Theory of the Spin and Charge Distribution in Aromatic Ion Radicals; Application to the Naphthalene Negative Ion

The valence-bond method is extended to positive- and negative-ion radicals. General formulas for the required energy, overlap, spin-density, and charge-density matrices are developed and specialized to pielectron systems. An application of the method to the pi electrons of the naphthalene negative ion is given. Included in the calculation are all unexcited structures with the negative charge in each of the ten possible positions. When approximate exchange and transfer integrals are used to determine the coefficients of valence-bond structures, the α to β position spin-density ratio is found to be equal to 2.60, in good agreement with the ``experimental'' value of 2.65. The magnitudes of the calculated spin densities are such that a Q of —26.3 gauss is required to obtain the measured hyperfine splittings. To test the validity of these valence-bond results, their sensitivity to the molecular integral values is examined. Also, comparisons with a variety of molecular-orbital calculations are given. It is of considerable interest that the charge distributions obtained from the valence-bond theory and the molecular-orbital theory are very different in spite of the similarity of the spin distributions calculated by the two methods.