molecular orbital theory
1
Molecular-Orbital Theory
Introduction
Orbitals in molecules are not necessarily localized on atoms or between atoms as suggested in the valence bond theory.
Molecular orbitals can also be formed the LCAO where more than two atomic orbitals are used. (Technically, we can use all of the atomic orbitals in the LCAO.)
Linear combinations of orbitals result in the interference of waves. Both constructive and destructive interference may result.
Within a diatomic molecule, N atomic orbitals on atom 1 and N atomic orbitals on atom 2 result in 2N molecular orbitals.
**In a practical sense, only those atomic orbitals that have similar energies and the appropriate symmetry can combine to form molecular orbitals.**
These molecular orbitals are classified as bonding orbitals, antibonding orbitals or nonbonding orbitals.
Types of Molecular Orbitals
Bonding Orbitals
For the linear combination of only two atomic orbitals, the bonding orbital is constructed from adding the wavefunctions together. ψ MO = ψ AO ( A ) + ψ AO ( B)
Thus, the probability density of the bonding orbital can be written as ψ MO = ψ AO ( A ) + ψ AO ( B ) + 2ψ AO ( A ) ψ AO ( B )
2
2
2
= A2 + B 2 + 2AB
The 2AB term is the constructive interference of the overlap of the atomic orbitals.
- The interference results in an increase of electron density between the nuclei.
- Thus, the nuclei have greater attraction to each other, via their mutual attraction to the increased electron density.
1s
1s
2px
2px
1sσ
2pπ
2
Aside: S = ∫ ABdτ is called overlap integral.
Antibonding Orbitals
For the linear combination of only two atomic orbitals, the antibonding orbital is constructed from subtracting the wavefunctions together.
ψ MO = ψ AO ( A ) − ψAO ( B)
Thus, the probability density of the bonding orbital can be written as ψ MO = ψ AO ( A ) + ψ AO ( B ) − 2ψ AO ( A ) ψ AO ( B )
2
2
2
= A2 + B 2 − 2AB
The -2AB term is the destructive
Molecular-Orbital Theory
Introduction
Orbitals in molecules are not necessarily localized on atoms or between atoms as suggested in the valence bond theory.
Molecular orbitals can also be formed the LCAO where more than two atomic orbitals are used. (Technically, we can use all of the atomic orbitals in the LCAO.)
Linear combinations of orbitals result in the interference of waves. Both constructive and destructive interference may result.
Within a diatomic molecule, N atomic orbitals on atom 1 and N atomic orbitals on atom 2 result in 2N molecular orbitals.
**In a practical sense, only those atomic orbitals that have similar energies and the appropriate symmetry can combine to form molecular orbitals.**
These molecular orbitals are classified as bonding orbitals, antibonding orbitals or nonbonding orbitals.
Types of Molecular Orbitals
Bonding Orbitals
For the linear combination of only two atomic orbitals, the bonding orbital is constructed from adding the wavefunctions together. ψ MO = ψ AO ( A ) + ψ AO ( B)
Thus, the probability density of the bonding orbital can be written as ψ MO = ψ AO ( A ) + ψ AO ( B ) + 2ψ AO ( A ) ψ AO ( B )
2
2
2
= A2 + B 2 + 2AB
The 2AB term is the constructive interference of the overlap of the atomic orbitals.
- The interference results in an increase of electron density between the nuclei.
- Thus, the nuclei have greater attraction to each other, via their mutual attraction to the increased electron density.
1s
1s
2px
2px
1sσ
2pπ
2
Aside: S = ∫ ABdτ is called overlap integral.
Antibonding Orbitals
For the linear combination of only two atomic orbitals, the antibonding orbital is constructed from subtracting the wavefunctions together.
ψ MO = ψ AO ( A ) − ψAO ( B)
Thus, the probability density of the bonding orbital can be written as ψ MO = ψ AO ( A ) + ψ AO ( B ) − 2ψ AO ( A ) ψ AO ( B )
2
2
2
= A2 + B 2 − 2AB
The -2AB term is the destructive