`=>` Lewis approach helps in writing the structure of molecules but it fails to explain the formation of chemical bond.

● It also fails to give any reason for the difference in bond dissociation enthalpies and bond lengths in molecules like `H_2 (435.8 kJ mol^(-1), 74 p m)` and `F_2 (150.6 kJ mol^(-1), 42 p m)`, although in both the cases a single covalent bond is formed by the sharing of an electron pair between the respective atoms.

● It also gives no idea about the shapes of polyatomic molecules.

`=>` Similarly the VSEPR theory gives the geometry of simple molecules but theoretically, it does not explain them and also it has limited applications.

`=>` To overcome these limitations the two important theories based on quantum mechanical principles are introduced.

● These are valence bond (VB) theory and molecular orbital (MO) theory.

`=>` Valence bond theory was introduced by Heitler and London (1927) and developed further by Pauling and others.

`=>` Valence bond theory is based on the knowledge of atomic orbitals, electronic configurations of elements, the overlap criteria of atomic orbitals, the hybridization of atomic orbitals and the principles of variation and superposition.

● For the sake of convenience, valence bond theory has been discussed in terms of qualitative and non-mathematical treatment only.

`=>` To start with, let us consider the formation of hydrogen molecule which is the simplest of all molecules.

● Consider two hydrogen atoms `A` and `B` approaching each other having nuclei `N_A` and `N_B` and electrons present in them are represented by `e_A` and `e_B`.

● When the two atoms are at large distance from each other, there is no interaction between them.

● As these two atoms approach each other, new attractive and repulsive forces begin to operate.

● `color{green}("Attractive forces arise between")` :

(i) nucleus of one atom and its own electron that is `N_A – e_A` and `N_B– e_B`.

(ii) nucleus of one atom and electron of other atom i.e., `N_A– e_B, N_B– e_A.`

● `color{green}("Similarly repulsive forces arise between")` :

(i) electrons of two atoms like `e_A – e_B,`

(ii) nuclei of two atoms `N_A – N_B.`

● Attractive forces tend to bring the two atoms close to each other whereas repulsive forces tend to push them apart.

● Experimentally, magnitude of new attractive force is more than the new repulsive forces.

● As a result, two atoms approach each other and potential energy decreases and a stage is reached where the net force of attraction balances the force of repulsion and system acquires minimum energy.

● At this stage two hydrogen atoms are said to be bonded together to form a stable molecule having the bond length of `74` pm.

● Since the energy gets released when the bond is formed between two hydrogen atoms, the hydrogen molecule is more stable than that of isolated hydrogen atoms. The energy so released is called as bond enthalpy, which is corresponding to minimum in the curve depicted in Fig.

● Conversely, `435.8` `kJ` of energy is required to dissociate one mole of `H_2` molecule.

`H_2 (g) +435.8 kJ mol^(-1) → H (g) +H (g)`

`=>` In the formation of hydrogen molecule, there is a minimum energy state when two hydrogen atoms are so near that their atomic orbitals undergo partial interpenetration. This partial merging of atomic orbitals is called overlapping of atomic orbitals which results in the pairing of electrons.

● The extent of overlap decides the strength of a covalent bond.

● In general, greater the overlap the stronger is the bond formed between two atoms.

● According to orbital overlap concept, the formation of a covalent bond between two atoms results by pairing of electrons present in the valence shell having opposite spins.

`=>` The formation of covalent bond depends on the overlapping of atomic orbitals.

`=>` The molecule of hydrogen is formed due to the overlap of `1s`-orbitals of two `H` atoms, when they combine with each other.

`=>` In case of polyatomic molecules like `CH_4`, `NH_3` and `H_2O`, the geometry of the molecules is also important in addition to the bond formation.

`color{red}("Example ")`

● `CH_4` molecule has tetrahedral shape and `HCH` bond angles are `109.5°`.

● The shape of `NH_3` molecule is pyramidal.

`=>` The valence bond theory explains the formation and directional properties of bonds in polyatomic molecules like `CH_4`, `NH_3` and `H_2O`, etc. in terms of overlap and hybridisation of atomic orbitals.

`=>` When two atoms come close to each other, there is overlapping of atomic orbitals.

● This overlap may be positive, negative or zero depending upon the properties of overlapping of atomic orbitals.

● The various arrangements of `s` and `p` orbitals resulting in positive, negative and zero overlap are depicted in Fig..

`=>` The criterion of overlap, as the main factor for the formation of covalent bonds applies uniformly to the homonuclear/heteronuclear diatomic molecules and polyatomic molecules.

● In the case of polyatomic molecules like `CH_4`, `NH_3` and `H_2O`, the `VB` theory has to account for their characteristic shapes as well.

● Now, we will find out if these geometrical shapes can be explained in terms of the orbital overlaps.

`=>` Let us first consider the `CH_4` (methane) molecule.

● The electronic configuration of carbon in its ground state is `[He]2s^2 2p^2` which in the excited state becomes `[He] 2s^1 2p_x^1 2p_y^1 2p_z^1`.

● The energy required for this excitation is compensated by the release of energy due to overlap between the orbitals of carbon and the hydrogen.

● The four atomic orbitals of carbon, each with an unpaired electron can overlap with the `1s` orbitals of the four `H` atoms which are also singly occupied.

● This will result in the formation of four `C-H` bonds.

● It will, however, be observed that while the three `p` orbitals of carbon are at `90°` to one another, the `HCH` angle for these will also be `90°`.

● That is three `C-H` bonds will be oriented at `90°` to one another. The `2s` orbital of carbon and the `1s` orbital of `H` are spherically symmetrical and they can overlap in any direction.

● Therefore the direction of the fourth `C-H` bond cannot be ascertained.

● This description does not fit in with the tetrahedral `HCH` angles of `109.5°`.

● Clearly, it follows that simple atomic orbital overlap does not account for the directional characteristics of bonds in `CH_4`.

● Using similar procedure and arguments, it can be seen that in the case of `NH_3` and `H_2O` molecules, the `HNH` and `HOH` angles should be `90°`.

● This is in disagreement with the actual bond angles of `107°` and `104.5°` in the `NH_3` and `H_2O` molecules respectively.

`=>` The covalent bond may be classified into two types depending upon the types of overlapping :

(i) Sigma (`σ`) bond, and (ii) pi (`π`) bond

(i) `color{green}("Sigma (σ) bond")` : This type of covalent bond is formed by the end to end (hand-on) overlap of bonding orbitals along the internuclear axis. This is called as head on overlap or axial overlap. This can be formed by any one of the following types of combinations of atomic orbitals.

● `color{green}("s-s overlapping")` : In this case, there is overlap of two half filled `s`-orbitals along the internuclear axis as shown in fig.

● `color{green}("s-p overlapping")` : This type of overlap occurs between half filled `s`-orbitals of one atom and half filled `p`-orbitals of another atom.

● `color{green}("p–p overlapping")` : This type of overlap takes place between half filled `p`-orbitals of the two approaching atoms.

(ii) `color{green}("pi (π) bond")` : In the formation of `π` bond the atomic orbitals overlap in such a way that their axes remain parallel to each other and perpendicular to the internuclear axis.

● The orbitals formed due to sidewise overlapping consists of two saucer type charged clouds above and below the plane of the participating atoms.

`=>` Basically the strength of a bond depends upon the extent of overlapping.

`=>` In case of sigma bond, the overlapping of orbitals takes place to a larger extent.

● Hence, it is stronger as compared to the pi bond where the extent of overlapping occurs to a smaller extent.

`color{red}("Note ")` π bond between two atoms is formed in addition to a sigma bond.

● It is always present in the molecules containing multiple bond (double or triple bonds)