Energy component analysis of the pseudo-Jahn-Teller effect in the ground and electronically excited states of the cyclic conjugated hydrocarbons: Cyclobutadiene, benzene, and cyclooctatetraene

To elucidate the nature of the pseudo-Jahn-Teller (JT) effect, an energy component analysis has been carried out for the ground and electronically excited states of the titled cyclic polyenes by using the MCSCF method with 6-31G(d) basis set. Examination of the energy components comprised in the total energy reveals that in the ground state of planar cyclobutadiene and cyclooctatetraene molecules, the stability of a bond-alternated structure is largely attributable to a decrease in the internuclear repulsion energy and the interelectronic repulsion energy due to a electrons. These observations are consistent with a totally symmetric expansion of the carbon skeleton brought about by the pseudo-JT distortion. Concomitantly, a contraction of the pi electron cloud takes place by polarization of the bond charges, and the nuclear-electron attraction energy of pi electrons also plays an important role in the pseudo-JT stabilization. Further, the stability of a nonplanar tub structure in cyclooctatetraene results from a lowering of the nuclear-electron attraction energy. In the excited states examined, the situation differs from molecule to molecule. In the lowest excited singlet state of cyclobutadiene, the stability of a rhombic structure originates from the energy lowerings of the nuclear-electron attractive term of a electrons and the kinetic term of pi electrons. While in the lowest excited triplet state of benzene, the stability of a quinoid structure arises from the energy lowerings of the internuclear repulsive term, the interelectronic repulsive term of sigma electrons, and the nuclear-electron attractive term of pi electrons.