Comparison of methods to study excitation energy transfer in molecular multichromophoric systems

Coarse-Grained Approach to Simulate Signatures of Excitation Energy Transfer in Two-Dimensional Electronic Spectroscopy of Large Molecular Systems

Two-dimensional electronic spectroscopy (2DES) has proven to be a highly effective technique in studying the properties of excited states and the process of excitation energy transfer in complex molecular assemblies, particularly in biological light-harvesting systems. However, the accurate simulation of 2DES for large systems still poses a challenge because of the heavy computational demands it entails. In an effort to overcome this limitation, we devised a coarse-grained 2DES method. This method encompasses the treatment of the entire system by dividing it into distinct weakly coupled segments, which are assumed to communicate predominantly through incoherent exciton transfer. We first demonstrate the efficiency of this method through simulation on a model dimer system, which demonstrates a marked improvement in calculation efficiency, with results that exhibit good concordance with reference spectra calculated with less approximate methods. Additionally, the application of this method to the light-harvesting antenna 2 (LH2) complex of purple bacteria showcases its advantages, accuracy, and limitations. Furthermore, simulating the anisotropy decay in LH2 induced by energy transfer and its comparison with experiments confirm that the method is capable of accurately describing dynamical processes in a biologically relevant system. This method presented lends itself to an extension that accounts for the effect of intrasegment relaxation processes on the 2DES spectra, which for computational efficiency are ignored in the implementation reported here. It is envisioned that the method will be employed in the future to accurately and efficiently calculate 2D spectra of more extensive systems, such as photosynthetic supercomplexes.

Excitation Energy Transfer between Higher Excited States of Photosynthetic Pigments: 1. Carotenoids Intercept and Remove B Band Excitations

Chlorophylls (Chls) are known for fast, subpicosecond internal conversion (IC) from ultraviolet/blue-absorbing ("B" or "Soret" states) to the energetically lower, red light-absorbing Q states. Consequently, excitation energy transfer (EET) in photosynthetic pigment-protein complexes involving the B states has so far not been considered. We present, for the first time, a theoretical framework for the existence of B-B EET in tightly coupled Chl aggregates such as photosynthetic pigment-protein complexes. We show that according to a Förster resonance energy transport (FRET) scheme, unmodulated B-B EET has an unexpectedly high range. Unsuppressed, it could pose an existential threat: the damage potential of blue light for photochemical reaction centers (RCs) is well-known. This insight reveals so far undescribed roles for carotenoids (Crts, this article) and Chl b (next article in this series) of possibly vital importance. Our model system is the photosynthetic antenna pigment-protein complex (CP29). Here, we show that the B → Q IC is assisted by the optically allowed Crt state (S2): The sequence is B → S2 (Crt, unrelaxed) → S2 (Crt, relaxed) → Q. This sequence has the advantage of preventing ∼39% of Chl-Chl B-B EET since the Crt S2 state is a highly efficient FRET acceptor. The B-B EET range and thus the likelihood of CP29 to forward potentially harmful B excitations toward the RC are thus reduced. In contrast to the B band of Chls, most Crt energy donation is energetically located near the Q band, which allows for 74/80% backdonation (from lutein/violaxanthin) to Chls. Neoxanthin, on the other hand, likely donates in the B band region of Chl b, with 76% efficiency. Crts thus act not only in their currently proposed photoprotective roles but also as a crucial building block for any system that could otherwise deliver harmful "blue" excitations to the RCs.

Surface hopping modeling of charge and energy transfer in active environments

An active environment is any atomic or molecular system changing a chromophore's nonadiabatic dynamics compared to the isolated molecule. The action of the environment on the chromophore occurs by changing the potential energy landscape and triggering new energy and charge flows unavailable in the vacuum. Surface hopping is a mixed quantum-classical approach whose extreme flexibility has made it the primary platform for implementing novel methodologies to investigate the nonadiabatic dynamics of a chromophore in active environments. This Perspective paper surveys the latest developments in the field, focusing on charge and energy transfer processes.

An efficient time-domain implementation of the multichromophoric Förster resonant energy transfer method

The excitation energy transfer (EET) process for photosynthetic antenna complexes consisting of subunits, each comprised of multiple chromophores, remains challenging to describe. The multichromophoric Förster resonance energy transfer theory is a popular method to describe the EET process in such systems. This paper presents a new time-domain method for calculating energy transfer based on the combination of multichromophoric Förster resonance energy transfer theory and the Numerical Integration of the Schrödinger Equation method. After validating the method on simple model systems, we apply it to the Light-Harvesting antenna 2 (LH2) complex, a light harvesting antenna found in purple bacteria. We use a simple model combining the overdamped Brownian oscillators to describe the dynamic disorder originating from the environmental fluctuations and the transition charge from the electrostatic potential coupling model to determine the interactions between chromophores. We demonstrate that with this model, both the calculated spectra and the EET rates between the two rings within the LH2 complex agree well with experimental results. We further find that the transfer between the strongly coupled rings of neighboring LH2 complexes can also be well described with our method. We conclude that our new method accurately describes the EET rate for biologically relevant multichromophoric systems, which are similar to the LH2 complex. Computationally, the new method is very tractable, especially for slow processes. We foresee that the method can be applied to efficiently calculate transfer in artificial systems as well and may pave the way for calculating multidimensional spectra of extensive multichromophoric systems in the future.

Dynamics of Excitons in Conjugated Molecules and Organic Semiconductor Systems

The exciton, an excited electron-hole pair bound by Coulomb attraction, plays a key role in photophysics of organic molecules and drives practically important phenomena such as photoinduced mechanical motions of a molecule, photochemical conversions, energy transfer, generation of free charge carriers, etc. Its behavior in extended π-conjugated molecules and disordered organic films is very different and very rich compared with exciton behavior in inorganic semiconductor crystals. Due to the high degree of variability of organic systems themselves, the exciton not only exerts changes on molecules that carry it but undergoes its own changes during all phases of its lifetime, that is, birth, conversion and transport, and decay. The goal of this review is to give a systematic and comprehensive view on exciton behavior in π-conjugated molecules and molecular assemblies at all phases of exciton evolution with emphasis on rates typical for this dynamic picture and various consequences of the above dynamics. To uncover the rich variety of exciton behavior, details of exciton formation, exciton transport, exciton energy conversion, direct and reverse intersystem crossing, and radiative and nonradiative decay are considered in different systems, where these processes lead to or are influenced by static and dynamic disorder, charge distribution symmetry breaking, photoinduced reactions, electron and proton transfer, structural rearrangements, exciton coupling with vibrations and intermediate particles, and exciton dissociation and annihilation as well.

Surface Hopping Dynamics with the Frenkel Exciton Model in a Semiempirical Framework

We present an implementation of the Frenkel exciton model in the framework of the semiempirical floating occupation molecular orbitals-configuration interaction (FOMO-CI) electronic structure method, aimed at simulating the dynamics of multichromophoric systems, in which excitation energy transfer can occur, by a very efficient approach. The nonadiabatic molecular dynamics is here dealt with by the surface hopping method, but the implementation we proposed is compatible with other dynamical approaches. The exciton coupling is computed either exactly, within the semiempirical approximation considered, or by resorting to transition atomic charges. The validation of our implementation is carried out on the trans-azobenzeno-2S-phane (2S-TTABP), formed by two azobenzene units held together by sulfur bridges, taken as a minimal model of multichromophoric systems, in which both strong and weak exciton couplings are present.

Computational spectroscopy of complex systems

Numerous linear and non-linear spectroscopic techniques have been developed to elucidate structural and functional information of complex systems ranging from natural systems, such as proteins and light-harvesting systems, to synthetic systems, such as solar cell materials and light-emitting diodes. The obtained experimental data can be challenging to interpret due to the complexity and potential overlapping spectral signatures. Therefore, computational spectroscopy plays a crucial role in the interpretation and understanding of spectral observables of complex systems. Computational modeling of various spectroscopic techniques has seen significant developments in the past decade, when it comes to the systems that can be addressed, the size and complexity of the sample types, the accuracy of the methods, and the spectroscopic techniques that can be addressed. In this Perspective, I will review the computational spectroscopy methods that have been developed and applied for infrared and visible spectroscopies in the condensed phase. I will discuss some of the questions that this has allowed answering. Finally, I will discuss current and future challenges and how these may be addressed.

Scaling relations of exciton diffusion in linear aggregates with static and dynamic disorder

Exciton diffusion plays an important role in many opto-electronic processes and phenomena. Understanding the interplay of intermolecular coupling, static energetic disorder, and dephasing caused by environmental fluctuations (dynamic disorder) is crucial to optimize exciton diffusion under various physical conditions. We report on a systematic analysis of the exciton diffusion constant in linear aggregates using the Haken-Strobl-Reineker model to describe this interplay. We numerically investigate the static-disorder scaling of (i) the diffusion constant in the limit of small dephasing rate, (ii) the dephasing rate at which the diffusion is optimized, and (iii) the value of the diffusion constant at the optimal dephasing rate. Three scaling regimes are found, associated with, respectively, fully delocalized exciton states (finite-size effects), weakly localized states, and strongly localized states. The scaling powers agree well with analytically estimated ones. In particular, in the weakly localized regime, the numerical results corroborate the so-called quantum Goldilocks principle to find the optimal dephasing rate and maximum diffusion constant as a function of static disorder, while in the strong-localization regime, these quantities can be derived fully analytically.

Quantum Dynamics of Exciton Transport and Dissociation in Multichromophoric Systems

Due to the subtle interplay of site-to-site electronic couplings, exciton delocalization, nonadiabatic effects, and vibronic couplings, quantum dynamical studies are needed to elucidate the details of ultrafast photoinduced energy and charge transfer events in organic multichromophoric systems. In this vein, we review an approach that combines first-principles parameterized lattice Hamiltonians with accurate quantum dynamical simulations using advanced multiconfigurational methods. Focusing on the elementary transfer steps in organic functional materials, we address coherent exciton migration and creation of charge transfer excitons in homopolymers, notably representative of the poly(3-hexylthiophene) material, as well as exciton dissociation at polymer:fullerene heterojunctions. We emphasize the role of coherent transfer, trapping effects due to high-frequency phonon modes, and thermal activation due to low-frequency soft modes that drive a diffusive dynamics.

Modeling nonlocal electron-phonon coupling in organic crystals using interpolative maps: The spectroscopy of crystalline pentacene and 7,8,15,16-tetraazaterrylene

Electron-phonon coupling plays a central role in the transport properties and photophysics of organic crystals. Successful models describing charge- and energy-transport in these systems routinely include these effects. Most models for describing photophysics, on the other hand, only incorporate local electron-phonon coupling to intramolecular vibrational modes, while nonlocal electron-phonon coupling is neglected. One might expect nonlocal coupling to have an important effect on the photophysics of organic crystals because it gives rise to large fluctuation in the charge-transfer couplings, and charge-transfer couplings play an important role in the spectroscopy of many organic crystals. Here, we study the effects of nonlocal coupling on the absorption spectrum of crystalline pentacene and 7,8,15,16-tetraazaterrylene. To this end, we develop a new mixed quantum-classical approach for including nonlocal coupling into spectroscopic and transport models for organic crystals. Importantly, our approach does not assume that the nonlocal coupling is linear, in contrast to most modern charge-transport models. We find that the nonlocal coupling broadens the absorption spectrum non-uniformly across the absorption line shape. In pentacene, for example, our model predicts that the lower Davydov component broadens considerably more than the upper Davydov component, explaining the origin of this experimental observation for the first time. By studying a simple dimer model, we are able to attribute this selective broadening to correlations between the fluctuations of the charge-transfer couplings. Overall, our method incorporates nonlocal electron-phonon coupling into spectroscopic and transport models with computational efficiency, generalizability to a wide range of organic crystals, and without any assumption of linearity.

Dynamic Disorder Drives Exciton Transfer in Tubular Chlorosomal Assemblies

Chlorosomes stand out for their highly efficient excitation energy transfer (EET) in extreme low light conditions. Yet, little is known about the EET when a chlorosome is excited to a pure state that is an eigenstate of the exciton Hamiltonian. In this work, we consider the dynamic disorder in the intermolecular electronic coupling explicitly by calculating the electronic coupling terms in the Hamiltonian using nuclear coordinates that are taken from molecular dynamics simulation trajectories. We show that this dynamic disorder is capable of driving the evolution of the exciton, being a stationary state of the initial Hamiltonian. In particular, long-distance excitation energy transfer between domains of high exciton population and oscillatory behavior of the population in the site basis are observed, in line with two-dimensional electronic spectroscopy studies. We also found that in the high exciton population domains, their population variation is correlated with their overall coupling strength. Analysis in a reference state basis shows that such dynamic disorder, originating from thermal energy, creates a fluctuating landscape for the exciton and promotes the EET process. We propose such dynamic disorder as an important microscopic origin for the high efficient EET widely observed in different types of chlorosomes, bioinspired tubular aggregates, or other light-harvesting complexes.