# 1.8: NH3 Molecular Orbitals

## Point Group of NH3

The symmetry elements of NH3 are E, 2C3, and 3 sigma-v. To elaborate, the molecule is of C3v symmetry with a C3 principal axis of rotation and 3 vertical planes of symmetry. The image of the ammonia molecule (NH3) is depicted in Figure $$\PageIndex{1}$$ and the following character table is displayed below.[1]

C3v E 2C3v 3 σv
A1 1 1 1 z x2+y2, z2
A2 1 1 -1 Rz
E 2 -1 0 (x,y)(Rx,Ry) (x2-y2,xy)(xz,yz)

## The Construction of Molecular Orbitals of NH3

The Molecular Orbital Theory (MO) is used to predict the electronic structure of a molecule. Molecular orbitals are formed from the interaction of 2 or more atomic orbitals, and the interactions between atomic orbitals can be bonding, anti-bonding, or non-bonding. A bonding orbital is the interaction of two atomic/group orbitals in phase while an anti-bonding orbital is formed by out-of-phase combinations.

In general, the energy level of molecular orbitals increases from bonding, to non-bonding, and anti-bonding molecular orbitals. Pi-bonding molecular orbitals generally have greater energies than sigma-bonding molecular orbitals because the pi interactions are less effective than sigma interactions. The energy of molecular orbitals increases when the number of nodes also increases, and vice versa.[6] Within bonding molecular orbitals of the same symmetry, the lowest energy are from completely symmetrical sigma bonding molecular orbitals.

### Projection Operator Methode:

The Projection Operator Methode can be used to determine MO of NH3, the next steps can be used:

1) Determine the point group of melecular;

2) Lable S orbital of H;

3) Generate a reducible representation (ᒥ) for H;

4) Reduce reducible representation to irreducible representation;

5) Generate the symmetry adapted linear combinations (SALCs) of orbitals that arise from these irreducible representations;

6) Drawing group orbital combinations and determine the atomic orbitals of the centeral atom;

7) MO

Example $$\PageIndex{1}$$