Modeling nonadiabatic dynamical processes in molecular aggregates
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A fundamental understanding of ultrafast nonequilibrium dynamical processes in molecular aggregates is crucially important for the design of nanodevices that utilize quantum mechanical effects. However, understanding the coupled electron-phonon dynamics of such high-dimensional systems remains a challenging issue. As a result of the ever-growing computational power that is available, realistic parameterization of model Hamiltonians and implementation of sophisticated quantum dynamics algorithms have become indispensable tools for gaining insight into these processes. The focus of this dissertation is the development and implementation of approximate path integral-based methods to compute the time-evolution as well as linear and nonlinear spectroscopic signals of molecular aggregates following photo-excitation. The developments and applications presented here are geared toward gaining a better understanding of the role that electron-phonon coupling plays in framing ultrafast excitation energy transfer networks in photosynthetic light-harvesting complexes. The ultrafast excitation energy transfer dynamics that occurs upon photo-excitation of a network of electronically coupled chromophores is remarkably sensitive to the strength of electronic coupling as well as the frequencies and coupling strengths that characterize electron-phonon interactions. Based on approximations to the diabatic representation of molecular Hamiltonians, energetic models of condensed phase molecular aggregates can be parameterized from a first principles description. Often times, computational parameterization of these models reveals comparable magnitudes for intermolecular electronic couplings and electron-phonon couplings, negating the applicability of popular perturbative algorithms (such as those based on Forster or Redfield theory) for describing their time-evolution. Moreover, non-perturbative exact methods (e.g. stochastic Schrodinger equations and the Hierarchical Equations of Motion) are generally inefficient for all but a few specific limiting forms of electron-phonon coupling, or make assumptions about autocorrelation timescales of the vibrational environment. Because of the failure of the energetic parameters determined through recent ab initio studies of natural molecular aggregates to abide by the rather restrictive requirements for efficient application of the above-mentioned methods, the development of approximate non-perturbative algorithms for predicting nonequilibrium dynamical properties of such systems is a central theme in this dissertation. Following a general introductory section describing the basic concepts that are fundamental to the remainder of the thesis, the derivation of path integral dynamics methods is presented. These include a cartesian phase space path integral derivation of the truncated Wigner approximation as applied to the Meyer-Miller-Stock-Thoss mapping model for describing vibronic systems as well as a novel derivation of the Partially Linearized Density Matrix algorithm, highlighting its emergence as a leading order approximation to an, in principle, exact expression for the density matrix. An algorithm for computing the nonlinear response function for higher-order optical spectroscopy signals is presented within the framework of the partially linearized density matrix formalism. Time-resolved two-dimensional electronic spectra are computed and compared with exact results as well as standard perturbation theory-based results, highlighting the accuracy and efficiency of the developed method. Additionally, the recently popularized symmetrical quasi-classical method for computing the reduced density matrix dynamics is extended for computing linear optical spectroscopy signals, and compared with results from the partially linearized density matrix treatment. A generalization of the model Hamiltonian form utilized in recent ab initio studies is presented, allowing for direct vibrational energy relaxation due to coupling between intramolecular normal modes and their environment. The consequences of including these interactions within a model Hamiltonian that is inspired by energetic parameters found in studies of a photosynthetic light-harvesting complex are highlighted in the context of density matrix dynamics and time-resolved two-dimensional electronic spectroscopy. The results indicate that this physical process can be utilized as a means of optimizing the efficiency of excitation energy transfer and localization. Inspired by ab initio characterization of model Hamiltonians for molecular aggregates, a new approximate semiclassical propagator for describing the time-evolution of a system consisting of discrete electronic states in the presence of both high-frequency harmonic vibrational modes as well as slow environmental DOFs with arbitrary potentials is presented. Results indicate that this algorithm provides a more accurate description in this parameter regime than standard linearized path integral methods such as the partially linearized density matrix algorithm and the truncated Wigner approximation. Finally, preliminary results of dynamics involving non-perturbative field-matter interactions is presented with emphasis on strategically shaped pulses, field design through optimal control, and non-perturbative pump-probe spectroscopy.
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