-4

Context

I am a teacher, and, during a class, my student asked me to draw the molecular orbital (MO) diagram of the hydroxide anion ($\ce{HO-}$). First, I made the diagram on the left, and then, when my student pointed out that the bond order is two, I corrected it by exciting some of the electrons to the antibonding orbitals, making the diagram on the right.

Note: This is a genuine attempt at explaining MO diagrams to a high school student. Please help me explain the concept right.

I attempted to draw the molecular orbital (MO) diagram of the hydroxide anion.

I have shown the one with electron filling according to Aufbau principle and the one with a simple fix I applied to correct the bond order.

The bonding ($\sigma_1$ and $\sigma_2$) and anti-bonding ($\sigma^\ast_1$ and $\sigma^\ast_2$) orbitals have been highlighted:

electron filling of molecular orbitals of hydroxide anion according to the Aufbau principle with bond order 2 and fixed filling of molecular orbitals of hydroxide anion with bond order 1

Now, according to the Wikipedia article on Aufbau principle, in the ground state, electrons fill subshells of the lowest available energy first, and subsequently the subshells of higher energy are filled, which is what I have done in the left diagram, $\mathrm{BO=2}$, and I have shown an excited state, with $\mathrm{BO=1}$, on the right.

Comments

  1. I am fully aware, as remarked by the student and in the comments, that $\ce{H}$ is not known to form a double bond.
  2. There might be somethings which are wrong with the MO diagrams.
  3. It has been pointed out that the number of MOs is more than the number of atomic orbitals (AOs), which is supposedly incorrect.
  4. According to the comments, one of the bonding orbitals I have drawn is non-bonding, though I do not yet know of this.
  5. Some comments have suggested reading a few textbooks, which I will, but it will take some time, and I will edit the question in due time, please be patient.

Question

Several comments have pointed out that this MO diagram is incorrect. What is wrong with this MO diagram and what is the correct MO diagram?

ananta
  • 2,289
  • 3
  • 22
  • 3
    You better start your editing already - with such title you're lucky I can't closehammer it. – Mithoron May 23 '23 at 20:45
  • @Mithoron any suggestions? – ananta May 23 '23 at 20:46
  • 3
    Ditch your alternate diagram and ask what's wrong with the "double bonding" pic. - one "bonding pair" is actually non-bonding. (I don't feel like this question can be good even then, though). – Mithoron May 23 '23 at 20:48
  • @Mithoron which bonding pair is non-bonding? – ananta May 23 '23 at 20:50
  • 5
    Your initial case is already wrong. You made 6 MOs out of 5 AOs. I'd suggest reading a textbook to check the MO diagram for hydroxide ion (or HF; it's the same thing, and you're more likely to find that in a book). – orthocresol May 23 '23 at 20:53
  • @Mithoron there is nothing wrong with that, a single AO can interact with multiple AOs while forming MOs. – ananta May 23 '23 at 20:55
  • @orthocresol yes, $\ce{HF}$ is isoelectronic to $\ce{HO^-}$. Would you recommend a textbook? – ananta May 23 '23 at 20:57
  • Of course, there are a few here: https://chemistry.stackexchange.com/a/37305/16683 I think Housecroft, or Miessler, are the better ones for this. I presume both your comments were directed at me. Yes, more than 2 AOs can interact; but that doesn't mean you can generate extra MOs out of nowhere. If you have 3 AOs with the same symmetry, they form 3 MOs, not 4. You've made 4 MOs out of the oxygen 2s, oxygen 2pz, and hydrogen 1s. – orthocresol May 23 '23 at 21:00
  • @orthocresol I will read the relevant sections from the recommended textbooks and edit this question asap. – ananta May 23 '23 at 21:01
  • 1
    @ToddMinehardt I teach remotely, online. – ananta May 23 '23 at 22:31
  • @Mithoron does the diagram in the answer address all the concerns? – ananta May 23 '23 at 23:51

1 Answers1

1

The following diagram is from Kinetics of the Reactions of Water, Hydroxide Ion and Sulfide Species with CO2, OCS and CS2: Frontier Molecular Orbital Considerations)$^1$ George W., Luther III (2004).

molecular orbital diagram of hydroxide anion

This diagram addresses the concerns raised in the comments and the question:

  1. Number of atomic orbitals is equal to number of molecular orbitals.
  2. One of the orbitals, shown wrongly as bonding, is actually non-bonding.
  3. Bond order of $\ce{O}\text{-}\ce{H}$ bond in $\ce{HO-}$ is 1.

Note: The $\mathrm{1s}$ orbital of $\ce{O}$ is not shown since it is low in energy and essentially does not interact.

References

  1. George W., Luther III. (2007). Kinetics of the Reactions of Water, Hydroxide Ion and Sulfide Species with CO2, OCS and CS2: Frontier Molecular Orbital Considerations. Aquatic Geochemsitry, 10, 81-97. 10.1023/B:AQUA.0000038957.18584.b0
ananta
  • 2,289
  • 3
  • 22
  • Honestly, even this one is kind of dubious. The σ MOs are correct now (we could argue about the best labels to give them, although that's not so important). More crucially, the π MOs shouldn't be raised in energy relative to 2px/2py when there is no overlap going on. – orthocresol May 25 '23 at 20:01
  • I would say that you can shift the π MOs down and it would be correct. But I also don't really think you should have gone to a geochemistry journal. No offence, but I don't generally think that would be the best place if you were looking for something theoretical, like MO analysis. You could google for 'HF MO diagram', find any of the top hits, replace F with O- and call it a day — and it would be accurate. – orthocresol May 25 '23 at 20:06