60. Covalent Bonding(6)- Hybridization(1).

From this post onwards, we start studying one of the most seminal theories in chemistry- THE HYBRIDIZATION THEORY.  This theory was a giant leap forward. It did not consider atomic orbitals as they are but proposed that they mix together and form new hybrid orbitals.

Need for the concept of hybridization.

The concept of hybridization was mainly needed as –

  1. Failure of VBT  to explain valencies for some elements


    Atomic number

    Electronic configuration

    No. of unpaired electrons in valence shells

    Ideal valency

    Seen valency


    Beryllium, Be


    1s2 2s2


    inert element as both s orbitals are filled (Zero valent)

    (has two unpaired electrons/valencies)

    BeCl2 , BeF2

    Boron, B


    1s2 2s2 2px1


    Monovalent as only one unpaired electron is present.

    (has three unpaired electrons/ valencies)

    BF3, BCl3

    Carbon, C


    1s2 2s2 2px1 2py1


    Divalent as two unpaired electrons are present

    (has four unpaired electrons / valencies)

    CH4, CHCl3

    As seen in the above table, based on VBT theory beryllium should be inert, boron should be monovalent and carbon should be divalent. However, in reality, we see that this is not true.

    Beryllium forms compound like beryllium dichloride (BeCl2) and beryllium difluoride (BeF2) indicating that it has two unpaired electrons, which form bonds with chlorine and fluorine atoms respectively.

    Similar observations were made for boron and carbon too. Physicists had discovered, with experimentation, that carbon had two subshells in its valence shell, with slightly different energy. So ideally, carbon should be bivalent (2 unpaired electrons in valence sub-shell). However, carbon exhibits tetravalency.

    Boron too has just one unpaired electron and yet it was trivalent.

    These compounds were forming more bonds than expected! VBT could not explain these observations.

  2. Some molecules’ bond angles and geometries could not be explained based on earlier theories.
    Ammonia molecule has Nitrogen atom at its center.
    N (7) ⇒ 1s2 2s2 2px1 2py1 2pz1.
    601According to VBT, the three 2p orbitals of N should overlap with three 1s orbitals of H to form an ammonia molecule. However, we know that the three p – orbitals are perpendicular(90º )to each other. So, the bond angle in the ammonia molecule should be 90º. However, the bond angle is found to be 107º. This observation could not be explained by any theory

So, a new theory had to be developed to explain these phenomena.

The Man Behind The Hybridization Theory.


It was Linus Pauling who introduced the concept of hybridization, in 1931. Remember him? Yes! He is the same chemist, who developed the Pauling scale for electronegativity! (post 46). He is regarded as one of the two great scientists of all time! He is the only person to be awarded two unshared Nobel Prizes!!

Carbon was studied extensively, as it formed the basis of all life. carbohydrates, fats, amino acids, all life had carbon in it.  Physicists had proposed that carbon had two valence sub-shells (with slightly different energies), and the outer valence sub-shell had only 2 electrons. Thus, carbon had to be bivalent. This proposition was negated by the recorded experimental data. Experiments showed that carbon was tetravalent, and it formed 4 bonds. This discrepancy needed to be resolved. Linus Pauling’s hybridization theory was the answer to this conflict.

In 1928, he first came up with some mathematical calculations, to believe that his idea of hybridization was even worth working on. He quoted,

It was so complicated that I thought people won’t believe it.And perhaps I don’t believe it, either. Anybody could see that the quantum mechanics must lead to the tetrahedral carbon atom, because we have it. But the equations were so complicated that I never could be sure that I could present the arguments in such a way that they would be convincing to anybody.

One night, while working on this complex problem, he had an important insight. It occurred to him that if he could somehow combine the two sub-shells into one valence shell, he could solve the problem! So, leaving behind some complex mathematical calculations, he simply combined the two wave functions. Subsequently, the hybridization theory was developed.

“One day, late in the day…I had an idea. It was the basic idea of hybrid orbitals. I was trying to understand why the carbon atom is tetrahedral, forms bonds directed towards the four corners of a tetrahedron. Even as early as 1924, I had made a model of methane, in which I said the four outer electrons of the carbon are in orbits directed towards the corners of a tetrahedron…. When quantum mechanics came along, a result was confirmed that had been accepted earlier, that the four outer electrons in the carbon are of two different kinds…. I thought ‘the basic principles of quantum mechanics permit us to combine these functions from the Schrödinger equation in another way.’ And I said to myself: ‘Let’s suppose that I look just at the distribution in various directions, and not worry about the difference in the radial distribution for those.’ This permitted rather simple calculations to be made in a straightforward manner. The first result I got was that the best bonds that the carbon atom can form are directed towards the four corners of a tetrahedron. So, in 1931, I had a simple theory of the tetrahedral carbon atom and an explanation of a great bit of organic chemistry.”

Linus Pauling
March 27, 1964

He kept working for hours. Using the same basic approach, he found he could apply this theory to other molecules too!

“I was so excited and happy, I think I stayed up all night, making, writing out, solving the equations, which were so simple that I could solve them in a few minutes,” he remembered. “Solve one equation, get the answer, then solve another equation about the structure of octahedral complexes such as the ferrocyanide ion in potassium ferrocyanide, or square planar complexes such as in tetrachloroplatinate ion, and various other problems. I just kept getting more and more euphorious as time went by.”

Let us begin discussing this theory in our next post. Till then,

Be a perpetual student of life and keep learning!

Good Day!

References and further reading –

Image source –

  1. By Library of Congress – http://www.notablebiographies.com/Ni-Pe/Pauling-Linus.html, Public Domain, https://commons.wikimedia.org/w/index.php?curid=17802529

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