Theoretical Study of H2+ Ground Electronic State Spectroscopic Properties

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Abstract
Born–Oppenheimer and adiabatic vibrational–rotational eigenvalues are determined for the (1sσg) 2Σg+ ground state of H2+ by a combination of Runge–Kutta and Adams–Moulton numerical techniques. These eigenvalues are believed to be more accurate than any previously reported. Dunham expansions of the potentials are used to determine Born–Oppenheimer and adiabatic spectroscopic constants; the adiabatic constants are considered to be the best set, theoretical or experimental, available for the ground state of H2+. The ΔG curve for this state has two points of inflection and a positive curvature tail, presumably to be associated with long-range 1 / R4 forces in the molecular ion. The Bυ curve has a shape similar to the ΔG curve; more striking, inflection points occur at essentially the same values of the vibrational quantum number υ. The Dυ curve has a negative slope at υ = 0, but rises rapidly near dissociation. The Hυ values decrease and become negative at large υ values. The sharp rise at high υ in | Hυ |, like that in Dυ, is probably due to the dominance of the centrifugal reaction over the true potential at large nuclear separations R.