Question

Explain how symmetry arguments are used to construct molecular orbitals.

Answer 1

solution:

  

We use atomic orbitals (AO) as a basis for constructing MO's.

LCAO-MO = linear combination of atomic orbitals.

The basic rules we developed for hybridization also apply here: orbitals are added with scalar coefficients (c) in such a way that the resulting orbitals are orthogonal and normalized. The difference is that in the MO case, the orbitals come from different atoms.

The linear combination of atomic orbitals always gives back the same number of molecular orbitals. So if we start with two atomic orbitals (e.g., an s and a p_z orbital as shown in Fig. 2.1.1), we end up with two molecular orbitals. When atomic orbitals add in phase, we get constructive interference and a lower energy orbital. When they add out of phase, we get a node and the resulting orbital has higher energy. The lower energy MOs are bonding and higher energy MOs are antibonding.

Fig. 2.1.1. Sigma bonding and antibonding combinations of an s and p orbital.

Molecular orbitals are also called wavefunctions (ψ), because they are solutions to the Schrödinger equation for the molecule. The atomic orbitals (also called basis functions) are labeled as φ's, for example, φ_1s and φ_3pz or simply as φ₁ and φ₂.