I. Application of the Equations-of-Motion Method to the Excited States of N₂, CO, and C₂H₄. II. Applicability of SCF Theory to Some Open-Shell States of CO, N₂, and O₂

Abstract

In Part I various low-lying electronic states of N2, CO, and ethylene are studied by the equations-of-motion-method. This approach attempts to describe excitation processes directly, without solving Schroedinger's equation separately for the excited and ground states. It reduces to a matrix eigenvalue problem in a space of single particle-hole excitations, and the effect of double excitations is determined by perturbation theory. Using extensive Gaussian basis sets, excitation energies and oscillator strengths are obtained for nine states of CO and eleven states of N2 at the equilibrium geometry. The typical error in frequency is about five per cent relative to experiment. Calculated oscillator strengths are also very good since the total intensity must very nearly satisfy the energy weighted sum rule. Results for ethylene show that the V state is a valence state but is more diffuse than the T state and ground state. Potential energy curves are constructed for all these states by solving the equations at a few points with slightly smaller basis sets. The theory is appropriate as long as the Hartree Fock approximation is a good one for the ground state -- within about thirty per cent of equilibrium. The Σ+ states of N2 and CO are most interesting because questions about perturbation and pre-dissociation can be answered. Part II describes open shell SCF calculations for some diatomic molecules. By working with the real functions πx and πy instead of π+ and π-, the SCF Hamiltonians for the Σ states of the configurations (πu)3(πg), (πu)3(πg)3,and (1π)3(2π) of diatomic molecules can be expressed in terms of Coulomb and exchange operators only. With these results, conventional SCF programs can solve for the wavefunctions of many interesting states of N2, O2, and CO, e.g., the B 3Σ-u state of O2. For many states, the SCF results are in good agreement with experiment. However, SCF theory runs into serious trouble if electron correlation is important in determining the relative locations of excited states.