The Impact of Ligand Field Symmetry on Molecular Qubit Coherence

Developing quantum bits (qubits) exhibiting room temperature electron spin coherence is a key goal of molecular quantum information science. At high temperatures, coherence is often limited by electron spin relaxation, measured by T₁. Here we develop a simple and powerful model for predicting relative T₁ relaxation times in transition metal complexes from dynamic ligand field principles. By considering the excited state origins of ground state spin-phonon coupling, we derive group theory selection rules governing which vibrational symmetries can induce decoherence. Thermal weighting of the coupling terms produces surprisingly good predictions of experimental T₁ trends as a function of temperature and explains previously confounding features in spin-lattice relaxation data. We use this model to evaluate experimental relaxation rates across S = 1/2 transition metal qubit candidates with diverse structures, gaining new insights into the interplay between spin-phonon coupling and molecular symmetry. This methodology elucidates the specific vibrational modes giving rise to decoherence, providing insight into the origin of room temperature coherence in transition metal complexes. We discuss the outlook of symmetry-based modeling and design strategies for understanding molecular coherence.