Multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) approach to the correlated exciton-vibrational dynamics in the FMO complex

All-DFTB Approach to the Parametrization of the System-Bath Hamiltonian Describing Exciton-Vibrational Dynamics of Molecular Assemblies

Spectral density functions are central to the simulation of complex many body systems. Their determination requires making approximations not only to the dynamics but also to the underlying electronic structure theory. Here, blending different methods bears the danger of an inconsistent description. To solve this issue we propose an all-DFTB approach to determine spectral densities for the description of Frenkel excitons in molecular assemblies. The protocol is illustrated for a model of a PTCDI crystal, which involves the calculation of monomeric excitation energies and Coulomb couplings between monomer transitions, as well as their spectral distributions due to thermal fluctuations of the nuclei. Using dynamically defined normal modes, a mapping onto the standard harmonic oscillator spectral densities is achieved.

Finite-temperature time-dependent variation with multiple Davydov states

The Dirac-Frenkel time-dependent variational approach with Davydov Ansätze is a sophisticated, yet efficient technique to obtain an accurate solution to many-body Schrödinger equations for energy and charge transfer dynamics in molecular aggregates and light-harvesting complexes. We extend this variational approach to finite temperature dynamics of the spin-boson model by adopting a Monte Carlo importance sampling method. In order to demonstrate the applicability of this approach, we compare calculated real-time quantum dynamics of the spin-boson model with that from numerically exact iterative quasiadiabatic propagator path integral (QUAPI) technique. The comparison shows that our variational approach with the single Davydov Ansätze is in excellent agreement with the QUAPI method at high temperatures, while the two differ at low temperatures. Accuracy in dynamics calculations employing a multitude of Davydov trial states is found to improve substantially over the single Davydov Ansatz, especially at low temperatures. At a moderate computational cost, our variational approach with the multiple Davydov Ansatz is shown to provide accurate spin-boson dynamics over a wide range of temperatures and bath spectral densities.

Tracing feed-back driven exciton dynamics in molecular aggregates

Excitation, exciton transport, dephasing and energy relaxation, and finally detection processes shift molecular systems into a specific superposition of quantum states causing localization, local heating and finally excitonic polaronic effects.

Quantum coherence as a witness of vibronically hot energy transfer in bacterial reaction center

Photosynthetic proteins have evolved over billions of years so as to undergo optimal energy transfer to the sites of charge separation. On the basis of spectroscopically detected quantum coherences, it has been suggested that this energy transfer is partially wavelike. This conclusion depends critically on the assignment of the coherences to the evolution of excitonic superpositions. We demonstrate that, for a bacterial reaction center protein, long-lived coherent spectroscopic oscillations, which bear canonical signatures of excitonic superpositions, are essentially vibrational excited-state coherences shifted to the ground state of the chromophores. We show that the appearance of these coherences arises from a release of electronic energy during energy transfer. Our results establish how energy migrates on vibrationally hot chromophores in the reaction center, and they call for a reexamination of claims of quantum energy transfer in photosynthesis.

Simulation of Quantum Dynamics of Excitonic Systems at Finite Temperature: an efficient method based on Thermo Field Dynamics

Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on Thermo Field Dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. The solution of Thermo Field Dynamics equations with a novel technique for the propagation of Tensor Trains (Matrix Product States) is implemented and discussed. The methodology is applied to the study of the exciton dynamics in the Fenna-Mathews-Olsen complex using a realistic structured spectral density to model the electron-phonon interaction. The results of the simulations highlight the effect of specific vibrational modes on the exciton dynamics and energy transfer process, as well as call for careful modeling of electron-phonon couplings.

Wavepacket dynamics and the multi-configurational time-dependent Hartree approach

Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.