Jan Wenzel

Investigating excited electronic states using the algebraic diagrammatic construction (ADC) approach of the polarisation propagator

The development of reliable theoretical methods and the provision of efficient computer programs for the investigation of optical spectra and photochemistry of large molecules in general is one of the most important tasks of contemporary theoretical chemistry. Here, we present an overview of the current features of our implementation of the algebraic diagrammatic construction scheme of the polarisation propagator, which is a versatile and robust approach for the theoretical investigation of excited states and their properties.

Calculating core‐level excitations and x‐ray absorption spectra of medium‐sized closed‐shell molecules with the algebraic‐diagrammatic construction scheme for the polarization propagator

Core‐level excitations are generated by absorption of high‐energy radiation such as X‐rays. To describe these energetically high‐lying excited states theoretically, we have implemented a variant of the algebraic‐diagrammatic construction scheme of second‐order ADC(2) by applying the core‐valence separation (CVS) approximation to the ADC(2) working equations. Besides excitation energies, the CVS‐ADC(2) method also provides access to properties of core‐excited states, thereby allowing for the calculation of X‐ray absorption spectra. To demonstrate the potential of our implementation of CVS‐ADC(2), we have chosen medium‐sized molecules as examples that have either biological importance or find application in organic electronics. The calculated results of CVS‐ADC(2) are compared with standard TD‐DFT/B3LYP values and experimental data. In particular, the extended variant, CVS‐ADC(2)‐x, provides the most accurate results, and the agreement between the calculated values and experiment is remarkable.

Statistical analysis of electronic excitation processes: Spatial location, compactness, charge transfer, and electron-hole correlation†

We report the development of a set of excited‐state analysis tools that are based on the construction of an effective exciton wavefunction and its statistical analysis in terms of spatial multipole moments. This construction does not only enable the quantification of the spatial location and compactness of the individual hole and electron densities but also correlation phenomena can be analyzed, which makes this procedure particularly useful when excitonic or charge‐resonance effects are of interest. The methods are first applied to bianthryl with a focus on elucidating charge–resonance interactions. It is shown how these derive from anticorrelations between the electron and hole quasiparticles, and it is discussed how the resulting variations in state characters affect the excited‐state absorption spectrum. As a second example, cytosine is chosen. It is illustrated how the various descriptors vary for valence, Rydberg, and core‐excited states, and the possibility of using this information for an automatic characterization of state characters is discussed.

Calculating X-ray Absorption Spectra of Open-Shell Molecules with the Unrestricted Algebraic-Diagrammatic Construction Scheme for the Polarization Propagator.

X-ray absorption spectroscopy (XAS) is a powerful tool that provides information about the electronic structure of molecules via excitation of electrons from the K-shell core region to the unoccupied molecular levels. These high-lying electronic core-excited states can be accurately calculated using the algebraic-diagrammatic construction scheme of second order ADC(2) by applying the core-valence separation (CVS) approximation to the ADC(2) working equations. For the first time, an efficient implementation of an unrestricted CVS-ADC(2) variant CVS-UADC(2) is presented for the calculation of open-shell molecules by treating α and β spins separately from each other. The potential of the CVS-UADC(2) method is demonstrated with a set of small organic radicals by comparison with standard TD-DFT/B3LYP values and experimental data. It turns out that the extended variant CVS-UADC(2)-x, in particular, provides the most accurate results with errors of only 0.1% compared to experimental values. This remarkable agreement justifies the prediction of yet nonrecorded experimental XAS spectra like the one of the anthracene cation. The cation exhibits additional peaks due to the half-filled single-occupied molecular orbital, which may help to distinguish cation from the neutral species.

Analysis and comparison of CVS-ADC approaches up to third order for the calculation of core-excited states

The extended second order algebraic-diagrammatic construction (ADC(2)-x) scheme for the polarization operator in combination with core-valence separation (CVS) approximation is well known to be a powerful quantum chemical method for the calculation of core-excited states and the description of X-ray absorption spectra. For the first time, the implementation and results of the third order approach CVS-ADC(3) are reported. Therefore, the CVS approximation has been applied to the ADC(3) working equations and the resulting terms have been implemented efficiently in the adcman program. By treating the α and β spins separately from each other, the unrestricted variant CVS-UADC(3) for the treatment of open-shell systems has been implemented as well. The performance and accuracy of the CVS-ADC(3) method are demonstrated with respect to a set of small and middle-sized organic molecules. Therefore, the results obtained at the CVS-ADC(3) level are compared with CVS-ADC(2)-x values as well as experimental data by calculating complete basis set limits. The influence of basis sets is further investigated by employing a large set of different basis sets. Besides the accuracy of core-excitation energies and oscillator strengths, the importance of cartesian basis functions and the treatment of orbital relaxation effects are analyzed in this work as well as computational timings. It turns out that at the CVS-ADC(3) level, the results are not further improved compared to CVS-ADC(2)-x and experimental data, because the fortuitous error compensation inherent in the CVS-ADC(2)-x approach is broken. While CVS-ADC(3) overestimates the core excitation energies on average by 0.61% ± 0.31%, CVS-ADC(2)-x provides an averaged underestimation of -0.22% ± 0.12%. Eventually, the best agreement with experiments can be achieved using the CVS-ADC(2)-x method in combination with a diffuse cartesian basis set at least at the triple-ζ level.

Physical Properties, Exciton Analysis, and Visualization of Core-Excited States: An Intermediate State Representation Approach

The theoretical simulation of X-ray absorption spectra is in general a challenging task. However, for small and medium-sized organic molecules, the algebraic diagrammatic construction scheme (ADC) for the polarization operator in combination with the core-valence separation approximation (CVS) has proven to yield core-excitation energies and transition moments with almost quantitative accuracy allowing for reliable construction of X-ray absorption spectra. Still, to understand core-excitation processes in detail, it is not sufficient to only compute energies, but also properties like static dipole moments and state densities are important as they provide deeper insight into the nature of core-excited states. Here, we present for the first time an implementation of the intermediate state representation (ISR) approach in combination with the CVS approximation (CVS-ISR), which gives, in combination with the CVS-ADC method, direct access to core-excited state properties. The performance of the CVS-ADC/CVS-ISR approach is demonstrated by means of small- and medium-sized organic molecules. Besides the calculation of core-excited state dipole moments, advanced analyses of core-excited state densities are performed using descriptors like exciton sizes and distances. Plotting electron and hole densities helps to determine the character of the state, and in particular, the investigation of detachment/attachment densities provides information about orbital relaxation effects that are crucial for understanding core excitations.

Matrix effects in the C 1s photoabsorption spectra of condensed naphthalene

High-resolution C 1s near-edge x-ray absorption fine structure (NEXAFS) spectra of naphthalene are investigated. By comparing the spectral signatures of condensed naphthalene molecules with those of naphthalene in the gas phase, we are able to unambiguously identify spectral features which are affected by the intermolecular interactions in the condensed phase. With the help of calculations using time-dependent density-functional theory and the second-order algebraic-diagrammatic construction scheme for the polarization propagator, resonances in the relevant energy range can be assigned to valence and Rydberg-like excitations. Thus, we obtain a more detailed identification of NEXAFS resonances beyond the present literature.

The All-Seeing Eye of Resonant Auger Electron Spectroscopy: A Study on Aqueous Solution Using Tender X-rays

X-ray absorption and Auger electron spectroscopies are demonstrated to be powerful tools to unravel the electronic structure of solvated ions. In this work for the first time, we use a combination of these methods in the tender X-ray regime. This allowed us to address electronic transitions from deep core levels, to probe environmental effects, specifically in the bulk of the solution since the created energetic Auger electrons possess large mean free paths, and moreover, to obtain dynamical information about the ultrafast delocalization of the core-excited electron. In the considered exemplary aqueous KCl solution, the solvated isoelectronic K+ and Cl- ions exhibit notably different Auger electron spectra as a function of the photon energy. Differences appear due to dipole-forbidden transitions in aqueous K+ whose occurrence, according to the performed ab initio calculations, becomes possible only in the presence of solvent water molecules.