Stability of polyatomic molecules in degenerate electronic states - I—Orbital degeneracy

Abstract
In the following we investigate the conditions under which a polyatomic molecule can have a stable equilibrium configuration when its electronic state has orbital degeneracy, i. e. degeneracy not arising from the spin. We shall show that stability and degeneracy are not possible simultaneously unless the molecule is a linear one, i. e. unless all the nuclei in the equilibrium configuration lie on a straight line. We shall see also that the instability is only slight if the degeneracy is due solely to electrons having no great influence on the binding of the molecule. We first note that if accidental degeneracy (i. e. degeneracy not caused by symmetry) is disregarded then a degenerate electronic state necessarily entails a symmetrical nuclear configuration. Thus in order to cover all cases we may first consider each possible type of symmetry separately and discuss what nuclear configurations are consistent with each symmetry. A given molecule will possess a continuous set of configurations consistent with one definite type of symmetry, and among these configurations there may be one with a minimum electronic energy. This configuration is then stable with respect to all totally symmetrical nuclear displacements (i. e. displacements which do not disturb the symmetry). We shall have to investigate its stability with respect to all other nuclear displacements.

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