Mass-reduced quantum numbers: Application to the isotopic mercury hydrides

Abstract

The concept of mass‐reduced quantum numbers is introduced and discussed. For a diatomic molecule, the mass‐reduced vibrational quantum number η= (v+1/2)/(μ)^1/2 and mass‐reduced rotational quantum number ξ=J (J+1)/μ are used and exemplified. Isotopically combined methods of potential determination from spectroscopic data follow from introduction of these quantum numbers, e.g., the isotopically combined Rydberg–Klein–Rees (RKR) method. These concepts are applied in detail to the isotopic mercury hydrides. It is shown that mass‐reduced functions exist which accurately describe, for example, vibrational spacings [ΔG (η)(=dG/dη) = μ^1/2ΔG (v+1/2)], rotational constants [B (η) =dE (η,ξ)/ dξ=μB (v)], and centrifugal distortion constants [D (η) =μ²D (v)]. The vibrational and rotational mass‐reduced functions are used to construct an isotopically combined RKR potential. This potential, when joined to the long‐range potential and extrapolated at short range reproduces the energy levels fairly well. In a companion paper, it is shown to yield the energy dependence of the total scattering cross section accurately. It should be noted that many other possible methods for potential determination are inadequate in this case. The interesting pseudocrossing region (∼3–5 Å), where an unusual flat shoulder in the potential occurs, is discussed, as are the two loci of barrier maxima (the extra locus arising from this shoulder). In Appendixes A, B, and C, new assignments of the 0–6 band of the A–X system of HgD are reported, the long‐range C₈ coefficient estimated, and the dissociation energies of HgH and HgD accurately determined to be D₀=3020⁺¹₋₇ cm⁻¹ and 3207±1 cm⁻¹, respectively.