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I am learning about MO theory in my advanced inorganic chemistry course and am starting to realize that it is truly the most accurate representation of how molecular orbitals look like, where they are located in the molecule, and their relative energies to each other and the original atomic orbitals from which they are composed of. We are using Symmetry Adapted Linear Combinations as the approximation method and so far this method has successfully explained all chemical/magnetic/electronic properties for any molecule investigated thus far.

My question is: Is MO theory perfect? Or does it have a flaw somewhere like every other bonding theory (Lewis, VB, hybridization) I have learned about so far in my chemistry career?

Martin - マーチン
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Nova
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    Everything is flawed because we can't solve the Schrodinger eqn. By MO theory I'd assume you are referring to a Hartree-Fock wavefunction, which gets electron correlation pretty wrong. – orthocresol Mar 29 '16 at 22:47
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    Thank you for orthocresol for the great answer. No thank you to the other two for making me feel stupid. I struggle enough with chemistry, no need to rub it in. Just trying to learn. – Nova Apr 02 '16 at 01:31
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    Nova, I don't think that anyone wanted to make you feel stupid. I believe the key problem is - and I came across that many times - that you are learning quantum chemistry from an inorganics point of view. The theory you learn there is usually a short version of the whole deal. It is good that you question the concept, stay curious. I think (hope) that @Karl wanted to express that to gain deeper insight into the matter it would have been better if you were introduced properly to quantum chemistry first. – Martin - マーチン Apr 06 '16 at 05:52
  • I do not think that this question is too broad. It is basically asking for the pitfalls and shortcomings of MO theory. While there are many, I think that a concise not too long answer is certainly possible. @orthocresol even provided the first stepping stone. – Martin - マーチン Apr 06 '16 at 05:54
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    Yea, sorry, I didn't mean to be snippish. It's just that studying advanced concepts without the complete basic training in physical chemistry is imo bound to be very hard for both you and your teacher, who then has the choice of loosing half his audience by overcharging them or the other half by boring them with endless repeating of introductory stuff. I know a lot of universities allow or even advocate that. :-/ – Karl Apr 06 '16 at 08:24
  • Some good additional context, as well as the beginnings of an answer to your question, can be found here and here. – hBy2Py Apr 06 '16 at 15:03
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    The problem with MO theory are... the orbitals themselves! Orbitals are, by definition, single particle wavefunctions and they have no real physical meaning since you are dealing with a many-body system. For this reason MO theory is far from perfect! –  Apr 11 '16 at 12:46
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    MO is a way to approach FCI by using orthogonal one-electron basis. Its limitation is quantum mechanics itself. Since FCI can reach the exact solution, even it typically takes infinity long expansion. – Rodriguez Jun 03 '16 at 19:56
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    The trouble with MO theory is that, in practice, it is largely descriptive, not predictive. When we see a molecular structure, MO theory often gives good explanations of why its properties exist. But the math is too complex to make high quality predictions before observation of some key properties like the symmetry. – matt_black Aug 16 '21 at 12:41
  • @matt_black Not sure what your point is. The trouble with any quantum-chemical procedure is that it is generally too complex to make robust, accurate predictions without doing the actual computational work. – Antimon Jan 10 '22 at 19:17
  • @Antimon My point was, partly, that the computational power needed for good calculations is too high for calculation to be a really useful tool for anything other than simple situations. You have to be prepared to do a humongous amount of work and that isn't worth it for most situations. – matt_black Jan 10 '22 at 19:29
  • I still fail to see how that is an exclusive feature of MO theory. – Antimon Jan 10 '22 at 19:35

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MO theory fails pretty fantastically in a wide-variety of cases.

While it works well near the equilibrium geometry of a molecule, it cannot dissociate even the simplest bonds correctly.

H2 dissociation curves, image taken from: https://chem.libretexts.org/Bookshelves/Organic_Chemistry/Book%3A_Basic_Principles_of_Organic_Chemistry_(Roberts_and_Caserio)/21%3A_Resonance_and_Molecular_Orbital_Methods/21.07%3A_Which_Is_Better-_MO_or_VB

It is well-known by computational chemists that any quantitative predictions of MO theory (ionization energies, HOMO-LUMO gaps, etc.) cannot be trusted, even for the simplest molecules.

In more complex molecules, such as those with transition metal centers, calculations can even fail to qualitatively describe the electronic structure correctly, even giving ground states with incorrect symmetries.

In my opinion, inorganic chemists like MO theory so much because it's is the simplest theory of molecular bonding and geometrically its results are quite intuitive. It is an excellent conceptual tool for understanding quantum chemistry, but a horrible one for actual predictions of chemical properties.

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    Depends on what exactly you call "MO theory". If you're talking about only Hartree-Fock, then you're right, but it's also a bit of a moot point because noone in their right mind uses HF as a standalone method. If you extend it to include post-HF methods that are based on those MOs, then your answer is not accurate. – Antimon Jan 10 '22 at 18:55
  • Post-HF or Multi-Reference methods, I should have said. - Also, what happened to UHF? That one describes the dissociation of e.g. H2 just fine. – Antimon Jan 10 '22 at 19:09
  • UHF has its own set of problems with spin-contamination. Also, UHF theory emphasizes spin-orbitals, most inorganic classes focus entirely on spatial orbitals. Of course post-HF methods can be used to improve HF results, but post-HF methods are no longer really orbital theories. For example it no longer makes sense to talk about a HOMO/LUMO, because even in the ground-state virtual orbitals can be partially occupied. –  Jan 10 '22 at 23:10
  • More concretely, you give a graph showing how far off things are, but for what molecule? (I'm guessing H2.) And what reference? – Oscar Lanzi Feb 12 '23 at 10:10