Person:

Valleau, Stephanie

Vibrational eigenfunctions are calculated on-the-fly using semiclassical methods in conjunction with ab initio density functional theory classical trajectories. Various semiclassical approximations based on the time-dependent representation of the eigenfunctions are tested on an analytical potential describing the chemisorption of CO on Cu(100). Then, first principles semiclassical vibrational eigenfunctions are calculated for the (CO_2) molecule and its accuracy evaluated. The multiple coherent states initial value representations semiclassical method recently developed by us has shown with only six ab initio trajectories to evaluate eigenvalues and eigenfunctions at the accuracy level of thousands trajectory semiclassical initial value representation simulations.

A remarkable amount of theoretical research has been carried out to elucidate the physical origins of the recently observed long-lived quantum coherence in the electronic energy transfer process in biological photosynthetic systems. Although successful in many respects, several widely used descriptions only include an effective treatment of the protein-chromophore interactions. In this work, by combining an all-atom molecular dynamics simulation, time-dependent density functional theory, and open quantum system approaches, we successfully simulate the dynamics of the electronic energy transfer of the Fenna-Matthews-Olson pigment-protein complex. The resulting characteristic beating of populations and quantum coherences is in good agreement with the experimental results and the hierarchy equation of motion approach. The experimental absorption, linear, and circular dichroism spectra and dephasing rates are recovered at two different temperatures. In addition, we provide an extension of our method to include zero-point fluctuations of the vibrational environment. This work thus presents, to our knowledge, one of the first steps to explain the role of excitonic quantum coherence in photosynthetic light-harvesting complexes based on their atomistic and molecular description.

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.

Phototrophic organisms such as plants, photosynthetic bacteria, and algae use microscopic complexes of pigment molecules to absorb sunlight. Within the light-harvesting complexes, which frequently have several functional and structural subunits, the energy is transferred in the form of molecular excitations with very high efficiency. Green sulfur bacteria are considered to be among the most efficient light-harvesting organisms. Despite multiple experimental and theoretical studies of these bacteria, the physical origin of the efficient and robust energy transfer in their light-harvesting complexes is not well understood. To study excitation dynamics at the systems level, we introduce an atomistic model that mimics a complete light-harvesting apparatus of green sulfur bacteria. The model contains approximately 4000 pigment molecules and comprises a double wall roll for the chlorosome, a baseplate, and six Fenna-Matthews-Olson trimer complexes. We show that the fast relaxation within functional subunits combined with the transfer between collective excited states of pigments can result in robust energy funneling to the initial excitation conditions and temperature changes. Moreover, the same mechanism describes the coexistence of multiple time scales of excitation dynamics frequently observed in ultrafast optical experiments. While our findings support the hypothesis of supertransfer, the model reveals energy transport through multiple channels on different length scales.

Fast and efficient calculations of optical responses using electromagnetic models require computational acceleration and compression techniques. A hierarchical matrix approach is adopted for this purpose. In order to model large-scale molecular structures, these methods should be applied over wide frequency spectra. Here, we introduce a novel parametric hierarchical matrix method that allows one for a rapid construction of a wideband system representation and enables an efficient wideband solution. We apply the developed method to the modeling of the optical response of bacteriochlorophyll tubular aggregates as found in green photosynthetic bacteria. We show that the parametric method can provide one with the frequency and time-domain solutions for structures of the size of 100 000 molecules, which is comparable to the size of the whole antenna complex in a bacterium. The absorption spectrum is calculated and the significance of electrodynamic retardation effects for relatively large structures, i.e., with respect to the wavelength of light, is briefly studied.

In the first part of this dissertation, we investigate on the presence of quantum effects in the exciton dynamics of the Fenna-Matthews-Olson photosynthetic complex of green sulfur bacteria using an atomistic Quantum Mechanics / Molecular Mechanics (QM/MM) model combined with open quantum systems methods. Subsequently, we explore the theoretical connection between the atomistic QM/MM approach and the open quantum system methods and propose the correct theoretical expressions to maintain consistency when using both approaches contemporarily. In particular we show that when using the correct prefactor to extract the spectral density - the strength of coupling between excitation and other degrees of freedom - the atomistic results are in good agreement with experimental predictions. We then describe a first atomistic study of the full light-harvesting complex of green sulfur bacteria. The various units are treated atomistically and the full system's exciton dynamics is obtained using a Markovian open quantum system master equation. To conclude the first part, we describe a Machine Learning algorithm which we developed and implemented to learn time-dependent density functional theory energies by using trained neural networks and supplying these with coulomb matrices extracted from molecular dynamics simulations. This approach provides a much more rapid solution to obtaining a QM/MM Hamiltonian and subsequently extracting dynamics. It is particularly useful when multiple identical molecules are found in similar environments as one can train the network on a single molecule and predict all others. We applied this method to the Fenna-Matthews-Olson complex.

In the second part of this dissertation we focus on model systems and synthetic aggregates. In particular, we investigate the exciton dynamics in thin-film J-aggregates using a Markovian stochastic Schrödinger equation approach. We derive expressions to obtain diffusion constants from the dynamics and compare a series of different thin-film J-aggregates. The parameters of the model are obtained atomistically. From this model we obtain information on the parameters which lead to optimal exciton diffusion. This can guide the design of new exciton transfer materials.

Obtaining the exciton dynamics of large photosynthetic complexes by using mixed quantum mechanics/molecular mechanics (QM/MM) is computationally demanding. We propose a machine learning technique, multi-layer perceptrons, as a tool to reduce the time required to compute excited state energies. With this approach we predict time-dependent density functional theory (TDDFT) excited state energies of bacteriochlorophylls in the Fenna-Matthews-Olson (FMO) complex. Additionally we compute spectral densities and exciton populations from the predictions. Different methods to determine multi-layer perceptron training sets are introduced, leading to several initial data selections. In addition, we compute spectral densities and exciton populations. Once multi-layer perceptrons are trained, predicting excited state energies was found to be significantly faster than the corresponding QM/MM calculations. We showed that multi-layer perceptrons can successfully reproduce the energies of QM/MM calculations to a high degree of accuracy with prediction errors contained within 0.01 eV (0.5%). Spectral densities and exciton dynamics are also in agreement with the TDDFT results. The acceleration and accurate prediction of dynamics strongly encourage the combination of machine learning techniques with ab-initio methods.

Organic molecules store the energy of absorbed light in the form of charge-neutral molecular excitations -- Frenkel excitons. Usually, in amorphous organic materials, excitons are viewed as quasiparticles, localized on single molecules, which diffuse randomly through the structure. However, the picture of incoherent hopping is not applicable to some classes of molecular aggregates -- assemblies of molecules that have strong near field interaction between electronic excitations in the individual subunits. Molecular aggregates can be found in nature, in photosynthetic complexes of plants and bacteria, and they can also be produced artificially in various forms including quasi-one dimensional chains, two-dimensional films, tubes, etc. In these structures light is absorbed collectively by many molecules and the following dynamics of molecular excitation possesses coherent properties. This energy transfer mechanism, mediated by the coherent exciton dynamics, resembles the propagation of electromagnetic waves through a structured medium on the nanometer scale. The absorbed energy can be transferred resonantly over distances of hundreds of nanometers before exciton relaxation occurs. Furthermore, the spatial and energetic landscape of molecular aggregates can enable the funneling of the exciton energy to a small number of molecules either within or outside the aggregate. In this review we establish a bridge between the fields of photonics and excitonics by describing the present understanding of exciton dynamics in molecular aggregates.

Green sulfur bacteria is an iconic example of nature’s adaptation: thriving in environments of extremely low photon density, the bacterium ranks itself amongst the most efficient natural lightharvesting organisms. The photosynthetic antenna complex of this bacterium is a self-assembled nanostructure, ≈ 60 × 150 nm, made of bacteriochlorophyll molecules. We study the system from a computational nanoscience perspective by using electrodynamic modeling with the goal of understanding its role as a nanoantenna. Three different nanostructures, built from two molecular packing moieties, are considered: a structure built of concentric cylinders of aggregated bacteriochlorophyll-d monomers, a single cylinder of bacteriochlorophyll-c monomers and a model for the entire chlorosome. The theoretical model captures both coherent and incoherent components of exciton transfer. The model is employed to extract optical spectra, concentration and depolarization of electromagnetic fields within the chlorosome, and fluxes of energy transfer for the structures. The second model nanostructure shows the largest field enhancement. Further, field enhancement is found to be more sensitive to dynamic noise rather than structural disorder. Field depolarization however is similar for all structures. This indicates that the directionality of transfer is robust to structural variations while on the other hand, the intensity of transfer can be tuned by structural variations.

Studies on light-harvesting (LH) systems have attracted much attention after the finding of long-lived quantum coherences in the exciton dynamics of the Fenna–Matthews–Olson (FMO) complex. In this complex, excitation energy transfer occurs between the bacteriochlorophyll a (BChl a) pigments. Two quantum mechanics/molecular mechanics (QM/MM) studies, each with a different force-field and quantum chemistry approach, reported different excitation energy distributions for the FMO complex. To understand the reasons for these differences in the predicted excitation energies, we have carried out a comparative study between the simulations using the CHARMM and AMBER force field and the Zerner intermediate neglect of differential orbital (ZINDO)/S and time-dependent density functional theory (TDDFT) quantum chemistry methods. The calculations using the CHARMM force field together with ZINDO/S or TDDFT always show a wider spread in the energy distribution compared to those using the AMBER force field. High- or low-energy tails in these energy distributions result in larger values for the spectral density at low frequencies. A detailed study on individual BChl a molecules in solution shows that without the environment, the density of states is the same for both force field sets. Including the environmental point charges, however, the excitation energy distribution gets broader and, depending on the applied methods, also asymmetric. The excitation energy distribution predicted using TDDFT together with the AMBER force field shows a symmetric, Gaussian-like distribution.