Electronic levels in simple conjugated systems, I. Configuration interaction in cyclobutadiene

In the simplest cyclic system of π-electrons, cyclobutadiene, a non-empirical calculation has been made of the effects of configuration interaction within a complete basis of antisymmetric molecular orbital configurations. The molecular orbitals are made up from atomic wave functions and all the interelectron repulsion integrals which arise are included, although those of them which are three- and four-centre integrals are only known approximately. In this system configuration interaction is a large effect with a strongly differential action between states of different symmetry properties. Thus the 1A1g state is several electron-volts lower than the lowest configuration of that symmetry, whereas for 1B1g the comparable figure is about one-tenth of an electron-volt. The other two states examined, 1B2g and 3A2g are affected by intermediate amounts. The result is a drastic change in the energy-level scheme compared with that based on configuration wave functions. Neither the valence-bond theory nor the molecular orbital theory (in which the four states have the same energy) gives a satisfactory account of the energy levels according to these results. One conclusion from the valence-bond theory which is, however, confirmed, is the somewhat unexpected one that the non-totally symmetrical 1B2g state is more stable than the totally symmetrical 1A1g. On the other hand, it is clear that the valence-bond theory, with the usual value for its exchange integral, grossly exaggerates the resonance splitting of the states, giving separations between them several times too great. Thus the valence-bond theory leads to large values of the resonance energy (larger, per π-electron, than in benzene) and so associates with the molecule a considerable π-electron stabilization. This expectation has no support in the present more detailed and non-empirical calculations.