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In the context of Frenkel exciton dynamics in aggregated molecules thepolaron transformation technique facilitates a treatment where diagonalelements attributed to electronic excited-state populations are decoupled fromfluctuations associated with vibrational degrees-of-freedom. In this article wedescribe for the first time how the polaron transformation can be applied inthe context of the "Hierarchical Equations of Motion" (HEOM) technique fortreatment of open quantum systems with all vibrational components attributed toan environment. By using a generating function approach to introduce a shift inthe excited state potential energy surface, we derive hierarchical equationsfor polaron transformation in analogy to those for time propagation. Wedemonstrate the applicability of the developed approach by calculating thedynamics of underdamped and overdamped oscillators coupled to electronicexcitation of a monomer without and with previous polaron transformation andstudy the dynamics of the expectation value of the respective vibrationalcoordinates. Furthermore, we investigate the dynamics of a dimer with a barriercomparable to the thermal energy between the minima of the lower excitonicpotential energy surface. It turns out that the assumption of localization atthe monomer unit with energetically higher potential minimum, introduced viapolaron transformation, has a substantial influence on the transfer dynamics.Here, it makes a clear difference whether the polaron transformation isperformed in the local or exciton basis. This reflects the fact that thepolaron transformation only accounts for equilibration of the vibrational, butnot of the excitonic dynamics. We sketch an approach to compensate thisshortcoming in view of obtaining an initial state for the calculation ofemission spectra of molecular aggregates.

Strong Exciton-Vibrational Coupling in Molecular Assemblies. Dynamics using the Polaron Transformation in HEOM Space