Doctor of Philosophy / Chemistry / Ryszard J. Jankowiak / The structure-function relationships of natural pigment–protein complexes are of great interest, as the electronic properties of the pigments are tuned by the protein environment to achieve high quantum yields and photon utilization. Determination of electronic structure and exciton dynamics in protein complexes is complicated by static disorder and uncertainties in the properties of system-bath coupling. The latter is described by the phonon profile (or spectral density), whose shape can only be reliably measured experimentally for the lowest energy state. Low-temperature, laser-based spectroscopies are applied towards model pigment–protein complexes, i.e., the Fenna-Matthews-Olson (FMO) and water-soluble chlorophyll-binding (WSCP) complexes, in order to study system-bath coupling and energy transfer pathways. Site-selective techniques, e.g., hole burning (HB) and fluorescence line narrowing, are utilized to overcome static disorder and reveal details on homogeneous broadening. In addition, excitonic calculations with non-Markovian lineshapes provide information on electronic structure and exciton dynamics. A new lognormal functional form of the spectral density is recommended which appropriately defines electron-phonon parameters, i.e., Huang-Rhys factor and reorganization energy. Absorbance and fluorescence spectral shifts and HB spectra reveal that samples of FMO may contain a subpopulation of destabilized proteins with modified HB efficiencies. Simulations of spectra corresponding to intact proteins indicate that the entire trimer has to be taken into account in order to properly describe fluorescence and HB spectra. The redshifted fluorescence spectrum of WSCP is described by uncorrelated energy transfer as opposed to previous models of excited state protein relaxation. Also, based on nonconservative HB spectra measured for WSCP, a mechanism of electron transfer between chlorophylls and aromatic amino acids is proposed.

<p>The Fenna-Matthews-Olson (FMO) complex is a photosynthetic pigment-protein complex that has been the subject of study of decades of research, both experimental and theoretical. The FMO complex is small enough that computational modeling is feasible, while the rich excitonic interactions between the pigments give rise to absorption and circulardichroism (CD) spectra with many interesting details. This makes FMO an excellent testing ground for new predictive modeling techniques.</p> <p><br></p> <p>In this work we model the FMO complex from first-principles, wherein the only input is the X-ray crystal structure of the protein. We compute steady-state absorption and CD spectra of wild-type (WT) FMO as well as two mutants, Y16F and Q198V, in which amino acid residues near pigment 3 and pigment 7 are replaced respectively. CD spectra contain extra structural information and thus provide another avenue of investigation into the electronic properties of the FMO complex. We find that while there are large structural changes in the mutants, not all of the structural changes produce significant spectral changes. We conclude that the primary contributor to the spectral changes in Y16F is the breaking of a hydrogen bond between the nearby tyrosine and pigment 3. On the other hand, the spectral changes in Q198V are due to a collection of effects cancelling one another out to varying degrees, all induced by widespread structural changes as a result of the mutation.</p> <p><br></p> <p>We then perform time-resolved absorption and CD spectroscopy measurements on WT, Y16F, and Q198V FMO to provide a high quality set of experimental data against which the first-principles spectra can be validated. We find that in order to accurately model the triplet energy transfer dynamics in FMO two effects must be accounted for in the modeling: (1) the Stark shift caused by the rotation of the bacteriochlorophyll’s permanent dipole moment upon entering a triplet state, and (2) decays must be modeled as Boltzmann populations rather than individual pigments.</p>

<div> <div> <div> <p>The Effective Fragment Potential (EFP) is a quantum-mechanical based model potential for accurate calculations of non-covalent interactions between molecules. It can be coupled with ab initio methods in so-called QM/EFP models to explore the electronic properties of extended molecular systems by providing rigorous description of surrounding environments. The current EFP formulation is, however, not well suited for large-scale simulations due to its inherent limitation of representing effective fragments as rigid structures. The process of utilizing EFP method for the molecular systems with flexible degrees of freedom entails multiple sets of parameter calculations requiring intensive computational resources. This work presents development of the EFP method for describing flexible molecular systems, so-called Flexible EFP. To validate the applicability of the Flexible EFP method, extensive benchmark studies on the amino acid interactions, binding energies, and electronic properties of flavin chromophore of the cryptochrome protein have been demonstrated. In addition to methodological developments, excitonic properties of the Fenna-Matthews-Olson (FMO) photosynthetic pigment-protein complex are explored. In biological systems where intermolecular interactions span a broad range from non-polar to polar and ionic forces, EFP is superior to the classical force fields. In the present study, we demonstrate excellent performance of the QM/EFP model for predicting excitonic interactions and spectral characteristics of the FMO wildtype complex. We characterize the key factors for accurate modeling of electronic properties of bacteriochlrophyll a (BChl a) photosynthetic pigments and suggest a robust computational protocol that can be applied for modeling other photosynthetic systems. Developed computational procedures were also successfully utilized to elucidate photostability and triplet dynamics in the FMO complex and spectroscopic effects of single-point mutagenesis in FMO. A combination of polarizable EFP molecular dynamics and QM/EFP vibrational frequency calculations were also applied to understanding and interpreting structures and Raman spectroscopy of tert-butyl alcohol solutions. </p> </div> </div> </div>

In the first part of this dissertation, recent efforts to understand quantum mechanical effects in biological systems are discussed. Especially, long-lived quantum coherences observed during the electronic energy transfer process in the Fenna-Matthews-Olson complex at physiological condition are studied extensively using theories of open quantum systems. In addition to the usual master equation based approaches, the effect of the protein structure is investigated in atomistic detail through the combined application of quantum chemistry and molecular dynamics simulations. To evaluate the thermalized reduced density matrix, a path-integral Monte Carlo method with a novel importance sampling approach is developed for excitons coupled to an arbitrary phonon bath at a finite temperature. In the second part of the thesis, simulations of molecular systems and applications to vibrational spectra are discussed. First, the quantum dynamics of a molecule is simulated by combining semiclassical initial value representation and density funcitonal theory with analytic derivatives. A computationally-tractable approximation to the sum-of-states formalism of Raman spectra is subsequently discussed.

Photosynthesis involves the absorption of photons by light-harvesting pigments and the subsequent transfer of excitation from the absorption centre to the reaction centre. This highly efficient phenomenon of excitation transfer has traditionally been explained by the Forster mechanism of incoherent hopping of excitation from one chromophore to another. Recently 2D electronic spectroscopic evidences were gathered by Fleming and coworkers on the photosynthetic Fenna-Matthews-Olson (FMO) complex in green sulfur bacteria [1]. Subsequent simulation studies by the same group [2] led to the proposition of a quantum-mechanical, coherent, wave-like transfer of excitation among the chromophores. However, Fleming's conclusions regarding retention of coherence appeared surprising because, the complex would interact with the numerous degrees of freedom of the protein scaffold surrounding it, leading to decoherence, which is expected to be rapid. Thus, we were interested in proposing an analytical treatment to rationalize the excitation transfer. Traditional approaches employed for studying excitation energy transfer involve the master equation techniques where the system-bath coupling is perturbative and is truncated after a few orders. It is important to note that the system-bath coupling causes both decoherence and population relaxation. Such a perturbative approximation is difficult to justify for the photosystem, as the system-bath coupling and the interchromophoric electronic coupling have comparable values. Also, these treatments are largely numerical studies and demand involved calculations. Thus, exact calculations for such a system (7-level) are very difficult. Consequently, we were interested in developing an analytical approach where the coupling is treated as non-perturbative. We devised a novel analytical treatment which employs a unitary transformation analogous to the one used for the theory of nonadiabatic effects in chemical reactions [3]. Our treatment rests on an adiabatic basis which are eigenstates calculated at each nuclear position (i.e. at each configuration of the bath) bearing a parametric dependence in Qi, where Qi denotes the shift of the exciton at site `i' due to the environment. The treatment is justified because in the case of coherent transfer, the excitation would travel mostly amongst the adiabatic states and the effects of non-adiabaticity are small. We observed that the system-bath coupling, after the unitary transformation, could be decoupled at the lowest order into two parts: a) an adiabatic contribution, which accounts solely for decoherence (this is evaluated almost exactly in our approach) and b) a non-adiabatic contribution which accounts for population relaxation from one adiabatic state to another (treated by a Markovian master equation). When we applied our technique to the FMO complex, our prediction for population evolution at the chromophores showed excellent correspondence with those obtained by Nalbach and coworkers using path-integral calculations [4], which are exact. These were calculations where the environment was modelled using a Drude spectral density. Our method allowed the calculations to be readily performed for different temperatures as well. It should be specifically emphasized that, unlike the involved and cumbersome path-integral calculations by Nalbach and coworkers [4] or the hierarchical equation calculations by Ishizaki et al. [2], our method is simple, easy to apply and computationally expedient. Further it became evident that the ultra-efficiency of energy transfer in photosynthetic complexes is not completely captured by coherence alone but is the result of an interplay of coherence and the dissipative influence of the environment (also known as ENAQT or Environment Assisted Quantum Transport [5]). An added advantage of our analytical treatment was the flexibility it offered. Thus, we could use our formalism to perform expedient analyses on the behavior of the system under various conditions. For example, we may wish to evaluate the consequences of introducing correlations among the bath degrees of freedom on the efficiency of transfer to the reaction centre. To this end, we applied our formalism by introducing correlations among the bath degrees of freedom and then by introducing anticorrelations among the bath degrees of freedom. The conclusions were interesting, for they suggested that the efficiency of transfer to the reaction centre was enhanced by the presence of anti-correlations, when compared with an uncorrelated bath. Uncorrelated baths, in turn, had a higher efficiency of energy transfer than correlated baths [6]. Thus, the population evolution is fastest for the anti-correlated bath, followed by the uncorrelated bath and is slowest for the correlated bath. Similar conclusions have been reached at by Tiwari et al. [7]. We could also extend the formalism for studying the system under different spectral densities for the environment, apart from just the Drude spectral density which is popularly used in literature associated with FMO calculations. For instance, the FMO system could be analyzed for the Adolphs-Renger spectral density [3, 8]. Once again our results showed excellent agreement with those reported by Nalbach. We also analyzed the FMO system under the spectral density proposed by Kleinekathofer and coworkers [9]. It was found that these latter spectral densities had more profound participation from the environment, therefore coherences were destroyed more effectively and population relaxation was faster. The excitation transfer to the final site (site closest to the reaction centre in the FMO complex) was found to be faster for the Adolphs and Renger spectral density and the spectral density proposed by Kleinekathofer and coworkers, when compared to the Drude spectral density. Also, the excitation transfer was fastest when we modelled the environment using the Kleinekathofer spectral density. This reinforced the previous conclusions that the dissipative effects of the environment promote a faster energy transport. Being an almost analytical approach, our technique could be applied to systems with larger number of levels as well. A good example of such a case is the MEH-PPV polymer. 2D electronic-spectroscopic experiments performed on this polymer in solution speculate that the excitation energy transfer might be coherent even at physiological temperatures [10]. A prototype for studying this system might be a conjugated polymer with around 80-100 chromophores. Linewidths and Lineshapes in the vicinity of Graphene It has been reported that a vibrating dipole may de-excite by transferring energy non-radiatively to a neighboring metal surface [11]. It is also understood that due to its delocalized pi-cloud, graphene has a continuum of energy states and can behave like a metal sheet and accept energies. Thus, we proposed that if a vibrationally excited dipole de-excites in the vicinity of a graphene sheet, graphene may get electronically excited and thus serve as an effective quencher for such vibrational excitations. Depending on the distance of the dipole from the graphene sheet, the transfer might be intense enough to be spectroscopically probed. We have investigated the rate of such an energy transfer. We use the Dirac cone approximation for graphene, as this enables us to obtain analyt-ical results. The Fermi Golden rule was used to evaluate the rate of energy transfer from the excited dipole to the graphene sheet [12]. The calculations were performed for both the instances: a) energy transfer from a dipole to undoped graphene and, b) energy trans-fer from a dipole to doped graphene. For undoped graphene, the carrier (electron) charge density in the conduction band is zero and we would only have transitions from the valence band to the conduction band. As a consequence of absence of carrier charge density in CB (conduction band), the screening of Coulombic interactions in the graphene plane is ineffective. Thus, one could use the non-interacting polarizability for undoped graphene in the rate expression [13]. However, when we consider the case of doped graphene where EF is shifted upwards into CB, the conduction band electrons will contribute to screening. In this case, we have two sets of transitions: a) from ki in VB (valence band) to kf in CB and b) ki in CB to kf in CB, where ki and kf are the wavevectors which correspond to the initial and final electronic states in graphene. So we have used the polarizability propagator in the random phase approximation [14] to calculate the rate following the approach of [13]. It is also known that the imaginary part of the frequency domain dipole-dipole corre-lation function is a measure of the lineshape [15]. We were, thus, interested in evaluating the lineshape for these transitions. For evaluating the correlation function, we used the partitioning technique developed by L•owdin [16] and subsequently extracted the lineshape from its imaginary part. Using this method, we calculated lineshape for the vibrational excitation of CO molecule in the vicinity of an undoped graphene lattice. The linewidth for this system also was obtained. It could be seen that the vibrational linewidth for 1 CO in the vicinity (5 A) of undoped graphene (EF = 0:00eV ) is small (0:012 cm ) but could be observed experimentally. The lineshape calculations were also extended to cases where it is possible to have atomic transitions by placing an electronically excited atom in the vicinity of the graphene sheet. We considered the following two cases: a) 3p ! 2s transition in hydrogen atom, at a distance of 12 A from the graphene sheet and, b) 4p ! 3s transition in hydrogen atom, at a distance of 20 A from the graphene sheet. The linewidths for atomic transitions could be easily probed in these cases ( 55 cm 1 for 3p ! 2s and 56 cm 1 for 4p ! 3s). In the preceding calculations, the transi-tion dipoles were considered perpendicular to the graphene surface. It is worthwhile to note that if the transition dipoles are considered parallel to the graphene surface, the respective linewidths would be half of those obtained for the case where the transition dipoles are perpendicular. Another interesting possibility would be to consider a lanthanide metal complex placed within a few nanometers from graphene. Lanthanides are known to have sharp f-f transitions [17] and consequently, one could easily observe the effects of broadening due to energy transfer to the electronic system of graphene. Energy Eigenmodes for arrays of Metal Nanoparticles In the final part of the thesis we consider organized assemblies of metal nanoparti-cles, specifically helical and cylindrical assemblies and investigate the plasmonic excitation transfer across these assemblies. These were motivated by recent studies which reported growth of chiral asymmetric assemblies of nanoparticles on D and L- isomers of dipheny-lalanine peptide nanotubes [18]. The plasmons in the helical/cylindrical assemblies are expected to couple with each other via electromagnetic interactions. We construct the Hamiltonian for such systems and evaluate the eigenmodes and energies pertaining to these modes in the wave vector space. We also perform calculations for the group velocity for each eigenmode as this gives us an idea of which eigenmode transports excitation the fastest.