Determining the Key Vibrations for Spin Relaxation in Ruffled Cu(II) Porphyrins via Resonance Raman Spectroscopy

Pinpointing vibrational mode contributions to electron spin relaxation (T1) 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 = ½ 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 (~50 cm-1) for spin-phonon coupling, thereby causing faster spin relaxation in distorted porphyrins. However, experimental T1 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 T1 lie in the energy regime of bond stretches (~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 T1. These results indicate that molecular spin-phonon coupling models systematically overestimate the contribution of ultra-low-energy distortion modes to T1, 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-function relationships in molecular quantum information science.