Ethylene is the simplest molecule that has a double bond.  As we saw from the valence bond model, we should find the presence of a σ-bond framework, and a π-bond between carbons.

 (Calculated at the B3LYP/cc-pvdz level using Jaguar, version 7.8, SchrÃ¶dinger, LLC, New York, NY, 2011.) Let's start with the π bond:  click on MO 6 in the list below.  You should clearly see the bonding interaction that forms between two pure p atomic orbitals, with a node in the molecular plane. Show the 12th MO; E>+5.5 eV Show the 11th MO; E=+5.03 eV Show the 10th MO; E=+3.02 eV Show the 9th MO; E=+2.83 eV Show the 8th MO; E=+2.18 eV Show the 7th MO: the antibonding π* MO; E=+0.22 eV Show the 6th MO: the π MO; E=-7.45 eV Show the 5th MO; E=-9.60 eV Show the 4th MO; E=-4.85 eV Show the 3rd MO; E=-12.68 eV Show the 2nd MO; E=-15.72 eV Show the lowest energy MO; E=-20.67 eV Next, let's click through the remaining bonding MOs (1-5).  We will see the same pattern as in methane:  the lowest energy MO has the electron density spread out along the sigma gramework, and higher energy MOs have electron density concentrated between atoms but still delocalized over the entire molecule. Note carefully that there are a total of 6 bonding MOs:  the pi system, plus combinations of 4 C-H and one C-C sigma bond. One of the crucial peatures of the pi bond is that it restricts bond rotation. Note that ethane (with only a C-C sigma bond) rotates freely; we will see in the next chapter that the barrier to rotation is low--2.9 kcal/mol (12 kJ/mol)--meaning that at room temperature, the bond spins at approximately 50 billion times per second! For ethene, the double bond increases this barrier to 65 kcal/mol (260 kJ/mol). At room temperature, this means that a molecule will rotate on average once every 1027 years.