Title: Quantum computing algorithms for quantum chemistry Author: Jakub Višňák Abstract: The topic of this study is the simulation of the quantum algorithm for the diagonalization of the matrix representation of the all-electron Dirac-Coulomb hamiltonian of the SbH molecule. Two different limited CI expansions were used to describe both the ground state (X 0+ ) and the first excited doublet (A 1) by simulating the Iterative Phase Estinamtion Algorith (IPEA). In the simulations numerically performed in this work, the "compact mapping" has been employed for the representation of the evolution operator exp(i Hˆ t); in the theoretical part of the work, the "direct mapping" is described as well. The influence of the metodics for choosing the initial eigenvector estimate is studied in both IPEA A and IPEA B variants. For those variants, the success probabilities pm are computed for different single-points on the SbH dissociation curves. The initial eigenvector estimates based on the "CISD(2)" method are found to be sufficient for both studied LCI-expansions up to internuclear distance R  6 a0. The pm dependence on the overlap between the eigenvector in question and its inital estimate - 2 0  is studied the for IPEA B method. The usability of the both variants of the IPEA in possible later calculations is...

Im Folgenden werden Transferprozesse in Nanohybridsystemen theoretisch untersucht. Diese Hybridsysteme sind vielversprechende Kandidaten für neue optoelektronische Anwendungen und erfahren daher ein erhebliches Forschungsinteresse. Jedoch beschränken sich Arbeiten darüber hauptsächlich auf experimentelle Untersuchungen und kaum auf die dazugehörige theoretische Beschreibung. Bei den theoretischen Betrachtungen treten entscheidende Limitierungen auf. Es werden entweder Details auf der atomaren Ebene vernachlässigt oder Systemgrößen betrachtet, die wesentlich kleiner als im Experiment sind. Diese Thesis zeigt, wie die bestehenden Theorien verbessert werden können und erweitert die bisherigen Untersuchungen durch die Betrachtung von vier neuen hoch relevanten Nanohybridsystemen. Das erste System ist eine Nanostruktur, die aus einem Au-Kern und einer CdS-Schale besteht. Beim zweiten System wurde eine ZnO/Para-Sexiphenyl Nanogrenzfläche untersucht. Die zwei anderen Systeme beinhalten jeweils einen CdSe-Nanokristall, der entweder mit einem Pheophorbide-a-Molekül oder mit einem röhrenförmigen Farbstoffaggregat wechselwirkt. In allen Systemen ist der Anregungsenergie-Transfer ein entscheidender Transfermechanismus und steht im Fokus dieser Arbeit. Die betrachteten Hybridsysteme bestehen aus zehntausenden Atomen und machen daher eine individuelle Berechnung der einzelnen Subsysteme sowie deren gegenseitiger Wechselwirkung notwendig. Die Halbleiter-Nanostrukturen werden mit der Tight-Binding-Methode und der Methode der Konfigurationswechselwirkung beschrieben. Für das molekulare System wird die Dichtefunktionaltheorie verwendet. Die dazugehörigen Rechnungen wurden von T. Plehn ausgeführt. Das metallische Nanoteilchen wird durch quantisierte Plasmon-Moden beschrieben. Die verwendeten Theorien ermöglichen eine Berechnung von Anregungsenergietransfer in Nanohybridsystemen von bisher nicht gekannter Systemgröße und Detailgrad. / In the following, transfer phenomena in nanohybrid systems are investigated theoretically. Such hybrid systems are promising candidates for novel optoelectronic devices and have attracted considerable interest. Despite a vast amount of experimental studies, only a small number of theoretical investigations exist so far. Furthermore, most of the theoretical work shows substantial limitations by either neglecting the atomistic details of the structure or drastically reducing the system size far below the typical device extension. The present thesis shows how existing theories can be improved. This thesis also expands previous theoretical investigations by developing models for four new and highly relevant nanohybrid systems. The first system is a spherical nanostructure consisting of an Au core and a CdS shell. By contrast, the second system resembles a finite nanointerface built up by a ZnO nanocrystal and a para-sexiphenyl aggregate. For the last two systems, a CdSe nanocrystal couples either to a pheophorbide-a molecule or to a tubular dye aggregate. In all of these systems, excitation energy transfer is an essential transfer mechanism and is, therefore, in the focus of this work. The considered hybrid systems consist of tens of thousands of atoms and, consequently, require an individual modeling of the constituents and their mutual coupling. For each material class, suitable methods are applied. The modeling of semiconductor nanocrystals is done by the tight-binding method, combined with a configuration interaction scheme. For the simulation of the molecular systems, the density functional theory is applied. T. Plehn performed the corresponding calculations. For the metal nanoparticle, a model based on quantized plasmon modes is utilized. As a consequence of these theories, excitation energy transfer calculations in hybrid systems are possible with unprecedented system size and complexity.

Disertacijos tikslai: išplėtoti biortogonalių orbitalių metodą energijų ir kitų svarbių atominių charakteristikų skaičiavimui; gauti tikslesnes atomines charakteristikas (energijos lygmenis, šuolių tikimybes, lygmenų gyvavimo trukmes) ab initio metodu. Disertacija sudaryta iš šešių skyrių. Pirmas skyrius yra įvadinis. Jame pristatomi disertacijos tikslai, uždaviniai ir ginamieji teiginiai. Antras skyrius skirtas disertacijoje naudojamiems ir kuriamiems teoriniams metodams aprašyti. Jame aprašomas naujai sukurtas PCFI artinys paremtas biortogonaliomis transformacijomis ir aprašomi, kokie pakeitimai buvo padaryti Breito ir Paulio operatorių matricinių elementų išraiškose, atsižvelgiant į biortogonalių orbitalių metodo specifiką. Kiti trys skyriai skirti disertacijoje gautiems rezultatams pristatyti. Kiekviename iš jų pateikiama mokslinių tyrimų apžvalga ir svarba. Trečiame skyriuje pateikiami apskaičiuoti spektroskopiniai duomenys boro, anglies, azoto ir deguonies izoelektronėms sekoms. Ketvirtame skyriuje pateikiami W24+ jono energijos lygmenys, stipriausi elektriniai dipoliniai šuoliai, gyvavimo trukmės. Penktame skyriuje pateikiami suskirstytų koreliacinių funkcijų sąveikos metodo taikymai ličio ir boro atomams. Neutralaus boro šuolio energijos tarp 2Po - 4P termų skaičiavimai atlikti naudojantis MCHF bei PCFI metodais. Paskutiniame skyriuje pateikiamos disertacijos išvados. / The main goals of the study are: to develop the biorthogonal orbital method for calculation of energies and other important atomic data; to obtain more accurate atomic data (energy levels, transition rates, and lifetimes) using ab initio method. The doctoral dissertation consists of six chapters. Chapter 1 introduces the main goals, main tasks of the study and statements presented for defence. Chapter 2 is designed to describe theoretical methods that were used in the thesis. There is also an account of the newly developed PCFI method based on biorthogonal transformations and the modifications in spin-angular part that were needed. The other three chapters are devoted to presenting the results obtained in the dissertation. Each of them has a scientific review of the research and importance. Also the results obtained in this work are compared with other authors’ theoretical and experimental data. Chapter 3 presents the calculation of spectroscopic data of boron, carbon, nitrogen and oxygen isoelectronic sequences. Chapter 4 presents the results of the W24+ calculations: energy spectra structure, the strongest electric dipole transitions, and the lifetimes. In Chapter 5 applications of PCFI approach are presented for lithium and boron. For neutral boron the 2Po and 4P transition energy was calculated using MCHF and PCFI methods. Chapter 6 presents the conclusions of the study.

The main goals of the study are: to develop the biorthogonal orbital method for calculation of energies and other important atomic data; to obtain more accurate atomic data (energy levels, transition rates, and lifetimes) using ab initio method. The doctoral dissertation consists of six chapters. Chapter 1 introduces the main goals, main tasks of the study and statements presented for defence. Chapter 2 is designed to describe theoretical methods that were used in the thesis. There is also an account of the newly developed PCFI method based on biorthogonal transformations and the modifications in spin-angular part that were needed. The other three chapters are devoted to presenting the results obtained in the dissertation. Each of them has a scientific review of the research and importance. Also the results obtained in this work are compared with other authors’ theoretical and experimental data. Chapter 3 presents the calculation of spectroscopic data of boron, carbon, nitrogen and oxygen isoelectronic sequences. Chapter 4 presents the results of the W(24+) calculations: energy spectra structure, the strongest electric dipole transitions, and the lifetimes. In Chapter 5 applications of PCFI approach are presented for lithium and boron. For neutral boron the 2Po and 4P transition energy was calculated using MCHF and PCFI methods. Chapter 6 presents the conclusions of the study. / Disertacijos tikslai: išplėtoti biortogonalių orbitalių metodą energijų ir kitų svarbių atominių charakteristikų skaičiavimui; gauti tikslesnes atomines charakteristikas (energijos lygmenis, šuolių tikimybes, lygmenų gyvavimo trukmes) ab initio metodu. Disertacija sudaryta iš šešių skyrių. Pirmas skyrius yra įvadinis. Jame pristatomi disertacijos tikslai, uždaviniai ir ginamieji teiginiai. Antras skyrius skirtas disertacijoje naudojamiems ir kuriamiems teoriniams metodams aprašyti. Jame aprašomas naujai sukurtas PCFI artinys paremtas biortogonaliomis transformacijomis ir aprašomi, kokie pakeitimai buvo padaryti Breito ir Paulio operatorių matricinių elementų išraiškose, atsižvelgiant į biortogonalių orbitalių metodo specifiką. Kiti trys skyriai skirti disertacijoje gautiems rezultatams pristatyti. Kiekviename iš jų pateikiama mokslinių tyrimų apžvalga ir svarba. Trečiame skyriuje pateikiami apskaičiuoti spektroskopiniai duomenys boro, anglies, azoto ir deguonies izoelektronėms sekoms. Ketvirtame skyriuje pateikiami W(24+) jono energijos lygmenys, stipriausi elektriniai dipoliniai šuoliai, gyvavimo trukmės. Penktame skyriuje pateikiami suskirstytų koreliacinių funkcijų sąveikos metodo taikymai ličio ir boro atomams. Neutralaus boro šuolio energijos tarp 2Po - 4P termų skaičiavimai atlikti naudojantis MCHF bei PCFI metodais. Paskutiniame skyriuje pateikiamos disertacijos išvados.