Quantum dynamics of ultrafast energy transfer processes in light harvesting systems

How to harvest sunlight efficiently for residential and industrial consumption is one of the most challenging problems faced by the modern energy-hungry world. However, underlying mechanisms of the nearly perfect energy transfer efficiency in light harvesting systems are not well understood despite many experimental and theoretical efforts devoted to unravelling these intricate processes. By formulating an accurate theoretical framework aided by the highly parallel Graphic Processing Unit (GPU) architecture, this thesis presents a comprehensive mechanistic study of the energy transfer processes in light harvesting systems. We first develop two theoretical methods, i.e., a time-dependent variational approach utilizing a superposition of the Davydov D1 and the Davydov D2 ans¨atze, and an extended discretized Hierarchy Equation of Motion (HEOM) method that can accurately and efficiently characterize dynamics of the Holstein polaron in the presence of both diagonal and off-diagonal exciton-phonon coupling. Polaron dynamics of the Holstein model in various parameter regimes are systematically scrutinized by a combination of the two methods. Our formalism making use of the Davydov D1 trial state is also applied to explore the coherent energy transport in engineered nano-arrays of pigments taken from natural photosynthetic systems. Next, the HEOM method is applied to study dissipative dynamics at a conical intersection, which plays an important role in the ultrafast energy relaxation processes in polyatomic systems. We analyze the ultrafast nonadiabatic dynamics for a two-state two-mode conical intersection in pyrazine which is bilinearly coupled to a bath of an infinite number of harmonic oscillators by calculating the diabatic and adiabatic populations of electronic states as well as wave packets of individual vibrational modes. While the population of the upper adiabatic electronic state is effectively quenched by the system-bath coupling, that of the diabatic electronic state exhibits long-lived quantum beating driven by the motion of the tuning mode. It is found that even weak coupling to the bath may effectively suppress the erratic oscillatory features of the nonadiabatic wave packet motion of an isolated two-mode conical intersection, and the main effect of the bath is to direct the wave packet to the lower adiabatic energy surface. Furthermore, a first principles recipe has been developed for describing femtosecond doublepump single molecule signals of molecular aggregates by incorporating the vibrational modes with significant exciton-phonon coupling into a system Hamiltonian and treating the corresponding dynamics in terms of the Davydov D1 ansatz, while the effect of remaining intra and inter-molecular modes treated as a bath are accounted for through the lineshape function formalism.We then apply our theory to calculate the single molecule signal of LHCII, and it is found that signal oscillations are of vibronic origin, and the oscillation periods are dependent on the exciton-phonon coupling strength. Finally, a theoretical framework is developed to calculate 2D spectra of molecular aggregates by integrating the Davydov trial states into the non-linear response theory. We first apply this theory to calculate a model J aggregate in the presence of exciton-phonon coupling and bath-induced relaxation and dephasing. It is found that the 2D spectra at weak diagonal (offdiagonal) exciton-phonon coupling exhibits similar patterns as those of a two-level system, while multi-peak structures accompanied with the population relaxation from high to low energy regions for large population time dominate for the large diagonal (off-diagonal) coupling. The application of our theory to the calculation of 2D spectra of LHCII reveals coherent energy transport between different excitonic states within Chlb and Chla bands. To summarize, through this work we have developed theoretical frameworks to systematically study energy transfer processes starting from basic model systems to realistic light harvesting systems. Specifically, we have investigated nonadiabatic wave packet motion of a two-state two-mode conical intersection in pyrazine, oscillatory features of the single molecule signal of LHCII, and the coherent energy transport between different excitonic states within Chlb and Chla bands of LHCII. It is our hope that this work may help provide guiding principles for the relationship between the structure of the light harvesting systems and optimal energy transfer pathways.Doctor of Philosophy (MSE