The Two Quantum Excited States of the Hydrogen Molecule

Theory of two quantum states of H₂.---There are sixteen possible wave functions for a pair of interacting H atoms which dissociate adiabatically into a normal H atom and a two quantum H atom. These wave functions give rise to eight distinct S states and four distinct P states (the latter are degenerate in the fixed nuclei problem). These states may be divided into four groups of three according to the symmetry of the wave functions with respect to (a) an interchange of electron coordinates, and (b) reflection in the plane which forms the perpendicular bisector of the internuclear axis. The principles of selection for transitions between these various types of electronic state are formulated and compared with the rules of Kronig. A first order perturbation theory computation of the potential energy curves for the P states shows that two of them have the form requisite for the formation of stable molecules. These two may be identified respectively with the C state (upper level for Werner bands) and the 2³P state reported by Richardson. The agreement between the computed curves and the empirical data is fair.Valence theory.---The computations show that in the case of the excited states of hydrogen the union of valence electrons to form symmetrical pairs is not the essential feature of molecule formation as London's original valence theory supposed. The rule that molecular formation is contingent on the removal of degeneracy from the wave functions of the interacting atoms seems to have a greater range of applicability than London's rule. The latter is no doubt correct for a great variety of cases, however.