Valence Bond Theory

Valence Bond Theory

Table of Contents

Introduction to Valence Bond Theory

The concept of covalent bond formation which occurs because of sharing of electrons does not provide us with any idea about the forces operating between the atoms. Also, why there is a difference between bond dissociation enthalpies and bond length in different molecules is not explained.

 For Example, both H2 and F2 molecules have a single covalent bond which is formed by sharing of an electron pair between the respective atoms but the difference in bond enthalpy and bond lengths is: 

Molecule

Bond Enthalpy

Bond length

H2

435.8 kJ mol-1

74 pm

F2

150.6 kJ mol-1

42 pm

Also the concept of covalent bonding doesn’t signify anything about the shapes of polyatomic molecules. Even though VSEPR theory gives the geometry of simple molecules, but it doesn’t explain them theoretically.
Because of these limitations, we use two important theories based on quantum mechanical principles. These are:

  • Valence Bond Theory
  • Molecular orbital Theory

 Valence Bond Theory

In the year 1927, Heitler and London came up with the concept of Valence Bond Theory. It was then modified and developed by L Pauling and J.C Slater in 1931. The valence bond theory is based on certain things like electronic configurations of elements, overlap criteria of atomic orbitals, atomic orbital and stability of the molecule.

Atoms consisting of unpaired electrons tend to bond with other atoms having unpaired electrons, which makes  unpaired electrons to get paired up, and the atoms which gets paired  achieves stable electronic arrangement, i.e. similar to that of a noble gas configuration. When 2 electrons are shared between atoms it forms a bond.

The number of bonds formed by an atom is usually the same as the number of unpaired electrons in the ground state, which is the lowest energy state, but the atom can form more bond in some cases, which is because of excitation of the atom. When electrons which were paired in the ground state gets unpaired and jump into empty orbitals, it result in increase in the number of unpaired electrons which participate in forming the bond. 
A covalent bond forms because of sharing of electrons. According to Pauli Exclusion Principle, the spin of 2 electrons must be opposite such that no two electrons in one atom can have all same four quantum numbers. 

  • In HF, H has a singly occupied s-orbital that overlaps with a singly filled 2p orbital of F. 
  • In   H2O, the O atom has two unpaired electrons in 2p orbitals, which overlaps with an unpaired electron in the s orbital of two hydrogen atoms to form a H2O molecule.

Structure of WaterFig. No. 1 Structure of Water

  • In NHthere are three singly occupied p orbitals on N which overlap with s orbitals of three H atoms.

Structure of AmmoniaFig. No. 2 Structure of Ammonia (NH3)

Basic Assumptions of VBT

The basic assumptions of this theory are: 

  • Even after the formation of the molecule the atoms do not lose their identity
  • When two atoms come close to each other, interaction occurs between the valence electron which results in the formation of a bond. The inner electrons do not participate in the bond formation.
  •  At the time of bond formation, only the valence electrons from each bonded atom lose their identity. The other electrons remain unaffected. 

The stability of the bond is accounted by the fact that the formation of bond results in the release of energy.The distance between the atoms at which the molecule has minimum energy is called internuclear distance. Larger the decrease in energy, stronger will be the bond formed. 

Let us consider the formation of the H2 molecule for better understanding.

Valence Bond Treatment for H2 Molecule

Let A and B be two hydrogen atoms having nuclei HA and HB and the corresponding electrons eA and eB respectively and are approaching each other. No interaction takes place between two atoms when there is a large distance between them, and the total energy of the system is the sum of the energies of the individual atoms. New attractive and repulsive forces come into picture when the two atoms starts to shift closer to each other. The forces which begins to operate are: 

(i) Attractive Forces - Attractive forces operate between electron of atom A (eA) and nucleus of atom B (HB) an electron the of atom B (eB) and the nucleus of A (HA). These two new attractive forces are shown in Figure No. 3

Forces of attraction and repulsion during formation of H2Fig. No. 3 Forces of attraction and repulsion during formation of H2

(ii) Repulsive Forces - Repulsive forces are present between the nuclei HA - HB and electrons of two atoms eA - eB, shown in Figure No. 3.
Thus, the forces operating in the molecule are: 

Attractive

(i) Between atom’s own electron and nucleus: HA - eA and HB - eB.
(ii) Electron of one atom and Nucleus of other atom: HA - eB and HB -.eA
Repulsive:

(i) Electrons of two atoms: eA - eB

(ii) Nuclei of two atoms : HA - HB

Attractive forces bring two atoms closer to each other while repulsive forces create more and more distance between the atoms. Experimentally, we came to know that magnitude of the new attractive forces is more than that of new repulsive force. So the potential energy of the system decreases when the two atoms approach each other.

 As the two atoms come closer and closer, the system becomes more and more stable due to decrease of energy. So there comes a stage where the force of attraction becomes equal to the repulsive forces and the system has minimum energy, the bonded Hydrogen atoms forms a stable molecule and the distance (r0) between the atoms is known as bond length.

For hydrogen molecule the distance between two hydrogen atoms having minimum energy is 74 pm. Potential energy is assumed to be zero when the two atoms are far apart as there is no attractive or repulsive interactions between them.

Potential Energy Diagram as Hydrogen atoms are brought closerFig. No. 4 Potential Energy Diagram as Hydrogen atoms are brought closer


Thus bond formation results in release of energy making the hydrogen molecule more stable than the individual hydrogen atoms. That is, 
H + H ----→H2 + 435.8 kJ mol-1
The energy corresponding to a minimum in the curve is called Bond Energy
Conversely, when one mole of H2 molecules is dissociated into two hydrogen atoms, 435.8 kJ of energy is needed. 
H2 (g) + 4435.8 kJ mol-1 ----- → H (g) + H (g) 
It must be kept in mind that the two hydrogen atoms cannot be brought closer than 74 pm because then the repulsive forces will become larger and the potential energy would rise.

Why a helium molecule does not form He2?

Now let us understand why He2 molecule is not formed. This can be easily understood by calculating the attractive and repulsive forces, when two helium atoms come closer to each other. Each helium atom has two electrons in its 1s-orbital. There are two attractive forces between the nucleus and the electrons of each atom. It has been found that when two helium atoms comes close to each other four new attractive force and five new repulsive force come into play. Therefore, repulsive force predominate and the potential energy of the system increases resulting in instability. Thus, He2 represents unstable state and a chemical bond is not formed between helium atoms.

Attractive and repulsive forces between Helium AtomFig. No. 5 Attractive and repulsive forces between Helium Atom

Orbital Overlapping of Covalent Bond

When two atoms comes closer to each other, and when two bonding orbital merges, it is  known as overlapping of the orbitals. The overlapping orbitals results in the pairing of electrons. The strength of a covalent bond depends upon the amount of overlapping taking place. Greater overlapping results in stronger bond formation between the atoms.
Let’s understand the formation of a molecule of hydrogen by this method. A hydrogen atom consists of a single electron in 1s-orbital. Now, according to Pauli’s exclusion principle, an orbital can hold two electrons of opposite spins. When these two atoms having electrons with the opposite spins approach each other closely, their orbitals overlap. Due to the overlapping the two atomic orbitals merge into a bigger cloud called molecular orbital. The molecular orbital contains both the electrons. The two electrons can be shared under these conditions. As a result, the two hydrogen atoms are held together in the form of a molecule. Thus, according to orbital theory, the formation of a covalent bond between two atoms is because of the pairing of electrons with opposite spins belonging to valence shells of the pairing atoms.

Types of Covalent Bond

 Depending upon the type of overlapping, the covalent bonds may be divided into following types (a) Sigma (σ) bond (b) Pi (π) bond 

Sigma bond (σ bond)

 The bond formed because of overlapping of two half-filled atomic orbitals along their axis is called as sigma (σ) bond. σ bond is a strong bond because overlapping is large as compared to pi bond. The hybrid orbitals always form σ-bond.

  • S-S Overlapping: Overlapping of two half-filled s-orbitals taking place along the inter-nuclear axis results in S-S overlapping.
  • S-P overlapping: Overlapping of half-filled s orbital of one atom with half-filled p orbital of another atom along the inter-nuclear axis to form bonds results in S-P overlapping.
  • P-P overlapping: In this type, overlapping of one half-filled p orbital from each bonding atom undergoes head-on overlapping along the inter-nuclear axis.

Types of Sigma Bond FormationFig. No. 5 Types of Sigma Bond Formation

Pi bond (π bond)

  • Lateral overlapping of half-filled atomic orbitals results in the formation of pi bond. The sidewise overlapping is quite less as compared to sigma bond. Therefore, a pi bond formed is a weak bond. π bond overlapping takes place only at the sides of two lobes. A π bond is formed only when a s bond already exists between combining atom.

Pi Bond FormationFig. No.6 Pi Bond Formation

Strength of sigma and pi- bonds

The strength of a covalent bond depends upon the amount of overlapping taking place in atomic orbitals at the time of bond formation. During the formation of a sigma bond the overlapping of orbitals takes place to a larger extent, but quite less at the time of formation of a pi-bond.
Therefore the sigma bond is stronger than a pi-bond. 
It is interesting to note that pi- bond between two atoms is formed in addition to a sigma bond. It is always present in the molecules having multiple bonds. 

Difference between sigma and pi-bond

Sigma Bond

Pi Bond

Formed by end to end filled atomic orbitals along the intermolecular axis. The overlapping takes place between two s-orbitals, one s and p orbitals.

Formed by sidewise overlap of two half-filled p-orbitals.

Overlapping takes place to a greater extent, thereby forming a stronger bond.

Overlapping takes place to lesser extent, thereby forming a weaker bond.

The molecular orbital is symmetrical about inter nuclear axis.

Molecular orbital are discontinuous.

Atoms can freely rotate around sigma bond.

Because of overlapping of electron cloud above and below the plane of atoms, they cannot rotate freely.

Bond may be present between two atoms either alone or along with sigma bond.

The bond is always present only when there is a sigma bond. They cannot exist alone.

S orbital participates in the formation of sigma bond.

S orbitals cannot participate in the formation of pi bond.


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