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At temperatures approaching absolute zero, atomic and molecular interactions are dominated by quantum effects. Cold (T<1 K) and ultracold (T<1 mK) atoms and molecules play central roles in low-temperature chemistry, precision tests of fundamental physics, quantum information, and quantum computation. Compared with atoms, molecules possess richer internal structure arising from reduced symmetry and from their rotational and vibrational degrees of freedom. This complexity enables a wide range of applications unique to (ultra)cold molecules. In particular, nearly degenerate states that are ubiquitous in open-shell molecules (free radicals) greatly enhance their sensitivity to extremely weak perturbations. As a result, high-resolution, high-precision spectra of (ultra)cold molecules provide exquisite probes for searches for new physical phenomena and for understanding low-temperature chemistry and physics. [1,2]

To fully exploit these opportunities, more detailed investigation and quantitative understanding of spin-rovibronic (spin-rotational-vibrational-electronic) energy levels and transition intensities through both laser spectroscopy and first-principles calculations are essential. [3,4] Recently, our group and collaborators have completed the first quantitative spin-vibronic analyses of the lowest electronic states of nonlinear alkaline-earth monoalkoxide (MOR) radicals, including calcium methoxide (CaOCH₃), [5] calcium ethoxide (CaOC₂H₅), [6] and calcium isopropoxide (CaOCH(CH₃)₂), [7] all of which have been proposed as candidates for laser cooling - a versatile approach to producing cold molecules. Experimentally, we recorded laser-induced fluorescence/dispersed fluorescence (LIF/DF) and cavity ring-down (CRD) spectra of theÃ-X̃electronic transitions of these radicals under jet-cooled conditions. Spin-orbit (SO) and vibronic (vibrational-electronic) interactions were quantified with the assistance of complete active space self-consistent field (CASSCF) and coupled-cluster (CC) calculations. Experimental transition intensities enabled accurate determination of vibrational branching ratios (VBRs), which inform the design of laser-cooling schemes and allow predictions of cooling efficiencies. Furthermore, we developed two spectroscopic models to predict (i) the spin-vibronic structure and VBRs [8] and (ii) the rotational and fine structure and the corresponding rotational branching ratios (RBRs). [9] Finally, I will present our ongoing efforts to achieve more accurate prediction and measurement of VBRs and RBRs of candidate molecules for laser cooling.

[1] J. Mol. Spectrosc. 300, 1 (2014).
[2] ChemPhysChem 17, 3581 (2016).
[3] Contemp. Phys. 59, 356 (2018).
[4] Science, 369, 1366 (2020).
[5] J. Chem. Phys. 151, 134303 (2019).
[6] J. Chem. Phys. 155, 024301 (2021).
[7] Phys. Chem. Chem. Phys. 24, 8749 (2022).
[8] Int. Rev. Phys. Chem.40, 165 (2021).
[9] J. Chem. Phys. 148, 124112 (2018).