Questions: Constructing Molecular Orbital Diagrams for Diatomics

Question 1

MO theory predicts that O₂ is paramagnetic. Which feature of the MO diagram explains this, and why can't the Lewis structure for O₂ predict it?

• A. O₂ has an odd total number of electrons, and odd-electron molecules are always paramagnetic
• B. The two degenerate π*₂p antibonding orbitals each hold one unpaired electron by Hund's rule, giving two unpaired electrons total — a feature Lewis structures have no mechanism to represent
• C. All of O₂'s electrons occupy bonding orbitals, releasing enough energy to produce a magnetic moment
• D. The σ₂p orbital in O₂ is singly occupied, providing one unpaired electron

Answer: (B)

O₂ has 12 electrons. After filling σ₂s (2), σ*₂s (2), σ₂p (2), and π₂p (4), the last 2 electrons enter the two degenerate π*₂p orbitals. By Hund's rule, they occupy these orbitals singly with parallel spins — giving two unpaired electrons and paramagnetism. The Lewis structure draws O₂ as O=O with all electrons paired, completely failing to predict this. This is the classic case where MO theory succeeds where Lewis structures fail, and it validates MO theory as the correct framework for understanding molecular electronic structure.

Question 2

N₂ has 14 electrons and a bond order of 3. If two electrons are added (forming N₂²⁻), what are the new bond order and magnetic properties?

• A. Bond order increases to 4 and N₂²⁻ is diamagnetic
• B. Bond order decreases to 2 and N₂²⁻ becomes paramagnetic
• C. Bond order stays at 3 but N₂²⁻ becomes paramagnetic due to electron repulsion
• D. Bond order decreases to 2.5 and N₂²⁻ remains diamagnetic

Answer: (B)

N₂'s 14 electrons (using s-p mixing ordering) fill: σ₂s(2), σ*₂s(2), π₂p(4), σ₂p(2) — 8 bonding, 2 antibonding, bond order = 3, diamagnetic. Adding 2 electrons fills both degenerate π*₂p orbitals: bonding = 8, antibonding = 4, bond order = (8−4)/2 = 2. By Hund's rule, the two new electrons each occupy one π*₂p orbital singly — two unpaired electrons, so N₂²⁻ is paramagnetic. Both the weakened bond and the paramagnetism follow directly from reading the MO diagram.

Question 3

For second-row diatomics lighter than O₂ (such as N₂ and C₂), the σ₂p molecular orbital lies at lower energy than the degenerate π₂p orbitals.

• T. True
• F. False

Answer: False

For Li₂ through N₂, s-p mixing (interaction between the σ₂s/σ*₂s orbitals and the σ₂p/σ*₂p orbitals) pushes σ₂p upward in energy above the π₂p orbitals. The correct ordering is: σ₂s < σ*₂s < π₂p < σ₂p < π*₂p < σ*₂p. For O₂ and F₂, the larger energy gap between 2s and 2p orbitals reduces this mixing, and σ₂p drops back below π₂p. Getting this switch wrong leads to incorrect electron filling and wrong predictions — for example, incorrectly predicting B₂ is diamagnetic when it is actually paramagnetic.

Question 4

A homonuclear diatomic molecule with bond order 0 predicted by its MO diagram is an unstable species that does not exist as an isolated molecule under ordinary conditions.

• T. True
• F. False

Answer: True

Bond order = (bonding electrons − antibonding electrons)/2. A bond order of 0 means equal numbers of bonding and antibonding electrons, so all bonding stabilization is cancelled out. There is no net attraction between the two atoms — no bond. Ne₂ is the canonical example: filling all MOs from σ₂s through σ*₂p with 18 total electrons gives 8 bonding and 8 antibonding electrons (ignoring core), bond order 0. Noble gas diatomics do not form stable molecules, exactly as MO theory predicts. Bond order is thus a direct existence criterion for molecules.

Question 5

Why can MO theory correctly predict that O₂ is paramagnetic while Lewis structures cannot, even though both are attempting to describe the same molecule's electrons?

Model answer: Lewis structures distribute electrons as localized pairs in bonds and lone pairs, with no concept of orbital degeneracy or Hund's rule. They inherently assume all electrons are paired. MO theory instead places electrons into molecular orbitals that are energy-ordered and may be degenerate. When electrons partially fill degenerate orbitals (like the two π*₂p in O₂), Hund's rule demands one electron per orbital before pairing — leaving unpaired electrons that cause paramagnetism. Lewis structures have no framework for representing degenerate antibonding orbitals, so they miss this entirely.

The Lewis structure of O₂ (O=O) correctly counts 12 electrons and shows a double bond, but forces all electrons into paired bonds and lone pairs. MO theory reveals that 2 of those 12 electrons must occupy two separate π* antibonding orbitals — a fact that emerges naturally from the energy level diagram and Hund's rule. The experimental paramagnetism of liquid oxygen (it sticks to a magnet) is a direct confirmation of MO theory over Lewis structures.