Theoretical methods for studying charge and spin separation in excited states of large molecules and condensed phase

Abstract

In recent years the GW/BSE approach as a sophisticated many-body method gained considerable attention for ab-initio calculations of a range of properties in finite and infinite systems. For instance, several benchmarks exist for ionization potentials, electron affinities, (band) gaps, and electronically excited states demonstrating an overall good performance of the GW/BSE approach at a computational cost comparable to time-dependent density functional theory (TD-DFT) which is a widely applied method in quantum chemistry. The GW/BSE method outperforms TD-DFT for accurate description of charge-transfer states due to explicit capture of non-local electron-hole interaction mediated by the screened Coulomb potential $W(r,r^{'},omega)$. Furthermore, dynamical correlation is properly described through explicit frequency dependency of $W(r,r^{'},omega)$. Long-range dispersion effects are accounted for by infinite summation of non-local electron correlation contributions; the so-called ring diagrams within the random-phase approximation (RPA). Therefore, the GW/BSE method provides a reliable theoretical tool with a satisfactory prediction power for electronic and optical properties of materials at different phases, and hence is consistently used in this thesis for different types of problems. <br /> In the first part of this thesis, the effect of electron-electron correlation, electron-phonon coupling and vertex corrections on the electronic band structure of ice and liquid water within the many-body Green's function formalism (the GW method) is investigated. Furthermore, within the same methodology and based on the Bethe-Salpeter equation (BSE) linear optical absorption spectra of antiferromagnetic zinc ferrite, water and ammonia in the condensed phase are calculated and analyzed in detail. Here, the electron-hole correlation which is responsible for the observed red-shift of absorption peaks and spectral weight redistributions is explicitly taken into account. The electron-hole effects are also of extreme importance for the non-linear absorption spectrum of liquid water (two-photon spectrum) in combination with quasi-particle (QP) effects. <br /> The good performance of the GW/BSE methodology is also shown on large donor-acceptor-type molecules, demonstrating its reliability for finite systems where the screening effects are much lower than in periodic systems and a correct description of the long-range behaviour of the exchange-correlation functional is essential. In order to enhance the predictive power of the GW/BSE theory for molecular systems starting from self-interaction free orbitals, a many-body based screening mixing scheme is introduced which remarkably improves the agreement of calculated excitation energies with reference data. <br /> In the second part, non-adiabatic excited-state dynamics of condensed water is studied. A combination of ab-initio Born-Oppenheimer molecular dynamics and time-dependent density functional theory is applied. The complex proton dynamics is investigated by large-scale excited-state calculations. It is found that instantaneous concerted hops of protons to the neighboring water molecules (Grotthuss mechanism) are highly unlikely. Furthermore, the solvated electron formed upon proton transfer in the excited state is not fully localized within a cavity-like environment as a consequence of attractive interaction with the surrounding water molecules.