Study of the Geometry and Spectra of the Allylic Systems by Ab Initio Methods

Ab initio SCF MO and CI calculations are reported for the allyl cation, radical, and anion and also for their cyclopropyl isomers. A large series of SCF calculations is employed to study the relationship between the position of the hydrogen atoms of C₃H₅⁺ and the magnitude of its CCC skeletal internuclear angle. The differences in the molecular geometry and heights of various rotational barriers observed between the cations and the related neutral species allene and cyclopropene are subsequently explained in terms of changes in electronic configuration induced upon protonation of these C₃H₄ systems. Analogous geometrical phenomena for the neutral C₃H₅ systems and the allyl anion are investigated via Koopmans' theorem. Finally the electronic spectrum of the allylic systems is studied by means of a large CI calculation in which excitations involving $\sigma$ MO's are given explicit consideration; the results of this treatment are seen to differ markedly from those obtained by semiempirical π‐electron calculations, especially in that many of the low‐lying excited states obtained herein are found to result from the $\mathrm{\sigma \hspace{0.17em}\to \hspace{0.17em}\pi }$ category of electronic transitions.