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arXiv:2607.27907

A Quantum Mechanical Approach to the Computation of Rovibrational Spectra of Diatomic Molecules in Strong Magnetic Fields

Nikhil Yenugu, Ashwani K Tiwari, Sangita Sen

physics.chem-phquant-phSubmitted Jul 30, 2026• Announced Jul 31, 2026
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Abstract

In the absence of experimental data for molecular spectra in strong magnetic fields, high resolution and reliable computational spectra are required for the interpretation of spectra collected from highly magnetic astrophysical objects. In this paper, we extend the Wilson-Hamiltonian framework, recently implemented and benchmarked by us (\textit{J. Chem. Theory Comput.}, \textbf{21}, 9753 (2025) ), to a general three-dimensional framework suitable for computing the rovibrational spectra of diatomic molecules in strong uniform magnetic fields. The field-dependent electronic and nuclear Hamiltonians capture full non-perturbative coupling between particle motion and the field making the method applicable to all field strengths. The electric quadrupole transition moment integrals for rovibrational transitions in external static magnetic fields are formulated, implemented, and computed to yield spectra which respect the selection rules of the molecule-field system. The spectral changes with increasing field strength such as shifting, splitting, merging, appearance and disappearance of peaks are noted. Contributions from electrons and nuclei are studied individually, as well as in unison to reveal the underlying physics such as stiffening of the bond, emergence of a rotational barrier, field-induced coupling/decoupling of states, and symmetry-breaking in rotational and vibrational states. These results provide the first fully quantum mechanical computational results for the rovibrational signature of $^1\mathrm{H}_{2}$ in extreme magnetic field environments with accuracy suitable for experimental interpretation. The methodology developed herein has direct relevance for high-field spectroscopy and astrochemical modeling, both for providing computational data as well as for understanding the spectral impact of strong magnetic fields on electronic structure and nuclear motion in molecules.

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In the absence of experimental data for molecular spectra in strong magnetic fields, high resolution and reliable computational spectra are required for the interpretation of spectra collected from highly magnetic astrophysical objects. In this paper, we extend the Wilson-Hamiltonian framework, recently implemented and benchmarked by us (\textit{J. Chem. Theory Comput.}, \textbf{21}, 9753 (2025) ), to a general three-dimensional framework suitable for computing the rovibrational spectra of diatomic molecules in strong uniform magnetic fields. The field-dependent electronic and nuclear Hamiltonians capture full non-perturbative coupling between particle motion and the field making the method applicable to all field strengths. The electric quadrupole transition moment integrals for rovibrational transitions in external static magnetic fields are formulated, implemented, and computed to yield spectra which respect the selection rules of the molecule-field system. The spectral changes with increasing field strength such as shifting, splitting, merging, appearance and disappearance of peaks are noted. Contributions from electrons and nuclei are studied individually, as well as in unison to reveal the underlying physics such as stiffening of the bond, emergence of a rotational barrier, field-induced coupling/decoupling of states, and symmetry-breaking in rotational and vibrational states. These results provide the first fully quantum mechanical computational results for the rovibrational signature of 1H2^1\mathrm{H}_{2}1H2​ in extreme magnetic field environments with accuracy suitable for experimental interpretation. The methodology developed herein has direct relevance for high-field spectroscopy and astrochemical modeling, both for providing computational data as well as for understanding the spectral impact of strong magnetic fields on electronic structure and nuclear motion in molecules.
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.
Rovibrational energies, wave functions, and Raman transition moments are reported for the lowest-energy states of the H_{3}^{+} molecular ion including the magnetic couplings of the proton spins and molecular rotation in the presence of a weak external magnetic field. The rovibrational-hyperfine-Zeeman Hamiltonian matrix is constructed and diagonalized using the rovibrational eigenstates and the proton spin functions. The developed methodology can be used to compute hyperfine-Zeeman effects also for higher-energy rovibrational excitations of H_{3}^{+} and other closed-shell polyatomic molecules. These developments will guide future experiments extending quantum logic spectroscopy to polyatomic systems.
We use ab initio electronic-structure methods to investigate random-matrix theory (RMT) universality in molecular electronic structure. Using single-reference electronic structure methods, including Hartree-Fock, configuration-interaction singles (CIS), density functional theory, and linear-response time-dependent density-functional theory, we compute single-particle orbital energies and many-electron excitations of several representative molecules (benzene, alanine, 1-phenylethylamine, methyloxirane, and helicene chains). For generic low-symmetry geometries, the unfolded spectra of these ab initio Hamiltonians exhibit Wigner-Dyson level statistics of the Gaussian orthogonal ensemble (GOE). For extended helicene chains we explicitly restrict to bound valence excitations below the ionization threshold and still observe GOE statistics, indicating that the RMT universality is present for physical states of direct relevance to real molecules. We further explore the electric and magnetic field dependence of the molecular electronic spectra. The variance of electric polarizability (level curvature K) is predicted to be non-analytic in the magnetic field which serves as an infrared cutoff, <K^2> proportional to log(1/|B|). We observe a transition to the Gaussian unitary ensemble (GUE) by increasing the magnetic fields, although it occurs only at magnetic fields far beyond experimentally accessible scales. Our results indicate that random matrix universality provides a general framework for organizing ab initio predictions of interacting electron spectra in complex systems.
We study the translational motions of homonuclear diatomic molecules prepared in their 3Σ electronic states, deeply bound vibrational states, and rotational states of well-defined parity. The trapping potential arises due to the interaction of the total spin of electrons and orbital angular momentum of nuclei with the trap's quadrupole magnetic field. The translational motion of a molecule is treated classically. We examine the Hamilton equations that govern the center-of-mass dynamics both numerically and analytically. Using data of a hydrogen molecule at the ground vibrational state, we present global dynamics using the Poincaré section method and various types of trajectories: periodic, quasiperiodic, and chaotic. We prove that the Hamiltonian system governing this motion is non-integrable. The particle's orbits are confined to a bound region of space that grows with energy, but for small energies (<1.8 K), the motion is restricted to a processing chamber (a few centimeters). Solutions of equations of motion occurring on the symmetry axis and the horizontal plane are expressed in terms of Jacobi elliptic functions.
We investigate the impact of combined electric and magnetic fields on the structure of ultralong-range polar Rydberg molecules. Our focus is hereby on the parallel as well as the crossed field configuration, taking into account both the s -wave and p -wave interactions of the Rydberg electron and the neutral ground state atom. We show the strong impact of the p -wave interaction on the ultralong-range molecular states for a pure B -field configuration. In the presence of external fields, the angular degrees of freedom acquire vibrational character, and we encounter two- and three-dimensional oscillatory adiabatic potential energy surfaces for the parallel and crossed field configuration, respectively. The equilibrium configurations of local potential wells can be controlled via the external field parameters for both field configurations depending on the specific degree of electronic excitation. This allows us to tune the molecular alignment and orientation. The resulting electric dipole moment is in the order of several kDebye, and the rovibrational level spacings are in the range of 2– . Both properties are analyzed with varying field strengths.
We investigate single-particle energy spectra of the hydroxyl free radical (OH) in the lowest electronic and rovibrational level under combined static electric and magnetic fields, as an example of heteronuclear polar diatomic molecules. In addition to the fine-structure interactions, the hyperfine interactions and centrifugal distortion effects are taken into account to yield the zero-field spectrum of the lowest 2 Π 3 / 2 manifold to an accuracy of less than 2 kHz. We also examine level crossings and repulsions in the hyperfine structure induced by applied electric and magnetic fields. Compared to previous work, we found more than 10% reduction of the magnetic fields at level repulsions in the Zeeman spectrum subjected to a perpendicular electric field. In addition, we find new level repulsions, which we call Stark-induced hyperfine level repulsions, that require both an electric field and hyperfine structure. It is important to take into account hyperfine structure when we investigate physics of OH molecules at micro-Kelvin temperatures and below.