Semiempirical Calculation on the Electronic Structure of the Nitrogen-Containing Heterocyclic Molecules. I. General Theory

A semiempirical theory for n — π and π — π spectra of nitrogen heterocycles is proposed. The theory is an extension of the semiempirical molecular‐orbital method of Pariser and Parr, and the nonbonding electrons localized at the nitrogen atoms as well as π electrons are considered explicitly into the interaction term in the Hamiltonian. The orbitals in which nonbonding electrons are contained may be any 2s—2p hybrids. The differential overlap between atomic orbitals are formally neglected. One‐center electronic‐interaction integrals are obtained from atomic spectral data and two‐center integrals at moderate internuclear distances are extrapolated, using corresponding one‐center integrals obtained from atomic spectral data together with the theoretical value of the two‐center integrals at larger internuclear distances. On account of the hybrid nature of the nonbonding AO's (AO's from which nonbonding MO's are constructed), various kinds of two‐center integrals as well as one‐center ones appear. The method of obtaining these integrals is described systematically. The method of obtaining the valence‐state ionization potential for nonbonding electrons in hybrid orbitals is also described. Finally, as an example of the application of the present scheme, the energy levels of the pyrazine molecule are calculated, assuming that the s character of the nonbonding AO at the nitrogen atom is one third and taking account only of interactions among the ground and the singly‐excited configurations. Only the singlet levels are considered in this paper. Although the calculated ${}^1{A}_g{\to }^1{B}_{\text{3u}}\mathrm{(\pi -\pi )}$ transition energy agrees fairly well with experiment, it is found for ${}^1{A}_g{\to }^1{B}_{\text{1u}}{,}^1{B}_{\text{3g}}\mathrm{(n-\pi )}$ transitions that the calculated values are considerably higher than the observed values. This is probably due either to the neglect of the doubly excited configurations or to the invalid assumption concerning the hybridization parameter of the nitrogen nonbonding AO. This point will be discussed in Part II of this series.