The unfavorable scaling of wavefunction storage severely impacts the feasibility of quantum dynamical calculations in the condensed phase. Feynman’s path integral formulation offers an attractive alternative, replacing wavefunctions by a sum of quantum mechanical amplitudes along all possible paths. However, the path sum involves astronomical numbers of terms, and stochastic methods are unable to deal with the oscillatory quantum phase.<br/>A series of developments have led to efficient real-time path integral methods for a variety of processes. The quasi-adiabatic propagator path integral (QuAPI) for system-bath dynamics achieves linear scaling with the number of time steps by propagating a tensor that spans the memory interval. Recent work showed that one can further disentangle the variables through the small matrix decomposition of the path integral (SMatPI), thereby allowing the simulation of long-memory processes and multistate systems. A different decomposition leads to the modular path integral (MPI) for extended systems, which also allows the inclusion of any number of finite-temperature vibrational modes and scales linearly system length. In addition to these numerically exact methods, the quantum-classical path integral (QCPI) offers a rigorous formulation of nonadiabatic dynamics in solution or biological environments.<br/>These methods are used to investigate quantum coherence and its destruction in charge, proton, and energy transfer processes in a variety of systems based on numerically exact simulations. This lecture will focus on the role of intramolecular vibrations on the excitation energy transfer in bacteriochlorophyll aggregates and the 18-unit LH2 ring, where the two electronic states and 50 vibrational modes in each molecular unit were treated explicitly at room temperature with spectroscopic parameters, and in long J-aggregates of a perylene bisimide (PBI) with 28 intramolecular vibrations per unit.

Real-time path integral dynamics of charge and exciton transfer in large systems

ACS Spring Meeting 2021

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