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I was asked to find out the magnetic behavior (and essentially electronic configuration) of heteroleptic complexes using Valence Bond Theory and Crystal Field Theory.

But I am confused about how to do it. Especially in the ones which have both strong field and weak field ligands together; how am I to decide whether pairing of electrons will take place or not ?

For a more concrete example consider the complex $\ce{[Cr(NH3)_4Cl_2]^{+}}$

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  • $\begingroup$ I think my first question is how many valence (d) electrons do you need to consider - what is the formal oxidation state on the Cr ion? $\endgroup$ – Geoff Hutchison May 20 '16 at 20:36
  • $\begingroup$ Are there electron counts where it doesn't matter whether the ligands are strong field or weak field? $\endgroup$ – Geoff Hutchison May 20 '16 at 20:36
  • $\begingroup$ @Geoff Cr is in +3 oxidation state so there are 3 electrons in d. $\endgroup$ – Abhirikshma May 21 '16 at 1:57
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Based on the available information, we would start by figuring out the 3D geometry of the complex. $\ce{Cr^3+}$ should be octahedral, with two possible "combinations", cis or trans. Let's start with the trans version. The symmetry of this system is $D_{4h}$ so we call this "tetragonal".

With a tetragonal geometry, the MO's would be arranged in such a way that there will be two degenerate orbitals at the lowest energy, and three higher-energy orbitals. The MO diagram typically looks something like this:

Octahedral and Tetragonal MO

Chromium(III) has an [Ar] $3d^3$ electronic configuration so we need to fill up three levels. Now the question is whether or not the splitting caused by the ligands are large enough to cause pairing.

We know for a fact that the trans version of the example is a green solution, so it absorbs red light (700 nm or ~14,300 $cm^{-1}$). Pairing energy is typically in the range of 20,000 - 30,000 $cm^{-1}$ so the 'gap' between yz and xy is probably about only ~14,000 $cm^{-1}$. As such, I would say the trans isomer is magnetic and not paired, because it is energetically more favorable to promote the 3rd electron to the higher energy level than to force it to pair.

Similarly, we know for a fact that the cis version is violet. This means it absorbs yellow light, about 570 nm or 17,000 $cm^{-1}$. This is still lower than the pairing energy, so I'd say that The tetraamminedichlorochromium(III) is magnetic.

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