# Explain on the basis of valence bond theory that tetracyanonickelate(II) ion with square planar structure is diamagnetic

Answers on the internet suggest that tetracyanonickelate ($$\ce{([Ni(CN)4]^{2-}}$$) with square planar structure is diamagnetic because $$\ce{CN-}$$ is a strong field ligand and causes pairing, but my book says that VBT does not distinguish between strong and weak field ligands. So can anyone explain the logic using VBT?

@M.L has already provided the solution as per VBT, but that answer seems to have some flaws when it comes to CFT (looks like he has corrected the mistakes now). So, I would like to take some time to answer this question using CFT.

According to crystal field theory, the degeneracy of the orbitals of a same orbital is lost in presence of a ligand and the pattern in which they are distorted depends upon the nature of the ligand. The spectrochemical series helps us understand the nature of a ligand.

In general there are two types of ligands, strong field and weak field. Strong field ligands have a greater power to distort the degeneracy of the sub-orbitals whereas weak field have a weaker power of distortion.

As per the spectrochemical series, $$\ce{CN-}$$ is a strong field ligand and thus creates a greater distortion in the degeneracy of $$\mathrm d$$ orbitals.

The central metal ion here is the $$\ce{Ni^2+}$$ with its $$\mathrm d^8$$ electronic configuration.

A $$\mathrm d^8$$ system prefers a square planar approach of ligands if the ligands are strong field. In such a condition the the degeneracy is disrupted and the energy diagram of the $$\mathrm d$$ orbitals is as below:

Now when trying to fill this diagram with electrons we have to take into consideration that an electron in the $$\mathrm d_{x^2-y^2}$$ orbital can pair up with the electron in $$\mathrm d_{xy}$$ in case of a strong field ligand. This is because the extent of splitting done by a strong field ligand is so high that it can overcome the energy gained due to pairing of electrons.

Thus the energy diagram filled with electrons looks as following:

Now the ligands donate their lone pairs in the $$3\mathrm d_{x^2-y^2}$$, $$4\mathrm s$$, $$4\mathrm p_x$$ and $$4\mathrm p_y$$ sub-orbitals.

In reality, no hybridization takes place but if forced to say the hybridization of this complex, we can say $$\mathrm{dsp}^2$$ because of the orbitals involved in the $$\sigma$$ bonds between the metal and ligands.

As you can see the energy diagram does not contain any unpaired electron and thus the complex is diamagnetic.

According to VBT, for $$\ce{[Ni(CN)_4]^{2-}}$$, because it is a square planar geometry, it will experience $$\ce{dsp^2}$$ hybridization. The following process and result will be the following:

The diagram clearly shows that using VBT, we get that $$\ce{[Ni(CN)_4]^{2-}}$$ is diamagnetic. However, in general, VBT is not used often to describe these bonds, and more and more complex theories of bonding have been developed, although all involve approximations/assumptions. One of them is crystal field theory which is what the internet answers were suggesting.

In terms of crystal field theory. $$\ce{Ni^{2+}}$$ has a $$\ce{d^8}$$ configuration, and the crystal field splitting diagram is square planar. Since $$\ce{CN-}$$ creates large splitting, only four orbitals will be filled in the following diagram:

We will find that only $$\ce{d_{yz}}$$, $$\ce{d_{xz}}$$, $$\ce{d_{z^2}}$$, and $$\ce{d_{xy}}$$ will be filled as $$\ce{d_{x^2-y^2}}$$ is too high in energy. Since there are 8 electrons, all of the 4 orbitals will be fully filled and this makes it diagmagnetic according to crystal field theory.

• May 5 at 15:55
• It is dsp2 because that is the hybridization of square planar geometries according to VBT. If it is tetrahedral in the case of $\ce{[Nicl_4]^{2-}}$, it will undergo sp3 hybridization.
– M.L
May 5 at 15:58
• @Mithoron I am not sure if you saw my comment but see this chemistry.stackexchange.com/questions/58012/…
– M.L
May 5 at 22:57
• And you saw Martin's comment there? VBT isn't what you think - it's part of class of computational methods - about as good approach as MOT and the calculations say there's almost always only negligible mixing of p and d orbitals - no actual hybridisation of d and p orbital together. May 5 at 23:11
• @Mithoron I know, that is what my second paragraph explains that VBT is not generally used to describe these bonds and so on. I know there are other theories like MOT, CFT, and Ligand Bond Theory (Which I posed a question about that hasn't been answered). It's just the question asked about how would VBT be used to model the bonding in $\ce{Ni(CN)_4}^{2-}$
– M.L
May 5 at 23:18