Laser-cooling molecules relies on rapid and continuous photon scattering events that provide the “momentum kicks” that slow down molecules. Experimental implementation of laser cooling with enough photons scattered per molecule (about 10⁴ or 10⁵) requires not only a highly diagonal Franck-Condon matrix but also rotational closure. Achieving rotationally closed photon cycling in laser cooling asymmetric-top molecules is nontrivialB. L. Augenbraun, J. M. Doyle, T. Zelevinsky, and I. Kozyryev, Phys. Rev. X 10, 031022 (2020).ue to the lowered symmetry and complex intramolecular interactions, including the spin-orbit interaction and vibronic interactions. In this talk, we will discuss transition intensities between rotational energy levels of electronic states involved in laser-cooling asymmetric-top molecules, rotational branching ratios, and selection rules. Using alkaline-earth monoalkoxide radicals as examples, we will predict the rotational branching ratios using a “coupled-state model” J. Liu, J. Chem. Phys. 148, 124112 (2018).nd discuss possible pumping and re-pumping schemes.

---

Footnotes:

B. L. Augenbraun, J. M. Doyle, T. Zelevinsky, and I. Kozyryev, Phys. Rev. X 10, 031022 (2020).d J. Liu, J. Chem. Phys. 148, 124112 (2018).a

Lambda-doubling is the splitting of rotational levels that have the same quantum numbers and differ only in their parity. This phenomenon has been understood for nearly a century to be caused by an asymmetric perturbation by an energetically remote electronic state acting on otherwise degenerate rovibronic states. The terms in the Hamiltonian responsible for this perturbation are ∧H^c=−B(∧J⁺∧L⁻ + ∧J⁻∧L⁺)+(B +\frac12 A)(∧L⁺∧S⁻ + ∧L⁻∧S⁺), where ∧J^±, ∧L^± and ∧S^± are ladder operators for total, orbital, and spin angular momenta, and B and A are the rotational and spin-orbit coupling constants. The time-honored method for calculating the level-splitting is to calculate off-diagonal matrix elements of this operator that connect macroscopic terms of the form |^2S+1Λ_Ω〉_e,f, using second-order perturbation theory (the Van Vleck transformation) to determine the energy difference between states of e- and f-symmetry. We have discovered that neglect of the microscopic electronic structure of the molecule may lead to incorrect values of the level-splitting and erroneous assignment of the parity of some of the levels. The breakdown of the macroscopic method lies in its failure to recognize that the rotational component of ∧H^c contains two-electron operators, whereas the spin-orbit component is a one-electron operator. In addition, the macroscopic formulation fails to account for exchange symmetry of electrons in partially-filled spin-orbitals. We have shown that the macroscopic formulation gives correct results for inhomogeneous (Ω-changing) perturbations and fails for homogeneous (Ω-preserving) perturbations produced by the rotational part of the Hamiltonian. The breakdown is especially marked for the splitting of ²Π_\frac12 by ²Σ_\frac12^± states, for which both homogeneous and inhomogeneous perturbations are involved.

Our longstanding goal has been achieving a global fit of the ground state and seven lowest excited states of HN₃ (ν₅, ν₆, ν₄, ν₃, 2ν₅, 2ν₆, and ν₅+ν₆), all of which are strongly connected by Coriolis, anharmonic, and Darling-Dennison resonance perturbations. From the combined effort of the Wisconsin and Prague groups, we observed and assigned most of the millimeter-wave spectrum from low-frequency microwave lines up to 720 GHz. Recently, we have acquired an extensive set of infrared (IR) spectral data at the Canadian Light Source (CLS), 30-5000 cm⁻¹ at 0.0009 cm⁻¹ resolution and pressures between 1 and 100 mTorr. This data supersedes all previous IR data, in that it provides higher sensitivity (providing transitions with higher J’s and K’s) and higher frequency accuracy for all the ground and fundamental states. More importantly, it has permitted assignment of thousands of lines in about 30 subbands involving the combination and overtone states. Using linear least-squares treatments of individual subbands (Fortrat or Q-branch plots), we have so far determined absolute energies of K_a = 0-7 of 2ν₅, K_a = 2-6 of ν₅+ν₆, and K_a = 0-6 of 2ν₆, using redundant measurements from multiple subbands confirmed by combination differences with known a-type lines in the mm-wave spectrum. Several additional mm-wave series were assigned using improved predictions from the IR spectra, and several others have been reassigned. We present our current spectral analysis and progress on the implementation of an eight-state global fit.

Intramolecular hydrogen bonds are of fundamental importance in chemistry, existing in a range of systems from small medicinal molecules to the macromolecules of DNA, proteins, and plastics. The strengths of these hydrogen bonds have important consequences on the structure, and consequently the function of such chemical systems. However, the strength of intramolecular hydrogen bonds cannot be either directly measured experimentally or computed theoretically through dissociation, like those in regular intermolecular hydrogen bonds. Computational approaches, such as the rotational bond method, can approximate these energies but rely on a series of assumptions that limit their application. This work proposes a scale based on the spectral-energy relationship first studied by Badger and Bauer to estimate the strength of intramolecular hydrogen bonds from the measured experimental infrared (IR) bands of the respective vibrations. A single regression between energy and shifts in vibrational frequency was derived for hydrogen bonds incorporating O, N, and F atoms. The linear regression between energy and underlying frequency was established at the MP2/aug-cc-pVDZ and MP2/aug-cc-pVTZ levels of theory and validated at both higher levels of electron correlation (CCSD(T)) and by using experimental IR spectra and zero-point energies. Our results reproduce the intramolecular hydrogen bond energies of enolones and amino alcohols obtained by the rotational bond method within 1 kcal/mol. We subsequently used our approach to estimate the hydrogen bond strengths of a variety of systems for which the experimental frequencies for the respective intra-molecular hydrogen bonds have been reported. Our results quantify the strengthening of the hydrogen bond in amino-ethanols under fluorination by over 2 kcal/mol and yield hydrogen bond strengths of about 4 kcal/mol in helical poly-peptides, making it possible, for the first time, to quantify the strengths of these elusive interactions in systems of biological importance.

We report for the first time highly precise differential microwave spectroscopy, carried out in a cavity-enhanced buffer gas cell. We report a statistically limited differential measurement of 0.08 ±0.72 Hz between (R)- and (S)-1,2-propanediol at frequencies around 15 GHz Symmetry 2022, 14(1), 28; https://doi.org/10.3390/sym14010028 This highly repeatable measurement opens new avenues in studying molecular structure at the 10⁻¹⁰ level. We also report the coupling of a neon buffer gas beam to this cavity, reaching linewidths of 3 kHz in methyltrioxorhenium, and future modifications to reach 1.5 kHz linewidth.

---

Footnotes:

Symmetry 2022, 14(1), 28; https://doi.org/10.3390/sym14010028.

Precision molecular experiments provide a unique tool in the search for physics beyond the Standard Model (SM) and exploration of the fundamental forces of nature. Compared to atoms, certain molecules can offer more than eleven orders of magnitude enhanced sensitivity to violations of fundamental symmetries, enabling precision tests of the SM and the possibility to probe energy scales beyond hundreds of TeV. Containing octupole-deformed nuclei, radium monofluoride (RaF) is expected to be particularly sensitive to symmetry violating nuclear properties [Phys. Rev. A 82, 052521 (2010); J. Chem. Phys. 152, 044101 (2020)]. In this talk, I will present the latest results obtained from a series of laser spectroscopy experiments performed on short-lived RaF molecules at the ISOLDE facility at CERN. Using a collinear resonant ionization setup, the rotational and hyperfine structure of ²²⁶RaF and ²²⁵RaF were measured with high precision. This allowed us to establish a laser cooling scheme for these molecules, and to explore nuclear structure effects at the molecular level. Our new results represent an increase in precision of at least 3 orders of magnitude compared to our previous studies [Nature 581, 396 (2020); Phys. Rev. Lett. 127, 033001 (2021)] being the first of their kind performed on radioactive, short-lived molecules and opening the way for future precision studies and new physics searches in these systems.

Pyrazole (C₃H₃N₂, C_s) is an aromatic heterocycle consisting of a 5-membered ring molecule doubly substituted with adjacent nitrogen atoms. Searches for similar heteroaromatic compounds (imidazole, furan, etc.) have been recently conducted in the interstellar medium. This study provides the necessary transition frequencies for a search for pyrazole across the frequency range of available radiotelescopes. We have collected the mm-wave spectrum of pyrazole from 130-750 MHz, which extends the previously published microwave studies from 13 to 35 MHz. The new data greatly expand the range of rotational quantum numbers observed in the ground vibrational state rotational transitions and provide transitions for over a dozen excited vibrational states. These rotational data are simultaneously analyzed with high-resolution rotation-vibration spectra of pyrazole between 500-1300 cm⁻¹ that we have obtained at the Canadian Light Source synchrotron’s far-infrared beam line. The considerable benefits of simultaneously analyzing mm-wave and high-res IR transitions that cover the same approximate ranges of J and K will be discussed. The results provide a thorough characterization of all eight vibrationally excited states below 950 cm⁻¹, of which the highest energy states (ν₁₆, ν₁₅, and ν₁₄) form a Coriolis-coupled triad.

We have recently observed the infrared spectrum of DN₃ at a resolution of 0.0009 cm⁻¹using the synchrotron at the Canadian Light Source between 30 and 5000 cm⁻¹at several pressures between 1 and 100 mTorr. A special heavy walled stainless steel apparatus was constructed to perform the synthesis of the highly toxic and explosive substance on site in way that met the stringent safety standards of the facility. We have also measured the millimeter wave spectrum of DN₃ at Wisconsin and at Prague covering altogether the range from 130-730 GHz. We are working toward combining all this spectral data to achieve a global eight state fit with SPFIT. While the many perturbing interactions between these lowest eight vibrational states cause somewhat less dramatic shifts than the same ones do in HN₃, it remains a very challenging problem in spectroscopy. A substantial additional complication in this isotopologue though is the fact that it has proved to be impractical to obtain an isotopically pure sample of DN₃ because of facile H/D exchange on the walls of the absorption cells employed. This makes it desirable at least to assign the HN₃ spectrum first, so that the corresponding features can be eliminated from consideration in the DN₃ work.