Zero-field splitting of the lowest triplet state of some aromatic hydrocarbons: Calculation and comparison with experiment

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Abstract
It is investigated how far the zero-field splitting of the lowest triplet state of aromatic hydrocarbons can quantitatively be accounted for with a π-electron representation of the wave function. The calculations are based on triplet SCF-MO's, as obtained from an extension by Colpa of Pariser's formalism to open-shell systems. Interaction with all π-electron configurations that are either singly or doubly excited relative to the lowest triplet configuration is included. The pertinent integrals over 2pz Slater AO's have been evaluated by numerical integration, with a result almost identical to that obtained by Gouterman and Moffitt for Gaussian AO's. When the calculated values of the parameters D and E in the spin Hamiltonian for naphthalene, anthracene and phenanthrene are compared with experiment, those of D are found to be 15–20 per cent too high, whereas those of E—though lying in the right order—are considerably too large. The contribution to the splitting parameters due to spin polarization of the σ-electrons in the C-C and C-H bonds by the π-electrons is then estimated. It is found that the effect is of the right order of magnitude to bring the calculated and observed values of D to agreement. Finally, a semi-empirical method of calculation is suggested to take account of σ-π polarization and the uncertainty in the precise values of the dipole-dipole integrals between two electrons on neighbouring atoms. Calculations for naphthalene, anthracene, phenanthrene and triphenylene with this modified method yield values of D which are in perfect agreement with experiment, but those of |E|—which are very sensitive to changes in the configurational mixing—are less reliably predicted. The value of D for the (trigonal) phenalenylium ion is also calculated; it is of the right order of magnitude.