What is quantum mechanical treatment of the valence bond theory?

Quantum mechanical treatment of valence bond theory refers to the relationship established between the quantum mechanical theory and the valence bond theory to describe the chemical bonding in a particular molecule.

Two scientists named Walter Heitler and Fritz London gave explanations regarding the quantum mechanical aspects of chemical bonding, which was further extended by scientists named John Slater and Linus Pauling. The latter scientists introduced the valence bond theory.

What is the relation between quantum mechanics and chemical bonding?

There were several theories for explaining the aspects related to chemical bonding. One among them was the Lewis theory, but it was not successful in explaining bond formation. Another one was the VSEPR theory, which also had certain limitations. Both these theories didn’t give precise information regarding the factors like bond length and angles. Later, quantum chemistry gave a quantitative description regarding chemical bonding.

Quantum chemistry deals with the applications of quantum mechanics in chemical moieties. It uses the wave equation given by Ervin Schrödinger for determining a molecule’s electronic structure. It gives information regarding the chemical bonding properties of the molecules.

The Schrödinger wave equation is  Hψ=Eψ.

Here,

• H^ is the Hamiltonian operator.
• ψ is the wave function
• E is the energy.

Quantum chemistry’s mathematical basics come from the Schrödinger wave equation. Several difficulties were observed when applying the Schrödinger wave equation to molecules. A perfect solution for this equation can only be produced on a hydrogen molecule as the nuclei of other molecules comprise a large number of electrons.

Valence bond theory

The Born-Oppenheimer approximation was introduced for explaining chemical bonding, that separated the motions of electrons and nuclei. It considers the nuclei to be heavier than electrons and hence move slowly. This approximation does not discuss anything related to solving the Schrodinger equation. So, approximations such as the valence bond theory (VB theory) and the molecular orbital theory (MO theory) were made to solve it.

Two scientists named Walter Heitler and Fritz London first explained the quantum mechanical aspects of chemical bonding. For this, they chose a hydrogen molecule. Later, the scientists named John Slater and Linus Pauling extended the findings of Heitler-London and gave the valence bond theory or the Heitler–London–Slater–Pauling (HLSP) method. This theory explains the combination of atomic orbitals to form chemical bonds, using factors like hybridization and resonance.

The molecular orbital theory or the MO theory was also developed with the aim of explaining chemical bonding in molecules. It explains that atomic orbitals combine to form molecular orbitals. Both these methods use the quantum mechanical aspects for explaining the nature of chemical bonding in molecules.

Molecule formation is accompanied by a chemical bond formation. The VB theory illustrates chemical bond formation as the combination of the atomic orbitals present in the atoms of the molecule. This combination of atomic orbitals is called atomic orbital overlapping, which occurs between two half-filled atomic orbitals. Covalent bonds are produced through this kind of overlapping.

Postulates of the VB theory

The VB theory describes bonding in various molecules through atomic orbital overlapping. Some postulates of this theory are:

• The covalent bond formation occurs because of the overlap of two valence orbitals or half-filled orbitals of different atoms occupying a molecule.
• The molecule’s stability increases because of the increment in electron density around the atoms involved in bond formation through orbital overlapping.
• The covalent bonds obtained through valence orbital overlapping are directional.
• If the valence orbital is occupied by many unpaired electrons, it may form multiple bonds with other atoms in the molecule.
• There is no role of paired electrons in the valence orbitals in chemical bond formation.
• According to the overlapping pattern, covalent bonds are categorized into sigma bonds and pi bonds.

Formation of sigma bond

Sigma bond or σ bond is formed through the head-on or head-to-head or end-to-end overlapping of valence atomic orbitals. This overlapping can occur between two s-orbitals, two p-orbitals, or between one s- and one p-orbital. This kind of overlapping can be a bonding interaction, involving overlapping between atomic orbitals in the same phase, or an antibonding interaction, involving overlapping atomic orbitals in different phases.

An example of sigma bond formation (between two s-orbitals) is shown in the figure given below.

Formation of Pi bond

Pi bond or π bond is formed through lateral or sidewise overlapping of valence atomic orbitals. This kind of overlap can occur only between two p-orbitals. Similar to the sigma bond formation, pi bond formation also occurs through bonding and antibonding interactions.

An example of pi bond formation through p-orbital overlapping (sidewise overlapping) is shown below.

Hybridization and resonance

Hybridization and resonance are two important factors that the VB theory uses for explaining chemical bonding. Hybridization deals with the combination of various atomic orbitals present in a molecule to form hybrid orbitals. These hybrid orbitals are good for electron pairing during the formation of chemical bonds. Based on the combining orbitals, hybridization can be different types such as ${\mathrm{sp}}^2, {\mathrm{sp}}^3, {\mathrm{d}}^2{\mathrm{sp}}^3$.

Resonance explains chemical bonding in molecules or ions with the help of the contributing structures. These structures can be called resonance or resonating structures. The combination of these structures gives a resonance hybrid.

Common Mistakes 

Students may get confused between the sigma bond and the pi bond. They may think that both are identical in formation, which is incorrect. Sigma and pi bonds are formed in different ways.

• Sigma bond is produced by the atomic orbitals when they overlap head-to-head, while pi bond is formed when the orbitals overlap sidewise.
• Sigma bond is formed by either s or p orbitals, while pi bond is formed only by p-orbitals.
• The only similarity in these bonds is that both can be obtained through bonding or antibonding interactions of orbitals.
• VB theory deals in the localization of bonds in two atoms but not in molecules, while in MO theory, localization of bonds is in both the atoms and molecules.

Context and Applications

This topic is helpful in the professional exams of undergraduate, and graduate courses, especially:

Bachelors in Chemistry

Bachelors in Physics

Bachelors in Industrial Chemistry

Masters in Industrial Chemistry

Masters in Pure and Applied Chemistry

Masters in Physics

Related Concepts

Molecular orbital theory

Resonance and aromaticity

Hybrid orbitals and hybridization

Bond length and bond angles

Practice Problems

Q1: Which among the following scientists first explained the quantum mechanical aspects of chemical bonding?

(a) Walter Heitler and Fritz London

(b) Schrondinger and Walter Heitler

(c) Walter Heitler and John Slater

(d) John Slater and Fritz London

Correct option: (a)

Q2: Which of the following statements is true about sigma bond formation?

(a) It can’t be formed through the overlap of one s and one p orbital.

(b) It can’t be formed through the overlap of two s-orbitals.

(c) It can be formed through the overlap of two p-orbitals.

(d) It can be formed through the sidewise overlap of two p-orbitals.

Correct option: (c)

Q3: Which among the following deals with the combination of various atomic orbitals present in a molecule?

(a) Resonance

(b) Hybridization

(c) Aromaticity

(d) Wave function

Correct option: (b)

Q4: In the Schrödinger equation, ψ denotes:

(a) Wavelength

(b) Intensity

(c) Operator

(d) Wave function

Correct option: (d)

Q5: Identify the false statement regarding covalent bond formation.

(a) The covalent bond formation occurs through the overlap of two valence orbitals of different atoms.

(b) There is no role of paired electrons in the valence orbitals in chemical bond formation.

(c) The covalent bond formation occurs through the overlap of two half-filled orbitals of different atoms.

(d) Even if the valence orbital of an atom has many unpaired electrons, it forms only a single bond with the other atom.

Correct option: (d)