Multireference Density Matrix Embedding for Spin-Phonon Relaxation

Spin-phonon coupling governs magnetic relaxation in numerous systems, including single-molecule magnets and molecular spin qubits. In most cases, the accurate prediction of spin relaxation rates requires multireference electronic structure methods, but their computational cost has largely restricted such calculations to isolated molecules. Here we show that spin-phonon relaxation rates can be computed within a multireference density matrix embedding framework. We apply the approach to three cobalt- and two dysprosium-based single-molecule magnets and to a cobalt-based molecular crystal. Across all systems, treating only the first coordination sphere of the magnetic center at the multireference level reproduces spin relaxation rates in good agreement with non-embedded CASSCF calculations, while reducing the correlated problem to 10-68% of the total basis functions. Periodic calculations further demonstrate that spin relaxation rates can be computed for a molecular crystal using an embedded active space of only 259 basis functions out of a total of 2569. These results show that multireference density matrix embedding extends quantitative spin-phonon relaxation calculations from isolated molecules to molecular crystals.