ANALYSIS OF THE DISTANCE DEPENDENCE AND MAGNITUDE OF THE PI+, PI- AND PI+ASTERISK, PI-ASTERISK SPLITTINGS IN A SERIES OF DIETHYNYL[N]STAFFANES - AN ABINITIO MOLECULAR-ORBITAL STUDY

Through-bond orbital interactions between the pi orbital and between the pi* orbitals of the first five members of the series of alpha,omega-diethynyloligo[1.1.1]propellanes, or alpha,omega-diethynyl[n]staffanes, 4(1)-4(5), have been investigated using ab initio MO theory. The pi+,pi- and pi+*,pi-* splittings of 4(1)-4(5) were obtained in the Koopmans' theorem approximation, using the STO-3G, 3-21G, and 6-31G* basis sets. For the first three members of the series, calculations were also performed with several other basis sets. It is found that the minimal STO-3G basis set failed to give satisfactory qualitative trends in the pi+,pi- and pi+*,pi-* splittings for 4(1)-4(5), whereas the 3-21G basis set is adequate in this regard. The pi+*,pi-* splittings (DELTAE) of 4(1)-4(5) followed a nearly exponential decay with increasing length of the staffane: DELTAE = A exp(-betam), where m refers to the number of C-C bonds in the relays connecting the acetylenic chromophores. On the other hand, the pi+,pi- splittings show a marked deviation from an exponential distance dependence. However, even in this case, the splittings'' settle down'' to a near-exponential distance dependence for the longer bridges. The average 3-21G beta values are 0.24 per bond (for the pi+,pi- splittings) and 0.37 per bond (for the pi+*,pi-* splittings). These beta values imply that the pi+,pi- and pi+*,pi-* splittings for 4(1)-4(5) fall off surprisingly slowly with increasing bridge length. The distance dependence of the pi+,pi- and the pi+*,pi-* splittings for 4(1)-4(5) is even weaker than that calculated for the polynorbornyl dienes, 3(2)-3(6), for which the average 3-21G beta values are 0.39 (pi+,pi-) and 0.54 (pi+*,pi-*) per bond. Based on this finding, it is predicted that the staffane bridges should be more effective than the polynorbornyl bridges at propagating electronic interactions over long distances, including intramolecular electron transfer and energy transfer processes. It is demonstrated, by means of a natural bond orbital analysis, that interactions that skip over bonds are very important for describing the coupling between adjacent staffane units.