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Exciton analysis tools for quantum-chemical investigation of molecular photochemistry

Mewes, Stefanie Andrea

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Abstract

A chromophore is a molecule that appears colorful to the human eye in sunlight. The recognized color is related to the wavelength of light, or in face of particle-wave dualism, to the energy of photons absorbed by the molecule. Light absorption, also called photo-excitation, corresponds to a transition of the molecule from its ground state to an electronically excited state. The energy gained during excitation allows the molecule to undergo manifold chemical and physical processes, giving rise to the presents of a plethora of chromophores in nature and technology. In order to rationalize these light-induced processes, the involved electronic ground and excited states of a molecule can be investigated by means of quantum-chemical methods. These allow to determine the energy and properties of the molecule in its different electronic states. An important step in the interpretation of the results of such calculations is to determine the character of an excited state, which is directly connected with many properties, such as the interaction with an environment, reaction pathways and deexcitation processes. The aim of this work is to develop new tools for the investigation of excited states, their characters, and quantum-chemical methods for their description. The central idea is to rationalize excited states in terms of correlated electron-hole quasiparticles, i.e. excitons, a concept from solid-state physics. The working hypothesis is to identify the one-particle transition density matrix (1TDM) as an effective electron-hole (i.e. exciton) wave function. The character of an excited state can in turn be determined from the calculated exciton properties. These properties are computed by evaluating expectation values of the exciton wave function with respect to operators of interest. In practice, several protocols have been developed, which characterize spatial and statistical properties of the electron-hole quasiparticle. These excited-state descriptors are directly comparable to results from solid-state physics as well as from experiments, emphasizing their physical significance. In contrast to standard approaches, deriving excited-state characters from exciton properties has some immediate advantages. Different types of excited states such as charge-transfer, Rydberg or local, can be directly determined according to a few exciton descriptors. The use of quantitative descriptors is comparably unbiased, since it does not rely on an ambiguous visual interpretation of molecular orbitals (MOs) involved in the electronic transition. Moreover, exciton descriptors allow to investigate excited states that are poorly represented in the MO picture. Since exciton analysis is based on the 1TDM, which is a method-independent quantity, the descriptors allow to investigate quantitative differences between the descriptions of excited states at various levels of theory. The presented approach is particularly relevant for molecules featuring excited states with exciton character. A particularly important substance class are large π-conjugated organic molecules. Here, delocalized π-electrons play a decisive role and require precise description of correlation effects, posing a challenge for quantum-chemical methods. The scientific interest in large π-conjugated organic molecules is triggered by their special electronic properties, which are applied in organic electronics. In the course of this work, a variety of excited states of extended π-conjugated organic molecules is calculated by means of correlated ab initio methods as well as by time-dependent density functional theory (TDDFT) and subjected to exciton analysis. In Chapter 3, exciton sizes are investigated for excited states of poly(para phenylene vinylene) (PPV) oligomers and polyacenes. Excited states are found to differ in exciton sizes depending on irreducible representations and multiplicities. In Chapter 4, PPV is thoroughly investigated as a prototypical organic semiconductor to rationalize its exciton properties from a quantum-chemical perspective. The emergence of excitonic states is examined for a series of PPV oligomers with different chain length. It is found that exciton formation takes place for oligomers with four or more building blocks. To gain insight into the spectroscopic properties of the PPV polymer, the largest still computationally feasible representative, the octamer (PV)7P is studied intensely. A systematic analysis of forty excited states allows to examine their exciton characters in detail. The investigated excitons are found to have well-defined structures that can be rationalized in terms of Frenkel and Wannier exciton models. The results are in good agreement with experimental findings and band-structure calculations of PPV. To investigate the effects of exciton formation for a more chemically diverse set of molecules, a variety of aromats as well as heteroaromats are investigated in Chapter 6. It is found that the first excited state of these π-systems has a uniform exciton character with an exciton size converging towards 7 A very similar to the trends in PPV. The explicit chemical structures and presence of heteroatoms have surprisingly little influence on this character. Shifting the focus to methodological aspects, Chapter 6 reveals the influence of exchange-correlation (xc) functionals on the description of exciton properties in TDDFT. By comparing exciton sizes and electron-hole correlation coefficients, it is found that there are major differences in the excited-state description for the tested xc-functionals. The trends amongst different xc-functionals suggest that these deviations are mostly governed by the amount of nonlocal orbital exchange (NLX) in the xc-functionals. This finding is of great significance showing that a single parameter can induce a complete change in the electron-hole interaction from repelling (anti-correlated) to strongly attractive (correlated). A more general investigation of the same effect is presented for Tozer's benchmark set in Chapter 5. This set is composed of a broad selection of molecules featuring different types of excited states and designed to develop diagnostic tools for TDDFT. It is well-known that excited states which involve nonlocal electron transitions, such as charge-transfer, Rydberg or π → π* states of extended π-systems, show systematic errors in excitation energy for different types of xc-functionals. Here, exciton descriptors reveal that these errors are related to substantial differences in the description of the respective excited states by the xc-functionals. Since exciton descriptors are able to identify all problematic cases, they are suggested as diagnostic tools for TDDFT.

Ultimately, Chapter 7 focuses on the evaluation of excited-state methods. For this purpose, the selection of methods is extended to include also equation-of-motion coupled-cluster singles doubles (EOM-CCSD) and a diverse set of applications is investigated. Exciton properties calculated with correlated ab initio methods (ADC(2), ADC(3) and EOM-CCSD), as well as TDDFT are compared, revealing strengths and weaknesses of the methods in different applications. The most important outcome of investigating exciton properties is that accuracy in terms of excitation energies is not necessary a measure for the quality of description of the underlying wave function and properties of a system. In fact, the best agreement in terms of exciton properties with respect to high level ab initio data is obtained with an xc-functional that is the least accurate in terms of excitation energies for several examples. The presented approach is publically available as open-source code package libwfa and integrated in the Q-Chem program package.

Item Type: Dissertation
Supervisor: Dreuw, Prof. Dr. Andreas
Place of Publication: Heidelberg
Date of thesis defense: 23 May 2018
Date Deposited: 19 Jun 2018 12:29
Date: 2018
Faculties / Institutes: Fakultät für Chemie und Geowissenschaften > Institute of Physical Chemistry
Subjects: 540 Chemistry and allied sciences
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