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NH3 Molecular Orbitals

Molecular structure of Ammonia with the principle rotational axis and projection labels

Ammonia has the following symmetry elements: E, 2C₃, 3σ_v. These symmetry elements classified Ammonia as a C_3v point group.

The character table of C_3v point group are shown below:

Character Table for C3v
C3v	E	2C3	3σv
A1	1	1	1	z	x2+y2, z2
A2	1	1	-1	Rz
E	2	-1	0	(xy), (Rx, Ry)	(x2-y2,xy), (xy, yz)

Reducible Representation

C3v	E	2C3	3σv	Irreducible Representation
Γσ	3	0	1	A1 + E
Γπ	6	0	0	A1 + A2 + 2E

The 2s and 2P_z orbital individually transforms as A₁ irreducible representation, while 2P_x and 2P_y both transforms as E irreducible representation.

Symmetry-Adapted Linear Combinations (SALCs)

(Left) Figure shows each direction of the C₃ rotation. (Right) Top view defining each mirror plane.

SALC A₁ = ${1 \over {\sqrt {3}}}(\Phi _{1}+\Phi _{2}+\Phi _{3})$

SALC E⁽¹⁾ = ${1 \over {\sqrt {3}}}(2\Phi _{1}-\Phi _{2}-\Phi _{3})$

Degeneracy

Ammonia has a doubly degenerate (E) orbital. Pauli exclusion principle dictates that any two electron can not have the same quantum state and any exchange must be antisymmetric, therefore the second SALC must be orthogonal to the first SALC (E).

SALC E⁽²³⁾ = ${1 \over {\sqrt {2}}}(\Phi _{2}-\Phi _{3})$

The Molecular Orbitals

Figures A to G are the representations of SALCs and its MOs. The shaded spheres or lobes corresponds to the positive projection coefficient, and similarly, the empty spheres or lobes corresponds to the negative projection coefficient. Figure D to I are derivatives of Figure A to C, where the s and the p orbitals were added.

Energy Levels

Each SALCs has different energy level. The node of each SALC roughly indicate how much energy is in the bond. The Nitrogen atom in ammonia can only participate in σ and π (P_x and P_y) bonding, whereas the Hydrogen atoms can only participate in σ bonding.

Molecular Orbitals of Ammonia (NH₃)

The non-bonding, 2P_z (a₁), orbital give raise to the lone pair on Nitrogen atom in Ammonia.