Average energy concept

Question

Problem

When the number of electrons in bonding molecular orbitals is equal to number of electrons in anti-bonding molecular orbitals bond cannot be formed between two atoms because

A) Bonding effect by the electrons in bonding M.O.s is cancelled by the antibonding effect of electrons in antibonding M.O.s

B) Antibonding effect by the electrons in antibonding orbitals is more than the bonding effect by the electrons in bonding M.O.s

C) Average energy of bonding and anti-bonding M.O.s is more than the average energy of atomic orbitals from which they are formed

D) Average energy of bonding and antibonding M.O.s is equal to the average energy of atomic orbitals from which they are formed

Answer

B and C

My thoughts

I get the reason for option B as anti-bonding orbitals have higher energy comparing to the bonding orbitals, so naturally their destabilizing effect must be greater than the stabilizing effect offered by the bonding orbitals.

But I really can't understand the average energy concept of orbitals as expressed in the option C . could you help clarify what exactly is the energy concept regarding the molecular orbital and atomic orbital ? and how they can be compared?

Correct me wherever I'm wrong.

Answer 1

Choices B and C are two different ways of saying the same thing. Say $E_{MO}(A)$ and $E_{MO}(AB)$ are the energies of electrons in bonding and anti-bonding orbitals, respectively, relative to the electrons in the original atomic orbitals from which the molecular orbitals are formed, or, to make matters simple, set the energy of electrons in the original atomic orbitals to zero, that is, set as a reference $E_{AO}(1)$ and $E_{AO}(2)=0$ (assuming for simplicity that there are two MOs formed from two AOs).

To say bonding occurs is equivalent to saying that the energy of electrons in the separate atomic orbitals is higher than the energy of the electrons in the bonding molecular orbital. Using that reference system, positive energies (>0) disrupt bonding, and negative lead to bonding. Then saying that the effect of the antibonding electrons is greater than that of the bonding ones is equivalent to the statement $$0\lt E_{MO}(B) + E_{MO}(AB)$$ or equivalently $$0\lt \frac{E_{MO}(B) + E_{MO}(AB)}{2} = E_{MO,\text{avg}} $$ but this is just what choice C says, since the average energy of the atomic orbitals is just zero, that is $$ \frac{E_{MO}(B) + E_{MO}(AB)}{2} = E_{MO,\text{avg}} \gt 0 = E_{AO,\text{avg}} $$

Answer 2

When a test question is so vague that you can't figure out what answer is best, it's difficult to formulate a question about the answers to the question. The test question specifies bonding electrons equal to antibonding electrons. No energy statements. There needs to be one more answer:

E. All of the above, although some answers are a little better than others.

In order to develop a bond, the decrease in energy, i.e., the stabilization, of bonding electrons, needs to be enough to prevent disruption of the bond. If the "bond" is stabilized and destabilized by the same amount, there is nothing holding it together. If the destabilization is greater than the stabilization, the "bond" never formed.

Even if, under extreme conditions, like high pressure, or very cold temperatures, molecules are formed that are metastable for short periods, bonding forces hold them together only until some vibration puts them into a state which is less stabilized; then the atoms move apart more and more until they are separated - no bond any more.