Pi Bonds

Ethene The atomic orbitals of the two carbon atoms, the 2py orbitals, are represented on the outsides by the two phased, dumbbell shaped orbitals.  In the middle are the in-phase and out-of-phase combinations for the molecule.  Remember, the "phase" of an orbital arises from the mathematical expression that describes the shape of the orbital. This is important in bonding since the two orbitals that will form the bond must have the same phases to overlap and produce a new bonding molecular orbital. If they are "out-of-phase" they can not overlap and share electrons. The in-phase combination (CA-2py + CB-2py) is at lower energy than the 2py orbitals we started from and is called the bonding molecular orbital since it is responsible for sharing the electron density between the two nuclei. This molecular orbital is not symmetrical with respect to rotation about an axis on which both C nuclei lie, the electron density is located in two lobes on either side of the internuclear axis. This type of bond is termed a "pi" orbital i.e.  π-orbital, and results from the side-to-side overlap of two "p" orbitals. In contrast to a σ-bond, π-bonds are not "free" to rotate about the internuclear axis. If this rotation occurred, the π-bond would break when the two "p" orbitals no longer overlapped (see below). This process can occur, but not at "low" temperatures, i.e. room temp. A "broken" π-bond. The orbitals do not overlap! The out-of-phase combination (CA-2py - CB-2py) is at higher energy than the 2py orbitals we started from. Again the out-of-phase combination produces a node in the orbital perpendicular the the internuclear axis and located at the mid-point of the C-C bond. This orbital is called the anti-bonding molecular orbital since the presence of electrons in this orbital will cause the bond to break. With a total of four electrons both the bonding and anti-bonding orbitals would be occupied and there would be no net bonding effect between the atoms. The anti-bonding π-orbital is again unsymmetrical with respect to rotation about an axis on which both C nuclei lie, so it is also a π-orbital, but because it is the out-of-phase combination it is termed a "pi-star" orbital  i.e. π*-orbital. The electrons are "placed" in the molecular orbitals following the same rules as for filling orbitals in atoms (i.e. lowest energy level first).  This means the two 2py electrons both go into the bonding molecular orbital, this results in the stabilization of the system. Hence, two C atoms combine to become more stable as a ethene molecule. A of the formation of a π-Bond. (Note: the animation is large, wait until the background turns white before playing.) IMPORTANT:  Only orbitals containing electrons contribute to the stability of the molecule, so the empty π*-orbital has no impact here. The π bond can be formed by the overlap between: two "p" orbitals (side-to-side) two "d" orbitals (side-to-side) i.e. any combination that produces a bonding molecular orbital with the electron density located off the internuclear axis.
	C 2py atomic orbital C2H4 molecular orbitals C 2py atomic orbital

Note:

• In general the overlap of "s" type orbitals is more efficient than the side-to-side overlap of "p" orbitals.
• In general this means that σ-bonds are stronger than π-bonds.
• In a chemical reaction the π-bond is much more likely to break first rather than the σ bond.
• In general it is not possible to form a π-bond with out also forming a σ-bond, thus a double bond consists of 1 σ and 1 π bond.
• Multiple π bonds are possible (triple bonds) they merely require the two atoms to each donate two "p" orbitals to the (side-to-side) formation of two π bonds.

Relationship between Bond Type, Strength & Length
Bond Type	# σ bonds	# π bonds	bond length	bond strength
Single	1	0	longest	weakest
Double	1	1	intermediate	intermediate
Triple	1	2	shortest	strongest