Dominant vibronic relaxation channels in a europium-based molecular qubit

Molecular spin qubits offer a versatile platform for quantum information processing due to their synthetic tunability and well-defined electronic structure. Here, a fitted-parameter-free computational framework combining density functional theory (DFT), time-dependent DFT (TD-DFT), and Redfield theory is applied to investigate the longitudinal spin-lattice relaxation time $T_1$ of the Eu nuclear spin qubit Eu(dpphen)(NO3)3. Using a single-molecule gas-phase model, the experimental long relaxation component $T_{1,\mathrm{long}} = 41.39$ s is reproduced within a factor of 1.4 (calculated: 55.88 s at 4.2 K), indicating that the slow relaxation channel is governed by intramolecular vibronic coupling. In contrast, the calculated $T_{1,\mathrm{short}}$ deviates by a factor of 66, highlighting the importance of crystal lattice and intermolecular effects absent from the model. The experimental $^5D_0 \rightarrow {}^7F_0$ optical transition is reproduced to within 1.1%, supporting the accuracy of the electronic structure description. Vibrational analysis identifies a large-amplitude dpphen rocking mode at a frequency of $332.02~\mathrm{cm}^{-1}$ as the dominant vibronic coupling channel, while electric field gradient (EFG) derivative analysis independently identifies another nitrate-rocking mode at $180.57~\mathrm{cm}^{-1}$ as the primary modulator of the nuclear spin environment via nitrate motion. These results are consistent with a near-maximal quadrupole asymmetry parameter $\eta = 0.941$, which creates state mixing through off-diagonal quadrupolar terms. Overall, the results establish a single-molecule relaxation baseline and suggest targeted ligand rigidification and substitution strategies to suppress decoherence.