Valence bond theory (VBT) of chemical bonding

Table of Contents

The valence bond theory (VBT) of chemical bonding was introduced by L. Pauling around 1916. VBT is described as the quantum mechanical treatment of the chemical bond formation. It is important to explain the chemical bonding process regarding orbital overlap.

What is VBT? – Its definition, postulates, importance, applications and limitations? Continue reading to learn all this valuable information and much more in this article.

What is VBT – Definition

The valence bond theory (VBT) explains covalent bond formation by the overlapping of atomic orbitals containing valence electrons. Different energy atomic orbitals hybridize to yield same energy hybrid orbitals. The hybrid orbitals overlap to form new chemical bonds. VBT assumes that the electrons are localized, i.e., occupy a fixed position in the bond region formed via orbital overlapping. In this way, atoms retain their individuality even after bond formation.

Main postulates of VBT

  • As per VBT, only valence electrons are involved in chemical bonding.
  • Therefore, the atomic orbitals of the outermost shell of an atom will be used. The inner shell atomic orbitals stay undisturbed.
  • Covalent chemical bonds are formed by the complete overlap of half-filled valence orbitals belonging to two different atoms.
  • Post chemical bonding, bonding electrons stay fixed in the bonding area, resulting in an overall molecular stability.
  • Atoms retain their individuality in the molecule.
  • A covalent bond possesses a specific direction which is the direction of two overlapping orbitals respectively.

Why was there a need for VBT after the VSEPR theory?

The need for VBT was realized as the valence shell electron pair repulsion (VSEPR) theory of chemical bonding failed to explain how different energy atomic orbitals combine to form new molecules. Also, the VSEPR theory could not explain the different shapes of isoelectronic molecules.

How does VBT explain covalent bonding?

As per VBT, when two different atoms approach each other, the valence electrons of one atom experience attraction to the nucleus of the other and vice versa. Similarly, a force of repulsion exists between the two nuclei and/or the valence electrons of the two atoms. A covalent chemical bond is formed by orbital overlap at the internuclear distance, where the force of attraction supersedes the repulsive force.

A sigma (σ) bond is formed by overlapping two s atomic orbitals, such as in H2 or an s and a p-orbital such as in HF.  A pi (π) bond is formed by the side-by-side overlap of two p orbitals. The first bond formed between two combining atoms is always a sigma bond. The second and third bonds are pi-bonds.

 A sigma bond is always stronger than a pi-bond. The electron cloud density is fixed between two atomic nuclei in a sigma bond. Contrarily the shared electron cloud lies above and below the atomic nuclei in a pi-bond. However, in both cases, the shared electron cloud stays uniformly localized in a specific overlapping region as per the valence bond theory.

Strengths of VBT

  • VBT explains how bonding occurs, where bonding occurs, and the direction of lone pair of valence electrons after chemical bond formation.
  • VBT differentiates between sigma and pi bonds.
  • Bond energies and bond lengths can be predicted based on orbital overlapping.

Schrodinger wave treatment of VBT

This concept is an extension of the valence bond theory of chemical bonding. It was introduced in 1927 by Heinrich Heitler and Wolfgang London. According to the quantum mechanical treatment of VBT, the three-dimensional space in which an electron resides can be represented by a wave. Each individual atom can thus be represented by a wave function Ψ. The wave function represents the probability of finding an electron within the atom.

A covalent chemical bond is formed as the electron wave of one atom completely overlaps with the valence electron wave of the other atom.

Further explanation:

When two different atoms, A and B, approach each other to form a new molecule called AB. The wave function of atom A can be represented as Ψa, while that of atom B is represented as Ψb. Similarly, the energies of the two independent atoms can be represented as Ea and Eb, respectively.  At an infinite distance from each other, when there is no interaction between atoms A and B, the total wave function Ψ of the system is represented by equation (i).

Ψ = Ψa Ψb  ….…. Equation (i)

The total energy of the system at this point is represented by equation (ii)

E = Ea + Eb ……………Equation (ii)

As per VBT, when the two atoms approach each other at a distance close enough for interaction, then the total wave function of the system can be represented by another wave function (Ψ1), as shown in equation (iii).

Ψ1 = Ψa (1). Ψb (2) …………. Equation (iii)

In the above equation, the numbers 1 and 2 denote the electrons of atoms A and B involved in chemical bonding, respectively. The value of wave functions Ψa and Ψb can be obtained from the solution of the Schrodinger wave equation (equation iii). We will not go into the details of how to solve a Schrodinger wave equation in this article.

However, what is important for you to note is that the valence bond theory explains how the system’s energy depends on the extent of orbital overlap. The potential energy of the system decreases as two atoms approach each other, and their Internuclear distance is decreased.

All the images in this article are by Ammara W.

A chemical bond is formed at a specific Internuclear distance where the potential energy of the system is minimum. Refer to the graph drawn below.

The minimum energy point represents the most stable state, i.e., the bonding stage. The internuclear distance at this point is known as bond length. The difference between the energy of the system when there was no interaction between the respective atoms and at the point of minimum energy is known as bond energy.   

VBT and hybridization

As we already discussed that according to VBT, a new chemical bond is formed by the orbital overlap of two independent atoms. But how is a successful overlap possible between two different energy atomic orbitals? Well, this problem is solved by the concept of hybridization.

Hybridization refers to intermixing different energy atomic orbitals to produce the same energy hybrid orbitals. Hybridization occurs before overlapping during bond formation. After a chemical bond is formed, the atomic orbitals retain their individual entity. Based on the number of atomic orbitals hybridized, an equal number of hybrid orbitals are formed.

For example, one s-atomic orbital mixes with one p-atomic orbital to produce two sp hybrid orbitals. Each sp hybrid possesses a 50% s-character and a 50% p-character. Both hybrid orbitals have an identical shape and direction in addition to having an equal energy content.

Why is hybridization important – VBT applications

The electronic configuration of a carbon atom is 1s2 2s2 2p2.

It has 2 unpaired electrons in its p-orbitals. So ideally, a C-atom should only form two C-H covalent chemical bonds by overlapping with the s-atomic orbitals of the respective H-atoms. But we are all familiar with the methane (CH4) molecule. It consists of four C-H bonds with the central C-atom. Each H-C-H bond angle is 109.5°.

This is possible because, during chemical bonding, the 2s electrons of carbon get unpaired. One 2s electron shifts to an empty 2p atomic orbital of carbon. One 2s and three half-filled 2p orbitals hybridize to yield four sp3 hybrid orbitals. Each sp3 hybrid orbital possesses a 25 s-character and a 75% p-character; each of these contains a single electron. Each sp3 hybrid orbital thus overlaps with the s-orbital of hydrogen to form the C-H sigma bond by sp3-s overlap.

The methane molecule thus adopts a symmetrical tetrahedral shape (as shown below).

The shared electron pair between each C-H bond is known as a bond pair. There are no un-bonded electrons or lone pairs of electrons present in the methane molecule.

Individual atomic orbitals reappear in their original forms after bond formation.

Let’s see another example.

The carbon dioxide (CO2) molecule consists of 4 bond pairs and 4 lone pairs. Each C=O double bond comprises 2 bond pairs. A C-O sigma bond is formed by sp-sp2 overlap. The carbon atom is sp hybridized, while the oxygen atom is sp2 hybridized during CO2 bond formation. As no lone pairs of electrons are present on the central C-atom, CO2 thus adopts a linear shape with a 180° bond angle.

Electronic repulsions present in a molecule strongly affect its molecular geometry or shape.

According to VBT: Lone pair-lone pair repulsions > lone pair-bond pair repulsions > bond pair-bond pair repulsions.

The bonded atoms in a molecule adopt a shape such that the electron-repulsive effect is as minimized in it as possible. In this way, VBT has a significant place in determining the shape or geometry of a covalently bonded molecule.

Read more about hybridization in our next article.

Limitations of VBT

Even though having a profound significance in explaining chemical bonding, VBT still has the following limitations:

  • Electron localization and atomic individuality after chemical bonding is an obsolete concept. Refer to MOT of chemical bonding to find out why.
  • VBT does not fully appreciate the tetravalency of a carbon atom. A double or triple covalent bond with a carbon atom is considered a single electron domain while determining the shape of a molecule as per VBT.
  • VBT fails to explain the colors exhibited by coordination complexes, unlike ligand field theory (LFT).

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1. Galbraith, John Morrison, Sason Shaik, David Danovich, Benoît Braïda, Wei Wu, Philippe Hiberty, David L. Cooper, Peter B. Karadakov, and Thom H. Dunning, Jr. 2021. ‘Valence Bond and Molecular Orbital: Two Powerful Theories that Nicely Complement One Another’, Journal of Chemical Education, 98: 3617-20.

2. Sanaullah. 2016. Inorganic Chemistry.

3. Shaik, S., D. Danovich, and P. C. Hiberty. 2021. ‘Valence Bond Theory-Its Birth, Struggles with Molecular Orbital Theory, Its Present State and Future Prospects’, Molecules, 26.

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