An effective Hamiltonian for the valence states of ethylene generated by canonical transformations

We calculate the vertical N→T, N→V, and T→V transition energies in the ethylene molecule by diagonalizing the effective valence shell Hamiltonian obtained by our first principles canonical transformation–cluster expansion formalism. Calculations are performed for five different partitions of the one-electron space into core, valence, and excited subspaces. Excellent results of 4.61, 7.67, and 3.06 eV are obtained for the three respective transitions, provided that the many-electron states arising from a given partition meet two criteria. In particular, we find it is necessary to include both a localized and a diffuse π* orbital explicitly in the valence space. In addition, care must be taken in partitioning the one-electron space so as to avoid the quasidegeneracy between a state in the model space and one of the same symmetry in the orthogonal complement.