The major difference between semiconductor quantum dots and bulk semiconductors is in the quantum confinement effect. It results the controllable exciton¡¦s absorption and emission spectra by tuning the size of the quantum dot. Moreover, multi-exciton states are reported to be observed in the highly symmetric quantum dot systems. In this dissertation, we use the single molecule fluorescence measurement to study the power dependence of multi-exciton state in single CdSe/ZnS semiconductor quantum dots. At low excitation fluence, anti-bunching behavior, and nearly single exponential relaxation dynamics are observed. By increasing the laser power, bi-exponential fluorescence decay dynamics as well as bunching behaviors from the same QD indicate the fast PL dynamics due to the relaxation from multi-exciton. The results indicate certain threshold energy level for multi-exciton generation. In addition, the multiple step cascade radiative relaxation processes are observed. Besides, we modulate linear polarization light to study the excitation orientation dependence. The results indicate the emission dipole of multi-exciton is similar to the single exciton, having a two dimensional transition dipole plane with c-axis symmetry. However, the absorption dipole of multi-exciton exhibits different orientation dependence from the single exciton.

Strongly correlated systems have been a major challenge for a long time in the field of theoretical chemistry. For such systems, the relevant portion of the Hilbert space scales exponentially, preventing efficient simulation on large systems. However, in many cases, the Hilbert space can be partitioned into clusters on the basis of strong and weak interactions. In this work, we mainly focus on an approach where we partition the system into smaller orbital clusters in which we can define many-particle cluster states and use traditional many-body methods to capture the rest of the inter-cluster correlations. This dissertation can be mainly divided into two parts. In the first part of this dissertation, the clustered ansatz, termed as tensor product states (TPS), is used to study large strongly correlated systems. In the second part, we study a particular type of strongly correlated system, correlated triplet pair states that arise in singlet fission. The many-body expansion (MBE) is an efficient tool that has a long history of use for calculating interaction energies, binding energies, lattice energies, and so on. We extend the incremental full configuration interaction originally proposed for a Slater determinant to a tensor product state (TPS) based wavefunction. By partitioning the active space into smaller orbital clusters, our approach starts from a cluster mean-field reference TPS configuration and includes the correlation contribution of the excited TPSs using a many-body expansion. This method, named cluster many-body expansion (cMBE), improves the convergence of MBE at lower orders compared to directly doing a block-based MBE from an RHF reference. The performance of the cMBE method is also tested on a graphene nano-sheet with a very large active space of 114 electrons in 114 orbitals, which would require 1066 determinants for the exact FCI solution. Selected CI (SCI) using determinants becomes intractable for large systems with strong correlation. We introduce a method for SCI algorithms using tensor product states which exploits local molecular structure to significantly reduce the number of SCI variables. We demonstrate the potential of this method, called tensor product selected configuration interaction (TPSCI), using a few model Hamiltonians and molecular examples. These numerical results show that TPSCI can be used to significantly reduce the number of SCI variables in the variational space, and thus paving a path for extending these deterministic and variational SCI approaches to a wider range of physical systems. The extension of the TPSCI algorithm for excited states is also investigated. TPSCI with perturbative corrections provides accurate excitation energies for low-lying triplet states with respect to extrapolated results. In the case of traditional SCI methods, accurate excitation energies are obtained only after extrapolating calculations with large variational dimensions compared to TPSCI. We provide an intuitive connection between lower triplet energy mani- folds with Hückel molecular orbital theory, providing a many-body version of Hückel theory for excited triplet states. The n-body Tucker ansatz (which is a truncated TPS wavefunction) developed in our group provides a good approximation to the low-lying states of a clusterable spin system. In this approach, a Tucker decomposition is used to obtain local cluster states which can be truncated to prune the full Hilbert space of the system. As a truncated variational approach, it has been observed that the self-consistently optimized n-body Tucker method is not size- extensive, a property important for many-body methods. We explore the use of perturbation theory and linearized coupled-cluster methods to obtain a robust yet efficient approximation. Perturbative corrections to the n-body Tucker method have been implemented for the Heisenberg Hamiltonian and numerical data for various lattices and molecular systems has been presented to show the applicability of the method. In the second part of this dissertation, we focus on studying a particular type of strongly correlated states that occurs in singlet fission material. The correlated triplet pair state 1(TT) is a key intermediate in the singlet fission process, and understanding the mechanism by which it separates into two independent triplet states is critical for leveraging singlet fission for improving solar cell efficiency. This separation mechanism is dominated by two key interactions: (i) the exchange interaction (K) between the triplets which leads to the spin splitting of the biexciton state into 1(TT),3(TT) and 5(TT) states, and (ii) the triplet-triplet energy transfer integral (t) which enables the formation of the spatially separated (but still spin entangled) state 1(T...T). We develop a simple ab initio technique to compute both the triplet-triplet exchange (K) and triplet-triplet energy transfer coupling (t). Our key findings reveal new conditions for successful correlated triplet pair state dissociation. The biexciton exchange interaction needs to be ferromagnetic or negligible compared to the triplet energy transfer for favorable dissociation. We also explore the effect of chromophore packing to reveal geometries where these conditions are achieved for tetracene. We also provide a simple connectivity rule to predict whether the through-bond coupling will be stabilizing or destabilizing for the (TT) state in covalently linked singlet fission chromophores. By drawing an analogy between the chemical system and a simple spin-lattice, one is able to determine the ordering of the multi-exciton spin state via a generalized usage of Ovchinnikov's rule. In the case of meta connectivity, we predict 5(TT) to be formed and this is later confirmed by experimental techniques like time-resolved electron spin resonance (TR-ESR). / Doctor of Philosophy / The study of the correlated motion of electrons in molecules and materials allows scientists to gain useful insights into many physical processes like photosynthesis, enzyme catalysis, superconductivity, chemical reactions and so on. Theoretical quantum chemistry tries to study the electronic properties of chemical species. The exact solution of the electron correlation problem is exponentially complex and can only be computed for small systems. Therefore, approximations are introduced for practical calculations that provide good results for ground state properties like energy, dipole moment, etc. Sometimes, more accurate calculations are required to study the properties of a system, because the system may not adhere to the as- sumptions that are made in the methods used. One such case arises in the study of strongly correlated molecules. In this dissertation, we present methods which can handle strongly correlated cases. We partition the system into smaller parts, then solve the problem in the basis of these smaller parts. We refer to this block-based wavefunction as tensor product states and they provide accurate results while avoiding the exponential scaling of the full solution. We present accurate energies for a wide variety of challenging cases, including bond breaking, excited states and π conjugated molecules. Additionally, we also investigate molecular systems that can be used to increase the efficiency of solar cells. We predict improved solar efficiency for a chromophore dimer, a result which is later experimentally verified.

Die Multiexzitonen-Theorie des Anregungsenergie-Transfers in Farbstoff-Protein-Komplexen und biologischen Antennensystemen wird um den Prozess der Exziton-Exziton-Vernichtung erweitert. Um eine mikroskopische Beschreibung zu erzielen, wird eine Herangehensweise benutzt, die auf der Internen Konversion der Anregungsenergie innerhalb der Farbstoffmoleküle basiert. Diese Interne Konversion führt zu nicht strahlenden Übergängen von höheren zu niedrigeren Exziton-Mannigfaltigkeiten. Neben der Einbeziehung der Exziton-Exziton-Vernichtung beinhaltet die hier verwendete Multiexziton-Dichtematrixtheorie auch die Kopplung zu niedrig-energetischen Schwingungs-Freiheitsgraden und dem elektrischen Feld. Für den Übergang von der Zwei- zu der Einexzitonen -Mannigfaltigkeit werden exakte und genäherte Ausdrücke hergeleitet. Die erste Anwendung der erweiterten Multiexziton-Dichtematrixtheorie ist die Berechnung von ultra-schnellen differentiellen Absoptionsspektren. Um den Prozess der Exziton-Exziton-Vernichtung in intensitätsabhängigen differenziellen Absorptionsspektren näher zu untersuchen, wird diese Herangehensweise auf den B850 Ring des LH2 von rhodobacter sphaeroides angewendet. Die Bedeutung der Exziton-Exziton-Vernichtung und der Einfluss von statischer Unordnung werden detailiert diskutiert. Die Simulationen der differentiellen Absorptionsspektren mit statischer Unordnung und Orientierungsmittelung zeigen gute Übereinstimmung mit experimentellen Beobachtngen. Durch die Veröffentlichung der Strukturdaten des Photosystem I (PS1) von Synechococcus elongatus wurde es zum ersten Mal möglich, ein Exziton-Modell für die 96 Chorophyllmoleküle einzuführen, die in die Proteinmatrix dieses Antennensystems eingebettet sind. Das Ziel dabei ist, sowohl die linearen Spektren in einem weiten Temperaturbereich, als auch die zeitaufgelöste Fluoreszenz zu reproduzieren. Die Kopplungen und die Dipolmomente der Chlorophyllmoleküle wurden den Strukturdaten entnommen. Da die Energien der einzelnen Farbstoffe stark von deren unmittelbarer Umgebung abhängt, werden diese bestimmt, indem simulierte Absorption, Lineardichroismus und Zirkulardichroismus bei niedrigen Temperaturen den experimentellen Spektren angepasst werden. Nachdem einige Chlorophyllmoleküle den Zuständen mit den niedrigsten Energien zugeordnet wurden, werden die Energien mit Hilfe eines evolutionären Algorithmus angepasst. Die Qualität des PS1 Modells wird durch die Berechnung der zeitabhängigen Fluoreszenz untermauert (mit zusätzlicher inhomogener Linienbreite), die Simulationen stimmen gut mit aktuellen experimentellen Resultaten überein. Die oben erwähnten Exziton-Modelle beschreiben die jeweiligen Experimente erfolgreich. Der nächste Schritt ist, diese Modelle zu nutzen, um einen neuen Typ von Experiment vorzuschlagen, das Exciton-Steuerungs-Experiment. Auf dem Exciton-Modell des FMO Komplexes von Prosthecochloris aestuarii und dem oben erwähnten PS1 Modell von Synechococcus elongatus aufbauend wird die Bildung von exzitonischen Wellenpaketen durch Laser-Anregung studiert. Diese stellen eine kohärente Überlagerung exzitonischer Zustände dar, ähnlich der bei Schwingungs-Wellenpaketen. Um die spezielle Form des Femtosekunden-Laserpulses zu bestimmen, der zu einer räumlichen Lokalisierung der Anregungsenergie führt, wird die Theorie der optimalen Steuerung verwendet. Die Möglichkeit, solch einen lokalisierten Zielzustand zu erreichen, wird aufgezeigt, auch unter dem Einfluss von energetischer Unordnung und Exziton-Exziton Vernichtung. Ferner wird gezeigt, dass die Effizienz der Lokalisierung und die Länge des optimalen Pulses stark von der Temperatur abhängen. / The multi-exciton description of excitation energy transfer in chromophore complexes and biological light harvesting antenna systems is extended to include the exciton-exciton annihilation processes. To achieve a complete microscopic description the approach is based on intra--chromophore internal conversion processes which leads to non-radiative transitions from higher to lower lying exciton manifolds. Besides an inclusion of exciton-exciton annihilation the used multi-exciton density matrix theory also accounts for a coupling to low-frequency vibrational modes and the radiation field. Concentrating on transitions from the two- to the single-exciton manifold exact and approximate expressions for the annihilation rate are derived. A first application of the introduced extended multi-exciton density matrix theory is given by the computation of ultrafast transient absorption spectra. To elucidate the process of exciton-exciton annihilation in intensity dependent transient absorption data the approach is applied to the B850 ring of the LH2 found in rhodobacter sphaeroides. The signatures of exciton-exciton annihilation as well as the influence of static disorder are discussed in detail. The simulations of transient absorption including static disorder and orientational averaging are in good agreement with experimental data. The recently published structure of the Photosystem I (PS1) of Synechococcus elongatus made it for the first time possible to introduce an excitonic model for the 96 chlorophylls embedded in the protein matrix of that core-antenna system, as presented in this work. The challenge has been to reproduce linear frequency domain spectra in a wide temperature range as well as the time resolved fluorescence. The couplings and the dipole-moments of the chlorophylls are extracted from the x-ray crystal structure. Since the position of the energetic levels of the chlorophylls depend on the respective surrounding their determination is achieved by fitting low temperature absorption, linear dichroism and circular dichroism at the same time. After assigning some chromophores to the red-most states, an evolutionary algorithm is used to get the best fit. The quality of the resulting PS1 model (additionally accounting for inhomogeneous line broadening) is confirmed in calculating time dependent fluorescence spectra which show a good agreement with recent experimental results. The outlined method is also applicable to other photosynthetic antenna systems. The above described exciton models successfully explain the respective measurements. In a second step, they will be used to propose a new type of experiment, the exciton control experiment. Based on an exciton model for the FMO complex of Prosthecochloris aestuarii and the proposed PS1 model of Synechococcus elongatus one studies the laser pulse formation of excitonic wavepackets, i.e. a coherent superposition of excitonic states similar to vibrational wavepackets. Optimal Control theory is used to calculate the shape of femtosecond laser pulses that leads to a spatial localization of excitation energy. The possibility to populate such a localized target state is demonstrated, even in the presence of disorder or exciton-exciton annihilation, and it is shown that the efficiency of localization as well as the length the most suited pulses strongly depend on temperature.