Sum over orbitals scaling of the second hyperpolarisabilities of polyenic chains: a case study

A sum over molecular orbitals scheme with a 6-31G basis set is tested to calculate the static second hyperpolarisabilities γ of polyenic chains with N double bonds (5⩽N⩽80). On scaling ab initio values by a factor that `substitutesʹ the HOMO–LUMO gap with the optical gap, the calculated γs are in good agreement with experimental results reported on substituted polyenic chains up to roughly 70 double bonds. This agreement is taken to indicate that the present simplified procedure can behave as an effective hamiltonian which may find further application. Alternatively, one can postulate that the nature of the response in polyenic chains can be reduced to a function of the molecular orbitals only.