# 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. Figure $$\PageIndex{1}$$: The structure of NH3

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. 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 $$\PageIndex{1}$$