The unfavorable scaling of wavefunction storage severely impacts the feasibility of quantum dynamical calculations on large molecular and condensed-phase systems. 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 over the past three decades have led to rigorous and 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 path integral variables through the small matrix decomposition (SMatPI), which eliminates tensor storage, enabling the simulation of long-memory processes and multistate systems. The modular path integral (MPI) decomposition offers linear scaling with system length. These methods converge to exact, fully quantum mechanical results with any number of harmonic modes coupled to the system states, at zero or finite temperature. The quantum-classical path integral (QCPI) offers a rigorous formulation of nonadiabatic dynamics in solution or biological environments.<br/>These methods have been used to investigate the complex interplay among quantum coherence, delocalization, vibrational damping and thermal fluctuations in charge, proton, and energy transfer processes, as well as the dynamics of coupled spins. Recent work on excitation energy transfer in large molecular aggregates will be presented.

<b>Award Address </b>(ACS Award in Theoretical Chemistry sponsored by the ACS Division of Physical Chemistry). Real-time path integral methods for quantum dynamics

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Award Address (ACS Award in Theoretical Chemistry sponsored by the ACS Division of Physical Chemistry). Real-time path integral methods for quantum dynamics