized carbon atom. The interaction of the 2p orbitals in a pi bond create one bonding molecular orbital and one antibonding molecular orbital. In a neutral state, the electrons in the 2p orbitals of ethylene will combine in phase, in the bonding molecular orbital. This occurs because the electrons in the pi bond will be in the lowest energy state and thus give the molecule the most stability. It is also important to realize that another molecular orbital exists. This is called the pi antibonding molecular orbitals and is shown above the pi bonding orbital. Remember, this orbital does exist but no electrons are present in this orbital if the molecule is neutral. Electrons move into the antibonding orbital only when they are excited, say by UV light, and thus attain a higher energy state. Also, note that the antibonding molecular orbital has a node between the two nuclei. Again, I have introduced the concept of antibonding orbital only for the sake of completeness. The main take home message from this graphic is what a pi bond looks like, namely the bonding pi molecular orbital shown on the bottom.