Molecular Orbital Theory (MOT)
Master the electronic configurations of diatomic molecules. Learn how s-p mixing changes the energy level diagram and predict bond order and magnetic behavior instantly.
Rule 1: Molecules with $\le 14$ Electrons
For molecules like $B_2$, $C_2$, and $N_2$, s-p mixing occurs. This pushes the $\sigma_{2p_z}$ orbital higher in energy, placing it above the $\pi_{2p_x}$ and $\pi_{2p_y}$ orbitals.
$$\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \color{#d946ef}{(\pi_{2p_x} = \pi_{2p_y}) < \sigma_{2p_z}} < (\pi^*_{2p_x} = \pi^*_{2p_y}) < \sigma^*_{2p_z}$$
Rule 2: Molecules with $> 14$ Electrons
For heavier molecules like $O_2$ and $F_2$, the energy gap between 2s and 2p is large. No s-p mixing occurs, meaning $\sigma_{2p_z}$ drops back down to its normal, lowest-energy position.
$$\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \color{#d946ef}{\sigma_{2p_z} < (\pi_{2p_x} = \pi_{2p_y})} < (\pi^*_{2p_x} = \pi^*_{2p_y}) < \sigma^*_{2p_z}$$
Bond Order (B.O.) = $\frac{N_b - N_a}{2}$
Where $N_b$ = Bonding Electrons, $N_a$ = Antibonding (*) Electrons
Where $N_b$ = Bonding Electrons, $N_a$ = Antibonding (*) Electrons
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Homoatomic Molecules
$$\ce{H2}$$
2 e⁻
$$\sigma_{1s}^2$$
Bond Order
1.0
Diamagnetic
$$\ce{H2+}$$
1 e⁻
$$\sigma_{1s}^1$$
Bond Order
0.5
Paramagnetic
$$\ce{H2-}$$
3 e⁻
$$\sigma_{1s}^2 \ \sigma_{1s}^{*1}$$
Bond Order
0.5
Paramagnetic
Less stable than $\ce{H2+}$ because the extra electron resides in an antibonding orbital.
$$\ce{He2}$$
4 e⁻
$$\sigma_{1s}^2 \ \sigma_{1s}^{*2}$$
Bond Order
0.0
Diamagnetic
Molecule does not exist.
$$\ce{He2+}$$
3 e⁻
$$\sigma_{1s}^2 \ \sigma_{1s}^{*1}$$
Bond Order
0.5
Paramagnetic
Unlike neutral $\ce{He2}$, this cation actually exists.
$$\ce{Li2}$$
6 e⁻
$$KK \ \sigma_{2s}^2$$
Bond Order
1.0
Diamagnetic
Exists in vapor phase. ($KK$ = closed 1s shells)
$$\ce{B2}$$
10 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ \pi_{2p_x}^1 = \pi_{2p_y}^1$$
Bond Order
1.0
Paramagnetic
Paramagnetic due to two unpaired electrons in degenerate $\pi$ orbitals.
$$\ce{C2}$$
12 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ \pi_{2p_x}^2 = \pi_{2p_y}^2$$
Bond Order
2.0
Diamagnetic
Highly unusual: Bond order is 2, but both are $\pi$ bonds! No $\sigma$ bond.
$$\ce{C2-}$$
13 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ (\pi_{2p_x}^2 \!=\! \pi_{2p_y}^2) \ \sigma_{2p_z}^1$$
Bond Order
2.5
Paramagnetic
$$\ce{N2}$$
14 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ (\pi_{2p_x}^2 = \pi_{2p_y}^2) \ \sigma_{2p_z}^2$$
Bond Order
3.0
Diamagnetic
Highest bond order, extremely stable. (1 $\sigma$ + 2 $\pi$)
$$\ce{N2+}$$
13 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ (\pi_{2p_x}^2 = \pi_{2p_y}^2) \ \sigma_{2p_z}^1$$
Bond Order
2.5
Paramagnetic
Removing an electron from a bonding orbital decreases B.O.
$$\ce{N2-}$$
15 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ (\pi_{2p_x}^2 \!=\! \pi_{2p_y}^2) \ \sigma_{2p_z}^2 \ \pi_{2p_x}^{*1}$$
Bond Order
2.5
Paramagnetic
Extra electron goes into antibonding $\pi^*$, decreasing B.O.
$$\ce{O2}$$
16 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ \sigma_{2p_z}^2 \ (\pi_{2p_x}^2 \!=\! \pi_{2p_y}^2) \ (\pi_{2p_x}^{*1} \!=\! \pi_{2p_y}^{*1})$$
Bond Order
2.0
Paramagnetic
MOT successfully explained the paramagnetism of liquid Oxygen, which VBT failed to do.
$$\ce{O2+}$$
15 e⁻
$$KK \ ... \ \sigma_{2p_z}^2 \ (\pi_{2p_x}^2 \!=\! \pi_{2p_y}^2) \ (\pi_{2p_x}^{*1} \!=\! \pi_{2p_y}^{*0})$$
Bond Order
2.5
Paramagnetic
Removing an anti-bonding electron increases the Bond Order!
$$\ce{O2-} \text{ (Superoxide)}$$
17 e⁻
$$KK \ ... \ \sigma_{2p_z}^2 \ (\pi_{2p_x}^2 \!=\! \pi_{2p_y}^2) \ (\pi_{2p_x}^{*2} \!=\! \pi_{2p_y}^{*1})$$
Bond Order
1.5
Paramagnetic
$$\ce{O2^{2-}} \text{ (Peroxide)}$$
18 e⁻
$$KK \ ... \ \sigma_{2p_z}^2 \ (\pi_{2p_x}^2 \!=\! \pi_{2p_y}^2) \ (\pi_{2p_x}^{*2} \!=\! \pi_{2p_y}^{*2})$$
Bond Order
1.0
Diamagnetic
Isoelectronic with $F_2$.
$$\ce{F2}$$
18 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ \sigma_{2p_z}^2 \ (\pi_{2p_x}^2 \!=\! \pi_{2p_y}^2) \ (\pi_{2p_x}^{*2} \!=\! \pi_{2p_y}^{*2})$$
Bond Order
1.0
Diamagnetic
$$\ce{Ne2}$$
20 e⁻
$$... \ (\pi_{2p_x}^{*2} = \pi_{2p_y}^{*2}) \ \sigma_{2p_z}^{*2}$$
Bond Order
0.0
Diamagnetic
Does not exist. $N_b = N_a$.
Heteroatomic Molecules
$$\ce{CO}$$
14 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ (\pi_{2p_x}^2 = \pi_{2p_y}^2) \ \sigma_{2p_z}^2$$
Bond Order
3.0
Diamagnetic
Isoelectronic with $N_2$. Extremely strong bond.
$$\ce{CN-}$$
14 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ (\pi_{2p_x}^2 = \pi_{2p_y}^2) \ \sigma_{2p_z}^2$$
Bond Order
3.0
Diamagnetic
Isoelectronic with $N_2$ and $CO$. Strong field ligand.
$$\ce{CN}$$
13 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ (\pi_{2p_x}^2 \!=\! \pi_{2p_y}^2) \ \sigma_{2p_z}^1$$
Bond Order
2.5
Paramagnetic
Cyanide radical.
$$\ce{CN+}$$
12 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ (\pi_{2p_x}^2 \!=\! \pi_{2p_y}^2)$$
Bond Order
2.0
Diamagnetic
Isoelectronic with $C_2$.
$$\ce{NO+}$$
14 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ \sigma_{2p_z}^2 \ (\pi_{2p_x}^2 = \pi_{2p_y}^2)$$
Bond Order
3.0
Diamagnetic
Nitrosonium ion. Highly stable due to B.O. of 3.
$$\ce{NO}$$
15 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ \sigma_{2p_z}^2 \ (\pi_{2p_x}^2 \!=\! \pi_{2p_y}^2) \ \pi_{2p_x}^{*1}$$
Bond Order
2.5
Paramagnetic
Fills similarly to $O_2$ pattern. Has one unpaired electron in anti-bonding $\pi^*$.
$$\ce{NO-}$$
16 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ \sigma_{2p_z}^2 \ (\pi_{2p_x}^2 \!=\! \pi_{2p_y}^2) \ (\pi_{2p_x}^{*1} \!=\! \pi_{2p_y}^{*1})$$
Bond Order
2.0
Paramagnetic
Isoelectronic with $O_2$. Possesses two unpaired electrons.
$$\ce{CO+}$$
13 e⁻
$$KK \ \sigma_{2s}^2 \ \sigma_{2s}^{*2} \ (\pi_{2p_x}^2 \!=\! \pi_{2p_y}^2) \ \sigma_{2p_z}^1$$
Bond Order
2.5 (or 3.5)
Paramagnetic
Standard MOT predicts 2.5. Actual B.O. is 3.5 (electron removed from weakly antibonding $\sigma_{2s}^*$).
