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Abstract
Nowadays, Xray absorption spectroscopy (XAS) techniques are important tools to investigate the electronic structure of molecules. Mostly, these methods are applied in the field of organic electronics to study unoccupied molecular levels, which provide information about charge generation and transport properties. With the help of modern synchrotron soft beam sources, molecules can absorb highenergy Xray photons, thereby promoting an electron from the core level, e.g. Kshell 1s orbitals, to the unoccupied molecular level. As a result, metastable bound coreexcited states are generated. Since core orbitals are energetically wellseparated from the remaining occupied and virtual orbital space, they are strongly contracted and the corresponding coreexcited states are very localized. As a consequence, the generated corehole interaction induces a rearrangement of the valence electrons, because the effective shielding of the nucleus is reduced. This effect leads to a lowering of the coreexcitation energy of the final state. This rearrangement of the electrons can be understood as an orbital relaxation effect. To fully understand and interpret experimental spectra, an accurate knowledge about coreexcitation energies, transition moments, the character of the coreexcited states as well as their corresponding properties is necessary. Such information can be obtained with quantum chemical (QC) methods. They help to analyze and interpret experimental spectra, thereby providing a deep insight into the nature of coreexcited states. Generally, a plethora of methods is available to calculate excited states and simulate absorption spectra. The larger the system, the more expensive are the computations. Hence, certain levels of approximation have to be introduced to lower the computational cost. This leads to a loss of reliability and accuracy of the results. The timedependent density functional theory (TDDFT), for example, currently is the prevalently used excitedstate method for the calculation of large molecules up to 300 atoms. However, TDDFT has several disadvantages like the selfinteraction error (SIE), which leads to wrong descriptions of certain kinds of excited states, e.g. chargetransfer states or coreexcited states. The excitation energies of these types of states are strongly underestimated, but if these issues are kept in mind, TDDFT is a useful tool, providing proper spectral features. The algebraic diagrammatic construction scheme (ADC) is a prominent QC method for the calculation of excited states, which is known to provide accurate valenceexcited states of small and mediumsized molecules in an adequate computational time. The ADC approach is based on a Green’s function formalism in combination with partitioning the Hamiltonian using perturbation theory. Due to its sizeconsistency and Hermitian ADC secular matrix structure, the level of approximation can be improved systematically and properties can be computed straightforwardly. It is possible to calculate oneparticle state properties in combination with the intermediate state representation (ISR) approach, e.g. static dipole moments and state densities, which altogether provide enhanced information about absorption spectra. A further advantage of ADC is the indirect inclusion of orbital relaxation effects via couplings to higherexcited configurations, which are important to describe coreexcited states properly. However, the calculation of core excitations is tedious using the unmodified ADC approach, because, in order to solve the ADC eigenvalue problem, numerical iterative eigenvalue solvers are employed usually only providing the energetically lowest eigenstates. Coreexcited states, however, are located in the high energy Xray region of the optical spectrum and in order to calculate them directly, one has to compute all energetically underlying valence excitations as well. This is computationally very expensive and not feasible for mediumsized systems. The direct calculation of the core excitations is prevented by couplings between the valence and coreexcited states. A solution to this issue is the application of the corevalence separation (CVS) approximation to the ADC approach, which results in the CVSADC method. This approximation is based on the fact that core orbitals are energetically wellseparated from the remaining orbital spaces and as a consequence, the couplings between core and valenceexcited states are small and can be neglected. In other words, the CVS approximation decouples the core and valence excitation spaces from each other and allows for a direct computation of coreexcited states. In former work, it was proven that a very good agreement with experiments can be obtained at the extended second order level CVSADC(2)x.
My PhD project mainly consists of two important parts. One was to enhance and develop variants of the CVSADC method and implement all approaches efficiently in the adcman program, which is part of the Qchem program package. Secondly, I benchmarked these implementations and simulated Xray absorption spectra of small and mediumsized molecules from different fields. In this thesis, I present my implementations, as well as the results and applications obtained with the CVSADC methods and give a general introduction into quantum chemical methods. At first, I implemented the CVSADC approach up to the extended second in an efficient way. The program is able to deal with systems up to 500 basis functions in an adequate computational time, which allows for accurate calculations of mediumsized closedshell molecules, e.g. acenaphthenequinone (ANQ). Afterwards, the CVSADC implementation was extended for the first time to deal with openshell systems, i.e. ions and radicals, which implies a treatment of unrestricted wave functions and spinorbitals. The resulting method is denoted as CVSUADC(2)x. For the first time, I applied the CVS approximation to the the third order ADC scheme, derived the working equations, and implemented the CVSADC(3) method in adcman. As the last step, I applied the CVS formalism for the first time to the ISR approach to enable calculations of coreexcited state properties and densities. This provides the basis for subsequent evaluations of transition and density matrices, which give access to exciton sizes, e.g. hole sizes or distances between hole and electron densities. All implementations are presented and discussed in the scope of my thesis.
To benchmark all restricted and unrestricted CVSADC/CVSISR methods up to third order in perturbation theory, I chose a set of small molecules, e.g. carbon monoxide (CO). The calculated values of coreexcitation energies, transition moments and static dipole moments are compared with experimental data or other approaches, thereby estimating complete basis set (CBS) limits. Furthermore, a comprehensive study of different basis sets is performed. As it turns out, the CVSADC(2)x method provides the best agreement with experiments, while CVSADC(3) overestimates the core excitation energies. In combination with the CBS limit of the augccseries, a mean error of 0.23%±0.12% for coreexcitation energies can be identified at the CVSADC(2)x level for carbon, nitrogen and oxygen Kedge excitations, whereas CVSADC(3) exhibits errors of 0.61%±0.32%. This is due to fortuitous error compensation of basis set truncation, electron correlation, orbital relaxation and neglect of relativistic effects at the CVSADC(2)x level. I show that this error compensation is broken at the third order level, because the ratio between terms describing relaxation and polarization effects is shifted in a way that the excitation energy increases. However, transition moments and spectral features, as well as static dipole moments, are excellently described with both CVSADC(2)x and CVSADC(3). Overall, considering the detailed investigation of the basis set influence on the results, I conclude that the use of restricted or unrestricted CVSADC(2)x in combination with a diffuse tripleζ basis set in its Cartesian version can be seen as a blackbox method for the calculation of coreexcited states of organic molecules. Especially the 6311++G** basis set provides an excellent ratio of accuracy to computational time. Another important topic is the description of orbital relaxation effects. In the scope of this thesis, I show, how these effects are included indirectly within the CVSADC approaches. For this purpose, two different descriptors are used, i.e. electron promotion numbers and the amount of doubly excited amplitudes. Furthermore, with the help of detachment/attachment (D/A) densities, which can be constructed via the CVSISR approach, relaxation effects can be visualized. For this purpose, the (D/A) densities are compared with hole/electron (h/e) densities based on the transition density matrix. With this knowledge, the Xray absorption spectra of mediumsized molecules and radicals from the fields of organic electronics and biology are investigated and analyzed. On the basis of these studies, the restricted and unrestricted versions of CVSADC(2)x in combination with the 6311++G** basis set exhibit mean errors of coreexcitation energies around 0.1%, compared to experimental values. Additionally, coreexcited state characters are analyzed with the help of state densities obtained via the CVSISR approach or the transition density matrix. To demonstrate that the CVSADC(2)x approach can be employed as a benchmark blackbox method, TDDFT results are compared directly with the ones at the CVSADC(2)x level. As expected, TDDFT underestimates coreexcitation energies up to 4% due to the SIE, which is about 10 eV in the case of carbon 1s excitations. Since the CVS approximation leads to both a simplification of the ADC working equations, as well as a restriction of the excitation space to correspond only to core excitations, the computational cost is reduced compared to the general ADC approach. To demonstrate the computational savings as a function of the size of the core space, several systems are investigated. CVSADC(3) calculations take about 8 – 10 times longer than CVSADC(2)x calculations and since the results are generally more accurate with the latter method, the use of CVS ADC(3) is not justified. Compared to general ADC(2)x, the speedup at the CVSADC(2)x level is about a factor of 4.0, but this factor strongly depends on the size of the system and the size of the core space. Next, I present applications from the field of organic electronics. The remarkable agreement with experimental data at the CVSADC(2)x level justifies the prediction of yet nonrecorded experimental Xray absorption spectra. Therefore, I chose the anthracene cation, which can be seen as a model system of pentacene and its derivatives, which are commonly used as hole conductors (ptype). Xray absorption spectra of the pentacene cation could provide deeper insight into its charge carrier properties, but measurements of experimental spectra of ionized species are usually very challenging. With the help of CVSUADC(2)x calculations, I show that the anthracene cation exhibits additional peaks due to the halffilled singleoccupied molecular orbital. They are located approximately 3.5 eV – 1.5 eV below the first peak of neutral anthracene, which may help to distinguish a cation from the neutral species. Furthermore, the cationic spectrum exhibits peak broadening, compared to the two first peaks of neutral anthracene. Other applications concentrate on the trends of coreexcited state properties along important potential energy surfaces (PES) of ANQ, phenol and bithiophene. Therefore, static dipole moments, energies, and exciton sizes are analyzed as a function of the C–O distances of ANQ and phenol, as well as the torsion around the central dihedral angle of bithiophene. Finally, another aspect of the CVSISR method is the accessibility of transition moments between two states, which can be used to calculate oscillator strengths for coreexcited state absorption (CESA) spectra. To the best of my knowledge, no experimental data of CESA processes between two coreexcited states have been recorded yet. However, such spectroscopic data could exhibit new insights and the calculation of CESA transition moments using the CVSADC/CVSISR approach is straightforward. Hence, first results of CESA processes were calculated and are presented in this thesis. In the case of ANQ, particularly bright transitions can be identified from the lowest oxygen 1s excitedstate to higher ones.
Item Type:  Dissertation 

Supervisor:  Dreuw, Prof. Dr. Andreas 
Date of thesis defense:  23 March 2016 
Date Deposited:  11 Apr 2016 09:37 
Date:  2016 
Faculties / Institutes:  Fakultät für Chemie und Geowissenschaften > Institute of Physical Chemistry Service facilities > Interdisciplinary Center for Scientific Computing 
Subjects:  500 Natural sciences and mathematics 530 Physics 540 Chemistry and allied sciences 
Controlled Keywords:  Excited States, CVSADC, CVSISR, CoreExcited States, Electronic Structure, Xray Absorption Spectroscopy, NEXAFS, Quantum Chemistry, Photochemistry, Organic Electronics, Exciton Analysis 
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 Development and Implementation of Theoretical Methods for the Description of Electronically CoreExcited States. (deposited 11 Apr 2016 09:37) [Currently Displayed]