Introduction to Molecular Orbital Theory
Valence Bond Theory fails to answer certain questions like Why He molecule does not exist and why O is paramagnetic? Therefore in 1932 F. Hood and RS. Mulliken came up with theory known as
Molecular Orbital Theory to explain questions like above. According to Molecular Orbital Theory individual atoms combine to form molecular orbitals, as the electrons of an atom are present in various atomic orbitals and are associated with several nuclei.
Fig. No. 1 Molecular Orbital Theory
Electrons may be considered either of particle or of wave nature. Therefore, an electron in an atom may be described as occupying an atomic orbital, or by a wave function Ψ, which are solution to the
Schrodinger wave equation . Electrons in a molecule are said to occupy molecular orbitals. The wave function of a molecular orbital may be obtained by one of two method:
1. Linear Combination of Atomic Orbitals (LCAO). 2. United Atom Method.
Linear Combination of Atomic Orbitals (LCAO)
As per this method the formation of orbitals is because of Linear Combination (addition or subtraction) of atomic orbitals which combine to form molecule . Consider two atoms A and B which have atomic orbitals described by the wave functions Ψ and Ψ .If electron cloud of these two atoms overlap, then the wave function for the molecule can be obtained by a linear combination of the atomic orbitals Ψ and Ψ i.e. by subtraction or addition of wave functions of atomic orbitals
Ψ = Ψ + Ψ
The above equation forms two molecular orbitals
Bonding Molecular Orbitals
When addition of wave function takes place, the type of molecular orbitals formed are called Bonding Molecular orbitals and is represented by Ψ = Ψ + Ψ
They have lower energy than atomic orbitals involved. It is similar to constructive interference occurring in phase because of which electron probability density increases resulting in formation of bonding orbital. Molecular orbital formed by addition of overlapping of two s orbitals shown in figure no. 2. It is represented by s .
Anti-Bonding Molecular Orbitals
When molecular orbital is formed by subtraction of wave function, the type of molecular orbitals formed are called Antibonding Molecular Orbitals and is represented by Ψ = Ψ - Ψ
They have higher energy than atomic orbitals. It is similar to destructive interference occurring out of phase resulting in formation of antibonding orbitals. Molecular Orbital formed by subtraction of overlapping of two s orbitals are shown in figure no. 2. It is represented by s* (*) is used to represent antibonding molecular orbital) called Sigma Antibonding.
Fig. No. 2 Formation of Bonding and Anti-Bonding Orbital
Therefore, Combination of two atomic orbitals results in formation of two molecular orbitals, bonding molecular orbital (BMO) whereas other is anti-bonding molecular orbital (ABMO).
BMO has lower energy and hence greater stability than ABMO . First BMO are filled then ABMO starts filling because BMO has lower energy than that of ABMO.
Formation of molecular orbitals occurs by the combination of atomic orbitals of proportional symmetry and comparable energy. Therefore, a molecular orbital is polycentric and atomic orbital is monocentric. Number of molecular orbitals formed is equal to the number of atomic orbitals.
Differences between Molecular Orbital and Atomic Orbital
Molecular Orbital Atomic Orbital
1. An electron Molecular orbital is under the influence of two or more nuclei depending upon the number of atoms present in the molecule.
2. Molecular orbitals are formed by combination of atomic orbitals
3. They have complex shapes. 1. An electron in atomic orbital is under the influence of only one positive nucleus of the atom.
2. Atomic orbitals are inherent property of an atom.
3. They have simple shapes.
Relative Energies of Molecular Orbitals
Bonding Molecular Orbitals (BMO) - Energy of Bonding Molecular Orbitals is less than that of Anti Bonding Molecular Orbitals because the attraction of both the nuclei for both the electron (of the combining atom) is increased.
Anti-Bonding Molecular Orbitals (ABMO) - Energy of Anti Bonding Molecular Orbitals is higher than Bonding Molecular Orbitals because the electron try to move away from the nuclei and are in repulsive state.
The Energies of Bonding Molecular Orbitals and Anti-Bonding Molecular Orbitals are shown in figure below:
Fig. No.3 Energies of BMO and ABMO
Energy Level Diagram
The factors upon which relative energies of molecular orbitals depend are:
(i) Energies of the Atomic orbitals combining to form Molecular Orbitals.
(ii) The extent of overlapping between the atomic orbitals. The greater the overlap, the more the bonding orbital is lowered and the anti-bonding orbital is raised in energy relative to AOs
1s Atomic Orbitals (AOs) of two atoms form two Molecular Orbitals (MOs) designated as s1s and s *1s.The 2s and 2p orbitals (eight AOs of two atoms) form four bonding MOs and four anti-bonding MOs as:
Bonding MOs: σ 2s , σ 2pz , π 2p , π 2p
Anti – Bonding MOσ: σ *2s , σ *2p , π *2p , π *2p
Using Spectroscopy, the energy levels of these molecular orbitals are determined experimentally. The order of increasing energy of molecular orbitals obtained by combination of 1s, 2s and 2p orbitals of two atoms is →
σ1s, σ *1s, σ 2s, σ *2s, σ 2p , π 2p = π 2p , π *2p = π *2p , σ *2p
( Energy Increases from left to right )
The molecular orbital diagram representing this order of energy levels is shown in fig.