Valence Bond Theory of Coordination Compounds

Introduction
The Valence Bond Theory is the basis upon which a very delicate interaction between metal ions and ligands is represented. The theory was put forth by Linus Pauling in 1930 which so lays a lot more emphasis on the atomic orbital overlap for the building of covalent bonds particularly in such complex structures called coordination compounds. These are very important compounds in catalysis, materials science, and biochemistry, having a central metal atom or ion surrounded by molecules or ions called ligands. One of the most important concepts of VBT arises from the ability of the ligand to donate electron pairs to the metal center, thereby forming coordinate bonds.
Hybridization is one of the most pronounced factors in the VBT perspective. It represents the process through which atomic orbitals hybridize to form new hybrid orbitals. The new hybrid orbitals are very energetically favored at bonding. In this respect, hybridization is the most important factor in the establishment of the geometrical characteristics of the coordination complexes. These change very much with different metal ions or ligands in the combination. For example, the geometry of a coordination complex can be octahedral, tetrahedral, and finally square planar, depending on the coordination number and the strength of the ligands.

Interpretation of Coordination Compounds According to VBT

Valence bond tells us that the covalent bond between two atoms is formed due to the overlap of the respective atomic orbitals. This, therefore, in coordination compounds requires the central metal atom or ion to have available vacant orbitals into which electron pairs donated by ligands would be accommodated. This starts with the metal ion; it would normally have unpaired electrons in its d-orbitals. As ligands come close, they could either be strong or weak, and so they either pair the electrons or take up vacant orbitals.
Strong-field ligands prefer to pair the electrons in the d orbitals of the metal, which gives rise to geometries such as octahedral or square planar by hybridization. Weak-field ligands do not direct pairing; generally, this results in geometries of common tetrahedral. Hybridization is very important as it gives the coordination complex shape and bonding features, finally determining chemical behavior and reactivity.

According to this theory, the metal atom or ion under the influence of ligands can use its (n-1)d or nd orbitals along with its ns and np for hybridization to yield a set of equivalent orbitals of definite geometry such as octahedral, tetrahedral, square planar and so on. These hybridized orbitals are allowed to overlap with ligand orbitals that can donate electron pairs for bonding. The different types of hybridization and their respective shapes are given below

Let us consider the case of [Ni(CN)₄]²⁺ and try to predict the hybridization of this complex

Here nickel is in a +2 oxidation state and the ion has a valence electronic configuration 3d⁸4s

In the presence of Cyanide ions, the electrons will be paired up and the hybridization of Ni in the complex will bed sp² as shown below

Each of the hybridized orbitals receives a pair of electrons from a cyanide ion. The compound is diamagnetic as evident from the absence of unpaired electrons.

Anomalous Example of Hybridisation

Hybridization in coordination compounds can vary from sp³ hybridization to an energy gap of several orders of magnitude, depending on the coordination number of the metal ion and the nature of the ligands. For instance, a coordination number of four can bring about sp³ hybridization in which the geometry is tetrahedral, or dma² hybridization in another instance. For example, sp³ hybridization is to be found in[ [NiCl₄] in which the weak ligand Cl⁻ allows nickel to avoid electron pairing.
The above observation may be explained by the fact that the complexes of the type [Ni(CN)₄]²⁺ are dsp² in nature, wherein the strong ligand CN⁻ is a cause to pair up the electrons in the 3d-orbitals and thus provides four equivalent dsp² hybrid orbitals; it may be the cause for square planar geometry. All the factors viewed above make it pretty clear that the nature of the ligand plays a large role in the hybridization and geometry of the complex.
On the basis of VBT, Magnetic Moment
The magnetic properties of coordination compounds can be rationalized by VBT by considering that all d-orbitals contain unpaired electrons. Consider, after which, magnetic moment calculated to be: μ= n(n+2) where pelites
Where n= number of unpaired electrons. A paramagnetic complex possesses a magnetic moment, and the electrons in the complex are unpaired, while in a diamagnetic complex, not a single electron is paired, and thus it does not possess a magnetic moment. This is indeed a slippery concept for comprehension, and an example will go a long way to clarify it. [MnBr₄]²⁻ will have 5 unpaired electrons, hence a high magnetic moment, and hence show paramagnetic behavior. Thus, there is a direct relation between hybridization and electron configuration and magnetic properties giving a further case for VBT to continue as mainstream.

[Cu(NH₃)₄]²⁺ is an exception for determining the hybridisation. On the experimental basis, it has been found that its geometry is square planar, thus atleast one d orbital is compulsory.

The electronic configuration of [Cu(NH₃)₄]²⁺ is as follows:

But in this case, the last electron can easily be removed and Cu²⁺ will become Cu³⁺, which does not exist in reality.

Thus to explain its square planar geometry, Huggins proposed sp²d hybridization that this last unpaired electron remains in the 3d orbital, and the hybridization is done by 4s orbital, 2 4p orbitals, and 1 4d orbital. The third 4p orbital does not participate in hybridization. Thus, in this way, its hybridization is sp²d and the geometry is square planar.

Weaknesses of VBT to Real-World Application

In as much as there are numerous strengths, the Valence Bond Theory has a couple of weaknesses that tend to limit its application to the real world. A major drawback of this theory is that it does not find enough explanation for the color and the electronic spectra of coordination compounds. VBT does not provide insight into the kinetic and thermodynamic stability of the complexes, which are of enormous utility in the fields related to catalysis and materials science.
In addition, VBT is not effective in the differentiation of strong and weak ligands. It occasionally makes some oversimplified predictions within the bonding behaviors as well. It also does not include some of the geometries of some of the complexes in reference to the expected hybridization models. On this basis, some of the transition metal complexes are distorted geometries that VBT does not explain.

The magnetic moment of coordination compounds can be measured by magnetic susceptibility experiments. The results can be used to obtain information about the number of unpaired electrons and hence structures adopted by metal complexes.
A critical study of the magnetic data of coordination compounds of metals of the first transition series reveals some complications. For metal ions with up to three electrons in the d orbitals, like$\mathrm{Ti}^{3+}(\mathrm{d}^1); \mathrm{V}^{5+}(\mathrm{d}^2); \mathrm{Cr}^{3+}(\mathrm{d}^5)$ two vacant d orbitals are available for octahedral hybridization with 4s and 4p orbitals. The magnetic behaviour of these free ions and their coordination entities is similar. When more than three 3d electrons are present, the required pair of 3d orbitals for octahedral hybridization is not directly available (as a consequence of Hund’s rule). Thus, for $\mathrm{d}^4(\mathrm{Cr}^{2+},\mathrm{Mn}^{3+}),\mathrm{d}^3(\mathrm{Mn}^{2+},\mathrm{Fe}^{3+}),\mathrm{d}^6(\mathrm{Fe}^{2+}, \mathrm{Co}^{5+})$ cases, a vacant pair of d orbitals results only by pairing of 3d electrons which leaves two, one and zero unpaired electrons, respectively.
The magnetic data agree with maximum spin pairing in many cases, especially with coordination compounds containing d⁶ ions. However, with species containing d⁴ and d⁵ ions, there are complications.$[{Mn}(\mathrm{CN})_6]$has a magnetic moment of two unpaired electrons while [MnCl₆]^3– has a paramagnetic moment of four unpaired electrons.$[\mathrm{He}(\mathrm{NV}) 6]$ has the magnetic moment of a single unpaired electron while [FeF₆]^3– has a paramagnetic moment of five unpaired electrons. [CoF₆]^3– is paramagnetic with four unpaired electrons while $[CO(C_4) 3]$ is diamagnetic. This apparent anomaly is explained by valence bond theory in terms of the formation of inner orbital and outer orbital coordination entities. $[\mathrm{Mn}(\mathrm{CN})]^{3-}[\mathrm{Fe}(\mathrm{CN})]^{3-}and [\mathrm{Co}(\mathrm{C}_2 \mathrm{O}_4)_3]$ are inner orbital complexes involving d²sp³ hybridization, the former two complexes are paramagnetic and the latter diamagnetic.

While the Valence Bond theory, to a larger extent, explains the formation, structures, and magnetic behavior of coordination compounds, it has some shortcomings which are listed below:
(i) It involves several assumptions.
(ii) It does not give a quantitative interpretation of magnetic data.
(iii) It does not explain the color exhibited by coordination compounds.
(iv) It does not give a quantitative interpretation of the thermodynamic or kinetic stabilities of coordination compounds.
(v) It does not make exact predictions regarding the tetrahedral and square planar structures of 4-coordinate complexes.
(vi) It does not distinguish between weak and strong ligands.

Some Solved Examples

Example 1
Question:

The molecule in which hybrid molecular orbitals involve only one d-orbital of the central atom is:

1)$\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$
2) $\mathrm{BrF}_5$
3) $\mathrm{XeF}_4$
4) $\left[\mathrm{CrF}_6\right]^{3-}$Solution:

Solution

Hybridization of the given molecules-

(1) $\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-} \rightarrow \mathrm{dsp}^2$
(2) $\mathrm{BrF}_5-\mathrm{Sp}^3 \mathrm{~d}^2$
(3) $\mathrm{XeF}_4-\mathrm{Sp}^3 \mathrm{~d}^2$
(4) $\left(\mathrm{CrF}_6\right)^{3-}-\mathrm{d}^2 \mathrm{Sp}^3$

So, in $[\mathrm{Ni}(\mathrm{CN})_4]^{2-} $molecule hybrid MOs involve only one d-orbital of the central atom.

Therefore, the correct option is (1).

Example 2
Question:

According to the valence bond theory, the hybridization of a central metal atom is dsp² for which one of the following compounds?

1)$
\mathrm{NiCl}_2 \cdot 6 \mathrm{H}_2 \mathrm{O}
$

2) $
\mathrm{K}_2\left[\mathrm{Ni}(\mathrm{CN})_4\right]
$

3)$
\left[\mathrm{Ni}(\mathrm{CO})_4\right]
$

4)$
\mathrm{Na}_2\left[\mathrm{NiCl}_4\right]
$

Solution

Configuration of $\mathrm{Ni}=[\mathrm{Ar}] 4 \mathrm{~s}^2 3 \mathrm{~d}^8$
Configuartion of $\mathrm{Ni}^{2+}=[\mathrm{Ar}] 3 \mathrm{~d}^8$

Thus, Ni²⁺ has 2 unpaired electrons which can be paired up in the presence of a strong field ligand like CN^-as depicted below

Thus, $\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$ has a $\mathrm{dsp}^2$ hybridisation.
Hence, the correct answer is option (2).

Example 3
Question:

In Wilkinson’s catalyst, the hybridization of the central metal ion and its shape are respectively :

1) $s p^3 d$, trigonal bipyramidal
2) $s p^3$ tetrahedral
3) $\mid d s p^2$,square planar
4) $d^2 s p^3$ octahedral

Solution:

As we learned in

Hybridization -

sp³d² - square bipyramidal or octahedral

d²sp³ - octahedral

sp³ - tetrahedral

dsp² - square planar

wherein

sp³d² - outer complex

d²sp³ - inner complex

\begin{aligned}
& \mathrm{sp}^3-\left[\mathrm{Ni}(\mathrm{Cl})_4\right]^{2-} \\
& \mathrm{dsp}^2-\left[\mathrm{Pt}(\mathrm{CN})_4\right]^{2-}
\end{aligned}

The Wilkinson catalyst is [ $\left.R h C l\left(p p h_3\right)_3\right]$ and the hybridization and its shape are $d s p^2$ and square planar respectively.

Hence, the answer is an option (3).

Example 4
Question:

Identify the pair in which the geometry of the species is T-shape and square-pyramidal, respectively :

1) $\mathrm{CIF}_3$ and $\mathrm{IO}_4^{-}$
2) $\mathrm{ICl}_2^{-}$and $\mathrm{ICl}_5$
3) $\mathrm{XeOF} F_2$ and $\mathrm{XeOF}_4$
4) $\mathrm{IO}_3^{-}$and $\mathrm{IO}_2 \mathrm{~F}_2^{-}$

Solution:

As we learned in

Structure of XeOF₂ -

Sp³d hybridized and T-shaped structure

- wherein

Structure of Xenon XeOF₄ (oxytetrafluoride) -

Sp³d² hybridized and square pyramidal structure

- wherein

Summary
In a nutshell, the Valence Bond Theory is maybe one of the most important tools in knowing the bonding and properties of coordination compounds, overhead in scientific and industrial use. In short, VBT describes how the metal ion interacts with ligands to form stable complexes while taking their geometrical arrangement on the principles of hybridization. This theory focuses on the level of strength of a ligand and the hybridization types that give rise to a diversity of structures, instituting tetrahedral and square planar geometries.
The most interesting aspect of VBT is that it can provide very functional insights into the magnetic properties of coordination compounds, relating unpaired electrons either to paramagnetism or diamagnetism. This relationship is of great practical interest, especially in concerns about material design and its use in electronics, catalysis, and medicine.
However, VBT has its own limitations. Many a time, the theory does not come up with a very satisfactory explanation for color and electronic spectra in the coordination compounds. It also further fails to explain the kinetic and thermodynamic stability of complexes. In real life, some geometries and magnetic properties for some coordination compounds cannot be accounted for by VBT alone.
VBT has to be combined with other theoretical approaches, such as crystal field theory and molecular orbital theory, to build an understanding of coordination chemistry. This becomes a multi-pronged approach to help the chemist or the researcher predict these characteristic features that coordination compounds exhibit and change them at his or her own will for better application in technology and industry.
The implications of the problem of coordination compounds for even the Valence Bond Theory are also an area that is very active—further developments here have promised to continue adding to our insight into these complex and tremendously important chemical entities. We enable innovation in just about everything, from pharmaceuticals to environmental science, by better understanding the subtleties of coordination compound bonding.