# 22: Summary of the Steps Involved in Constructing Molecular Orbitals

- Choose a basis set of functions \(f_i\) consisting of the valence atomic orbitals on each atom in the system, or some chosen subset of these orbitals.
- With the help of the appropriate character table, determine which irreducible representations are spanned by the basis set using Equation (15.20) to determine the number of times \(a_k\) that the \(k^{th}\) irreducible representation appears in the representation. \[a_k = \dfrac{1}{h}\sum_C n_C \chi(g) \chi_k(g) \label{22.1}\]
- Construct the SALCs \(\phi_i\) that transform as each irreducible representation using Equation 16.1 \[\phi_i = \sum_g \chi_k(g) g f_i \label{22.2}\]
- Write down expressions for the molecular orbitals by taking linear combinations of all the irreducible representations of the same symmetry species.
- Write down the secular equations for the system.
- Solve the secular determinant to obtain the energies of the molecular orbitals.
- Substitute each energy in turn back into the secular equations and solve to obtain the coefficients appearing in your molecular orbital expressions in step 4.
- Normalize the orbitals.

### Contributors

Claire Vallance (University of Oxford)