Spin and Phonon Design in Modular Arrays of Molecular Qubits

The transformative applications of quantum information science (QIS) require precise design and integration of networks of qubits, the fundamental units of QIS systems. Chemical synthesis is a powerful approach, offering routes to modular, atomically precise arrangements of identical qubits. Herein, we employed the versatility of framework chemistry to investigate spin and lattice dynamics of the expanded copper(II) porphyrinic framework Zr-Cu-NU-1102 (2) possessing Cu-Cu distances of 18.0 Å. Pulse electron paramagnetic resonance spectroscopy revealed a significant reduction in relaxation processes mediated by qubit-qubit interactions compared with the more spin-dense Cu-PCN-224 (1) framework. With the reduction in the spin-spin relaxation process, phonon-mediated processes emerged as the primary driver of spin-lattice relaxation. We synthesized the isoreticular Hf-Cu-NU-1102 (3) to elucidate the impact of the nodes versus the ligands on the phonon-mediated relaxation process. Measurement of 3 revealed identical spin-lattice relaxation dynamics to 2, thereby excluding involvement of node-centered or bulk framework acoustic modes. Supported by theoretical calculations of the ligand vibrational modes, these results implicated linker-based motions as dominant contributors to phonon-mediated spin-lattice relaxation. These findings provide clear guidelines for synthetic design to control spin and phonon interactions in modular arrays of molecular qubits.