MO Diagrams Li2 to Ne2: Bond Order and Magnetism Guide

Molecular orbital theory builds molecules by merging atomic orbitals into molecular orbitals spread over the whole molecule. For Li2 through Ne2, the MO energy diagrams predict bond strength and magnetism that simpler theories miss.

They matter because they explain real facts: why B2 and O2 are magnetic though their Lewis structures show paired electrons, and why Be2 and Ne2 simply do not exist.

Key Concepts

• Bonding vs antibonding: sigma 2s, sigma 2pz, pi 2px, pi 2py lower the energy and bind; starred orbitals (sigma star 2s, pi star 2px, sigma star 2pz) raise energy and weaken the bond.
• Bond order: half the difference between bonding and antibonding electrons; higher means shorter and stronger bonds.
• s-p mixing: in Li2 to N2 the 2s and 2pz orbitals mix, pushing sigma 2pz above pi 2px/pi 2py. From O2 onward the gap widens, mixing stops, and sigma 2pz sits below the pi star set.
• Order Li2-N2: sigma 2s < sigma star 2s < pi 2px = pi 2py < sigma 2pz < pi star set < sigma star 2pz.
• Order O2-Ne2: sigma 2s < sigma star 2s < sigma 2pz < pi 2px = pi 2py < pi star set < sigma star 2pz.

Formulas

• Bond order: BO = (Nb - Na) / 2. Nb counts bonding electrons, Na antibonding. BO = 0 means no stable molecule.
• Magnetic moment: mu = sqrt(n(n + 2)) Bohr magnetons, with n unpaired electrons. n = 0 is diamagnetic; n > 0 is paramagnetic.
• Results table: Li2: BO 1, diamagnetic. Be2: BO 0, absent. B2: BO 1, paramagnetic (2 unpaired). C2: BO 2, diamagnetic. N2: BO 3, diamagnetic. O2: BO 2, paramagnetic (2 unpaired). F2: BO 1, diamagnetic. Ne2: BO 0, absent.

Worked Example

Question: Find the bond order and magnetism of O2 from its MO diagram.

Step 1: O2 has 12 valence electrons. Using the O2-Ne2 order: (sigma 2s)2 (sigma star 2s)2 (sigma 2pz)2 (pi 2px)2 (pi 2py)2 (pi star 2px)1 (pi star 2py)1.

Step 2: Bonding electrons: 2 + 2 + 2 + 2 = 8. Antibonding: 2 + 1 + 1 = 4.

Step 3: BO = (8 - 4)/2 = 2, a double bond, matching the 121 pm bond length and 498 kJ/mol dissociation energy.

Step 4: The two pi star electrons occupy separate orbitals singly (Hund's rule), so n = 2: O2 is paramagnetic, which is why liquid oxygen clings to a magnet.

Common Misconceptions

• "O2 is diamagnetic because its Lewis structure pairs everything." The MO diagram leaves two pi star electrons unpaired; experiment confirms paramagnetism.
• "One MO order fits all eight molecules." s-p mixing flips sigma 2pz above the pi pair for B2, C2, N2. The wrong order wrongly predicts B2 as diamagnetic.
• "Bond order must be a whole number." Ions like O2+ (2.5) and O2- (1.5) have fractional bond orders with matching bond lengths.

Real-World Applications

• Explains the N triple N bond (BO 3, 945 kJ/mol) and nitrogen's inertness, forcing the Haber process to use extreme conditions.
• Predicts C2 has a double bond with no unpaired electrons, guiding spectroscopy of carbon vapour in stars and furnaces.
• Oxygen analysers exploit O2's paramagnetism: a magnet deflects an O2 stream so sensors can measure oxygen in medical and industrial gases.
• BO = 0 correctly predicts Be2 and Ne2 are absent, while the same method predicts the stable ion He2+ (BO 0.5).

MO diagrams for Li2 to Ne2 fill 2 to 16 valence electrons into two energy orders split by s-p mixing. Bond order = (Nb - Na)/2 gives bond strength; unpaired electrons give paramagnetism. Memorize the two orderings and the B2/O2 surprises.