Development and implementation of theoretical methods for the description of electronically core-excited states

My PhD project mainly consists of two important parts. One was to enhance and develop variants of the core-valence-separation-algebraic-diagrammatic-construction (CVS-ADC) method and implement all approaches efficiently in the adcman program, which is part of the Q-chem program package. Secondly, I benchmarked these implementations and simulated X-ray absorption spectra of small- and medium-sized molecules from different fields. In this thesis, I present my implementations, as well as the results and applications obtained with the CVS-ADC methods and give a general introduction into quantum chemical methods. At first, I implemented the CVS-ADC 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 medium-sized closed-shell molecules, e.g. acenaphthenequinone (ANQ). Afterwards, the CVS-ADC implementation was extended for the first time to deal with open-shell systems, i.e. ions and radicals, which implies a treatment of unrestricted wave functions and spin-orbitals. The resulting method is denoted as CVS-UADC(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 CVS-ADC(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 core-excited state properties and densities. To benchmark all restricted and unrestricted CVS-ADC/CVS-ISR methods up to third order in perturbation theory, I chose a set of small molecules, e.g. carbon monoxide (CO). The calculated values of core-excitation 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. In combination with the CBS limit of the aug-cc-series, a mean error of -0.23% ±0.12% for core-excitation energies can be identified at the CVS-ADC(2)-x level for carbon, nitrogen and oxygen K-edge excitations, whereas CVS-ADC(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 CVS-ADC(2)-x level. Transition moments and spectral features, as well as static dipole moments, are excellently described with both CVS-ADC(2)-x and CVS-ADC(3). Especially the 6-311++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 CVS-ADC 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 CVS-ISR 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 X-ray absorption spectra of medium-sized 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 CVS-ADC(2)-x in combination with the 6-311++G** basis set exhibit mean errors of core-excitation energies around 0.1%, compared to experimental values. Additionally, core-excited state characters are analyzed with the help of state densities obtained via the CVS-ISR approach or the transition density matrix. To demonstrate the computational savings as a function of the size of the core space, several systems are investigated. CVS-ADC(3) calculations take about 8-10 times longer than CVS-ADC(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 speed-up at the CVS-ADC(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. I present X-ray absorption spectra of the pentacene and the anthracene cation. Other applications concentrate on the trends of core-excited 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. The calculation of coreexcited state absorption (CESA) transition moments using the CVS-ADC/CVS-ISR approach is straightforward. Hence, first results of CESA processes were calculated and are presented in this thesis.