The distortions of the ethylene molecule in its low-lying excited states—A four-electron treatment

Calculations have been carried out on the low-lying excited states of ethylene, with a view of determining whether there appears a pyramidal arrangement of the bonds around each carbon atom, in addition to the twisting of the two CH2 groups. The two π-electrons and the two electrons of the CC σ-bond are treated as valence electrons; the core is formed by four hybrids pointing toward the hydrogen atoms, whose effect is neglected. The interaction between the valence electrons and the core is taken explicitly into account, but variation of the core energy with the distortions is neglected. It is found that in the (twisted) T state a flapping of the two CH2 groups produces a significant stabilization (0·7 ev for a tetrahedral arrangement of the bonds), whereas in the V state it causes an increase in energy. It appears from the study of the flapping in the non-twisted molecule that the relative stabilities of the cis- and trans-conformations in the ground state are not predicted correctly. This lack of success, which has been encountered also with other approximations in similar problems, stresses the need for more accurate calculations.