Development and application of reliable methods for the calculation of excited states [Elektronische Ressource] : from light-harvesting complexes to medium-sized molecules / von Michael Wormit

Michael Wormit

Informations

• Publié par: goethe_universitat_frankfurt_am_main
• Publié le: 01 janvier 2009
• Nombre de lectures: 12
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

Development and Application of Reliable
Methods for the Calculation of Excited States:
From Light-Harvesting Complexes to
Medium-Sized Molecules
Dissertation
zur Erlangung des Doktorgrades
der Naturwissenschaften
vorgelegt beim Fachbereich 14
der Johann Wolfgang Goethe – Universita¨t
in Frankfurt am Main
von
Michael Wormit
aus Speyer
Frankfurt, Januar 2009vom Fachbereich FB 14 Biochemie, Chemie und Pharmazie der
Johann Wolfgang Goethe–Universitat als Dissertation angenommen.¨
Dekan: .........................................................
Gutachter: .....................................................
Datum der Disputation: ........................................In memory of my father.Abstract
Photo-initiated processes, like photo-excitation and -deexcitation, internal conversion,
excitation energy transfer and electron transfer, are of importance in many areas of
physics, chemistryandbiology. Fortheunderstanding ofsuchprocesses, detailedknowl-
edge of excitation energies, potential energy surfaces and excited state properties of the
involved molecules is an essential prerequisite. To obtain these informations, quantum
chemicalcalculationsarerequired. Severalquantumchemicalmethodsexistwhichallow
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 sys-
tems, 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 par-
ticularly 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
transferprocessesinlight-harvestingcomplexes. Sincelight-harvestingcomplexes,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
complexesareusedtocalculatepotentialenergycurvesalongmeaningfulreactioncoordi-
nates. Artificialchargetransferstatesarecorrectedwiththehelpoftheso-calledΔDFT
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 ob-
served formation of carotenoid radical cations is studied. It is shown that the carotenoid
radicalcationisformedmostlikelyviatheopticallyforbiddenS stateofthecarotenoid.1
In light-harvesting complex LHC-II of green plants the fast component of the so-called
non-photochemicalquenching(NPQ)isinvestigated. Twoofseveraldifferenthypotheses
onthemechanismofNPQ,whichhavebeenproposedrecently,arestudiedindetail. The
first one suggests that NPQ proceeds via simple replacement of violaxanthin by zeaxan-
thin in the binding pocket in LHC-II. However, the calculated potential energy curves
exhibitnodifferencebetweenviolaxanthinandzeaxanthininthebindingpocket. Incom-
bination with experimental results it is thus shown that simple replacement alone does
not mediate NPQ in LHC-II. The second hypothesis proposes conformational changesof 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.
ThoughseveralconclusionscanbedrawnfromtheinvestigationsusingTD-DFT,the
interpretability of the results is limited due to the deficiencies of the method and of the
models. Toovercomethemethodologicaldeficiencies, moreaccuratemethodshavetobe
employed. Therefore, the so-called algebraic diagrammatic construction scheme (ADC)
is implemented. ADC is a widely overlooked ab initio method for the calculation of ex-
cited states, which is based on propagator theory. Its theoretical derivation proceeds via
perturbation expansion of the polarization propagator, which describes electronic exci-
tations. 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
cheapestexcitedstatemethodwhichcancorrectlydescribedoublyexcitedstates,aswell
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 S state which is known1
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
equationsofADC(2)aretransformedintoabasisoflocalorbitals. Inthisbasisnegligible
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
thecomputationtimesbecomeminimal,whiletheerrorsintheexcitationenergiesdueto
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
arebelow0.15eVforalltestsystems. Additionally, notrendisvisiblefortheerrorsthat
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).Zusammenfassung
Lichtinduzierte Prozesse, wie Absorption, Emission, interne Konversion und Energie-
und Elektrontransfer, sind in vielen Bereichen von Physik, Chemie und Biologie von
Bedeutung. Zum Verstandnis solcher Prozesse ist die genaue Kenntnis von Anregungs-¨
energien, Potentialenergiefla¨chen und Eigenschaften angeregter Zusta¨nde unabdingbar.
Zum Erwerb dieser Informationen werden quantenchemische Verfahren benotigt, die die¨
Berechnung angeregter Zusta¨nde erlauben. Die meisten der entsprechenden Methoden
sind aufgrund ihrer Hardware-Anforderungen nur auf kleine Molekule 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 Me-
thoden fu¨r die Berechnung dieser Systeme in Frage kommen. Eine ha¨ufig verwendete
Methode ist die zeitabha¨ngige Dichtefunktionaltheorie (TD-DFT), mit deren Hilfe sich
Systeme von bis zu 200–300 Atomen berechnen lassen, ohne dass die Fehler in den
Anregungsenergien mancher Zust¨ande 0.5 eV u¨berschreiten. Allerdings, hat TD-DFT
auch einige Nachteile. Der schwerwiegendste davon ist das Versagen bei der Berechnung
von Ladungstransferzusta¨nden, was besonders fu¨r große Systeme zu einer Fu¨lle solcher
Zustande mit viel zu niedrigen Anregungsenergien fuhrt. Desweiteren konnen auch soge-¨ ¨ ¨
nannte Rydberg-Zusta¨nde und Zusta¨nde mit starkem Doppelanregungscharakter nicht
richtig beschrieben werden. Trotzdem lasst sich die Methode gut zur Berechnung von¨
angeregten Zust¨anden einsetzen, wenn man bei der Interpretation der entsprechenden
Ergebnisse die vorhandenen Probleme beru¨cksichtigt.
In dieser Arbeit wird TD-DFT zur Untersuchung von Energie- und Elektronentrans-
ferprozessen in Lichtsammelkomplexen eingesetzt. Da Lichtsammelkomplexe mit ihren
weituber1000AtomenauchfurTD-DFT