Torsionally mediated spin-rotation hyperfine splittings at moderate to high J values in methanol

• Published in: The Journal of chemical physics 2016-07, Vol.145 (2), p.024307-024307
• Main Authors: Belov, S. P., Golubiatnikov, G. Yu, Lapinov, A. V., Ilyushin, V. V., Alekseev, E. A., Mescheryakov, A. A., Hougen, J. T., Xu, Li-Hong
• Format: Article
• Language: English
• Subjects: Angular momentum; ANGULAR MOMENTUM OPERATORS; GROUND STATES; INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; MATRIX ELEMENTS; METHANOL; Millimeter waves; Operators (mathematics); Quantum numbers; Rotation; SELECTION RULES; SPIN; Splitting; Symmetry; Torsion
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.4954941

This paper presents an explanation based on torsionally mediated proton-spin–overall-rotation interaction for the observation of doublet hyperfine splittings in some Lamb-dip sub-millimeter-wave transitions between ground-state torsion-rotation states of E symmetry in methanol. These unexpected doublet splittings, some as large as 70 kHz, were observed for rotational quantum numbers in the range of J = 13 to 34, and K = − 2 to +3. Because they increase nearly linearly with J for a given branch, we confined our search for an explanation to hyperfine operators containing one nuclear-spin angular momentum factor I and one overall-rotation angular momentum factor J (i.e., to spin-rotation operators) and ignored both spin-spin and spin-torsion operators, since they contain no rotational angular momentum operator. Furthermore, since traditional spin-rotation operators did not seem capable of explaining the observed splittings, we constructed totally symmetric “torsionally mediated spin-rotation operators” by multiplying the E-species spin-rotation operator by an E-species torsional-coordinate factor of the form e ±niα. The resulting operator is capable of connecting the two components of a degenerate torsion-rotation E state. This has the effect of turning the hyperfine splitting pattern upside down for some nuclear-spin states, which leads to bottom-to-top and top-to-bottom hyperfine selection rules for some transitions, and thus to an explanation for the unexpectedly large observed hyperfine splittings. The constructed operator cannot contribute to hyperfine splittings in the A-species manifold because its matrix elements within the set of torsion-rotation A1 and A2 states are all zero. The theory developed here fits the observed large doublet splittings to a root-mean-square residual of less than 1 kHz and predicts unresolvable splittings for a number of transitions in which no doublet splitting was detected.