THEORETICAL RESONANCE ENERGIES OF BENZENE, CYCLOBUTADIENE, AND BUTADIENE

A valence bond method, namely the bonded tableau unitary group approac h, is applied to analyze the pi electron delocalization of benzene, cy clobutadiene, and butadiene, and the resonance energies are also calcu lated and extensively compared with experimental data and theoretical results in the literature. In the frame of ab initio calculations, we optimize the geometries of hypothetical molecules with localized nonre sonating double bonds without any artificial approximation. Our result s show that the Csp(2)-Csp(1) single bend length (1.509 Angstrom with the 6-31G basis set) is only about 0.021 Angstrom shorter than the Csp (3)-Csp(3) bond, and the delocalization is a driving force in conjugat ed systems. If the delocalization energy can compensate the energy nee ded by the shortening of some Csp(2)-Csp(2) bonds, the system will pre fer a regular geometry with uniform C-C bond lengths, otherwise the sy stem will be stable toward an alternate geometry where delocalization is still important. An interesting result is that even in cyclobutadie ne the delocalization is energetically beneficial and the theoretical resonance energy is 3.16 kcal/mol with the STO-6G basis set or 5.67 kc al/mol with the 6-31G basis set, which is close to the value of butadi ene. Moreover, the pi orders of the long bonds in C4H4 and C4H6 are ve ry close. Thus it can be concluded that the antiaromacity of C4H4 is a direct outcome of the sigma frame's ring strain rather than pi electr onic delocalization.