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I am trying to construct the diagram of $\mathrm{d}$ orbitals in the tetraammineplatinum(II) complex. According to the angular overlap model, $\mathrm{d}$ orbitals are going to look like those in the picture. However, planar square complexes are drawn completely differently according to other approaches and this makes me doubt the validity of my diagram.

To arrive to this diagram, I used the following table:[citation needed]

As $\ce{NH3}$ is a σ only ligand, I am not taking into account the π interactions, for which there is a separate table. In the square planar shape, the ligands in the 1 and 6 positions are absent, so they do not contribute to the rise of the d orbital energies, only the 2, 3, 4, and 5 positions do. According to this, the $\mathrm{d}_{z^2}$ orbital should be raised in energy by $(1/4)+(1/4)+(1/4)+(1/4)=1 \mathrm{e}_\sigma$, and $\mathrm{d}_{x^2-y^2}$ should be raised by $(3/4)+(3/4)+(3/4)+(3/4)= 3 \mathrm{e}_\sigma$. The rest of the orbitals should stay the same energy they are as their coefficients are zero.

AOM sigma-only square planar splitting

Is this a correct diagram for a planar square coordination complex, with sigma only ligands, such as $\ce{[Pt(NH3)4]2+}$?

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    $\begingroup$ What is the angular overlap model? If you are considering crystal field theory then your diagram doesn't look right. Take a look at the diagram in this page: chem.libretexts.org/Bookshelves/Inorganic_Chemistry/… $\endgroup$
    – S R Maiti
    Jul 8 at 9:08
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    $\begingroup$ Hmm I have never heard of that method, but I feel that both methods should give the same result. Perhaps you could share all of the steps that you did in the calculation? $\endgroup$
    – S R Maiti
    Jul 8 at 10:03
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    $\begingroup$ @Holyshmarckel Even though Shoubhik isn't familiar with the concept, you should add the details. In a couple of days this question this question will get many views and there is a high likelihood that someone who is familiar with the concept will find it. $\endgroup$ Jul 8 at 11:09
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    $\begingroup$ I also hadn't come across AOM previously, possibly because it fits in a somewhat small niche between the mostly qualitative crystal/ligand field theory and the more quantitative semiempirical electronic structure methods like Huckel theory. Based on question 10.15 of this solution sheet, you have the right idea. While this question was for a square pyramidal splitting, it seems clear from your table that in going to square planar, the xy/xz/yz orbitals would be unaffected and z^2 would shift down by 1 sigma as you suggest. $\endgroup$
    – Tyberius
    Jul 8 at 17:09
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    $\begingroup$ @Holyshmarckel yes, if you used LFT, you would get the same qualitative result. This is because $t_{2g}$ orbitals are nonbonding (since there are only $\sigma$ interactions), so their energies won't change when going from octahedral $\ce{[Pt(NH3)6]^2+}$ to square planar $\ce{[Pt(NH3)4]^2+}$. But as you remove the ligands on $z$-axis, there will be less overlapping with $d_{z^2}$ so it will decrease in energy because $e_{g}^*$ is antibonding in this case. $\endgroup$
    – Azamat
    Jul 16 at 14:51
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Yes, you have correctly produced the diagram according to the angular overlap model, and the result is qualitatively in agreement with what you would get from other models. The reason it looks different from some canonical diagrams that you may find in textbooks for square planar complexes where dxy is raised in energy is because of the lack of $\pi$ interactions in this complex. It is the $\pi$ interactions that affect the dxy in the more general case.

Also, a general comment on the AOM since it seems not to be widely known. For what it's worth, it is described in the lecture notes that Richard Holm distributed for his undergraduate Inorganic Chemistry class at Harvard University in the 90's. He describes it thus:

The Angular Overlap Model (AOM) is a simple first approximation to the full MO model and embodies all of the characteristics of metal-ligand interactions important to understanding of the principles of structure, magnetism, and absorption spectra (color). Its primary value is the rapid establishment of d-orbital degeneracies (or lack thereof) and relative energies. It provides a guide to the metal-ligand orbital interactions as a basis of geometric and electronic structure and reactivity of MLn complexes. The model utilizes two parameters:

$e_\sigma$: $*$ a parameter defining energies of d-orbitals involved in $\sigma$-bonding in a given molecule $*$ depends on the overlap integral and $d_{z^2}$/L$\sigma$ energy difference; always positive

$e_\pi$: $*$ a parameter defining energies of d-orbitals involved in $\pi$-bonding in a given molecule $*$ +ve --$\pi$ donor $*$ -ve --$\pi$ acceptor

This text is taken from the 1996 version of the lecture notes for Chemistry 40: Inorganic Chemistry written by R.H. Holm. The pages are not numbered. Given Holm's stature in the inorganic chemistry community and the general reputation of the Harvard chemistry department, I would assume that the approach was more widely accepted and taught (at least at that time), but I do not have evidence of that. Perhaps someone can add a reference to a commercially published text?

UPDATED REFERENCE: The AOM is also described in detail (with many references) in

Cotton, F.A., and Wilkinson, G. Advanced Inorganic Chemistry 4th Edition, John Wiley & Sons, 1980, p.652-655.

Given the popularity of this text, I would argue that AOM was more than a niche model, though quite possibly no longer taught.

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  • $\begingroup$ +1 But perhaps adding diagrams (MO or AOM) of the sigma-only and sigma+pi bonding case would make the answer more easily understandable? $\endgroup$
    – S R Maiti
    Jul 19 at 14:09
  • $\begingroup$ I'm sorry, but I cannot take any book seriously, if they abbreviate positive and negative in that form. $\endgroup$ Jul 19 at 18:26
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    $\begingroup$ @Martin-マーチン as noted, it's lecture notes, not a book. If you want formal writing, read the cited section in Cotton and Wilkinson. $\endgroup$
    – Andrew
    Jul 19 at 21:45
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    $\begingroup$ The Angular Overlap model is still appreciated, at least at the research level. I don't know how much it is taught. See this very recent Coordination Chemistry Reviews "The angular overlap model of ligand field theory for f elements: An intuitive approach building bridges between theory and experiment" doi.org/10.1016/j.ccr.2021.213981 $\endgroup$ Jul 20 at 5:46

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