LONG-RANGE INTERACTIONS IN A SERIES OF RIGID NONCONJUGATED DIENES .1. DISTANCE DEPENDENCE OF THE PI+,PI- AND PI+STAR,PI-STAR SPLITTINGS DETERMINED BY ABINITIO CALCULATIONS

The splittings between the two lowest energy cation states and the two lowest energy anion states are calculated in both the Koopmans' theorem and DELTA-SCF approximations for a series of rigid nonconjugated dienes, with the two double bonds separated by 4-12 C-C sigma bonds. To determine the role of long-range through-bond coupling on the splittings, the calculations are carried out using several basis sets-STO-3G, 3-21G, 6-311G, 6-31+G, and D95v-which differ in the radial extent of the outermost basis functions. The dependence of the various splittings on n, the number of C-C sigma bonds separating the ethylenic groups, is examined. The pi+,pi- splittings for the dienes with bridges containing 8, 10, and 12 C-C bonds are consistent with an exponential dependence on n, independent of the basis set employed. Similarly, when the STO-3G basis set is used, the pi+*,pi-* splittings for these compounds are also consistent with an exponential n dependence. However, with more flexible basis sets, the pi+*,pi-* splittings for the longer dienes show small, but significant, deviations from an exponential n dependence. Moreover, when the results for the dienes with the four- and six-bond bridges are included, single exponentials no longer provide good fits to the pi+,pi- or the pi+*,pi-* splittings for the entire series of compounds. The deviations from exponential behavior are greater with the nonminimal basis sets and at the Koopmans' theorem than at the DELTA-SCF level of theory. It is suggested that the nonexponential distance dependence is due to the importance of multiple through-bond pathways.