Valence Bond Theory (VBT)

Theory

Valence bond theory (VBT) involves knowledge of 

• Atomic orbitals
• Electronic configuration of elements
• Overlap criteria of atomic orbitals
• Principles of variation and superposition

Formation of bonds leads to lowering the energy and thus making the molecule stable. Lets consider an example of H₂ molecule. H₂ molecule is formed when two hydrogen atoms come closer. When they start appraoching, the following interactions take place.

The magnitude of two attractive force is more than the new repulsive forces. That is why, they approach each other and potential energy decreased. When the distance between them is critical distance (r_o), the repulsive forces just balance. At this point, maximum lowering of energy takes place. If distance is less than r_o, then attractive forces dominate. If distance is more than r_o, then repulsive forces dominate, which results in increase of potential energy. Therefore, the critical distance is the bond length. 

Orbital overlap concept:

Hydrogen atom has half filled atomic orbital as it has one electron is 1s orbital. So, when two hydrogen atoms overlap, a part of electron cloud of each of the two half filled atomic orbitals become common. This is called overlapping of atomic orbitals.

The electrons are said to be shared. The probability of finding the electrons is maximum in the region of overlap. Thus, overlapping is necessary. The electrons must have opposite spins. The overlap between the atomic orbitals can be positive, negative or zero depending upon the characteristics of the orbitals participating to overlap.

Positive overlap involves the overlap of lobes of same sign which leads to attractive interactions.

Negative overlap involves overlap of lobes of opposite signs which leads to repulsive interactions.

Zero overlap implies inability of any kind of interactions.

Types of overlapping and nature of covalent bonds:

 The covalent bond can be classified into two categories depending on the overlapping:

1. Sigma () bond

2. pi () bond

1. Sigma () bond: 

• This is formed by the axial overlapping of half filled atomic orbitals. 
• The atomic orbitals overlap along internuclear axis and involve end to end or head on overlap.
• The electron cloud formed is cylindrically symmetrical about internuclear axis.
• The electron involved are called sigma electrons.
• There are three types of axial overlap among s and p-orbitals.

(A) s-s overlap: two half filled s-orbitals overlap along internuclear axis. Example is formation of H₂ molecule 

(B) s-p overlap: half filled s-orbitals of one atom overlap with the half filled p-orbitals of other atom. Example is formation of HF molecule by overlapping of 1s orbital of H and half filled 2p_z orbital of fluorine atom.

(C) p-p overlap: co-axial overlapping between half-filled p-orbitals of one F atom with half-filled p-orbitals of other F atom. Example is formation of F2 molecule where 2p_z orbitals of one F atom co-axially overlap with 2p_z orbitals of other F atom.

2. pi () bond: 

• This is formed when the atomic orbitals overlap in such a way that their axis remain parallel to each other and perpendicular to internuclear axis.
• There is sidewise overlapping betwen the orbitals.
• The electrons involved are called pi-electrons.

• It consists of two saucer type charge clouds above and below the plane of the participating atoms.

A pi bond always follows a sigma bond. Thus, a double bond involves one sigma bond and one pi bond. And a triple bond involves one sigma and two pi bonds. Sigma bond is stronger than pi bond because in sigma bond, the extent of overlapping is more.