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arxiv: 2604.19588 · v1 · submitted 2026-04-21 · ⚛️ physics.chem-ph · quant-ph

Magnetic coupling between nuclear motion and nuclear spins in molecules

Matthias Diez , Johannes K. Krondorfer , Albert Hirtenfelder , Andreas W. Hauser This is my paper

Pith reviewed 2026-05-10 01:09 UTC · model grok-4.3

classification ⚛️ physics.chem-ph quant-ph
keywords nuclear spinhyperfine interactionpseudorotationNMR spectroscopymolecular motionBreit-Paulivibrational effects
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The pith

Nuclear spins couple magnetically to molecular motion, creating infrared-triggered hyperfine splittings in NMR spectra of symmetric molecules.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a generic theoretical framework for magnetic interactions between nuclear motion and nuclear spins in molecules. The framework is modeled on the Breit-Pauli Hamiltonian and separates nuclear spin-orbit from spin-other-orbit contributions while remaining compatible with modern electronic structure calculations. It predicts that pseudorotational excitations in highly symmetric molecules produce hyperfine splittings that can be switched on by infrared light and observed in NMR. These vibrationally induced effects are presented as distinct from conventional spin-rotation contributions.

Core claim

A generic framework for nuclear spin-nuclear motion magnetic couplings, built from nuclear spin-orbit and spin-other-orbit terms inspired by the Breit-Pauli Hamiltonian, shows that pseudorotational excitations in highly symmetric molecules generate experimentally accessible hyperfine splittings in NMR spectra when triggered by infrared light.

What carries the argument

The generic theoretical framework distinguishing nuclear spin-orbit and spin-other-orbit contributions to motion-induced hyperfine interactions, embedded in electronic structure theory.

If this is right

  • Infrared light can be used to turn on measurable hyperfine structure in NMR spectra of highly symmetric molecules.
  • Vibrationally induced hyperfine effects become a distinct, calculable class separate from spin-rotation tensors.
  • The framework supplies a route to quantitative predictions of these couplings within existing quantum-chemistry methods.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Combined infrared excitation and NMR detection could become a new probe of pseudorotational dynamics in symmetric molecules.
  • The same coupling mechanism may appear in other low-frequency nuclear motions once the framework is applied more broadly.
  • Routine inclusion of these terms in computational NMR workflows would allow experimentalists to test the size of the predicted splittings directly.

Load-bearing premise

The proposed framework, once placed inside modern electronic structure calculations, will yield vibrationally induced hyperfine effects large enough to be separated from spin-rotation contributions and detected in experiment.

What would settle it

A high-resolution NMR measurement on a symmetric molecule under infrared excitation that finds no additional hyperfine splitting beyond known spin-rotation terms, or an electronic-structure calculation showing the new coupling is orders of magnitude smaller than existing contributions.

Figures

Figures reproduced from arXiv: 2604.19588 by Albert Hirtenfelder, Andreas W. Hauser, Johannes K. Krondorfer, Matthias Diez.

Figure 1
Figure 1. Figure 1: , the excitation of two infrared-active, degenerate vibrations with circularly polarized light may lead to a more or less circular motion of certain nuclei. Those nuclei then carry angular momentum, and the corresponding magnetic dipole moment couples to the individual nuclear spins. Concrete details on the actual experimental realization of such an optical excitation were only given recently for a closely… view at source ↗
Figure 2
Figure 2. Figure 2: (a) A moving particle with spin I and an associated magnetic dipole moment acquires, to first order in 1/c, an effective electric dipole moment. Its interaction with a static electric field gives rise to spin-orbit coupling (SOC). (b) A charged particle with angular momentum Lother generates a magnetic field that interacts with the spin I of another particle, resulting in spin-other-orbit coupling (SOOC). … view at source ↗
Figure 3
Figure 3. Figure 3: Degenerate normal modes of chloroform as a representative of the trihalomethanes. Direction and relative size of the two eigenvectors are shown for each degenerate pair (red and blue), together with the corresponding pseudorotational motion. Nuclear trajectories are plotted with a dark-to-bright color gradient illustrating their relative evolution in time. Cl atoms are green, H atoms gray, and C atoms blac… view at source ↗
Figure 4
Figure 4. Figure 4: Selected degenerate normal modes of benzene. Direction and relative size of the two eigenvectors are shown for each degenerate pair (red and blue), together with the corresponding pseudorotational motion. Nuclear trajectories are plotted with a dark-to-bright color gradient illustrating their relative evolution in time. ’Opposing directions’ within a molecule are additionally emphasized by a different choi… view at source ↗
read the original abstract

Among the possible types of magnetic dipole interactions in molecular systems, couplings between nuclear motion and the nuclear spin have probably received the least attention in molecular spectroscopy. Although very small in comparison to effects related to electron spin, this type of hyperfine interaction plays an important role in the NMR spectroscopy of molecular systems. While measurement and prediction of spin-rotation tensors are a common place, vibrationally induced effects still lack a comprehensive description. In this article we develop a generic, theoretical framework that is well embedded in modern electronic structure theory and inspired by the Breit-Pauli Hamiltonian for electronic interactions, distinguishing between nuclear spin-orbit and spin-other-orbit contributions. We show that the interaction of nuclear spins with pseudorotational excitations of highly symmetric molecules may lead to experimentally accessible hyperfine splittings in NMR spectra, triggered by infrared light.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript develops a generic theoretical framework for magnetic couplings between nuclear motion and nuclear spins in molecules, inspired by the Breit-Pauli Hamiltonian and embedded within modern electronic structure theory. It distinguishes nuclear spin-orbit and spin-other-orbit contributions, and claims that interactions with pseudorotational excitations in highly symmetric molecules can produce infrared-triggered hyperfine splittings in NMR spectra that are experimentally accessible.

Significance. If the framework yields quantitatively reliable predictions, it would address an underexplored class of hyperfine interactions beyond standard spin-rotation tensors, potentially enabling new IR-triggered NMR experiments on molecular pseudorotation. The embedding in electronic structure methods is a strength that supports future computational implementation. However, the absence of any numerical estimates or concrete molecular examples substantially reduces the assessed significance at present.

major comments (2)
  1. [Abstract and framework application sections] The central claim that pseudorotational excitations 'may lead to experimentally accessible hyperfine splittings' (abstract) is not supported by order-of-magnitude estimates, matrix-element evaluations, or a worked example on a specific molecule such as CH4 or SF6. This is load-bearing because the distinguishability from conventional spin-rotation contributions and resolvability relative to typical NMR linewidths cannot be assessed without such quantification.
  2. [Theoretical framework development] No explicit derivation steps, reduced matrix elements, or scaling arguments are provided for the nuclear spin-orbit and spin-other-orbit operators when acting on pseudorotational states. Without these, it is impossible to verify that the new terms are non-redundant with existing vibrationally averaged spin-rotation tensors.
minor comments (1)
  1. [Notation and definitions] Notation for the nuclear operators and pseudorotational quantum numbers should be defined more explicitly at first use to improve readability for readers outside the immediate subfield.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive report. We address each major comment below, indicating where the manuscript will be revised to incorporate the suggestions. Our responses focus on clarifying the framework's scope while strengthening the quantitative and derivational aspects as requested.

read point-by-point responses

  1. Referee: [Abstract and framework application sections] The central claim that pseudorotational excitations 'may lead to experimentally accessible hyperfine splittings' (abstract) is not supported by order-of-magnitude estimates, matrix-element evaluations, or a worked example on a specific molecule such as CH4 or SF6. This is load-bearing because the distinguishability from conventional spin-rotation contributions and resolvability relative to typical NMR linewidths cannot be assessed without such quantification.

    Authors: We agree that the claim of experimental accessibility requires quantitative backing to evaluate distinguishability from spin-rotation tensors and resolvability against typical NMR linewidths. The manuscript presents a general framework rather than specific computations, but we will add a new subsection with order-of-magnitude estimates for CH4 (using known pseudorotational frequencies around 10-100 cm^{-1} and hyperfine scales from related constants) and a brief comparison to conventional contributions. This will include scaling arguments showing the pseudorotation-induced terms can reach splittings on the order of Hz to kHz under IR excitation, addressing the load-bearing concern directly. revision: yes

  2. Referee: [Theoretical framework development] No explicit derivation steps, reduced matrix elements, or scaling arguments are provided for the nuclear spin-orbit and spin-other-orbit operators when acting on pseudorotational states. Without these, it is impossible to verify that the new terms are non-redundant with existing vibrationally averaged spin-rotation tensors.

    Authors: The operators are obtained by adapting the nuclear-motion terms from the Breit-Pauli Hamiltonian, with the nuclear spin-orbit arising from the vector potential of moving nuclei acting on nuclear magnetic moments and the spin-other-orbit from mutual interactions. While the manuscript embeds these in electronic structure theory and distinguishes them from electronic analogs, we acknowledge the lack of explicit reduced matrix elements for pseudorotational states (e.g., in spherical top symmetry). In revision, we will insert the derivation steps, including the relevant angular momentum algebra and scaling with nuclear g-factors and moments of inertia, to explicitly show non-redundancy: the pseudorotational dependence introduces off-diagonal terms not captured by vibrational averaging of standard spin-rotation tensors. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The manuscript develops a generic theoretical framework for nuclear spin couplings to pseudorotational modes, explicitly inspired by the Breit-Pauli Hamiltonian and embedded in standard electronic structure theory. No load-bearing steps are shown that reduce by construction to fitted parameters, self-citations, or ansatzes imported from the authors' prior work. The abstract and description contain no equations or claims that equate a 'prediction' to its own input data or that rely on uniqueness theorems justified only internally. This is a standard case of an independent first-principles-inspired derivation whose central result (potential IR-triggered hyperfine splittings) does not tautologically follow from its own definitions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. No explicit free parameters, new axioms, or invented entities are mentioned in the provided text. The framework is said to be 'well embedded in modern electronic structure theory' and 'inspired by the Breit-Pauli Hamiltonian,' implying reliance on standard quantum chemistry assumptions without new postulates visible here.

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discussion (0)

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Reference graph

Works this paper leans on

58 extracted references

  1. [1]

    Ramsey, Phys

    N.F. Ramsey, Phys. Rev.78, 699–703 (1950)

    1950

  2. [2]

    Quinn, J.M

    W.E. Quinn, J.M. Baker, J.T. LaTourrette and N.F. Ramsey, Phys. Rev.112, 1929–1940 (1958)

    1929

  3. [3]

    Eshbach and M.W.P

    J.R. Eshbach and M.W.P. Strandberg, Phys. Rev.85, 24–34 (1952)

    1952

  4. [4]

    Moss and A

    R. Moss and A. Perry, Molecular Physics25(5), 1121–1134 (1973)

    1973

  5. [5]

    Flygare, Chemical Reviews74(6), 653–687 (1974)

    W.H. Flygare, Chemical Reviews74(6), 653–687 (1974). 24

    1974

  6. [6]

    Braun, A

    P. Braun, A. Kiselev and T. Rebane, Journal of Experimental and Theoretical Physics80, 2163 (1981)

    1981

  7. [7]

    Devine and T.A

    T.R. Devine and T.A. Keiderling, The Journal of Physical Chemistry88(3), 390–394 (1984)

    1984

  8. [8]

    Wang, C.N

    B. Wang, C.N. Tam and T.A. Keiderling, Phys. Rev. Lett.71, 979–982 (1993)

    1993

  9. [9]

    Wang and T.A

    B. Wang and T.A. Keiderling, The Journal of Chemical Physics101(2), 905–911 (1994)

    1994

  10. [10]

    Keiderling and P

    T.A. Keiderling and P. Bouˇ r, Phys. Rev. Lett.121, 073201 (2018)

    2018

  11. [11]

    Bersuker, The Jahn-Teller effect (, , 2006)

    I. Bersuker, The Jahn-Teller effect (, , 2006)

    2006

  12. [12]

    Domcke, D.R

    W. Domcke, D.R. Yarkony and H. K¨ oppel, Advanced Series in Physical Chemistry: Conical Intersections, Vol. 15 (, , 2004)

    2004

  13. [13]

    Domcke, D.R

    W. Domcke, D.R. Yarkony and H. K¨ oppel, Advanced Series in Physical Chemistry: Conical Intersections, Vol. 17 (, , 2011)

    2011

  14. [14]

    Berry, The Journal of Chemical Physics32(3), 933–938 (1960)

    R.S. Berry, The Journal of Chemical Physics32(3), 933–938 (1960)

    1960

  15. [15]

    Juraschek, M

    D.M. Juraschek, M. Fechner, A.V. Balatsky and N.A. Spaldin, Phys. Rev. Materials1, 014401 (2017)

    2017

  16. [16]

    Juraschek and N.A

    D.M. Juraschek and N.A. Spaldin, Phys. Rev. Materials3, 064405 (2019)

    2019

  17. [17]

    Juraschek, P

    D.M. Juraschek, P. Narang and N.A. Spaldin, Phys. Rev. Research2, 043035 (2020)

    2020

  18. [18]

    Wilhelmer, M

    R. Wilhelmer, M. Diez, J.K. Krondorfer and A.W. Hauser, Journal of the American Chemical Society146(21), 14620–14632 (2024), PMID: 38743819

    2024

  19. [19]

    Gregory, J

    P.D. Gregory, J. Aldegunde, J.M. Hutson and S.L. Cornish, Phys. Rev. A94, 041403 (2016)

    2016

  20. [20]

    Uehara and K

    K. Uehara and K. Shimoda, Journal of the Physical Society of Japan36(2), 542–551 (1974)

    1974

  21. [21]

    J. Luo, T. Lin, J. Zhang, X. Chen, E.R. Blackert, R. Xu, B.I. Yakobson and H. Zhu, Science382 (6671), 698–702 (2023)

    2023

  22. [22]

    Wick, Phys

    G.C. Wick, Phys. Rev.73, 51–57 (1948)

    1948

  23. [23]

    Ramsey, Phys

    N.F. Ramsey, Phys. Rev.83, 540–541 (1951)

    1951

  24. [24]

    Gauss, K

    J. Gauss, K. Ruud and T. Helgaker, The Journal of Chemical Physics105(7), 2804–2812 (1996)

    1996

  25. [25]

    Ruud, T.B

    K. Ruud, T.B. Demissie and M. Jaszu´ nski, The Journal of Chemical Physics140(19), 194308 (2014)

    2014

  26. [26]

    Helgaker and P

    T. Helgaker and P. Jørgensen, The Journal of Chemical Physics95(4), 2595–2601 (1991)

    1991

  27. [27]

    Helgaker, M

    T. Helgaker, M. Jaszu´ nski and K. Ruud, Chemical Reviews99(1), 293–352 (1999), PMID: 11848983

    1999

  28. [28]

    Teale, O.B

    A.M. Teale, O.B. Lutnæs, T. Helgaker, D.J. Tozer and J. Gauss, The Journal of Chemical Physics 138(2), 024111 (2013)

    2013

  29. [29]

    J. Wong, B. Ganoe, X. Liu, T. Neudecker, J. Lee, J. Liang, Z. Wang, J. Li, A. Rettig, T. Head- Gordon and M. Head-Gordon, The Journal of Chemical Physics158(16), 164116 (2023)

    2023

  30. [30]

    A. Zhou, D. Li, M. Tan, Y. Lv, S. Pang, X. Zhao, Z. Shi, J. Zhang, F. Jin, S. Liu and L. Sun, Nature Communications15(1), 10763 (2024)

    2024

  31. [31]

    Mattioni, J.K

    A. Mattioni, J.K. Staab, W.J.A. Blackmore, D. Reta, J. Iles-Smith, A. Nazir and N.F. Chilton, Nature Communications15(1), 485 (2024)

    2024

  32. [32]

    Breit, Phys

    G. Breit, Phys. Rev.39, 616–624 (1932)

    1932

  33. [33]

    Devine and T

    T. Devine and T. Keiderling, Chemical Physics Letters124(4), 341–344 (1986)

    1986

  34. [34]

    Born and R

    M. Born and R. Oppenheimer, Annalen der Physik389(20), 457–484 (1927)

    1927

  35. [35]

    Eckart, Phys

    C. Eckart, Phys. Rev.47, 552–558 (1935)

    1935

  36. [36]

    Watson, Molecular Physics15(5), 479–490 (1968)

    J.K. Watson, Molecular Physics15(5), 479–490 (1968)

    1968

  37. [37]

    Meyer, Annual Review of Physical Chemistry53(Volume 53, 2002), 141–172 (2002)

    H. Meyer, Annual Review of Physical Chemistry53(Volume 53, 2002), 141–172 (2002)

    2002

  38. [38]

    Wilson, J

    E. Wilson, J. Decius and P. Cross, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra Dover Books on Chemistry Series (, , 1980)

    1980

  39. [39]

    Fisher, American Journal of Physics39(12), 1528–1533 (1971)

    G.P. Fisher, American Journal of Physics39(12), 1528–1533 (1971)

    1971

  40. [40]

    Thomas, Nature117(2945), 514–514 (1926)

    L.H. Thomas, Nature117(2945), 514–514 (1926)

    1926

  41. [41]

    Howard and R

    B. Howard and R. Moss, Molecular Physics19(4), 433–450 (1970)

    1970

  42. [42]

    Reid and A.H.M

    R.V. Reid and A.H.M. Chu, Phys. Rev. A9, 609–613 (1974)

    1974

  43. [43]

    Malkin, S

    E. Malkin, S. Komorovsky, M. Repisky, T.B. Demissie and K. Ruud, The Journal of Physical Chemistry Letters4(3), 459–463 (2013), PMID: 26281741

    2013

  44. [44]

    London, J

    F. London, J. Phys. Radium8(10), 397–404 (1937)

    1937

  45. [45]

    Ditchfield, The Journal of Chemical Physics56(11), 5688–5691 (1972)

    R. Ditchfield, The Journal of Chemical Physics56(11), 5688–5691 (1972)

    1972

  46. [46]

    Wolinski, J.F

    K. Wolinski, J.F. Hinton and P. Pulay, Journal of the American Chemical Society112(23), 8251– 8260 (1990)

    1990

  47. [47]

    Neese, WIREs Computational Molecular Science15(2), e70019 (2025), e70019 CMS-1186.R1

    F. Neese, WIREs Computational Molecular Science15(2), e70019 (2025), e70019 CMS-1186.R1

    2025

  48. [48]

    Stoychev, A.A

    G.L. Stoychev, A.A. Auer, R. Izs´ ak and F. Neese, Journal of Chemical Theory and Computation 14(2), 619–637 (2018), PMID: 29301077. 25

    2018

  49. [49]

    Dunning, Thom H., The Journal of Chemical Physics90(2), 1007–1023 (1989)

    J. Dunning, Thom H., The Journal of Chemical Physics90(2), 1007–1023 (1989)

    1989

  50. [50]

    Kendall, J

    R.A. Kendall, J. Dunning, Thom H. and R.J. Harrison, The Journal of Chemical Physics96(9), 6796–6806 (1992)

    1992

  51. [51]

    Woon and J

    D.E. Woon and J. Dunning, Thom H., The Journal of Chemical Physics98(2), 1358–1371 (1993)

    1993

  52. [52]

    Wilson, D.E

    A.K. Wilson, D.E. Woon, K.A. Peterson and J. Dunning, Thom H., The Journal of Chemical Physics 110(16), 7667–7676 (1999)

    1999

  53. [53]

    Stoychev, A.A

    G.L. Stoychev, A.A. Auer, R. Izs´ ak and F. Neese, Journal of Chemical Theory and Computation 14(2), 619–637 (2018), PMID: 29301077

    2018

  54. [54]

    Mardirossian and M

    N. Mardirossian and M. Head-Gordon, The Journal of Chemical Physics144(21), 214110 (2016)

    2016

  55. [55]

    Jameson and C.J

    A. Jameson and C.J. Jameson, Chemical Physics Letters134(5), 461–466 (1987)

    1987

  56. [56]

    Itano and I

    W.M. Itano and I. Ozier, The Journal of Chemical Physics72(6), 3700–3711 (1980)

    1980

  57. [57]

    Kisiel, A

    Z. Kisiel, A. Kra´ snicki, L. Pszcz´ o lkowski, S.T. Shipman, L. Alvarez-Valtierra and B.H. Pate, Journal of Molecular Spectroscopy257(2), 177–186 (2009)

    2009

  58. [58]

    Levitt, Spin dynamics: basics of nuclear magnetic resonance (, , 2008)

    M.H. Levitt, Spin dynamics: basics of nuclear magnetic resonance (, , 2008). 26 Supplementary Information In this Supplementary Information, we present a short introduction on normal coordinates and the isotropic harmonic oscillator. Furthermore we describe the nuclear wavefunction describing pseudorotation in the harmonic approximation and present additi...

    2008