Unraveling vibronic interactions in molecules functionalized with optical cycling centers

TL;DR

This work addresses vibronic interactions between closely spaced excited states in OCC-functionalized molecules and their impact on laser cooling. It combines a three-state KDC vibronic Hamiltonian, parameterized with EOM-CC calculations and quasi-diabatic NACs, with high-resolution 2D DLIF experiments on SrOPh and SrOPh-d5 to reveal A–B mixing via a higher C state. The key finding is that A–B mixing is a second-order effect mediated by C, with an effective coupling around $0.5 cm^{-1}$; isotope substitution strengthens the mixing by reducing the energy gap, enabling observable A21 33 1 features in SrOPh-d5 and validating the model. The results emphasize that non-adiabatic couplings must be incorporated to predict decay channels in complex molecules, guiding future design of OCC-based laser cooling strategies and extending to related systems like CaOPh.

Abstract

We report detailed characterization of the vibronic interactions between the first two electronically excited states, A and B, in SrOPh (Ph = phenyl, -C6H5) and its deuterated counterpart, SrOPh-d5 (-C6D5). The vibronic interactions, which arise due to non-adiabatic coupling between the two electronic states, mix the B,v0 state with the energetically close vibronic level A,v21v33, resulting in extra transition probability into the latter state. This state mixing is more prominent in the deuterated molecule because of the smaller energy gap between the interacting states. We model the mixing of the A and B states using the Koppel-Domcke-Cederbaum (KDC) Hamiltonian parametrized in the diabatic framework of Ichino, Gauss, and Stanton on the basis of equation-of-motion coupled-cluster calculations. The simulation attributes the observed mixing to a second-order effect mediated by linear quasi-diabatic couplings between the A-C and B-C states. Based on the measured spectra, we deduce an effective coupling strength of 0.5 cm-1. Non-adiabatic couplings between different electronic states is an important factor that should be considered in the design of laser-cooling protocols for complex molecules.

Figures (10)

• Figure 1: Low-lying electronic states in OCC-functionalized molecules illustrated by the Dyson orbitals in SrOH and a cartoon illustrating vibrational wavefunction overlaps between two electronic states. Reproduced from Ref. Ivanov:MFOCC:19 with permission from the Royal Society of Chemistry.
• Figure 2: Non-adiabatic coupling mixes vibrational levels from different electronic states, which are non-interacting within Born--Oppenheimer approximation. The mixed vibronic states lead to more decay pathways.
• Figure 3: Schematic illustration of molecular Hamiltonian in the adiabatic (or Born--Oppenheimer) basis, naive diabatic (here, static Born--Huang) basis, and quasi-diabatic basis. $T_N$ represents the nuclear kinetic energy operator and $H_e$ is the electronic Hamiltonian. In the quasi-diabatic basis, the states are close to the adiabatic states and the small derivative couplings remain, but the dominant couplings are now appear as off-diagonal terms in the electronic Hamiltonian. Reproduced from Ref. Stanton:EOMIPdeg:09, with the permission of AIP Publishing.
• Figure 4: SrOPh. (a) Dyson orbitals. (b) Vertical excitation energies ($E ^{(\alpha)}$ from Eq. \ref{['eq:kdc_Vdiag']}) and the linear diabatic couplings ($\lambda$ from Eq. \ref{['eq:kdc_Voff']}).
• Figure 5: Simulated absorption spectra of SrOPh and SrOPh-d$_5$. Colors denote the symmetries of the vibronic peaks: blue B$_2$, orange B$_1$, green A$_1$. The insets list the states and modes active in the simulation. The peaks are labeled as $^{S}\nu_{i}^{f}$, where $S$ denotes the electronically excited state, $v$ denotes the vibrational mode, $i$ and $f$ define the vibrational quantum number in the excited and ground electronic state. (a) Simulated spectra of SrOPh with vibronic coupling. (b) Simulated spectra of SrOPh without coupling (i.e., Franck--Condon simulation). (c) Zoomed-in version of (a) showing details of peaks resulted from the vibronic couplings. The corresponding vibrational modes are also assigned. (d) Zoomed-in version of SrOPh-d$_5$ spectra simulated with the same model. Deuteration shifts the frequency of the vibrational modes. The increased mixing is a result of smaller energy gap between the vibronically coupled states.