Entwicklung und Anwendung von verläßlichen Methoden zur Berechnung angeregter Zustände : von Lichtsammelkomplexen bis zu mittelgroßen Molekülen

Photo-initiated processes, like photo-excitation and -deexcitation, internal conversion, excitation energy transfer and electron transfer, are of importance in many areas of physics, chemistry and biology. For the understanding of such processes, detailed knowledge of excitation energies, potential energy surfaces and excited state properties of the involved molecules is an essential prerequisite. To obtain these informations, quantum chemical calculations are required. Several quantum chemical methods exist which allow for the calculation of excited states. Most of these methods are computationally costly what makes them only applicable to small molecules. However, many biological systems where photo-processes are of interest like light-harvesting complexes in photosynthesis or the reception of light in the human eye by rhodopsin are quite large. For large systems, however, only few theoretical methods remain applicable. The currently most widely used method is time-dependent density functional theory (TD-DFT), which can treat systems of up to 200–300 atoms with the excitation energies of some excited states exhibiting errors of less than 0.5 eV. Yet, TD-DFT has several drawbacks. The most severe failure of TD-DFT is the false description of charge transfer states which is particularly problematic in case of larger systems where it yields a multitude of artificially low-lying charge transfer states. But also Rydberg states and states with large double excitation character are not described correctly. Still, if these deficiencies are kept in mind during the interpretation of results, TD-DFT is a useful tool for the calculation of excited states. In my thesis, TD-DFT is applied in investigations of excitation energy and electron transfer processes in light-harvesting complexes. Since light-harvesting complexes, which consist of thousands of atoms, are by far too large to be calculated, model complexes for the processes of interest are constructed from available crystal structures. The model complexes are used to calculate potential energy curves along meaningful reaction coordinates. Artificial charge transfer states are corrected with the help of the so-called ∆DFT method. The resulting potential energy curves are then interpreted by comparison with experimental results. For the light-harvesting complex LH2 from purple bacteria the experimentally observed formation of carotenoid radical cations is studied. It is shown that the carotenoid radical cation is formed most likely via the optically forbidden S1 state of the carotenoid. In light-harvesting complex LHC-II of green plants the fast component of the so-called non-photochemical quenching (NPQ) is investigated. Two of several different hypotheses on the mechanism of NPQ, which have been proposed recently, are studied in detail. The first one suggests that NPQ proceeds via simple replacement of violaxanthin by zeaxanthin in the binding pocket in LHC-II. However, the calculated potential energy curves exhibit no difference between violaxanthin and zeaxanthin in the binding pocket. In combination with experimental results it is thus shown that simple replacement alone does not mediate NPQ in LHC-II. The second hypothesis proposes conformational changes of LHC-II that lead to quenching at the central lutein and chlorophyll molecules during NPQ. My TD-DFT calculations demonstrate that if this mechanism is operative, only the lutein 1 which is one of two central luteins present in LHC-II can take part in the quenching process. This is corroborated by recent experiments. Though several conclusions can be drawn from the investigations using TD-DFT, the interpretability of the results is limited due to the deficiencies of the method and of the models. To overcome the methodological deficiencies, more accurate methods have to be employed. Therefore, the so-called algebraic diagrammatic construction scheme (ADC) is implemented. ADC is a widely overlooked ab initio method for the calculation of excited states, which is based on propagator theory. Its theoretical derivation proceeds via perturbation expansion of the polarization propagator, which describes electronic excitations. This yields separate schemes for every order of perturbation theory. The second order scheme ADC(2), which is employed here, is the equivalent to the Møller-Plesset ground state method MP(2), but for excited states. It represents the computationally cheapest excited state method which can correctly describe doubly excited states, as well as Rydberg and charge transfer states. The quality of ADC(2) results is demonstrated in calculations on linear polyenes which serve as model systems for the larger carotenoid molecules. The calculations show that ADC(2) describes the three lowest excited states of polyenes sufficiently well, particularly the optically forbidden S1 state which is known to possess large double excitation character. Yet, the applicability of the method is limited compared to TD-DFT due to the much larger computational requirements. To facilitate the calculation of larger systems with ADC(2) a new variant of the method is developed and implemented. The variant employs the short-range behavior of electron correlation to reduce the computational effort. As a first step, the working equations of ADC(2) are transformed into a basis of local orbitals. In this basis negligible contributions of the equations which are due to electron correlation can be identified based on the distances of local orbitals. A so-called “bumping” scheme is implemented which removes the negligible parts during a calculation. This way, the computation times as well as the disk space requirements can be reduced. With the “bumping” scheme several new parameters are introduced that regulate the amount of “bumping” and thereby the speed and the accuracy of computations. To determine useful values for the parameters an evaluation is performed using the linear polyene octatetraene as test molecule. From the evaluation an optimal set of parameter values is obtained, so that the computation times become minimal, while the errors in the excitation energies due to the “bumping” do not exceed 0.15 eV. With further calculations on various molecules of different sizes it is tested if these parameter values are universal, i.e. if they can be used for all molecules. The test calculations show that the errors in the excitation energies are below 0.15 eV for all test systems. Additionally, no trend is visible for the errors that their magnitude might depend on the system. In contrast, the amount of disregarded contributions in the calculations increases drastically with growing system size. Thus, the local variant of ADC(2) can be used in future to reliably calculate excited states of systems which are not accessible with conventional ADC(2).Lichtinduzierte Prozesse, wie Absorption, Emission, interne Konversion und Energie- und Elektrontransfer, sind in vielen Bereichen von Physik, Chemie und Biologie von Bedeutung. Zum Verständnis solcher Prozesse ist die genaue Kenntnis von Anregungsenergien, Potentialenergieflächen und Eigenschaften angeregter Zustände unabdingbar. Zum Erwerb dieser Informationen werden quantenchemische Verfahren benötigt, die die Berechnung angeregter Zustände erlauben. Die meisten der entsprechenden Methoden sind aufgrund ihrer Hardware-Anforderungen nur auf kleine Moleküle anwendbar. Viele der hier interessierenden Systeme, wie z.B. die Lichtsammelkomplexe in Pflanzen oder das Rhodopsin im menschlichen Auge, sind jedoch sehr groß, so dass nur wenige Methoden für die Berechnung dieser Systeme in Frage kommen. Eine häufig verwendete Methode ist die zeitabhängige Dichtefunktionaltheorie (TD-DFT), mit deren Hilfe sich Systeme von bis zu 200–300 Atomen berechnen lassen, ohne dass die Fehler in den Anregungsenergien mancher Zustände 0.5 eV überschreiten. Allerdings, hat TD-DFT auch einige Nachteile. Der schwerwiegendste davon ist das Versagen bei der Berechnung von Ladungstransferzuständen, was besonders für große Systeme zu einer Fülle solcher Zustände mit viel zu niedrigen Anregungsenergien führt. Desweiteren können auch sogenannte Rydberg-Zustände und Zustände mit starkem Doppelanregungscharakter nicht richtig beschrieben werden. Trotzdem lässt sich die Methode gut zur Berechnung von angeregten Zuständen einsetzen, wenn man bei der Interpretation der entsprechenden Ergebnisse die vorhandenen Probleme berücksichtigt. In dieser Arbeit wird TD-DFT zur Untersuchung von Energie- und Elektronentransferprozessen in Lichtsammelkomplexen eingesetzt. Da Lichtsammelkomplexe mit ihren weit über 1000 Atomen auch für TD-DFT viel zu groß sind, werden zunächst anhand von Röntgenstrukturen Modellkomplexe für die jeweiligen Prozesse konstruiert. Mit diesen werden dann Potentialenergiekurven entlang geeigneter Reaktionskoordinaten berechnet. Die dabei auftretenden, schon erwähnten artifiziellen Ladungstransferzustände werden mit Hilfe der sogenannten ∆DFT-Methode korrigiert bzw. aussortiert. Durch Vergleich mit experimentellen Daten lassen sich die Potentialenergiekurven interpretieren. Beim in Purpurbakterien vorkommenden Lichtsammelkomplex LH2 wurde die photoinduzierte Bildung von Radikalkationen von Karotenoiden theoretisch studiert. Dabei zeigt sich, dass die Radikalkationen höchstwahrscheinlich über die S1 Zustände der jeweiligen Karotenoide entstehen. Desweiteren wurde der Mechanismus des nicht-photochemischen Quenchens (NPQ) in Lichtsammelkomplexen LHC-II von Pflanzen untersucht. Für den NPQ werden verschiedene mögliche Prozesse diskutiert, von denen hier zwei betrachtet wurden. Bei dem einen soll NPQ schon durch bloßen Austausch von Violaxanthin gegen Zeaxanthin in der Bindungstasche des LHC-II ablaufen. Allerdings zeigen die berechneten Potentialenergiekurven für Violaxanthin und Zeaxanthin keine entsprechenden Unterschiede. Daher lässt sich, gestützt durch weitere experimentelle Befunde, folgern, dass dieser einfache Mechanismus für NPQ nicht in Frage kommt. Beim zweiten Prozess lässt eine Konformationsänderung des LHC-II das Quenchen an den zentralen Lutein- und Chlorophyll-Molekülen stattfinden. Aus den Rechnungen dazu ergibt sich, dass, sollte dies der maßgebliche Mechanismus für NPQ sein, höchstens eins der zwei zentralen Luteine im LHC-II, das Lutein 1, am Quenchen teilnehmen kann. Trotz der obigen, aus TD-DFT-Rechnungen gewonnenen Erkenntnisse, bleibt die Interpretierbarkeit der Ergebnisse aufgrund der Unzulänglichkeiten der Methode und den stark vereinfachten Modellen doch beschränkt. Um die Probleme von TD-DFT zu umgehen, ist die Verwendung genauerer Methoden unausweichlich. Daher wurde hier als genauere Methode zur Berechnung angeregter Zustände die algebraisch-diagrammatische Konstruktion (ADC) weiterentwickelt. ADC ist eine weitgehend übersehene ab initio-Methode zur Berechnung angeregter Zustände, die auf dem Propagator-Formalismus beruht. Die Herleitung der Methode erfolgt über die störungstheoretische Entwicklung des Polarisationspropagators, der elektronische Anregungen beschreibt. Dabei ergibt sich für jede Ordnung der Störungstheorie eine neue Variante von ADC. In zweiter Ordnung ist das die im Folgenden verwendete ADC(2)-Methode. Sie entspricht für angeregte Zustände in etwa dem, was die bekannte Møller-Plesset-Störungstheorie MP(2) für Grundzustände darstellt. ADC(2) ist außerdem die am wenigsten aufwändige Methode, mit der doppelt angeregte Zustände, als auch Rydberg- und Ladungstransferzustände prinzipiell richtig beschrieben werden können. Die Qualität der ADC(2)-Ergebnisse wird in dieser Arbeit durch Rechnungen an linearen Polyenen demonstriert, die als Modelle für Karotenoide dienen. Die dabei erhaltenen, niedrigsten drei angeregten Zustände weisen eine ausreichende Genauigkeit auf. Allerdings lässt sich ADC(2) aufgrund des erhöhten Rechenaufwands nur auf wesentlich kleinere Systeme anwenden als TD-DFT. Um auch größere Systeme mit ADC(2) beschreiben zu können, habe ich in meiner Arbeit eine neue lokale Variante von ADC(2) entwickelt und implementiert. Diese Variante nutzt die Kurzreichweitigkeit der Elektronenkorrelation, um Rechenaufwand zu verringern. Für die Implementierung der Variante wurden die ADC-Gleichungen zunächst in eine Basis aus lokalen Orbitalen transformiert. In dieser Basis können mit Hilfe eines sogenannten ,,Bumping”-Schemas Teile der Berechnungen aufgrund des Abstandes der lokalen Orbitale vernachlässigt werden, was sowohl Rechenzeit verkürzt, als auch benötigten Speicher reduziert. Die Einführung des ,,Bumping”-Schemas resultiert in einer Reihe zusätzlicher Parameter. Diese Parameter sollten so gewählt sein, dass möglichst viel vernachlässigt werden kann, ohne dass jedoch der durch das ,,Bumping”-Schema verursachte Fehler in den Anregungsenergien 0.15 eV übersteigt. Ein Satz optimaler Parameterwerte wurde mittels Rechnungen an trans-Octatetraen bestimmt. Anschließend wurde die Qualität der Parameterwerte durch Rechnungen an mehreren, verschieden großen Molekülen überprüft. Dabei zeigt sich, dass die Fehler in den Anregungsenergien unabhängig vom Molekül etwa konstant bleiben. Gleichzeitig lässt sich bei den Rechnungen mit wachsender Systemgröße aber immer mehr vernachlässigen. Daher können mit der neuen, lokalen Variante von ADC(2) Rechnungen an Systemen durchgeführt werden, die mit dem konventionellen Verfahren nicht möglich sind, ohne dass dabei die Qualität der Ergebnisse leidet

Advances in molecular quantum chemistry contained in the Q-Chem 4 program package

A summary of the technical advances that are incorporated in the fourth major release of the Q-CHEM quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube

Advances in Molecular Quantum Chemistry Contained in the Q-Chem 4 Program Package

A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Møller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube

der Johann Wolfgang Goethe – Universität in Frankfurt am Main

Photo-initiated processes, like photo-excitation and-deexcitation, internal conversion, excitation energy transfer and electron transfer, are of importance in many areas of physics, chemistry and biology. For the understanding of such processes, detailed knowledge of excitation energies, potential energy surfaces and excited state properties of the involved molecules is an essential prerequisite. To obtain these informations, quantum chemical calculations are required. Several quantum chemical methods exist which allow for the calculation of excited states. Most of these methods are computationally costly what makes them only applicable to small molecules. However, many biological systems where photo-processes are of interest like light-harvesting complexes in photosynthesis or the reception of light in the human eye by rhodopsin are quite large. For large systems, however, only few theoretical methods remain applicable. The currently most widely used method is time-dependent density functional theory (TD-DFT), which can treat systems of up to 200–300 atoms with the excitation energies of some excited states exhibiting errors of less than 0.5 eV. Yet, TD-DFT has several drawbacks. The mos

Tracing Electronic Dynamics of Molecules in Real Time and Space: A Study of Excitation Transfer and Charge Separation

Understanding energy transfer and charge separation after excitation has enormous relevance to biological processes, such as photosynthesis, as well as being of purely fundamental interest and having potential applications in molecular electronics. We have developed a method for studying the movement of electrons and energy within and between electronically excited molecules, which produces descriptive animations of quasi-particle (particlehole) motion. The dynamically changing state is a manyelectron wavepacket, for which we numerically integrate the Schrödinger equation using the ADC(2) effective Hamiltonian for the particle-hole propagator. We apply this to examples of simple resonant energy transfer and transfer through non-resonant intermediaries. Excitation transfer rates depend strongly on alignment of transition dipole moments, and, already in a system with three constituents, an important aspect of multiple coupled systems appears, in that one absorbing system essentially shields another. In specific hole-doped and particle-doped π systems, we observe a difference in particle and hole mobilities which causes charges to separate periodicall

Tracing Electronic Dynamics of Molecules in Real Time and Space: A Study of Excitation Transfer and Charge Separation

Understanding energy transfer and charge separation after excitation has enormous relevance to biological processes, such as photosynthesis, as well as being of purely fundamental interest and having potential applications in molecular electronics. We have developed a method for studying the movement of electrons and energy within and between electronically excited molecules, which produces descriptive animations of quasi-particle (particlehole) motion. The dynamically changing state is a manyelectron wavepacket, for which we numerically integrate the Schrödinger equation using the ADC(2) effective Hamiltonian for the particle-hole propagator. We apply this to examples of simple resonant energy transfer and transfer through non-resonant intermediaries. Excitation transfer rates depend strongly on alignment of transition dipole moments, and, already in a system with three constituents, an important aspect of multiple coupled systems appears, in that one absorbing system essentially shields another. In specific hole-doped and particle-doped π systems, we observe a difference in particle and hole mobilities which causes charges to separate periodicall

Ultrafast charge separation driven by differential particle and hole mobilities.

The process of a local excitation evolving into an intramolecular charge-separated state is followed and compared for several systems by directly simulating the time propagation of the electronic wavefunction. The wavefunction and Hamiltonian are handled using the extended second-order algebraic diagrammatic construction (ADC(2)-x), which explicitly accounts for electron correlation in the dynamic many-particle state. The details of the charge separation can be manipulated according to the chemical composition of the system; atoms which dope the conjugated system with either particles or holes are shown to effect whether the particle or hole is more mobile. Initially, the charges oscillate between the ends of linear molecules (with different rates), separating periodically, but, at long times, both charges tend to spread over the whole molecule. Charge separation is also shown to occur for asymmetric systems, where it may eventually be experimentally feasible to excite a localized resonance (nonstationary state) on one end of the molecule preferentially and follow the ensuing dynamics

Correction: Strong enhancement of parity violation effects in chiral uranium compounds

International audienceCorrection for ‘Strong enhancement of parity violation effects in chiral uranium compounds’ by Michael Wormit et al., Phys. Chem. Chem. Phys., 2014, 16, 17043–1705