Rotational and fine structure of open-shell molecules in nearly degenerate electronic states. II. Interpretation of experimentally determined interstate coupling parameters of alkoxy radicals

A combined experimental and computational study on the transition of the calcium isopropoxide radical as a candidate for direct laser cooling

Vibronically resolved laser-induced fluorescence/dispersed fluorescence (LIF/DF) and cavity ring-down (CRD) spectra of the electronic transition of the calcium isopropoxide [CaOCH(CH₃)₂] radical have been obtained under jet-cooled conditions. An essentially constant energy separation of 68 cm^-1 has been observed for the vibrational ground levels and all fundamental vibrational levels accessed in the LIF measurement. To simulate the experimental spectra and assign the recorded vibronic bands, Franck-Condon (FC) factors and vibrational branching ratios (VBRs) are predicted from vibrational modes and their frequencies calculated using the complete-active-space self-consistent field (CASSCF) and equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) methods. Combined with the calculated electronic transition energy, the computational results, especially those from the EOM-CCSD calculations, reproduced the experimental spectra with considerable accuracy. The experimental and computational results suggest that the FC matrix for the studied electronic transition is largely diagonal, but transitions from the vibrationless levels of the à state to the X̃-state levels of the CCC bending (ν₁₄ and ν₁₅), CaO stretch (ν₁₃), and CaOC asymmetric stretch (ν₉ and ν₁₁) modes also have considerable intensities. Transitions to low-frequency in-plane [ν₁₇(a')] and out-of-plane [ν₃₀(a'')] CaOC bending modes were observed in the experimental LIF/DF spectra, the latter being FC-forbidden but induced by the pseudo-Jahn-Teller (pJT) effect. Both bending modes are coupled to the CaOC asymmetric stretch mode via the Duschinsky rotation, as demonstrated in the DF spectra obtained by pumping non-origin vibronic transitions. The pJT interaction also induces transitions to the ground-state vibrational level of the ν₁₀(a') mode, which has the CaOC bending character. Our combined experimental and computational results provide critical information for future direct laser cooling of the target molecule and other alkaline earth monoalkoxide radicals.

Electronic spectroscopy of the A1̃2A''/A2̃2A'-X̃2A' transitions of jet-cooled calcium ethoxide radicals: Vibronic structure of alkaline earth monoalkoxide radicals of Cs symmetry

Laser-induced fluorescence/dispersed fluorescence (LIF/DF) and cavity ring-down spectra of the A₁̃²A^''/A₂̃²A^'-X̃²A^' electronic transition of the calcium ethoxide (CaOC₂H₅) radical have been obtained under jet-cooled conditions. An essentially constant Ã₂-Ã₁ energy separation for different vibronic levels is observed in the LIF spectrum, which is attributed to both the spin-orbit (SO) interaction and non-relativistic effects. Electronic transition energies, vibrational frequencies, and spin-vibrational eigenfunctions calculated using the coupled-cluster method, along with results from previous complete active space self-consistent field calculations, have been used to predict the vibronic energy level structure and simulate the recorded LIF/DF spectra. Although the vibrational frequencies and Franck-Condon (FC) factors calculated under the Born-Oppenheimer approximation and the harmonic oscillator approximation reproduce the dominant spectral features well, the inclusion of the pseudo-Jahn-Teller (pJT) and SO interactions, especially those between the A₁̃²A^″/A₂̃²A^' and the B̃²A^' states, induces additional vibronic transitions and significantly improves the accuracy of the spectral simulations. Notably, the spin-vibronic interactions couple vibronic levels and alter transition intensities. The calculated FC matrix for the A₁̃²A^''/A₂̃²A^'-X̃²A^' transition contains a number of off-diagonal matrix elements that connect the vibrational ground levels to the levels of the ν₈ (CO stretch), ν₁₁ (OCC bending), ν₁₂ (CaO stretch), ν₁₃ (in-plane CaOC bending), and ν₂₁ (out-of-plane CaOC bending) modes, which are used for vibrational assignments. Transitions to the ν₂₁(a″) levels are allowed due to the pJT effect. Furthermore, when LIF transitions to the Ã-state levels of the CaOC-bending modes, ν₁₃ and ν₂₁, are pumped, A₁̃²A^''/A₂̃²A^'→X̃²A^' transitions to the combination levels of these two modes with the ν₈, ν₁₁, and ν₁₂ modes are also observed in the DF spectra due to the Duschinsky mixing. Implications of the present spectroscopic investigation to laser cooling of asymmetric-top molecules are discussed.

Laser-Induced Fluorescence Spectroscopy of Large Secondary Alkoxy Radicals: Part I. Spectral Overviews and Vibronic Analysis

We report vibronically resolved laser-induced fluorescence (LIF) spectra of jet-cooled C5-C10 secondary alkoxy radicals. The LIF spectra demonstrate vibronic structures similar to smaller (C3-C4) secondary alkoxies. For 2-pentoxy and 2-hexoxy, rotationally resolved LIF spectra have also been recorded. Two types of rotational structures have been observed in vibronic bands of each molecule. Extensive quantum chemistry calculations have been performed on 2-pentoxy and 2-hexoxy. The computed results include the relative energies of conformers, their geometries, and the energy separations between the nearly degenerate à and X̃ electronic states (ΔE^Ã-X̃). Based on the similarity between the vibronic structures of different secondary alkoxies and calculated molecular parameters, including the relative energies of conformers, the B̃ ← X̃ transition frequencies, and the vibrational frequencies, strong vibronic bands in the LIF spectra are assigned to the origin bands and CO stretch bands of the two lowest-energy conformers of each secondary alkoxy radical. The distinct rotational structures of the two different conformations of 2-pentoxy and 2-hexoxy will be simulated and analyzed in Part II of this series ( J. Phys. Chem. A 2021, DOI: 10.1021/acs.jpca.0c10663).

Laser-Induced Fluorescence Spectroscopy of Large Secondary Alkoxy Radicals: Part II. Rotational and Fine Structure

Selected vibronic bands of the B̃ ← X̃ laser-induced fluorescence (LIF) spectra of jet-cooled 2-pentoxy and 2-hexoxy, including the origin and CO-stretch bands, have been measured with rotational resolution and analyzed using (1) an effective Hamiltonian that comprises a rotational part and a spin-rotation (SR) part (the "isolated-states model") and (2) a recently developed Hamiltonian in which the nearly degenerate à and X̃ states are treated together (the "coupled-states model") (see Liu, J., J. Chem. Phys. 2018, 148, 124112). The observed rotational and fine structures of the strongest vibronic bands have first been simulated using a genetic algorithm with the isolated-states model. The parameters for the simulation include rotational constants for both the X̃ and B̃ states, which can be calculated from the electronic structure theory, as well as the electronic SR constants of the X̃ state and the transition dipole moments (TDMs), both of which are predicted based on their transferability in an "orbital-fixed coordinate system" using iso-propoxy as the reference molecule. Quantum chemistry calculations suggest that the lowest two electronic (X̃ and Ã) states of secondary alkoxy radicals have small energy separations on the order of 100 cm^-1 (see Part I of this series: J. Phys. Chem. A 2021, DOI: 10.1021/acs.jpca.0c10662). The electron configurations of these two nearly degenerate states have been determined by comparing the experimentally determined rotational constants and the TDMs to the ones predicted for the X̃ and à states. The experimental LIF spectra were also simulated with the coupled-states model, in which the effective spin-orbit (SO) constants (aζ_ed) and the SO-free separation between the à and the X̃ states (ΔE₀) have been determined. Molecular constants derived from fitting the rotational and fine structures of the experimental LIF spectra enabled unambiguous assignment of the observed vibronic bands to specific conformers of 2-pentoxy and 2-hexoxy as reported in Part I.