# Valence Bond Theory

Actually speaking treatment of the covalent bond is far more difficult than treatment of the electrovalent bond. Because here we have to understand what type of forces exist which keep the electron pair in contact with the tow atoms. What is the bond energy in a covalent bond and what is the geometry of the covalent compound?

The answer of such questions may be given by:

(i) Valency Bond Theory as formulated by Heitler and London (1931) and developed by Pauling and Slater (1931) and

(ii) Molecular Orbit  Theory as postulated by Hund and Mulliken.

Valence Bond Theory (VBT) or Heitler London Theory is based on the following two principles:

1. If two atoms are described by the wave functions $\Psi_A \text{and} \Psi_B$, then the wave function $\Psi$ for the system of independent atoms will be given by:

$\Psi = \Psi_A- \Psi_B$ ……………(1)

2. If there are several wave functions such as $\Psi_1, \Psi_2, \Psi_3, \cdots \Psi_n$ for the same system, then the wave function $\Psi$ for the system may be given by

$\Psi = C_1 \Psi_1 + C_2 \Psi_2 + C_3 \Psi_3 + \cdots + C_n \Psi_N$ …………(2)

Where $C_1, C_2, C_3 \cdots C_n$ are the various coefficients. The above equation is based on law of linear combination of atomic orbitals.

Now we consider the formation of hydrogen molecule $(H_2)$ on the basis of this theory. The bond length and bond energy of hydrogen molecule are $0.751 \AA \text{and} 436.0 Kj \text{mole}^{-1}$ values we consider that the hydrogen molecule is also ionic in nature. Hence the hydrogen molecule may be represented as:

$H - H \leftrightarrow H^- - H^+ \leftrightarrow H^+ - H^-$

Thus the structure of hydrogen molecule is the resonance hybrid of the above structures.

The important features of the Heitler-London Theory are given below:

(i) The atom should have unpaired electrons to form bond

(ii) A bond is formed by pairing of electrons

(iii) The maximum electron density lies between the bonded atoms

(iv) There is a tendency to form close shells of the atoms, though the octet is not attained in $BeCl_2, BF_3$ etc. and is exceeded in $PCl_5, SF_6, IF_7$ etc.

Limitations of Heitler-London Theory

(i)  It does not explain the formation of odd electron molecule such as $O_3, NO, H^+_2$ etc. in such molecules no electron pairing takes place.

(ii) It cannot explain the formation of coordinate bond, where only one atom donates a lone pair of electrons to the other atom, molecule or ion.

(iii) It cannot explain the formation of $\pi$-bond.

(iv) Stereo-chemistry of the molecules and ions cannot be explained by this theory.

Pauling and Slater’s Theory

This deals with the directional nature of the bond formed and is simply and extension of Heitler-London theory. According to this theory:

(i) Greater is the overlapping* stronger will be the bond formed.  It means bond strength depends upon overlapping and is directly proportional to the extent of overlapping.

(ii)  A spherically symmetrical orbital e.g. s-orbital will not show any preference in direction** whereas non-spherical orbitals e.g. p-orbitals will tend to form a bond in the direction of maximum electron density with the orbital.

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