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This thesis is concerned with quantum dynamical propagation methods suitable for high-dimensional systems, and their application to excitation energy transfer (EET), electron transfer (ET), and intra-molecular vibrational redistribution (IVR) in molecular aggregates. The theoretical description of these processes, which are often ultrafast – with time scales in the range of femtoseconds to picoseconds – is challenging, both with regard to quantum dynamical simulations and electronic structure calculations.
The present thesis comprises two parts. The first part concerns the implementation of a novel quantum dynamical method based on Gaussian Wavepackets (GWPs): the 2-Layer Gaussian-MCTDH (2L-GMCTDH) method. This method, which has recently been proposed in [S. Römer, M. Ruckenbauer, I. Burghardt, The Journal of Chemical Physics, 2013, 138, 064106] was implemented in a Fortran90 code and applied to various high-dimensional test systems. The second part of the thesis addresses the combined electronic structure and dynamical study of a novel type of donor-acceptor systems that have been investigated in a joint project with experimental collaboration partners at Strasbourg University. In both parts, numerical applications focus on high-dimensional model Hamiltonians for EET and ET processes.
Regarding the first part, the interest of using GWP-based methods is two-fold: First, GWPs represent spatially localized basis sets that are useful for on-the-fly dynamics in conjunction with electronic structure calculations. Second, they are naturally suited for the explicit representation of quantum mechanical system-bath type problems where a large number of vibrational bath modes are weakly perturbed from equilibrium. In this context, various methods exist that are based upon classically evolving GWP bases. A major improvement results from variational methods which involve optimized, non-classical GWP trajectories. In particular, the variational Gaussian-based Multi-Configuration Time-Dependent Hartree (GMCTDH) and its variational Multi-Configurational Gaussians (vMCG) variant were originally derived as semiclassical variants of the Multi-Configuration Time-Dependent Hartree (MCTDH) method. However, the G-MCTDH and vMCG methods mostly use Frozen Gaussian (FG) basis sets that are far less flexible than the single-particle (SPF) representation of standard MCTDH. As a consequence, a significantly larger number of GWPs are generally required to reach convergence. To remedy the lack of flexibility of the FG basis sets, the abovementioned two-layer (2L-G-MCTDH) approach has been introduced: Here, the first layer is composed of flexible SPFs, while the second layer is composed of low-dimensional FGs. The numerical scaling properties are significantly improved as compared with the conventional G-MCTDH and vMCG schemes. The first implementation of the method in an in-house Fortran90 code is presented, along with applications to (i) a model of site-to-site vibrational energy flow in the presence of intra-site vibrational energy redistribution (IVR) and (ii) a multidimensional donor-acceptor electron transfer system described within a linear vibronic coupling model. The second system relates to a model for ET at an oligothiophene-fullerene interface relevant to organic photovoltaics. Besides the description of the implementation, a detailed assessment of the convergence properties and comparison with multi-layer MCTDH (ML-MCTDH) benchmark calculations is presented. Finally, a perspective is given on the future combination with the existing ML-MCTDH scheme; indeed, such a combination is straightforward since the first layer of the 2L-G-MCTDH approach can be chosen to be orthogonal.
Regarding the second part of the thesis, two generations of a novel donor-acceptor (DA) system for organic photovoltaics applications, involving self-assembled block co-oligomers DA dyads and triads with perylene-diimide (PDI) accepter units, are addressed within a collaborative project with S. Haacke and S. Mery (University of Strasbourg). Based upon detailed excited-state electronic structure investigations along with quantum dynamical and kinetic studies, the relevant ET formation and recombination steps are characterized quantitatively, in view of optimizing the chemical design and reducing recombination losses.
In a first-generation variant of the abovementioned DA systems, which involves liquid-crystalline triads, we were able to show that a highly efficient inter-chain ET process prevails over intra-molecular ET, leading to fast recombination. Due to the latter, this system turns out to be inefficient for photovoltaic applications. To fully understand the elementary steps, high-dimensional quantum dynamics simulations were carried out using the ML-MCTDH method, in collaboration with Matthias Polkehn from our group. In the second-generation variant, which is in the focus of the present thesis, both the nanomorphology and the chemical design were modified. The present work, focuses upon the aspect of chemical design, by characterizing a series of modified DA’s, with donor units of varying length while the PDI accepter units remain unchanged. The intra-molecular ET is observed in these systems, but the processes are comparatively slow, of the order of tens to hundreds of picoseconds. Hence, a kinetic analysis using the Marcus-Levich-Jortner rate theory is employed. Among the main results of the study is that addition of an electron donating amine unit strongly increases the lifetime of the charge-separated state, and therefore reduced recombination losses.
Overall, the present thesis shows how a combination of high-dimensional quantum dynamics, electronic structure calculations, and vibronic coupling model Hamiltonians can be employed to obtain an accurate picture of EET, ET, and IVR in high-dimensional molecular assemblies. Furthermore, the 2L-GMCTDH method paves the way for accurate and efficient on-the-fly calculations; a suitable set-up for such calculations is currently in progress.