Which of the following is not correctly matched?
Complex ionCFSE
c${{[Fe{{F}_{6}}]}^{3-}}$ -4Dq

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Hint: The answer to this question includes the calculation of the outer electronic configuration of each of the complexes that tells us about the further calculation for CFSE based on the type of splitting.

Complete answer:
The concepts that are familiar to us include the crystal field stabilization energy of the tetrahedral and octahedral complexes.
Now, let us see in detail what is CFSE and how can it be calculated.
- The crystal field stabilization is defined as the difference in the energy of the electronic configuration in the ligand field and that of the isotropic fields.
- Pairing energy is the energy that is required to accommodate two electrons in one orbital.
Since, the above given complexes are all octahedral ligands the CFSE formula will be as follows which is based on the strong field or weak field ligand.
- From option a.${{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}$, the outer electronic configuration is ${{t}_{2g}}^{6}{{e}_{g}}^{0}$ and here ammonia is moderately strong field ligand.
Thus, CFSE for this will be,
CFSE = $6(-4Dq)+0(6Dq)=-24Dq$
Thus, the option is correctly matched.
In option b.${{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}$, the outer electronic configuration will be, ${{t}_{2g}}^{3}{{e}_{g}}^{0}$ and CFSE is calculated as,
CFSE =$3(-4Dq)+0(6Dq)=-12Dq$
Thus, this option is also correctly matched.
In option c.${{[Fe{{F}_{6}}]}^{3-}}$, the fluorine is weak field ligand and hence configuration will be ${{t}_{2g}}^{3}{{e}_{g}}^{2}$ and the CFSE will be,
CFSE = $3(-4Dq)+2(6Dq)=0Dq$
Thus, here the option is incorrectly matched.
In option d.${{[Fe{{(CN)}_{6}}]}^{3-}}$, the electronic configuration will be ${{t}_{2g}}^{5}{{e}_{g}}^{0}$ and thus the CFSE is,
CFSE = $5(-4Dq)+0(6Dq)=-20Dq$
Thus, this option is correctly matched.

Therefore, the correct answer is option c.${{[Fe{{F}_{6}}]}^{3-}}$

Note that the crystal field stabilization energy depends on several factors among which mainly on the geometry as it changes the d – orbital splitting patterns and the other factors include number of d – electrons, spin pairing energy and ligand character which is according to the spectrochemical series (weak field or strong field ligands).