Molecular Orbital Theory
This theory was developed by F. Hund and R. S. Mulliken in 1932. Following are the key features of Molecular Orbital Theory:
- Electrons in a molecule are present in various molecular orbitals.
- Atomic orbitals of comparable energies and proper symmetry combine to form molecular orbitals.
- An electron in a molecule orbital is influenced by two or more nuclei; depending upon the number of atoms in a molecule. Thus, a molecular orbital is polycentric.
- Number of molecular orbitals formed is equal to the number of combining atomic orbitals. So, combination of two atomic orbitals results in the formation of two molecular orbitals. One is called the bonding molecular orbital while another is called the antibonding molecular orbital.
- The bonding molecular orbital has lower energy and greater stability compared to the corresponding antibonding molecular orbital.
- Electron probability distribution around a group of nuclei in a molecule is given by a molecular orbital.
- Molecular orbitals are filled in accordance with the aufbau principle, obeying Pauli’s exclusion principle and Hund’s rule.
Linear Combination of Atomic Orbitals (LCAO)
According to wave mechanics, atomic orbitals can be expressed by wave functions (ψ's pronounced as psi). Wave functions represent the amplitude of the electron waves. Since it cannot be solved for any system containing more than one electron, molecular orbitals which are one electron wave functions for molecules are difficult to obtain directly from the solution of Schrodinger wave equation. An approximate method has been adopted to overcome this problem. This method is called Linear Combination of Atomic Orbitals (LCAO).
Let us take example of hydrogen molecule to understand this. Let us assume that a hydrogen molecule consists of two atoms A and B. The atomic orbitals of these atoms may be represented by wave functions ψA and ψB.
The formation of molecular orbitals may be described by linear combination of atomic orbitals which can be shown by addition or subtraction of wave functions of individual atomic orbitals; as shown by following equation.
ψMO = ψA ± ψB
So, the two molecular orbitals σ and σ* are formed as follows:
σ = ψA + ψB
σ* = ψA - ψB
The molecular orbital σ (formed by addition of atomic orbitals) is called the bonding molecular orbital. On the other hand, the molecular orbital σ* (formed by subtraction of atomic orbitals) is called the antibonding molecular orbital.
Difference between bonding and antibonding molecular orbitals:
- Bonding Molecular Orbital: In case of bonding molecular orbital, the two electron waves of bonding atoms reinforce each other due to constructive interference. So, electron density is located between the nuclei of bonded atoms in a bonding molecular orbital. Hence, repulsion between nuclei is very less. Electrons in a bonding molecular orbital tend to hold the nuclei together and stabilize the molecule. So, a bonding molecular orbital always has lower energy.
- Antibonding Molecular Orbital: In case of antibonding molecular ortbital, the two electron waves of bonding atoms cancel out each other due to destructive interference. So, electron density is located away from the space between the nuclei. Hence, repulsion between the nuclei is high. Hence, electrons in antibonding molecular orbital tend to destabilize the molecule. Energy of antibonding molecular orbital remains high. However, the total energy of two molecular orbitals remains the same as that of two original atomic orbitals.
Conditions for combination of Atomic Orbitals:
- The combining atomic orbitals must have same energy or nearly the same energy: This means that 1s orbital can combine with another 1s orbital but not with 2s orbital.
- The combining atomic orbitals must have the same symmetry about the molecular axis: This means that 2pz orbital of one atom can combine with 2pz orbital but not with 2px or 2py orbitals.
- The combining atomic orbitals must overlap to the maximum extent
Types of Molecular Orbitals
- Molecular orbitals are named as σ, π, δ, etc.
- σ molecular orbitals are symmetrical around the bond axis.
- π molecular orbitals are not symmetrical.
Energy Level Diagram of Molecular Orbitals
We have seen that 1s atomic orbitals on two atoms form two molecular orbitals, viz. σ1s and σ* 1s. Similarly, combination of 2s and 2p atomic orbitals makes following eight molecular orbitals.
Antibonding MOs: π*2s π *2pz π *2px π *2py
Bonding MOs: π2s π2pz π2px π2py
The increasing order of energies for various molecular orbitals for O2 and F2 is as follows:
σ1s < σ* 1s < σ2s < σ *2s < σ2pz < (π2px = π2py) < (π*2px = π*2py) < σ*2px
Electronic Configuration and Molecular Behavior
If Nb is the number of electrons occupying bonding orbitals, and Na is the number occupying anntibonding orbitals, then:
- If Nb is greater than Na, molecule is stable
- If Nb < Na, molecule is unstable
Half of the difference between the number of electrons present in the bonding and antibonding orbitals is called bond order.
Bond Order (b. o.) `=1/2(N_b-N_a)`
A positive bond order means a stable molecule, while negative bond order means an unstable molecule.
Magnetic Nature: If all the molecular orbitals in a molecule are doubly occupied, the substance is diamagnetic, i.e. repelled by magnetic field. If one or more molecular orbitals are singly occupied, the substance is paramagnetic, i.e. attracted by magnetic field.
When a highly electronegative element forms covalent bond with hydrogen atom, the electrons of the covalent bond are shifted towards the more electronegative atom. This results in a partially positively charged hydrogen atom. The partially positively charge hydrogen atom forms a bond with the other more electronegative atom. This bond is called the hydrogen bond and is weaker than the covalent bond. The attractive force which binds hydrogen atom of one molecule with the electronegative atom of another molecule is called hydrogen bond. For example; hydrogen bond exists between hydrogen atom of one molecule and fluorine atom of another molecule in case of HF molecule. This is shown below:
Hydrogen acquires fractional positive charge while electronegative element acquires fractional negative charge. It results in the formation of a polar molecule having electrostatic force of attraction. Magnitude of H-bonding is maximum in solid state and minimum in gaseous state.
Types of H-Bond
- Intermolecular Hydrogen Bond: It is found between two different molecules of same or different compounds.
- Intramolecular Hydrogen Bond: It is formed when hydrogen atom is in between two highly electronegative atoms (F, O, N) present within the same molecule.