The existence of secondary orbital interactions

B3LYP/6-311+G** (and MP2/6-311+G**) computations, performed for a series of Diels-Alder (DA) reactions, confirm that the endo transition states (TS) and the related Cope-TSs are favored energetically over the respective exo-TSs. Likewise, the computed magnetic properties (nucleus-independent chemical shifts and magnetic susceptibililties) of the endo- (as well as the Cope) TS's reveal their greater electron delocalization and greater aromaticity than the exo-TS's. However, Woodward and Hoffmann's original example is an exception: their endo-TS model, involving the DA reaction of a syn- with an anti-butadiene (BD), actually is disfavored energetically over the corresponding exo-TS; magnetic criteria also do not indicate the existence of SOI delocalization in either case. Instead, a strong energetic preference for endo-TSs due to SOI is found when both BDs are in the syn conformations. This is in accord with Alder and Stein's rule of "maximum accumulation of double bonds:" both the dienophile and the diene should have syn conformations. Plots along the IRC's show that the magnetic properties typically are most strongly exalted close to the energetic TS. Because of SOI, all the points along the endo reaction coordinates are more diatropic than along the corresponding exo pathways. We find weak SOI effects to be operative in the endo-TSs involved in the cycloadditions of cyclic alkenes, cyclopropene, aziridine, cyclobutene, and cyclopentene, with cyclopentadiene. While the endo-TSs are only slightly lower in energy than the respective exo-TSs, the magnetic properties of the endo-TS's are significantly exalted over those for the exo-TS's and the Natural Bond Orbitals indicate small stabilizing interactions between the methylene cycloalkene hydrogen orbitals (and lone pairs in case of aziridine) with pi-character and the diene pi MOs.