All-Mode Quantum–Classical Path Integral Simulation of Bacteriochlorophyll Dimer Exciton-Vibration Dynamics

Abstract

We use the quantum–classical path integral (QCPI) methodology to report numerically exact, fully quantum mechanical results for the exciton-vibration dynamics in the bacteriochlorophyll dimer, including all 50 coupled vibrational normal modes of each bacteriochlorophyll explicitly with parameters obtained from spectroscopic Huang–Rhys factors. We present a coordinate transformation that maps the dimer on a spin-Boson Hamiltonian with a single collective bath. We consider two vibrational initial conditions which correspond to a Franck–Condon excitation or to modes initially equilibrated with the excited monomer. Our calculations reveal persistent, underdamped oscillations of the electronic energy between the two pigments at room temperature. Static disorder leads to additional damping, but the population dynamics remains oscillatory. The population curves exhibit atypical, nonsmooth features that arise from the complexity of the bacteriochlorophyll vibrational spectrum and which cannot be captured by simple analytical spectral density functions.