Hyperfine structure in internal rotor molecules

Heuvel, J.E.M.; Dymanus, A.

doi:10.1016/0022-2852(73)90088-x

Cited by 7 publications

(22 citation statements)

References 13 publications

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“…The pair of torsional basis functions (e +iα , e −iα ), as well as the pair (e −2iα , e +2iα ), are both ( t E + , t E − ) functions transforming 14 according to Eqs. (3) and (4) above. In many fitting programs based on effective torsion-rotation Hamiltonians for methanol, the degenerate torsional eigenfunctions after a matrix diagonalization are represented by basis-set sums of the form…”

Section: Group Theory Applied To the Torsion-rotationnuclear-spin mentioning

confidence: 93%

“…We expect that spin-spin splittings (arising from the product of two nuclear spin angular momenta) 3,4 and spin-torsion splittings (arising from the product of one nuclear spin angular momentum and the torsional angular momentum) 3,4 will not increase with J value. On the other hand, spin-rotation splittings (arising from the product of one nuclear spin angular momentum and the total angular momentum) 3,4 are known to increase approximately linearly with J. We thus assume that spin-spin and spin-torsion interactions can be ignored and concentrate on selecting appropriate terms for our effective hyperfine Hamiltonian from among the group-theoretically allowed spin-rotation operators.…”

Section: A Intuitive Considerations and Experimental Findingsmentioning

confidence: 99%

“…Magnetic hyperfine coupling in a methyl group undergoing internal rotation has been discussed for methanol 3,4 and methyl formate. 15 We use here many ideas from Refs.…”

Section: Construction Of Symmetry-allowed Spin-rotation Operators mentioning

confidence: 99%

“…Hyperfine splittings in methanol were considered previously in the classic papers of Heuvel and Dymanus, 2,3 where a number of high-resolution measurements were presented, 2 and much of the necessary theory was developed. 3 A very recent paper by Coudert et al 4 uses the results of Ref. 3 to set up a rather complete hyperfine Hamiltonian formalism and to compute numerically, using modern quantum chemistry techniques, many of the hyperfine interaction parameters occurring in that Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

“…3 A very recent paper by Coudert et al 4 uses the results of Ref. 3 to set up a rather complete hyperfine Hamiltonian formalism and to compute numerically, using modern quantum chemistry techniques, many of the hyperfine interaction parameters occurring in that Hamiltonian. In addition, Coudert et al 4 carried out least-squares fits of the hyperfine splittings in 12 low-J transitions to a spin-spin, spin-rotation, and spintorsion hyperfine Hamiltonian containing a number of terms from their formalism.…”

Section: Introductionmentioning

confidence: 99%

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

Белов

Golubiatnikov

Lapinov

et al. 2016

The Journal of Chemical Physics

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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.

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Section: Group Theory Applied To the Torsion-rotationnuclear-spin mentioning

confidence: 93%

Section: A Intuitive Considerations and Experimental Findingsmentioning

confidence: 99%

“…Magnetic hyperfine coupling in a methyl group undergoing internal rotation has been discussed for methanol 3,4 and methyl formate. 15 We use here many ideas from Refs.…”

Section: Construction Of Symmetry-allowed Spin-rotation Operators mentioning

confidence: 99%