Accurate Analytic Potential and Born–Oppenheimer Breakdown Functions for MgH and MgD from a Direct-Potential-Fit Data Analysis

Abstract

New high-resolution visible Fourier transform emission spectra of the A (2)Π → X (2)Σ(+) and B' (2)Σ(+) → X (2)Σ(+) systems of (24)MgD and of the B' (2)Σ(+) → X (2)Σ(+) systems of (25,26)MgD and (25,26)MgH have been combined with earlier results for (24)MgH in a multi-isotopologue direct-potential-fit analysis to yield improved analytic potential energy and Born-Oppenheimer breakdown functions for the ground X (2)Σ(+) state of MgH. Vibrational levels of the ground state of (24)MgD were observed up to v" = 15, which is bound by only 30.6 ± 0.10 cm(-1). Including deuteride and minor magnesium isotopologue data allowed us also to determine the adiabatic Born-Oppenheimer breakdown effects in this molecule. The fitting procedure used the recently developed Morse/Long-Range (MLR) potential energy function, whose asymptotic behavior incorporates the correct inverse-power form. A spin-splitting radial correction function to take account of the (2)Σ spin-rotation interaction was also determined. Our refined value for the ground-state dissociation energy of the dominant isotopologue ((24)MgH) is D(e) = 11,104.25 ± 0.8 cm (-1), in which the uncertainty also accounts for the model dependence of the fitted D(e) values for a range of physically acceptable fits. We were also able to determine the marked difference in the well depths of (24)MgH and (24)MgD (with the deuteride potential curve being 7.58 ± 0.30 cm(-1) deeper than that of the hydride) as well as smaller well-depth differences for the minor (25,26)Mg isotopologues. This analytic potential function also predicts that the highest bound level of (24)MgD is v" = 16 and that it is bound by only 2.73 ± 0.10 cm(-1).

LEVEL: A computer program for solving the radial Schrödinger equation for bound and quasibound levels

“…Note that the equation and reference numbering appearing in this Supplemental Material document refer to those in this journal article, so for completeness we hereby cite nine papers referenced there that are associated with particular applications of this code, but had not been referred to above [68][69][70][71][72][73][74][75][76].…”

The ExoMol Atlas of Molecular Opacities

“…Weck et al [13] constructed a purely ab initio line list, which covers this band but is of limited accuracy. More recently, experimentally-driven studies [135,136] have sought to remedy this problem.…”

Deviations from Born-Oppenheimer mass scaling in spectroscopy and ultracold molecular physics

“…When characterizing a particular electronic state spectroscopically, it is sometimes possible to isolate small mass-dependent effects not accounted for by rudimentary mass-scaling. Such Born-Oppenheimer breakdown functions have been derived empirically for a number of relatively light diatomic molecules by least-squares fitting of measured line positions for a pair or series of isotopologs [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. The purpose of this section is to compare examples of Born-Oppenheimer breakdown functions from the literature with the results obtained using ab initio techniques.…”

“…Quantitative investigations of such deviations go back at least to the theoretical work of Ko los and Wolniewicz on H 2 [1,2], which stimulated reinterpretation of the experimental spectrum by Herzberg [3]. They are also important for H + 3 [4], and they have been characterized spectroscopically for hydrides such as HeH + [5], BeH + [6], HF [7,8,9], HCl [10,9], HBr and HI [9], AgH [11,12], LiH [13], BeH [14] and MgH [15] and for CO [16], Li 2 [17,18,19], LiK [20], and LiRb [21]. For molecules without such light nuclei, the deviations have been hard to detect [22,23,24], although indications of them have been seen in K 2 [25], Rb 2 [22,26], and I 2 [27,28].…”