Energy Gap Fluctuations Research Articles

Spin-wave resonance frequency and quantum fluctuation of the (anti)ferri-(anti)ferrimagnetic double-layer superlattice

The Hamiltonian of a four-sublattice simple cubic superlattice was solved by applying the linear spin-wave theory and the retarded Green's function technique. This study focused on the spin-wave resonance frequency, energy gap, sublattice magnetization, and quantum fluctuations of the system. The results show that the spin quantum number, interlayer (intralayer) exchange couplings, and intralayer anisotropy have a significant influence. In the ground state, the magnetizations of the sublattices are smaller than their spin quantum numbers, indicating the existence of quantum zero-point vibrations in the (anti)ferrimagnetic-(anti)ferrimagnetic bilayer system.

From Coherence to Function: Exploring the Connection in Chemical Systems.

ConspectusThe role of quantum mechanical coherences or coherent superposition states in excited state processes has received considerable attention in the last two decades largely due to advancements in ultrafast laser spectroscopy. These coherence effects hold promise for enhancing the efficiency and robustness of functionally relevant processes, even when confronted with energy disorder and environmental fluctuations. Understanding coherence deeply drives us to unravel mechanisms and dynamics controlled by order and synchronization at a quantum mechanical level, envisioning optical control of coherence to enhance functions or create new ones in molecular and material systems. In this frontier, the interplay between electronic and vibrational dynamics, specifically the influence of vibrations in directing electronic dynamics, has emerged as the leading principle. Here, two energetically disparate quantum degrees of freedom work in-sync to dictate the trajectory of an excited state reaction. Moreover, with the vibrational degree being directly related to the structural composition of molecular or material systems, new molecular designs could be inspired by tailoring certain structural elements.In the realm of chemical kinetics, our understanding of the dynamics of chemical transformations is underpinned by fundamental theories, such as transition state theory, activated rate theory, and Marcus theory. These theories elucidate reaction rates by considering the energy barriers that must be overcome for reactants to transform into products. Those barriers are surmounted by the stochastic nature of energy gap fluctuations within reacting systems, emphasizing that the reaction coordinate, the pathway from reactants to products, is not rigidly defined by a specific vibrational motion but encompasses a diverse array of molecular motions. While less is known about the involvement of specific intramolecular vibrational modes, their significance in certain cases cannot be overlooked.In this Account, we summarize key experimental findings that offer deeper insights into the complex electronic-vibrational trajectories encompassing excited states afforded from state-of-the-art ultrafast laser spectroscopy in three exemplary processes: photoinduced electron transfer, singlet-triplet intersystem crossing, and intramolecular vibrational energy flow in molecular systems. We delve into the rapid decoherence, or loss of phase and amplitude correlations, of vibrational coherences along promoter vibrations during subpicosecond intersystem crossing dynamics in a series of binuclear platinum complexes. This rapid decoherence illustrates the vibration-driven reactive pathways from the Franck-Condon state to the curve crossing region. We also explore the generation of new vibrational coherences induced by impulsive reaction dynamics rather than by the laser pulse in these systems, which sheds light on specific energy dissipation pathways and thereby on the progression of the reaction trajectory in the vicinity of the curve crossing on the product side. Another property of vibrational coherences, amplitude, reveals how energy can flow from one vibration to another in the electronic excited state of a terpyridine-molybdenum complex hosting a nonreactive dinitrogen substrate. A slight change in vibrational energy triggers a quasi-resonant interaction, leading to constructive wavepacket interference and ultimately intramolecular vibrational redistribution from a Franck-Condon active terpyridine vibration to a dinitrogen stretching vibration, energizing the dinitrogen bond.

Axial H-Bonding Solvent Controls Inhomogeneous Spectral Broadening, While Peripheral H-Bonding Solvent Controls Vibronic Broadening: Cresyl Violet in Methanol.

The dynamics of the nuclei of both a chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both force field and ab initio molecular dynamics trajectories along with the inclusion of only certain solvent molecules in the excited-state calculations, we determine that the methanol molecules axial to the chromophore are responsible for the majority of inhomogeneous broadening, with a single methanol molecule that forms an axial hydrogen bond dominating the response. The strong peripheral hydrogen bonds do not contribute to spectral broadening, as they are very stable throughout the dynamics and do not lead to increased energy-gap fluctuations. We also find that treating the strong peripheral hydrogen bonds as molecular mechanical point charges during the molecular dynamics simulation underestimates the vibronic coupling. Including these peripheral hydrogen bonding methanol molecules in the quantum-mechanical region in a geometry optimization increases the vibronic coupling, suggesting that a more advanced treatment of these strongly interacting solvent molecules during the molecular dynamics trajectory may be necessary to capture the full vibronic spectral broadening.

Dynamic embedding of effective harmonic normal mode vibrations in all-atomistic energy gap fluctuations: Case study of light harvesting 2 complex.

Environmental effects in excitation energy transfer have mostly been modeled by baths of harmonic oscillators, but to what extent such modeling provides a reliable description of actual interactions between molecular systems and environments remains an open issue. We address this issue by investigating fluctuations in the excitation energies of the light harvesting 2 complex using a realistic all-atomistic simulation of the potential energy surface. Our analyses reveal that molecular motions exhibit significant anharmonic features, even for underdamped intramolecular vibrations. In particular, we find that the anharmonicity contributes to the broadening of spectral densities and substantial overlaps between neighboring peaks, which complicates the meaning of mode frequencies constituting a bath model. Thus, we develop a strategy to construct a minimally underdamped harmonic bath that has a clear connection to all-atomistic dynamics by utilizing actual normal modes of molecules but optimizing their frequencies such that the resulting bath model can best reproduce the all-atomistic simulation results. By subtracting the underdamped contribution from the entire fluctuations, we also show that identifying a residual spectral density representing all other contributions with overdamped behavior is possible. We find that this can be fitted well with a well-established analytic form of a spectral density function or, alternatively, modeled as explicit time dependent fluctuations with muti-exponential or power law type correlation functions. We provide an assessment and the implications of these possibilities. The approach presented here can also serve as a general strategy to construct a simplified bath model that can effectively represent the underlying all-atomistic bath dynamics.

Taming the third order cumulant approximation to linear optical spectroscopy.

The second order cumulant method offers a promising pathway to predicting optical properties in condensed phase systems. It allows for the computation of linear absorption spectra from excitation energy fluctuations sampled along molecular dynamics (MD) trajectories, fully accounting for vibronic effects, direct solute-solvent interactions, and environmental polarization effects. However, the second order cumulant approximation only guarantees accurate line shapes for energy gap fluctuations obeying Gaussian statistics. A third order correction has recently been derived but often yields unphysical spectra or divergent line shapes for moderately non-Gaussian fluctuations due to the neglect of higher order terms in the cumulant expansion. In this work, we develop a corrected cumulant approach, where the collective effect of neglected higher order contributions is approximately accounted for through a dampening factor applied to the third order cumulant term. We show that this dampening factor can be expressed as a function of the skewness and kurtosis of energy gap fluctuations and can be parameterized from a large set of randomly sampled model Hamiltonians for which exact spectral line shapes are known. This approach is shown to systematically remove unphysical contributions in the form of negative absorbances from cumulant spectra in both model Hamiltonians and condensed phase systems sampled from MD and dramatically improves over the second order cumulant method in describing systems exhibiting Duschinsky mode mixing effects. We successfully apply the approach to the coumarin-153 dye in toluene, obtaining excellent agreement with experiment.

Beyond the Condon limit: Condensed phase optical spectra from atomistic simulations.

While dark transitions made bright by molecular motions determine the optoelectronic properties of many materials, simulating such non-Condon effects in condensed phase spectroscopy remains a fundamental challenge. We derive a Gaussian theory to predict and analyze condensed phase optical spectra beyond the Condon limit. Our theory introduces novel quantities that encode how nuclear motions modulate the energy gap and transition dipole of electronic transitions in the form of spectral densities. By formulating the theory through a statistical framework of thermal averages and fluctuations, we circumvent the limitations of widely used microscopically harmonic theories, allowing us to tackle systems with generally anharmonic atomistic interactions and non-Condon fluctuations of arbitrary strength. We show how to calculate these spectral densities using first-principles simulations, capturing realistic molecular interactions and incorporating finite-temperature, disorder, and dynamical effects. Our theory accurately predicts the spectra of systems known to exhibit strong non-Condon effects (phenolate in various solvents) and reveals distinct mechanisms for electronic peak splitting: timescale separation of modes that tune non-Condon effects and spectral interference from correlated energy gap and transition dipole fluctuations. We further introduce analysis tools to identify how intramolecular vibrations, solute-solvent interactions, and environmental polarization effects impact dark transitions. Moreover, we prove an upper bound on the strength of cross correlated energy gap and transition dipole fluctuations, thereby elucidating a simple condition that a system must follow for our theory to accurately predict its spectrum.

Influence of non-adiabatic effects on linear absorption spectra in the condensed phase: Methylene blue.

Modeling linear absorption spectra of solvated chromophores is highly challenging as contributions are present both from coupling of the electronic states to nuclear vibrations and from solute-solvent interactions. In systems where excited states intersect in the Condon region, significant non-adiabatic contributions to absorption line shapes can also be observed. Here, we introduce a robust approach to model linear absorption spectra accounting for both environmental and non-adiabatic effects from first principles. This model parameterizes a linear vibronic coupling (LVC) Hamiltonian directly from energy gap fluctuations calculated along molecular dynamics (MD) trajectories of the chromophore in solution, accounting for both anharmonicity in the potential and direct solute-solvent interactions. The resulting system dynamics described by the LVC Hamiltonian are solved exactly using the thermalized time-evolving density operator with orthogonal polynomials algorithm (T-TEDOPA). The approach is applied to the linear absorption spectrum of methylene blue in water. We show that the strong shoulder in the experimental spectrum is caused by vibrationally driven population transfer between the bright S1 and the dark S2 states. The treatment of the solvent environment is one of many factors that strongly influence the population transfer and line shape; accurate modeling can only be achieved through the use of explicit quantum mechanical solvation. The efficiency of T-TEDOPA, combined with LVC Hamiltonian parameterizations from MD, leads to an attractive method for describing a large variety of systems in complex environments from first principles.

Spectral Diffusion of Excitons in 3,4,9,10-Perylenetetracarboxylic-diimide (PTCDI) Thin Films.

In this work, we study spectral diffusion of molecular excitons in thin films of 3,4,9,10-perylenetetracarboxylic-diimide by using two-dimensional electronic spectroscopy (2DES). Temperature dependence of the spectral diffusion is studied from 105 to 471 K by analyzing the center line slope (CLS) of the ground-state bleach in the 2DES signal. A significant acceleration of the decay of the CLS with increasing the temperature is observed, which cannot be explained by a linear system-bath coupling model with a harmonic bath. We propose an anharmonic coupling model as the underlying mechanism, in which the exciton energy gap fluctuations by a high-frequency intramolecular vibration are enhanced by coupling with a low-frequency phonon mode.

Enhanced Exciton Quantum Coherence in Single CsPbBr3 Perovskite Quantum Dots using Femtosecond Two-Photon Near-Field Scanning Optical Microscopy.

Cesium-halide perovskite quantum dots (QDs) have gained tremendous interest as quantum emitters in quantum information processing applications due to their optical and photophysical properties. However, engineering excitonic states in quantum dots requires a deep knowledge of the coherent dynamics of their excitons at a single-particle level. Here, we use femtosecond time-resolved two-photon near-field scanning optical microscopy (NSOM) to reveal coherences involving a single cesium lead bromide perovskite QD (CsPbBr3) at room temperature. We show that, compared to other nonperovskite nanoparticles, the electronic coherence on a single perovskite QD has a relatively long lifetime of ca. 150 fs, whereas CdSe QDs have exciton coherence times shorter than 75 fs at room temperature. One possible explanation for the longer coherence time observed for the CsPbBr3 perovskite system is related to the exciton fine structure of these perovskite QDs compared to other nanoparticles. These perovskite QDs exhibit interesting optical properties that differ from those of the traditional QDs including bright triplet exciton states. In fact, due to the small amplitude of the energy gap fluctuations of dipole-allowed triplet states in perovskite QDs, the coherent superposition could be preserved for longer times. Furthermore, single-particle excitation approach implemented in this work allows us to remove effects of heterogeneity that are usually present in ensemble averaging experiments at room temperature. The realization of quantum-mechanical phase-coherence of a charge carrier that can operate at room temperature is an issue of great importance for the potential application of coherent electronic phenomena in electronic and optoelectronic devices. These interesting findings provide further evidence of the great potential of these perovskite QDs as candidates for quantum computing and information processing applications.

Anomalous Temperature Dependence of Exciton Spectral Diffusion in Tetracene Thin Film.

In this work, an ultrafast spectral diffusion of the lowest exciton in a tetracene ultrathin film is studied by two-dimensional electronic spectroscopy. From the analysis of the nodal line slope, the frequency-fluctuation correlation function (FFCF) of the exciton band is extracted. The FFCF contains two components with decay times of 400 and 80 fs; while the former can be understood by a linear exciton-phonon coupling model, the latter shows an order of magnitude increase in its amplitude from 96 to 186 K that cannot be explained by the same model. A novel scheme of the energy-gap fluctuations is examined, in which an intramolecular high-frequency mode causes the spectral diffusion that is enhanced through an anharmonic coupling to low-frequency phonon modes. This finding provides a valuable input for future theoretical predictions on the ultrafast nonadiabatic dynamics of the molecular exciton.

Ergodicity Breaking in Thermal Biological Electron Transfer? Cytochrome C Revisited II

It was recently suggested that cytochrome c operates in an ergodicity-breaking regime characterized by unusually large energy gap thermal fluctuations and associated reorganization free energies for heme oxidation of up to 3.0 eV. The large fluctuations were reported to lower activation free energy for oxidation of the heme cofactor by almost a factor of 2 compared to the case where ergodicity is maintained. Our group has recently investigated this claim computationally at several levels of theory and found no evidence for such large energy gap fluctuations. Here we address the points of our earlier work that have raised criticism and we also extend our previous investigation by considering a simple linear polarizability model for cytochrome c oxidation. We find very consistent results among all our computational approaches, ranging from classical molecular dynamics, to the linear polarizability model to QM(PMM)/MM to full QM(DFT)/MM electrostatic emdedding. None of them support the notion of very large energy gap fluctuations or ergodicity breaking. The deviation between our simulations and the ones reported in [ J. Phys. Chem. B 2017, 121, 4958] is traced back to rather large electric fields at the Fe site of the heme c cofactor in that study, not seen in our simulations, neither with the AMBER nor with the CHARMM force field. While ergodicity breaking effects may well occur in other biological ET, our numerical evidence suggests that this is not the case for cytochrome c.

Optical spectra in the condensed phase: Capturing anharmonic and vibronic features using dynamic and static approaches.

Simulating optical spectra in the condensed phase remains a challenge for theory due to the need to capture spectral signatures arising from anharmonicity and dynamical effects, such as vibronic progressions and asymmetry. As such, numerous simulation methods have been developed that invoke different approximations and vary in their ability to capture different physical regimes. Here, we use several models of chromophores in the condensed phase and ab initio molecular dynamics simulations to rigorously assess the applicability of methods to simulate optical absorption spectra. Specifically, we focus on the ensemble scheme, which can address anharmonic potential energy surfaces but relies on the applicability of extreme nuclear-electronic time scale separation; the Franck-Condon method, which includes dynamical effects but generally only at the harmonic level; and the recently introduced ensemble zero-temperature Franck-Condon approach, which straddles these limits. We also devote particular attention to the performance of methods derived from a cumulant expansion of the energy gap fluctuations and test the ability to approximate the requisite time correlation functions using classical dynamics with quantum correction factors. These results provide insights as to when these methods are applicable and able to capture the features of condensed phase spectra qualitatively and, in some cases, quantitatively across a range of regimes.

Relation between Vibrational Dephasing Time and Energy Gap Fluctuations.

Dephasing processes are present in basically all applications in which quantum mechanics plays a role. These applications certainly include excitation energy and charge transfer in biological systems. In a previous study, we have analyzed the vibrational dephasing time as a function of energy gap fluctuation for a large set of molecular simulations. In that investigation, individual molecular subunits were the focus of the calculations. The set of studied molecules included bacteriochlorophylls in Fenna-Matthews-Olson and light-harvesting system 2 complexes as well as bilins in PE545 aggregates. The present work extends this study to entire complexes, including the respective intermolecular couplings. Again, it can be concluded that a universal and inverse proportionality exists between dephasing time and variance of the excitonic energy gap fluctuations, whereas the respective proportionality constants can be rationalized using the energy gap autocorrelation functions. Furthermore, these findings can be extended to the gaps between higher-lying neighboring excitonic states.

Is back-electron transfer process in Betaine-30 coherent?

The possible role of coherent vibrational motion in ultrafast photo-induced electron transfer remains unclear despite considerable experimental and theoretical advances. We revisited this problem by tracking the back-electron transfer (bET) process in Betaine-30 with broadband pump-probe spectroscopy. Dephasing time constant of certain high-frequency vibrations as a function of solvent shows a trend similar to the ET rates. In the purview of Bixon-Jortner model, high-frequency quantum vibrations bridge the reactant-product energy gap by providing activationless vibronic channels. Such interaction reduces the effective coupling significantly and thereby the coherence effects are eliminated due to energy gap fluctuations, making the back-electron transfer incoherent.

Dephasing Times in the Phycobiliprotein Antenna Complexes PE545 and PE555

Since long-lived quantum coherence have not only been observed in the Fenna-Matthews-Olson (FMO) complex of green sulfur bacteria but also in the phycoerythrin 545 (PE545) photosynthetic antenna system, the interest in these systems has been increased significantly. Moreover, similar results have been found for the PE555 complex in which the two alpha-beta monomers are rotated compared to the PE545 structure leading to a water filled channel. By now, all three complexes have been investigated by a sequential combination of molecular dynamics (MD) simulations, calculations of vertical excitation energies along the trajectory and quantum dynamics for the exciton transfer [1-3]. A comparison of the obtained spectral densities and dynamics will be provided. An interesting property for the systems is the dephasing time which can give an estimate for how long quantum coherences might survive in the respective system. In a first step, the relationship between dephasing time and energy gap fluctuations of the individual pigments has been determined [4]. For the above mentioned complex but also additional exciton and charge transfer systems it can be confirmed that that an inverse proportionality exists between dephasing time and average gap energy fluctuation. Interestingly, an interestingly very similar behavior has been found for all these systems. In a subsequent step, the relationship between dephasing time and excitonic energy gap fluctuations for entire complexes including the respective inter-molecular couplings has been studied.[1] C. Olbrich, J. Strumpfer, K. Schulten, U. Kleinekathofer, J. Phys. Chem. Lett. 2, 1771 (2011).[2] M. Aghtar, J. Strumpfer, C. Olbrich, K. Schulten, U. Kleinekathofer, J. Phys. Chem. Lett. 5, 3131 (2014).[3] S. Chandrasekaran, K. R. Pothula, U. Kleinekathofer, J. Phys. Chem. B, DOI: 10.1021/acs.jpcb.6b05803 (2016).[4] M. I. Mallus, M. Aghtar, S. Chandrasekaran, G. Ludemann, M. Elstner, U. Kleinekathofer, J. Phys. Chem. Lett. 7, 1102 (2016).

Relation between Dephasing Time and Energy Gap Fluctuations in Biomolecular Systems.

Excitation energy and charge transfer are fundamental processes in biological systems. Because of their quantum nature, the effect of dephasing on these processes is of interest especially when trying to understand their efficiency. Moreover, recent experiments have shown quantum coherences in such systems. As a first step toward a better understanding, we studied the relationship between dephasing time and energy gap fluctuations of the individual molecular subunits. A larger set of molecular simulations has been investigated to shed light on this dependence. This set includes bacterio-chlorophylls in Fenna-Matthews-Olson complexes, the PE545 aggregate, the LH2 complexes, DNA, photolyase, and cryptochromes. For the individual molecular subunits of these aggregates it has been confirmed quantitatively that an inverse proportionality exists between dephasing time and average gap energy fluctuation. However, for entire complexes including the respective intermolecular couplings, such a relation still needs to be verified.

Frustrated Solvation Structures Can Enhance Electron Transfer Rates.

Polar surfaces can interact strongly with nearby water molecules, leading to the formation of highly ordered interfacial hydration structures. This ordering can lead to frustration in the hydrogen bond network, and, in the presence of solutes, frustrated hydration structures. We study frustration in the hydration of cations when confined between sheets of the water oxidation catalyst manganese dioxide. Frustrated hydration structures are shown to have profound effects on ion-surface electron transfer through the enhancement of energy gap fluctuations beyond those expected from Marcus theory. These fluctuations are accompanied by a concomitant increase in the electron transfer rate in Marcus's normal regime. We demonstrate the generality of this phenomenon-enhancement of energy gap fluctuations due to frustration-by introducing a charge frustrated XY model, likening the hydration structure of confined cations to topological defects. Our findings shed light on recent experiments suggesting that water oxidation rates depend on the cation charge and Mn-oxidation state in these layered transition metal oxide materials.

Charge transfer in dynamical biosystems, or the treachery of (static) images.

ConspectusThe image is not the thing. Just as a pipe rendered in an oil painting cannot be smoked, quantum mechanical coupling pathways rendered on LCDs do not convey electrons. The aim of this Account is to examine some of our recent discoveries regarding biological electron transfer (ET) and transport mechanisms that emerge when one moves beyond treacherous static views to dynamical frameworks.Studies over the last two decades introduced both atomistic detail and macromolecule dynamics to the description of biological ET. The first model to move beyond the structureless square-barrier tunneling description is the Pathway model, which predicts how protein secondary motifs and folding-induced through-bond and through-space tunneling gaps influence kinetics. Explicit electronic structure theory is applied routinely now to elucidate ET mechanisms, to capture pathway interferences, and to treat redox cofactor electronic structure effects. Importantly, structural sampling of proteins provides an understanding of how dynamics may change the mechanisms of biological ET, as ET rates are exponentially sensitive to structure. Does protein motion average out tunneling pathways? Do conformational fluctuations gate biological ET? Are transient multistate resonances produced by energy gap fluctuations? These questions are becoming accessible as the static view of biological ET recedes and dynamical viewpoints take center stage.This Account introduces ET reactions at the core of bioenergetics, summarizes our team’s progress toward arriving at an atomistic-level description, examines how thermal fluctuations influence ET, presents metrics that characterize dynamical effects on ET, and discusses applications in very long (micrometer scale) bacterial nanowires. The persistence of structural effects on the ET rates in the face of thermal fluctuations is considered. Finally, the flickering resonance (FR) view of charge transfer is presented to examine how fluctuations control low-barrier transport among multiple groups in van der Waals contact. FR produces exponential distance dependence in the absence of tunneling; the exponential character emerges from the probability of matching multiple vibronically broadened electronic energies within a tolerance defined by the rms coupling among interacting groups. FR thus produces band like coherent transport on the nanometer length scale, enabled by conformational fluctuations. Taken as a whole, the emerging context for ET in dynamical biomolecules provides a robust framework to design and interpret the inner workings of bioenergetics from the molecular to the cellular scale and beyond, with applications in biomedicine, biocatalysis, and energy science.

A stochastic reorganizational bath model for electronic energy transfer.

Environmentally induced fluctuations of the optical gap play a crucial role in electronic energy transfer dynamics. One of the simplest approaches to incorporate such fluctuations in energy transfer dynamics is the well known Haken-Strobl-Reineker (HSR) model, in which the energy-gap fluctuation is approximated as white noise. Recently, several groups have employed molecular dynamics simulations and excited-state calculations in conjunction to account for excitation energies' thermal fluctuations. On the other hand, since the original work of HSR, many groups have employed stochastic models to simulate the same transfer dynamics. Here, we discuss a rigorous connection between the stochastic and the atomistic bath models. If the phonon bath is treated classically, time evolution of the exciton-phonon system can be described by Ehrenfest dynamics. To establish the relationship between the stochastic and atomistic bath models, we employ a projection operator technique to derive the generalized Langevin equations for the energy-gap fluctuations. The stochastic bath model can be obtained as an approximation of the atomistic Ehrenfest equations via the generalized Langevin approach. Based on this connection, we propose a novel scheme to take account of reorganization effects within the framework of stochastic models. The proposed scheme provides a better description of the population dynamics especially in the regime of strong exciton-phonon coupling. Finally, we discuss the effect of the bath reorganization in the absorption and fluorescence spectra of ideal J-aggregates in terms of the Stokes shifts. We find a simple expression that relates the reorganization contribution to the Stokes shifts - the reorganization shift - to the ideal or non-ideal exciton delocalization in a J-aggregate. The reorganization shift can be described by three parameters: the monomer reorganization energy, the relaxation time of the optical gap, and the exciton delocalization length. This simple relationship allows one to understand the physical origin of the Stokes shifts in molecular aggregates.

On the alternatives for bath correlators and spectral densities from mixed quantum-classical simulations

We investigate on the procedure of extracting a "spectral density" from mixed QM/MM calculations and employing it in open quantum systems models. In particular, we study the connection between the energy gap correlation function extracted from ground state QM/MM and the bath spectral density used as input in open quantum system approaches. We introduce a simple model which can give intuition on when the ground state QM/MM propagation will give the correct energy gap. We also discuss the role of higher order correlators of the energy-gap fluctuations which can provide useful information on the bath. Further, various semiclassical corrections to the spectral density, are applied and investigated. Finally, we apply our considerations to the photosynthetic Fenna-Matthews-Olson complex. For this system, our results suggest the use of the Harmonic prefactor for the spectral density rather than the Standard one, which was employed in the simulations of the system carried out to date.