Bond Order and Magnetic Behaviour from MOT Explained

Bond order and magnetic behaviour are the two most testable predictions of molecular orbital theory. Bond order tells you how strong and short a bond is; magnetism reveals whether unpaired electrons hide inside the molecule.

Together they settle what Lewis structures cannot: why O2 is attracted to a magnet, why losing an electron can strengthen a bond, and how bond length shifts when a molecule is ionized.

Key Concepts

• Bond order (BO): the net number of electron pairs binding two atoms. 1 = single, 2 = double, 3 = triple; ions can have fractional values.
• BO trends: higher BO means shorter, stronger bonds. N2 (BO 3): 110 pm, 945 kJ/mol. F2 (BO 1): 142 pm, 158 kJ/mol.
• Paramagnetic: at least one unpaired electron; attracted into a magnetic field. Examples: O2, B2, NO.
• Diamagnetic: all electrons paired; weakly repelled by a magnetic field. Examples: N2, F2, CO.
• Ionization rule: removing a bonding electron lowers BO; removing an antibonding electron raises BO. Adding electrons reverses the effect.

Formulas

• Bond order: BO = (Nb - Na) / 2, from the MO electron count.
• Spin-only moment: mu = sqrt(n(n + 2)) Bohr magnetons, n = unpaired electrons. n = 1 gives 1.73 BM; n = 2 gives 2.83 BM.
• Check: O2 has 2 unpaired electrons, so mu = sqrt(8) = 2.83 BM, paramagnetic. N2 has 0, so mu = 0, diamagnetic.

Worked Example

Question: Compare N2, N2+, and N2- for bond order and magnetism.

Step 1: N2 (10 valence electrons): (sigma 2s)2 (sigma star 2s)2 (pi 2px)2 (pi 2py)2 (sigma 2pz)2. Bonding = 8, antibonding = 2: BO = 3, 0 unpaired, diamagnetic.

Step 2: N2+ loses one electron from sigma 2pz (bonding). BO = (7-2)/2 = 2.5, one unpaired electron: paramagnetic, bond longer and weaker.

Step 3: N2- gains one electron in pi star 2px (antibonding). BO = (8-3)/2 = 2.5, one unpaired electron: paramagnetic, bond weaker.

Step 4: Ionization weakens the N-N bond in both directions, and both ions are paramagnetic while neutral N2 is diamagnetic.

Common Misconceptions

• "Losing an electron always weakens a bond." O2+ is stronger than O2: the lost electron leaves an antibonding pi star orbital, so BO rises from 2 to 2.5 and the bond shortens from 121 pm to 112 pm.
• "Even-electron molecules are always diamagnetic." O2 has 12 valence electrons yet is paramagnetic: Hund's rule keeps its two pi star electrons unpaired in separate orbitals.
• "Lewis structures give bond order." They cannot give fractional bond orders or explain O2's magnetism; only the MO count does.

Real-World Applications

• Superoxide (O2-, BO 1.5) and peroxide (O2 2-, BO 1) in bleaches have O-O lengths of 133 pm and 149 pm, exactly following bond order.
• NO (BO 2.5, paramagnetic) is a signalling molecule in the body; its odd electron makes it reactive enough to relax blood vessels.
• Hospital oxygen analysers use O2's paramagnetism to monitor breathing gases continuously.
• Haber catalysts work by donating electrons into the N2 antibonding orbitals, lowering its bond order as the first step of ammonia synthesis.

Bond order = (Nb - Na)/2 links the MO count to bond length and strength, and the unpaired count gives magnetism via mu = sqrt(n(n+2)). Remember: antibonding electrons hurt the bond, and Hund's rule can leave even-electron molecules like O2 and B2 magnetic.