LONG-RANGE INTERACTIONS IN A SERIES OF RIGID NONCONJUGATED POLYNORBORNYL DIENES .2. ROLE OF ELECTRON CORRELATION IN DETERMINING THE DISTANCE DEPENDENCE OF THE PI(+),PI(-) AND PI(+)ASTERISK,PI(-)ASTERISK SPLITTINGS

The role of electron correlation effects in determining the splittings between the two pi cation and between the two pi* anion states of a series of rigid polynorbomyl dienes, in which the bridge length separating the double bands ranges from 4 to 12 C-C bonds, is investigated by means of second-order perturbation theory (MP2) and density functional theory (DFT) calculations. The results of these calculations are compared with those obtained previously in the Koopman's theorem (KT) and Delta SCF approximations. Far the longer members of the series, the inclusion of relaxation effects causes the pi and pi* splittings to decrease, whereas the inclusion of correlation effects causes them to increase, with the MP2 splittings being larger than the KT splittings. The MP2 and KT approximations give qualitatively similar rates of falloff of the splittings with increasing bridge length. The Delta SCF approximation predicts a much more rapid attenuation of the splittings. For the pi splittings the deviation from an exponential distance dependence is more pronounced in the KT than in the Delta SCF or MP2 methods. Relaxation and correlation effects prove less important for the splittings between the pi* anion states than for those between the pi cation states. The overall reasonable agreement between the MP2 and KT splittings lends justification for the use of the KT procedure as a computationally inexpensive way of estimating the splittings. The pi and pi* splittings obtained from the DFT calculations are appreciably smaller than the MP2 splittings, and for the longer members of the series, the pi cation and the pi* anion splittings calculated with the DFT method fall off somewhat more slowly with increasing bridge length than those calculated with the MP2 method.