Controlling Spin-Vibrational Coupling and Spin Relaxation in Cu(II) Molecular Spin Qubits via Ligand Rigidity

Abstract

A clear understanding of spin relaxation is central to the design and development of molecular spin qubits. A detailed computational study of spin-vibrational coupling and spin–lattice relaxation is presented here for a series of Cu(II) complexes with varying ligand rigidity. Density functional theory combined with multireference ab initio methods establishes a direct magneto-structural correlation among the ligand framework, electronic structure, and spin relaxation dynamics. Increasing ligand stiffness from bis(N,N′-dimethyl-4-amino-3-penten-2-imine) copper(II) (1) to bis(acetylacetone)ethylenediamine copper(II) (2) and tetramethyltetraazaannulene copper(II) (3) favors a square-planar ligand field, increases the ground-state to excited-state energy gaps, and quenches spin–orbit coupling, resulting in smaller g-shifts and weaker spin-vibrational coupling. The dynamic stability of the rigid coordination environment is further verified by ab initio molecular dynamics simulations at relevant temperatures. Vibrational mode-specific analyses reveal that modes involving chelate-ring twisting and out-of-plane distortions that perturb the dxy orbital govern T1 relaxation anisotropy. These results provide a molecular-level framework for understanding spin relaxation in Cu(II) systems and establish design principles for molecular spin qubits with enhanced coherence.