Rigorous Quantum-Mechanical Modeling of Tunneling-Based Structural Changes Associated with Line Shifts in Optical Spectroscopy Experiments in Pigment–Protein Complexes

Light-induced and spontaneously occurring (in the dark) spectral shifts can be observed in a wide variety of systems where pigments are embedded in a somewhat amorphous environment, for instance, organic glasses, polymers, and proteins. They are observed directly in single-molecule spectroscopy experiments and serve as the basis for nonphotochemical spectral hole burning (NPHB). These shifts reflect small rearrangements of the local environment of the pigment that can be represented as transitions between the minima of the respective energy landscape. While methodology for determining the parameters of the energy landscapes from the results of optical spectroscopy experiments has been developed over the years, rigor has been sometimes sacrificed for the sake of clarity, and this may be the reason for the discrepancies between theories and experiments. Here, we demonstrate an application of rigorous quantum-mechanical (QM) approaches to modeling the results of single molecule (or single pigment-protein complex) spectroscopy and nonphotochemical hole burning. We employ rectangular and parabolic energy landscapes, with a linear or an angular generalized coordinate, and include phonon-assisted tunneling. Under these assumptions, the same transition rates are obtained for lower barriers and/or <i>md</i>² or moment of inertia compared with those predicted by the semiclassical model generally utilized in the analysis of NPHB data.