# How to determine if a complex has a crystal field stabilization energy of zero?

I have encountered with the following question:

The complex having zero crystal field stabilisation energy is:

(A) $\ce{[Mn(H_2O)6]^3+}$ (B) $\ce{[Fe(H_2O)6]^3+}$ (C) $\ce{[Co(H_2O)6]^2+}$ (D) $\ce{[Co(H_2O)6]^3+}$

Zero crystal field stabilisation energy will be the case when the metal has either $d^{10}$ configuration or $d^5$ configuration with every orbital having one electron. For Iron($\ce{Fe^3+}$) the d orbital is half filled. Now the problem is, water is in the middle of the spectrochemical series, i.e. it is moderately strong ligand. So, how to decide whether the d orbital will have the 'every orbital half filled' condition or not ?

• In principle crystal field theory is an obsolete, empirically derived, incomplete concept/model, which gives tempting explanations that are not necessary right. It was combined with molecular orbital theory to form ligand field theory. In none of these complexes the $\ce{M-OH2}$ bonds will be of significant strength to cause the metal to adopt a low spin configuration. $\ce{Fe^3+}$ is your only choice because it had $d^5$ configuration. – Martin - マーチン Nov 25 '16 at 6:58
• Trivalent hexa Aqua complexes of the first row transition metals don't go low spin until Cobalt 3+ (where the highly favourable t2g 6 configuration is reached). So the answer to your question is the iron complex. – RobChem Nov 25 '16 at 13:10
• @RobChem Yes, that explains it. – Shoubhik R Maiti Nov 26 '16 at 6:13
• @Martin-マーチン I have read that the theory is now changed with the molecular orbital concept to give a more reasonable explanation. But it is in my syllabus. So, I have to read it nevertheless. – Shoubhik R Maiti Nov 26 '16 at 6:15
• By the way, I am wondering why Martin-マーチン and RobChem did not answer the question, but instead wrote it by comment. – Shoubhik R Maiti Nov 26 '16 at 6:17

## 1 Answer

In the given example it is pretty simple to chose B as the correct answer, as it is the only option that could possibly create a spin forbidden transition $d^5$ or a $d^{10}$ configuration. For most situatons I have encountered it is sufficient to assume high-spin filling, until you encounter very stable configurations: completely full or half full orbitals (like $d^6$)