CHM 501 Lecture

Molecular Orbital Theory

Linear Combination of Atomic Orbitals LCAO

Basic assumptions:

1) Orbitals in molecules look a lot like atomic orbitals

2) Perturbations are caused by wave interference (overlap) of atomic orbitals;

3) The new molecular orbitals fill with electrons according to the Aufbau and Pauli Principles

Constructive interference - lowers energy

Destructive interference - raises energy

Only orbital of the same irreducible representation can overlap with each other.

Increase of electron density in bonding orbitals between nuclei has two effects:

1) Screening of nuclear-nuclear repulsion by the extra electrons between nuclei

2) Electron-nuclear attraction in the direction that moves nuclei toward each other

Consider mixing orbitals in a linear diatomic molecule (D_h)

s orbitals: a_1g

p orbitals:

p_z a_1u

(p_x, p_y) e_1u

To distinguish various types of molecular orbitals

• No node perpendicular to the atom-atom axis : bonding
• One node perpendicular to the atom-atom axis : antibonding
• No nodes parallel to the atom-atom axis : sigma
• 1 node parallel to the atom-atom axis : pi
• 2 nodes parallel to the atom-atom axis : delta

Constructing Molecular Orbital energy diagrams:

Basic principles

1. Choose atomic orbitals as basis set; #AOs initially = #MOs created

2. AOs of like size and energy overlap better with each other

3. Only orbitals of the same symmetry can overlap with each other

4. A larger overlap leads to a larger energy change

5. Fill electrons into orbitals following the Pauli and Aufbau principles

H₂

electron configuration ²

BO = bond order = ½(N_b-N_a)

where

N_a = number of electrons in antibonding orbitals;

N_b = number of electrons in bonding orbitals

BO = 1 (in agreement with VBT)