Estimation of Electron-Phonon Coupling Parameters from Low-temperature Optical Spectra

In low-temperature spectroscopy, one is often interested in learning how strongly a chromophore interacts with its host matrix * . For example, by studying dye molecules embedded in frozen solutions or glassy matrices, one can learn interesting information about the matrix itself. Of more immediate interest for us is that the interaction of chromophores with their environment can have important consequences on the electronic properties of the chromophore itself, altering its optical (absorption and emission) spectra as well as coupling and energy transfer rates between chromophores. The particular system in which we are interested is the Photosystem II (PSII) chlorophyll-protein complex, consisting of a set of chlorophyll molecules (the chromophores) embedded in a protein “matrix.” Since we are interested in understanding how PSII functions in harvesting solar energy for photosynthesis, it is important to understand how the chlorophyll molecules interact both with each other (inter-molecular coupling and energy transfer) and with their environment. Knowledge of such properties can, for example, be used to model the optical and electronic properties of photosynthetic complexes 1-3 , giving detailed insight on its function in photosynthesis. Essentially, what we are interested in here is how transitions between the eigenstates of a chromophore affect (and are affected by) the vibrational motions of the matrix. A molecule can undergo several types of eigenstate transitions: usually we are interested in vibrational transitions and electronic transitions (which involve changes in the distribution of electrons within the molecule and are much more energetic than vibrational transitions). When a molecule undergoes a transition from one eigenstate to another, its interaction with the environment can trigger changes in the vibrational eigenstates of the environment—which we call phonons—as well. Since matrix phonons and molecular vibrational transitions are of roughly similar energies, they can each induce changes in each other—a phonon interacting with the molecule can trigger vibrational transitions, and a molecular vibrational transition can cause the creation or annihilation of a matrix phonon. Because electronic transitions are much more energetic than vibrational transitions, matrix phonons are very unlikely to induce molecular electronic transitions, but a molecular electronic transition can easily create or destroy matrix phonons. This interaction is termed electron-phonon coupling, and is an important feature of low-temperature spectroscopy. Several important parameters describing electron-phonon coupling (which can be obtained by low-temperature