Knowledge Bank

A simple and general quantum mechanical perturbation formula, valid even in the case of finite degeneracy of the unperturbed system, has been derived. By using this formula, organic compounds having the character of a perturbed benzene ring have been treated, using the molecular-orbital method and the perturbation idea introduced by $Hu¨ckel$^{1}$ and Pauling and $Wheland.2$ The perturbation may depend on the fact that one, two, or more carbon atoms in the ring are replaced by other atoms, for instance nitrogen, or they may be due to substituents having none, one, or more $\pi$-orbitals available. Second-order formulas are given for the energy levels of the mobile electrons, the charge distributions, the bond orders, the dipole moments, and the transition moments with and without the inclusion of the overlap integrals. The theoretical results will be compared with experience in the subsequent paper.