The theory of electronic spectra and electronic structure, the elucidation of which was begun in the first paper of this series, is further developed and applied to ethylene, butadiene, benzene, pyridine, pyrimidine, pyrazine, and s-triazine. A realistic and consistent LCAO-MO π-electron theory should allow the σ-electrons to adjust themselves to the instantaneous positions of the mobile π-electrons. This is accomplished in the theory by assignment of empirical values to the Coulomb electronic repulsion integrals and Coulomb penetration integrals which enter the formulas, these values being obtained in a prescribed way from valence state ionization potentials and electron affinities of atoms. Use of the empirical values in the molecular orbital theory reduces the magnitude of computed singlet-triplet splittings and the effects of configuration interaction without complicating the mathematics. From the valence-bond point of view, ionic structures may be said to be enhanced. The applications to hydrocarbons and heteromolecules which are considered show that the theory can correlate known π-electron spectral wavelengths and intensities very successfully, which, together with the simple structure of the theory, signals that manifold applications of the theory are in order elsewhere.

A semi-empirical theory is outlined which is designed for the correlation and prediction of the wavelengths and intensities of the first main visible or ultraviolet absorption bands and other properties of complex unsaturated molecules, and preliminary application of the theory is made to ethylene and benzene. The theory is formulated in the language of the purely theoretical method of antisymmetrized products of molecular orbitals (in LCAO approximation), including configuration interaction, but departs from this theory in several essential respects. First, atomic orbital integrals involving the core Hamiltonian are expressed in terms of quantities which may be regarded as semi-empirical. Second, an approximation of zero differential overlap is employed, and an optional uniformly charged sphere representation of atomic π-orbitals is introduced, which greatly simplify the evaluation of electronic repulsion integrals and make applications to complex molecules containing heteroatoms relatively simple. Finally, although the theory starts from the π-electron approximation, in which the unsaturation electrons are treated apart from the rest, provision is included for the adjustment of the σ-electrons to the π-electron distribution in a way which does not complicate the mathematics. Electronic energy levels in the theory are expressed in terms of ionization potentials of atoms, resonance integrals of bonds, Coulomb repulsion integrals between two π-electrons on the same atom and between two π-electrons on different atoms, and penetration integrals between π-electrons and neutral atoms. Preliminary applications to ethylene and benzene in which only the carbon-carbon resonance integral is treated as an empirical quantity show that the theory can reproduce the results of the purely theoretical method with very little labor. The reasonableness of considering all of the above quantities as semi-empirical is pointed out, however, and it is through a detailed examination and exploitation of this in the second paper of this series that correction for the inadequacies of the π-electron approximation is made and improved agreement with experiment is attained.

A previously given theory of the electronic spectra and structure of complex unsaturated molecules is further elucidated by listing specific formulas for the charge density, bond order, transition moment, and configuration interaction matrix elements. The theory is then applied to give a number of simple rules for alternant hydrocarbons. These refer to the energies of the singly excited states and the effects of configuration interaction, the degeneracy between certain singlet and triplet states, the prohibition of certain electronic transitions which would be allowed from a group theoretical point of view, and the charge density distribution of the ground and singly excited states. A mechanism is proposed to explain some of the anomalously rapid singlet-triplet radiationless transitions which are observed in connection with studies of the lower triplet states of complex molecules. Quantitative application of the theory is made to the spectra of the polyacenes, benzene through pentacene, and to the bond orders of naphthalene and anthracene, employing a high-speed digital computer. The calculated results are compared with experiment. Some previous assignments of electronic bands are confirmed, and some new assignments are suggested. The location of a number of excited states which have not, as yet, been observed is predicted.

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A rapid method for determining the degree of crosslinking in elastomers is described which involves measuring equilibrium compression modulus at very small deformations on solvent‐swollen samples. The elastomer used was a polyether urethane vulcanized by an accelerated sulfur recipe. The degree of crosslinking as measured by the compression method agreed with that measured by the extension method within 1–3%. Both methods agreed reasonably well with the theoretical values calculated from the sulfur level, polymer molecular weight, and crosslink structure.

A previously given theoretical method is applied to the azulene molecule. π-electron energies, transtion moments, dipole moments, charge distributions, and bond orders are calculated for the ground state and for the lower singlet and triplet excited states. The same detailed procedure which had previously given good results for the polyacenes is used here. Configuration interaction is included for all singly excited configurations. Two parallel calculations, one starting with conventional Hückel MOs and the other with perimeter MOs, are carried through. Hückel MOs lead to numerical results in good agreement with available experimental spectral data. In this connection some previous assignments are confirmed and some new ones are proposed. For the π-electron dipole moment for the ground state, one calculates 1.88 D with Hückel MOs and 3.36 D with perimeter MOs; the experimental value is 1 D. One may conclude that the present procedure gives results in substantial agreement with experiment provided that good MOs, e.g., Hückel MOs, are employed. For computation of excited state energies it is essential to include interaction among nearly degenerate configurations. More extensive configuration interaction, however, appears to improve the transition energies and especially the transition moments and dipole moments.

The concept of Markov chains has been employed to derive the degree-of-polymerization distribution, the over-all composition, and the compositional distribution for copolymers containing any number of different monomers. The results are then used to obtain explicit expressions for systems of two monomers. It is shown that this method, because of its conciseness and ease of generalization, is particularly well adapted for problems in copolymerization statistics.

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