Molecular Orbital Theory Localized Chemical Bonding

Molecular Orbital Theory in Localized Chemical Bonding - Organic Chemistry

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Molecular Orbital

The molecular orbital (MO) theory of bonding is mainly based on the work of Hund, Lennard-Jones, HUckel, and Mulliken. According to this theory the molecule is regarded as being formed by the overlap of all atomic orbitals (n) of the bonded atoms. When two atoms are brought closer to one another, their all atomic orbitals combine to give a set of new molecular orbitals (wave functions) in equivalent number (n) that encompass the entire molecule. Thus, every molecule is supposed to have orbitals associated with it in much the same way as a single isolated atom has. The Pauli's exclusion principle is applied to the MO's in the same way as it is applied to the atomic orbitals. MO's also follow Aufbau principle and Hund's rule.

According to molecular orbital theory, the atomic orbitals combine (overlap) and form a resultant orbital known as the molecular orbital in which the identity of both atomic orbitals is lost. All the electrons pertaining to, both the atoms are considered to be moving along the entire molecule under the influence of all the nuclei.
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Basic Principles of Molecular Orbital Theory 

1. When nuclei of two atoms come close to each other, their atomic orbitals interact resulting in the formation of molecular orbitals (MO). In molecule atomic orbitals of atoms lose their identity after the formation of molecular orbitals.
2. Each molecular orbital may be described by the wave function Ψ, which is known as MO, wave function, Ψ² represents the electron density.
3. Each MO wave function (Ψ) is associated with a set of quantum numbers which represent energy and shape of the occupied MO.
4. Each MO wave function (Ψ) is associated with a definite energy value. The total energy of the molecule is the sum of the energies of the occupied MO.
5. Molecular orbitals follow Pauli's exclusion principle, Hund's rule and Aufbau principle.
6. Each electron in a molecular orbital belongs to all the nuclei present in the molecule.
7. Each electron moving in the molecular orbital is having clockwise or counter-clock wise

8. Number of molecular orbitals are always equal to the number of atomic orbitals. The molecular orbitals can be obtained by the method of Linear combination of atomic orbitals (LCA,O). Let two atoms A and B form AB molecule which is hetero diatomic molecule. Their atomic orbitals are represented by Ψ_A and Ψ_B, respectively. There are following two way~ of their combination:
(i) Additive Overlap: Additive overlap is also known as positive overlap or ++ overlap. In this type of linear combination the positive lobe (i.e., the lobe having positive sign) of Ψ_A overlaps with the positiv~ lobe of Ψ_B, thus a molecular orbital is formed. This molecular orbital has lower energy than that of atomic orbitals of atom A and B due to attraction between the nuclei of A and B. Such type of molecular orbitals are known as bonding molecular orbitals (BMO) and represented as Ψ_b
(ii) Subtractive Overlap: Subtractive overlap is also known as negative overlap or +– overlap. In this type of the linear combination the positive lobe of Ψ_A overlaps with the negative lobe of Ψ_B thus a moleGular orbital is formed. This molecular orbital has higher energy than that of atomic orbitals of atom A and B due to repulsion between nuclei of A and B. Such type of molecular orbitals are known as anti-bonding molecular orbitals (ABMO) and represented as Ψ_a or Ψ
On the basis of above discussion, the formation of BMO and ABMO by the LCAO of Ψ_A and Ψ_B may be represented as :

When we show the contribution made by Ψ_A and Ψ_B in Ψ^a and Ψ^b molecular orbitals, the above equations may be written as :

The relative order of the energy of Ψ_A, Ψ_B. Ψ^b and Ψ^a is shown in Fig. 1.3.

It is to be noted that in the case of a bonding molecular orbital electron density is concentrated between two nuclei of the two atoms (Fig. 1.4), while in the case of anti-bonding molecular orbital nuclei of the two atoms come close to each other due to same charge and absence of the electron density, the nuclei repel each other (Fig. 1.5). We know that the square of the wave function (Ψ²) is known as probability of finding the electrons hence :

It is clear from the equation (5) that the value of Ψ^b₂is greater than the sum of Ψ²_A and Ψ²_B. It means that the probability of finding the electrons in the molecular orbitals obtained by the LCAO in accordance with equation 1 is greater than that in either of the AO's Ψ_A and Ψ_B In other words, the energy of Ψ_b is lower than either of ΨA and ΨB. Hence this orbital forms a stable chemical bond and named as bonding molecular orbital.
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In the same way we can say that from equation (6) that the value of Ψ²_a  is lesser than Ψ²_A  + Ψ²_B It means that the probability of finding the electron in the MO's obtained by the LCAO in accordance with equation (2) is lesser than that in either of the AO's Ψ_A and Ψ_B In other words, the energy of Ψ_a is higher than either of Ψ_A and Ψ_A Hence, this orbital catlnot form a stable chemical bond and is named as anti-bonding molecular orbital.