Direct cluster expansion method. Application to glyoxal

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Abstract
The direct cluster expansion formalism for large‐scale wave function calculations, based on an integral‐list driven procedure, is presented in a new form. The new approach allows us to calculate the correlated ground state wave function and to make the direct determination of excitation energies and various detachment and attachment energies, such as ionization potentials and electron affinities, in the symmetry‐adapted‐cluster (SAC) and SAC–CI framework. Applications are made to the ground state and low‐lying singlet and triplet excited states of glyoxal (CHO)2, and its positive and negative ions. Cluster expansion calculations indicate that correlation effects are very important both in the ground and excited states of glyoxal. The trans conformation is predicted to lie 4.6 kcal below the cis isomer in the ground state. The calculated adiabatic excitation energies are 22 000 cm−1 (3Au), 28 700 cm−1 (3Bg), and 30 400 cm−1 (3Bu). The ordering of the vertical ionization potentials of trans glyoxal is 7ag (n+), 6bu (n−), 1bg (π−), 1au (π+), and the agreement with experiment is fairly satisfactory. It is concluded that the present theory is applicable equally well to the study of the ground state and various excited states.