Determining the key vibrations for spin relaxation in ruffled Cu(II) porphyrins via resonance Raman spectroscopy

Pinpointing vibrational mode contributions to electron spin relaxation (T-1) constitutes a key goal for developing molecular quantum bits (qubits) with long room-temperature coherence times. However, there remains no consensus to date as to the energy and symmetry of the relevant modes that drive relaxation. Here, we analyze a series of three geometrically-tunable S = 1/2 Cu(ii) porphyrins with varying degrees of ruffling distortion in the ground state. Theoretical calculations predict that increased distortion should activate low-energy ruffling modes (similar to 50 cm(-1)) for spin-phonon coupling, thereby causing faster spin relaxation in distorted porphyrins. However, experimental T-1 times do not follow the degree of ruffling, with the highly distorted copper tetraisopropylporphyrin (CuTiPP) even displaying room-temperature coherence. Local mode fitting indicates that the true vibrations dominating T-1 lie in the energy regime of bond stretches (similar to 200-300 cm(-1)), which are comparatively insensitive to the degree of ruffling. We employ resonance Raman (rR) spectroscopy to determine vibrational modes possessing both the correct energy and symmetry to drive spin-phonon coupling. The rR spectra uncover a set of mixed symmetric stretch vibrations from 200-250 cm(-1) that explain the trends in temperature-dependent T-1. These results indicate that molecular spin-phonon coupling models systematically overestimate the contribution of ultra-low-energy distortion modes to T-1, pointing out a key deficiency of existing theory. Furthermore, this work highlights the untapped power of rR spectroscopy as a tool for building spin dynamics structure-property relationships in molecular quantum information science.