Quantum Dynamics of Electronic Excitations in Biomolecular Chromophores: Role of the Protein Environment and Solvent

Joel Gilmore, Ross H. McKenzie

A biomolecular chromophore can be viewed as a quantum system with a small number of degrees of freedom interacting with an environment (the surrounding protein and solvent) which has many degrees of freedom, the majority of which can be described classically. The system-environment interaction can be described by a spectral density for a spin-boson model. The quantum dynamics of electronic excitations in the chromophore are completely determined by this spectral density, which is of great interest for describing quantum decoherence and quantum measurements. Specifically, the spectral density determines the time scale for the "collapse" of the wave function of the chromophore due to continuous measurement of its quantum state by the environment. Although of fundamental interest, there very few physical systems for which the spectral density has been determined experimentally and characterized. In contrast, here, we give the parameters for the spectral densities for a wide range of chromophores, proteins, and solvents. Expressions for the spectral density are derived for continuum dielectric models of the chromophore environment. There are contributions to the spectral density from each component of the environment: the protein, the water bound to the protein, and the bulk solvent. Each component affects the quantum dynamics of the chromophore on distinctly different time scales. Our results provide a natural description of the different time scales observed in ultrafast laser spectroscopy, including three pulse photon echo decay and dynamic Stokes shift measurements. We show that even if the chromophore is well separated from the solvent by the surrounding protein, ultrafast solvation can be still be dominated by the solvent. Consequently, we suggest that the subpicosecond solvation observed in some biomolecular chromophores should not necessarily be assigned to ultrafast protein dynamics. The magnitude of the chromophore-environment coupling is sufficiently strong that the quantum dynamics of electronic excitations in most chromophores at room temperature is incoherent, and the time scale for "collapse" of the wave function is typically less than 10 fs.