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Development and Implementation of High-Level Propagator Methods for the Description of Electronically Stable and Unstable States

Dempwolff, Adrian Ludwig

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Abstract

Interactions of atoms or molecules with electromagnetic radiation or free electrons can induce a variety of transformations. Apart from elastic scattering processes, in which the quantum states of the involved particles are preserved, inelastic scattering may occur. The distribution of product states depends on the kind of the interacting particles and the energy transferred in the scattering process.

Among the possible transformations are electronic excitation, photoionization and the formation of electronic resonances, i.e., metastable electronic states which undergo subse quent decay by emission of an electron. The latter states can evolve in electronic excitation processes or as a result of electron attachment. In this dissertation, the implementation and application of quantum chemical propagator methods for the description of the above-mentioned processes are presented.

More specifically, a number of perturbation theoretical methods based on the algebraic diagrammatic construction (ADC) schemes for the electron propagator and the polarization propagator are considered. In the framework of these methods, one-electron properties are available via the intermediate state representation (ISR) approach, which enables the computation of the explicit form of the respective wave functions. The third-order static self-energy Σ(3) appearing in the third-order ADC(3) equations can thereby be replaced by an improved fourth-order quantity resulting from the so-called Σ(4+)-procedure, and this option has been explored in the context of ADC for ionization potentials (IP-ADC), electron affinities (EA-ADC) and, for the first time, excitation energies (PP-ADC).

In the first part of this dissertation, photoionization processes are considered, whose theoretical treatment is possible using IP-ADC(3). In the course of this work, the existing implementation of IP-ADC(3) in the Q-Chem quantum chemical program package has been extended by the possibility to compute photoelectron intensities, and therefore, to simulate photoelectron spectra. Other newly implemented features enable the interpretation of ionization transitions by means of visualization of Dyson orbitals and one-particle density matrix-based quantities as, e.g., detachment and attachment densities, which are available via the second-order ISR(2) approach.

The accuracy of the IP-ADC(3)/ISR(2) methodology with respect to ionization potentials and one-particle properties of electron-detached states has been evaluated in a subsequent benchmark study. Therein, the results obtained for 44 electronic states of small molecules are compared to high-level configuration interaction results. For this set of transitions, ionization potentials exhibit a mean absolute error of |∆| ≈ 0.2 eV. For dipole moments, a relative error of |∆| = 19 % is found. In a second IP-ADC(3) study, the applicability of the newly implemented density matrix-based analyses for the interpretation of photoelectron spectra is demonstrated using the example of the galvinoxyl free radical.

In the second part of this dissertation, electronic resonances are addressed. Due to the unbound nature of the involved electronic states, their theoretical treatment is challenging. Different theoretical approaches for their description within the framework of standard quantum chemical methods have been devised, two of which are considered in this work.

First, the efficient implementation of the Fano-Stieltjes-ADC method in the Q-Chem program is presented. For the first time, the third-order PP-ADC(3) scheme as well as various unrestricted PP-ADC schemes have been combined with the Fano-Stieltjes formalism. The applicability of the implementation for the description of resonances in medium-sized organic molecules is demonstrated in a study of a Feshbach resonance in the naphthalene molecule.

As a second option for the theoretical treatment of electronic resonances, the combination of the subspace-projected complex absorbing potential (CAP) method with PP- ADC(3) and EA-ADC(3) is considered. Results obtained using the novel CAP-EA-ADC and CAP-PP-ADC methods as implemented in the Q-Chem quantum chemical program package show an excellent agreement with theoretical best estimates and experimental data in studies of π* shape resonances in unsaturated molecules. Among the studied resonance states are the ²Πg resonance of the dinitrogen anion as well as the lowest π* resonances of the anions of the non-conjugated organic dienes norbornadiene and 1,4-cyclohexadiene. CAP-EA-ADC(3) calculations are in line with previous findings and show that a strong through-bond interaction mechanism reverses the natural ordering of the π* molecular orbitals in 1,4-cyclohexadiene.

Item Type: Dissertation
Supervisor: Dreuw, Prof. Dr. Andreas
Place of Publication: Heidelberg
Date of thesis defense: 8 April 2020
Date Deposited: 29 Apr 2020 07:32
Date: 2020
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: quantum chemistry, electronic structure theory, ionization, electronic resonance
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