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In this thesis, several contributions to the understanding and modeling of chemical phenomena using computational approaches are presented. These investigations are characterized by the usage of non-standard computational modeling techniques, which is necessitated by the complex nature of the electronic structure or atomic fluctuations of the target molecules.
Multiple biradical-type molecules and their spectroscopic properties were modeled. In the course of the investigation, it is found that especially the impact of correct molecular geometries on the computationally predicted absorption properties may be critical. In order to find the correct minimum geometries, Multi-Reference methods may have to be invoked.
The impact of geometry relaxation on the excitonic properties of Perylene Bisimide dimers were investigated. Oftentimes, these geometry factors are neglected in Organic Semiconductor modeling as an approximation. This present investigation suggests that this approximation is not always valid, as certain regimes are identified where geometrical parameters have critical impact on the localization and energetic properties of excitons.
The mechanism of the Triazolinedione (TAD) tyrosine bioconjugation reaction is investigated using quantum-chemical methods. By comparison of different conceivable mechanisms and their energetic ordering, the TAD tyrosine bioconjugation is found to proceed by means of a base-mediated electrophilic aromatic substitution reaction.
The kth nearest neighbor entropy estimation protocol is investigated. This estimator promises accurate entropy estimates even for flexible molecules with multiple structural minima. Our granular investigation of formal and practical properties of the estimator suggests that the uneven variance of a molecule’s vibrational modes is the cause of the observed slow convergence of the estimator. A rescaling procedure to reestablish fast convergence is suggested and benchmarks are performed.
Paclitaxel (PTX) is one of the leading drugs against breast and ovarian cancer. Due to its low solubility, treatment of the patients with this drug requires a very well-suited combination with a soluble pharmaceutical excipient to increase the bioavailability and reduce the strong side ef-fects. One efficient way to achieve this in the future could be the incorporation of PTX into pol-ymeric micelles composed of poly(2-oxazoline) based triblock copolymers (POL) which ena-bles PTX loadings of up to 50 wt.%. However, structural information at an atomic level and thus the knowledge of interaction sites within these promising but complex PTX-POL formula-tions were not yet available. Such results could support the future development of improved excipients for PTX and suitable excipients for other pharmaceutical drugs. Therefore, a solid-state MAS NMR investigation of these amorphous formulations with different POL-PTX com-positions was performed in this thesis as this gives insights of the local structure at an atomic level in its solid state. NMR in solution showed very broad 13C signals of PTX for this system due to the reduced mobility of the incorporated drug which exclude this as an analytical meth-od.
In a first study, crystalline PTX was structurally characterized by solid-state NMR as no com-plete 13C spectrum assignment and no 1H NMR data existed for the solid state. In addition, the asymmetric unit of the PTX crystal structure consists of two molecules (Z'=2) that can only be investigated in its solid state. As crystalline PTX in total has about 100 different 13C and 1H chemical shifts with very small differences due to Z’=2, and furthermore, its unit cell consisting of more than 900 atoms, accompanying GIPAW (CASTEP) calculations were required for NMR signal assignments. These calculations were performed using the first three available purely hydrous and anhydrous PTX structures, which were determined by XRD and published by Vel-la-Zarb et al. in 2013. Within this thesis, is was discovered that two investigated batches of commercially available PTX from the same supplier both contained an identical and so far un-known PTX phase that was elucidated by PXRD as well as solid-state NMR data. One of the two batches consists of an additional phase that was shown to be very similar to a known hy-drated phase published in 2013.[1] By heating the batch with the mixture of the two phases un-der vacuum, it is transformed completely to the new dry phase occurring in both PTX batches. Since the drying conditions to obtain anhydrous PTX in-situ on the PXRD setup described by Vella-Zarb et. al.[1] were much softer than ours, we identify our dry phase as a relaxed version of their published anhydrate structure. The PXRD data of the new anhydrate phase was trans-ferred into a new structural model, which currently undergoes geometry optimization. Based on solid-state NMR data at MAS spinning frequencies up to 100 kHz, a 13C and a partial 1H signal assignment for the new anhydrous structure were achieved. These results provided sufficient structural information for further investigations of the micellar POL-PTX system.
In a second study, the applicability and benefit of two-dimensional solid-state 14N-1H HMQC MAS NMR spectra for the characterization of amorphous POL-PTX formulations was investi-gated. The mentioned technique has never been applied to a system of similar complexity be-fore and was chosen because around 84% of the small-molecule drugs contain at least one nitrogen atom. In addition, the number of nitrogen atoms in both POL and PTX is much smaller than the number of carbons or hydrogens, which significantly reduces the spectral complexity. 14N has a natural abundance of 99.6% but leads to quadrupolar broadening due to its nuclear spin quantum number I = 1. While this is usually undesirable due to broadening in the resulting 1D 14N NMR spectra, this effect is explicitly used in the 2D 14N-1H HMQC MAS experiment. The indirect 14N measurement can avoid the broadening while maintaining the advantage of the high natural abundance and making use of the much more dispersed signals due to the additional quadrupolar shifts as compared to 15N.
This measurement method could be successfully applied to the complex amorphous POL-PTX mixtures. With increasing PTX loading of the formulations, additional peaks arise as spatial proximities of the amide nitrogens of POL to NH or OH groups of PTX. In addition, the 14N quadrupolar shift of these amide nitrogens decreases with increasing PTX content indicating a more symmetric nitrogen environment. The latter can be explained by a transformation of the trigonal planar coordination of the tertiary amide nitrogen atoms in pure POL towards a more tetrahedral environment upon PTX loading induced by the formation of hydrogen bonds with NH/OH groups of PTX.
In the third and last project, the results of the two abovementioned studies were used and ex-tended by solid state 13C and two-dimensional 1H-13C as well as 1H-1H MAS NMR data with the aim to derive a structural model of the POL-PTX formulations at an atomic level. The knowledge of the NMR signal assignments for crystalline PTX was transferred to amorphous PTX (present in the micelles of the formulations). The 13C solid-state NMR signals were evalu-ated concerning changes in chemical shifts and full widths of half maximum (FWHM) for the different PTX loadings. In this way, the required information about possible interaction sites at an atomic level becomes available. Due to the complexity of these systems, such proximities often cannot be assigned to special atoms, but more to groups of atoms, as the individual de-velopments of line widths and line shifts are mutually dependent. An advantageous aspect for this analysis was that pure POL already forms unloaded micelles. The evaluation of the data showed that the terminal phenyl groups of PTX seem to be most involved in the interaction by the establishment of the micelle for lowest drug loading and that they are likely to react to the change in the amount of PTX molecules as well. For the incorporation of PTX in the micelles, the following model could be obtained: For lowest drug loading, PTX is mainly located in the inner part of the micelles. Upon further increasing of the loading, it progressively extends to-ward the micellar shell. This could be well shown by the increasing interactions of the hydro-phobic butyl chain of POL and PTX, proceeding in the direction of the polymer backbone with rising drug load. Furthermore, due to the size of PTX and the hydrodynamic radius of the mi-celles, even at the lowest loading, the PTX molecules partially reach the core-shell interface of the micelle. Upon increasing the drug loading, the surface coverage with PTX clusters increas-es based on the obtained model approach. The latter result is supported by DLS and SANS data of this system. The abovementioned results of the 14N-1H HMQC MAS investigation of the POL-PTX formulations support the outlined model.
As an outlook, the currently running geometry optimization and subsequently scheduled calcu-lation of the chemical shieldings of the newly obtained anhydrous PTX crystal structure can further improve the solid-state NMR characterization through determination of further spatial proximities among protons using the existing 2D 1H(DQ)-1H(SQ) solid-state MAS NMR spec-trum at 100 kHz rotor spinning frequency. The 2D 14N-1H HMQC MAS NMR experiments were shown to have great potential as a technique for the analysis of other disordered and amor-phous drug delivery systems as well. The results of this thesis should be subsequently applied to other micellar systems with varying pharmaceutical excipients or active ingredients with the goal of systematically achieving higher drug loadings (e.g., for the investigated PTX, the similar drug docetaxel or even different natural products). Additionally, it is planned to transfer the knowledge to another complex polymer system containing poly(amino acids) which offers hy-drogen bonding donor sites for additional intermolecular interactions. Currently, the POL-PTX system is investigated by further SANS studies that may provide another puzzle piece to the model as complementary measurement method in the future. In addition, the use of MD simu-lations might be considered in the future. This would allow a computerized linking of the differ-ent pieces of information with the aim to determine the most likely model.
The scope of computational chemistry can be broadened by developing new methods and more efficient algorithms. However, the evaluation of the applicability of the methods for the different fields of chemistry is equally important. In this thesis systems with an unusual and complex electronic structure, such as excitonic states in organic semiconductors, a boron-containing bipolaron and the excited states of pyracene were studied and the applicability of the toolkit of computational chemistry was investigated. Concerning the organic semiconductors the focus was laid on organic solar cells, which are one of the most promising technologies with regard to satisfying the world's need for cheap and environmentally sustainable energy. This is due to the low production and material costs and the possibility of using flexible and transparent devices. However, their efficiency does still not live up to the expectations. Especially the exciton diffusion lengths seem to be significantly too short. In order to arrive at improved modules, a fundamental understanding of the elementary processes occurring in the cell on the molecular and supramolecular level is needed. Computational chemistry can provide insight by separating the different effects and providing models for predictions and prescreenings. In this thesis, the focus was laid on the description of excitonic states in merocyanines and perylene-based dyes taking the influence of the environment into account.
At first, the photochemical isomerization between two configurations of 6-nitro BIPS observed experimentally was studied by first benchmarking several functionals against SCS-ADC(2) in the gas phase and subsequently calculating the excited-state potential energy surface. The geometries obtained from a relaxed scan in the ground state as well as from a scan in the excited state were used. The environment was included using different polarizable continuum models. It was shown that the choice of the model and especially the question of the state specificity of the approach is of vital importance. Using the results of the calculations, a two-dimensional potential energy surface could be constructed that could be used to explain the experimental findings. Furthermore, the importance of the excited-state isomerization as a potential deactivation channel in the exciton transport was pointed out.
Then the assessment of the suitability of different merocyanines for optoelectronic applications with quantum-chemical methods was discussed. At first, the effect of the environment on the geometry, especially on the bond length alternation pattern, was investigated. It was shown that the environment changes the character of the ground-state wave function of several merocyanines qualitatively, which means that the results of gas-phase calculations are meaningless - at least when a comparison with solution or device data is desired. It was demonstrated that using a polarizable continuum model with an effective epsilon, a qualitative agreement between the calculated geometry and the geometry in the crystal structure can be obtained. Therefore, by comparing the bond length alternation in solution and in the crystal, a rough estimate of the effect of the crystal environment can be made.
It was further shown that the connection between the HOMO energy and the open-circuit voltage is not as simple as it is often implied in the literature. It was discussed that it is not clear whether the HOMO of a single molecule or a $\pi$-stack containing several monomers should be used and if the environmental charges of the bulk phase or the interface should be included. Investigating the dependence of the HOMO energy on the stack size yielded no definitive trend. Furthermore, it was discussed that the effect due the optimization of the modules (solvent, bulk heterojunction) during the production masks any potential correlation between the HOMO energy and measured open-circuit values. Therefore, a trend can only be expected for unoptimized bilayer cells. It was concluded that ultimately, the importance of the HOMO energy should not be overestimated.
The correlation between the exciton reorganization energy and the so-called cyanine limit, which is predicted by a simple two-state model, was also discussed. By referring to the results of VB calculations, it was discussed that the correlation indeed exists and is non-negligible, although the effect is not as strong as one might have expected. In this context, a potential application of a VB/MM approach was covered briefly. The importance of the molecular reorganization energy and the device morphology was also discussed.
It was concluded that the optimization of merocyanines for organic optoelectronic devices is inherently a multiparameter problem and one cannot expect to find one particular parameter, which solely controls the efficiency.
The perylene-based dyes were studied with a focus on the description of a potential trapping mechanism involving an intermolecular motion in a dimer. The aim was to find methods which can be applied to larger model systems than a dimer and take the effect of the environment into account. As a test coordinate the longitudinal shift of two monomers against each other was used. At first, it was demonstrated how the character of an excited state in a dimer can be defined and how it can be extracted from a standard quantum-chemical calculation. Then several functionals were benchmarked and their applicability or failure was rationalized using the character analysis. Two recipes could be proposed, which were applied to a constraint optimization (only intermolecular degrees of freedom) in the excited states of the PBI dimer and to the description of the potential energy surfaces of ground and excited states along a longitudinal displacement in the perylene tetramer, respectively.
It was further demonstrated that the semi-empirical OMx methods fail to give an accurate description of the excited-state potential energy surfaces as well as the ground-state surface along the test coordinate. This failure could be attributed to an underestimation of overlap-dependent terms. Consequently, it could be shown that the methods are applicable to large intermolecular distances, where the overlap is negligible. The results of DFT calculations with differently composed basis sets suggested that adding an additional single p-function for each atom should significantly improve the performance.
QM/MM methods are ideally suited to take the effect of the environment on a a dimer model system into account. However, it was shown that standard force fields also give an incorrect description of the interaction between the monomers along the intermolecular coordinate. This failure was attributed to the isotropic atom-atom interaction in the repulsion term of the Lennard-Jones potential. This was corroborated using two simple proof-of-principle anisotropy models. Therefore, a novel force field called OPLS-AA_O was presented that is based on OPLS-AA, but uses an anisotropic model for the repulsion. The model involves the overlap integral between the molecular densities, which are modeled as a sum of atom-centered p-type Gaussian functions. It was shown that using this force field an excellent agreement with the DFT results can be obtained when the correct parameters are used. These parameters, however, are not very generalizable, which was attributed to the simplicity of the model in its current state (using the same exponential parameter for all atoms). As a short excursion, the applicability of an MO-based overlap model was discussed.
It was demonstrated that the repulsion term based on the density overlap can be used to correct the failure of the OMx methods for the ground states. This is in accord with the assumption that an underestimation of the overlap terms is responsible for the failure.
It was shown that OPLS-AA_O also gives an excellent description of the longitudinal shift in a PBI tetramer. Using the tetramer as a test system and applying the recipe obtained in the TDDFT benchmark for the QM-part and OPLS-AA_O for the MM-part in conjunction with an electrostatic embedding scheme, a QM/MM description of the excited states of the PBI dimer including the effect of the environment could be obtained.
In the last chapter the theoretical description of the Bis(borolyl)thiophene dianion and the excited states of pyracene were discussed. The electronic structure of the Bis(borolyl)thiophene dianion - a negative bipolaron - was elucidated using DFT and CASPT2 methods. Furthermore, an estimation of the extent of triplet admixture to the ground state due to spin-orbit coupling was given.
In the second project the S1 and S2 states of pyracene were computed using SCS-CC2 and SCS-ADC(2) and an estimation for the balance between aromaticity and ring strain was given. This also involved computing the vibrational frequencies in the excited states.
In both studies the results of the computations were able to rationalize and complete experimental results.
In the context of this dissertation very long ranged exciton diffusion lengths (LD) were simulated for perylene-based materials under ideal conditions. This leads to the conclusion that the short LD values in existing materials result from an extrinsic and intrinsic immobilization. The latter, which is a specific material property, is based on a relaxation of the exciton into self-trapping states. An in-depth understanding of the atomistic processes defining self-trapping is essential to developing materials with long LD in the future, in which intrinsic immobilization is prevented. For the development of such a mechanistic understanding it is crucial that a clear relationship between molecular structure and LD is available. This is given by single crystals of diindeno perylene (DIP) and α-perylene tetracarboxylic anhydride (α-PTCDA). An extraordinary large LD of 90 nm was measured for the first one, while the latter possesses only 22 nm. Part of this thesis was to deliver reasons for this discrepancy. Only self-trapping comes into question to explain the different LD values. One reason for the different self-trapping in DIP and α-PTCDA could lie in the electronic structure. However, it was possible to demonstrate that a wide range of perylene-based materials possess no significant differences in their electronic structures. Consequently, such differences can be neglected for the explanation of immobilization mechanisms for the exciton. A further possible explanation could be polarization effects in the crystal, which influences the electronic structure of perylene based materials differently. Especially their influence on charge transfer (CT) states, which are located above the optically bright Frenkel state, was in question because such states could be stabilized by a polarizable surrounding. A significant influence of polarization effects on all considered states were excluded by using a polarizable continuum model. Hence, the small LD values in α-PTCDA are an evidence for self-trapping, which produces a crystal structure built up by π-stacks, while the one of DIP is of herringbone type. Since polarization effects can be neglected, is the dimer only via steric restrictions influenced by the crystal. Hence, a method describing self-trapping has to consider such effects, so that a mechanical embedding QM/MM approach is sufficient. Now, potential energy surfaces were calculated, on which wave packet dynamics were subsequently performed. In this way, atomistic mechanisms for the immobilization of excitons were described for the first time in organic materials. Self-trapping was studied in crystals of α-PTCDA by potential energy surfaces, which map an intermolecular shift motion of the dimer in the crystal. An immobilization of excitons occurs within 500 fs, which results from an irreversible energy loss together with a local deformation of the crystal lattice. This prevents a further transport of the exciton. In the case of DIP, this immobilization does not proceed due to high barriers. These barriers result from the herringbone type packing motif in the DIP crystal. This discrepancy in the dynamics explains the different LD values in DIP and α-PTCDA. In a further example, an exciton immobilization was found in helical π-aggregates of perylene tetracarboxylic bisimide (PBI) molecules. Self-trapping is caused by a relaxation mechanism, in which the exciton is transferred by asymmetric vibrations of the aggregate from the bright to a dark Frenkel state within 200 fs, whereby the transition is mediated by a CT state. However, the CT state is almost non-populated during the whole mechanism so that its participation could not yet be proven experimentally. This entire procedure is solely possible in helical aggregates, because only for such structures is there a CT state located next to the bright Frenkel state. At the final Frenkel state a torsional motion around the π-stacking axis is possible so that the loss in energy and the local rearrangement of the aggregate structure occurs, which means a self-trapping of the exciton. This mechanism is in perfect agreement with all available experimental data. These insights allow the conclusion that in future materials for organic solar cells an irreversible and ultrafast deformation of aggregates after photo-absorption must be avoided. Only in this way long LD values can be achieved and exciton self-trapping can be prevented. However, small LD values are always predicted in helical aggregates of perylene-based materials, because exciton immobilization occurs already due to small molecular motions. For this reason such aggregates are inappropriate for the use in organic solar cells. Long LD values are expected for aggregate structures with long intermolecular shifts or molecules with bulky substituents.
Quantum chemical calculations of circular dichroism (CD) spectra in combination with experimental CD studies are one of the most efficient analytical tools for the elucidation of the three-dimensional structure of a chiral molecule. In the present work 18 chiral compounds of most different molecular structures and origins were investigated using various theoretical methods (the semiempirical CIS methods, the time-dependent DFT and DFT/MRCI approaches). The advantages and limitations of the applied methods were discussed in the context of the studied compounds. Furthermore, the last part of this work deals with the CD investigations of a chiral compound in the crystalline state. A well-known natural product with a specific conformation/CD spectrum behavior was used as a model compound to examine a novel solid-state CD method and to investigate the possibility of its improvement to provide a higher reliability for the assignment of the absolute configuration.
This work focuses on theoretical approaches for predicting the valence and core excited states of aggregate systems. For the valence excitations, TD-HF and TD-DFT with different functionals have been tested at the Perylene bisimide (PBI) system. A simple character analysis method based on the calculated transition dipole moments is proposed. However, this method does not work for excited states without any transition dipole moment. Thus, we proposed a more general and more valid method based on a calculated CIS type wavefunction for the character analysis. Furthermore, a model Hamiltonian method is derived from a localized picture. The energies of the diabatic states and the corresponding coupling parameters were also determined on the basis of ab initio calculations. For the core excitation, three different methods were validated for C 1s-excited and ionized states if several small molecules. Also we tested the basis sets dependence of these core excited states. Based on those results, we chose the frozen core approximation method to evaluate the core excited states of NTCDA molecules. In order to explain the findings in the experiments, we developed an algorithm to evaluate the exciton coupling parameter where non-orthogonal MOs are used.
Für die Lösung der quantenmechanischen Bewegungsgleichungen, die komplexe, molekulare Systeme beschreiben, sind effiziente und verlässliche Näherungsverfahren erforderlich. Die Dichtefunktionaltheorie (DFT) stellt für die Behandlung der Elektronenwechselwirkung in vielen Fällen den besten Kompromiss zwischen Effizienz und Genauigkeit dar. Im Rahmen der DFT wird die gesamte nicht-klassische Elektron-Elektron-Wechselwirkung im so genannten Austausch-Korrelationsfunktional angenähert. Viele solcher Näherungen sind semi-empirischer Natur, andere wurden ausschließlich von physikalischen Überlegungen abgeleitet. In globalen Hybridfunktionale wird ein konstanter Anteil der integrierten DFT-Austauschenergiedichte durch exakten Austausch aus der Hartree-Fock Näherung ersetzt. Das populärste Funktional B3LYP enthält 20 % exakten Austausch und mehrere empirische Parameter. Der optimale Prozentsatz hängt allerdings sehr stark von den zu berechnenden Systemen und molekularen Eigenschaften ab. Eine Lösung dieses Problems sollten lokale Hybridfunktionale liefern, in denen die Beimischung der exakten Austauschenergiedichte über eine lokale Mischfunktion (LMF) gesteuert wird und daher positions- und molekülabhängig ist. In dieser Arbeit wird ein semi-empirischer Ansatz für die Entwicklung neuer lokaler Hybridfunktionale verfolgt: während die Energiedichten unverändert aus etablierten Näherungen zum Austauschkorrelationsfunktional übernommen werden, stehen parametrisierte LMFs im Zentrum der Untersuchungen. Die verschiedenen LMFs beinhalten neben mindestens einem empirischen Parameter eine Variable die vom Quotienten der von-Weizsäcker kinetischen Energiedichte und der korrelierten kinetischen Energiedichte (sogenannte t-LMFs) bzw. dem reduzierten Dichtegradienten (bezeichnet als t-LMFs) abhängt. Weitere LMFs werden durch zusätzliche Berücksichtigung der Spinpolarisation erhalten. Alle Parameter werden an Atomisierungsenergien bzw. Reaktionsbarrieren bekannter molekularer Testsätze gefittet. Durch Visualisierung der LMFs können zusätzlich Einblicke in den physikalischen Hintergrund und in Möglichkeiten der Weiterentwicklung gewonnen werden. Es wurde beispielsweise beobachtet, dass entlang einer gedehnten Bindung höhere Werte der LMF und damit größere Beimischungen exakter Austauschenergie in Übergangszuständen einhergehen. Dieser Effekt ist für t-LMFs am ausgeprägtesten und korreliert mit besseren Ergebnissen für Reaktionsbarrieren mit lokalen Hybridfunktionalen, die auf einer t-LMF basieren. Bis auf wenige Ausnahmen leiten sich die lokalen Hybridfunktionale in dieser Arbeit aus dem Austausch- und Korrelationsfunktional der lokalen Dichtenäherung (LSDA) ab und enthalten keine Gradientenkorrektur im Sinne der GGA (generalized gradient approximation). Die neuen Funktionale wurden zunächst nicht-selbstkonsistent in eine Entwicklerversion des quantenchemischen Programmpaketes Turbomole implementiert. Das bedeutet, für gegebene Molekülorbitale bzw. eine gegeben Elektronendichte kann lediglich die Gesamtenergie berechnet werden. Dies ist eine anerkannte Näherung, die vor allem für die Optimierung der Parameter eine große Zeitersparnis darstellt. Um letztlich orbitalabhängige, molekulare Eigenschaften berechnen zu können wird neben der Gesamtenergie auch noch das zugehörige lokale Hybridpotential benötigt. Für die selbstkonsistente Implementierung wird die funktionale Ableitung der Austauschkorrelationsenergie nach den Orbitalen bestimmt. Daraus resultierend müssen neben den üblichen lokalen Austauschkorrelationspotentialtermen auch Integrale berechnet werden, die das mit der LMF gewichtete nicht-lokale exakte Austauschpotential enthalten. Die entsprechenden Terme kann man, genauso wie die exakte Austauschenergiedichte an sich, nicht analytisch berechnen. Früheren Ansätzen folgend wurden sie in der vorliegenden Arbeit in einer Basissatzentwicklung angenähert, wobei der Einfachheit halber die atomaren Basisfunktionen verwendet wurden. Um die Genauigkeit dieser sogenannten RI (resolution of the identity)-Näherung validieren zu können und auch schon im Hinblick auf die Anpassung einer Hilfsbasis, wurde darüber hinaus die numerische Berechnung aller Integrale, die das exakte Austauschpotential und die entsprechende Energiedichte enthalten, implementiert. Unter Verwendung der RI-Näherung ist der Rechenaufwand lokaler Hybride vergleichbar mit dem globaler Hybridfunktionale: Während die formale Skalierung in Abhängigkeit der Systemgröße gleich ist, ergab sich ein etwas höherer Vorfaktor für die lokalen Hybride. Verschiedene Literaturbekannte Testsätze mit Atomisierungsenergien, Reaktionsbarrieren, Dissoziationsenergien oder Gleichgewichtsabständen, die teilweise einige Schwächen bisheriger Dichtefunktionalnäherungen aufdecken, wurden berücksichtigt. Für die 223 Atomisierungsenergien des G3 Testsatzes stellen alle unsere Funktionale eine signifikante Verbesserung gegenüber B3LYP dar. Atomisierungsenergien sind insofern ein sensibler Test, da alle Bindungen gebrochen werden und Fehlerkompensation eine untergeordnete Rolle spielt. Vor allem lokale Hybridfunktionale, deren LMFs neben der kinetischen Energiedichte explizit von der Spinpolarisation abhängen, lieferten hervorragende Resultate. Obwohl im Vergleich zu Atomisierungsenergien für die korrekte Berechnung von Reaktionsbarrieren im Allgemeinen mehr exakter Austausch benötigt wird, sind unsere Funktionale auch für zwei Testsätze mit jeweils 38 Reaktionsbarrieren besser als B3LYP. Zwar kann mit einem globalen Hybrid mit 50 % exaktem Austausch eine geringere Abweichung von den Richtwerten erzielt werden, aber ein solches Funktional ist für thermochemische Daten unzureichend. Hier wurde erstmals gezeigt, dass lokale Hybridfunktionale ohne Gradientenkorrektur sowohl für Thermochemie als auch für Kinetik zufrieden stellende Ergebnisse liefern können. Das Dissoziationsverhalten symmetrischer Radikalkationen stellt für die hier diskutierten Dichtefunktionale nach wie vor eine Herausforderung dar: Die Dissoziationsenergien von sieben Modellsystemen werden mit unseren Funktionalen stark überschätzt und Gleichgewichtsabstände unterschätzt. Insgesamt sind die Werte nur marginal besser als mit B3LYP. Neben Eigenschaften von Hauptgruppenverbindungen wurden zudem Übergangsmetalldimere und -monohydride untersucht. Für erstere ist eine gute Beschreibung dynamischer sowie statischer Elektronenkorrelation ausschlaggebend. In den Hydriden andererseits dominiert mit gängigen Dichtefunktionalen die unphysikalische Selbstwechselwirkung eines Elektrons mit sich selbst. Für die 3d-Übergangsmetalldimere sind die getesteten Funktionale genauso gut wie B3LYP und für die Hydride etwas besser. Atomare s-d Transferenergien von 3d Übergangsmetallen verbleiben auch für unsere lokalen Hybridfunktionale, die insgesamt schlechtere Ergebnisse erzielen als B3LYP, noch problematisch. Das hierfür geeignetste lokale Hybridfunktional basiert auf einer s-LMF und beinhaltet LYP Korrelation. Für die isotropen Hyperfeinkopplungskonstanten (HFCCs) kleiner Hauptgruppenverbindungen wurden zufriedenstellende Ergebnisse (ähnlich wie B3LYP) mit einem t-LMF basierten lokalen Hybrid erzielt. Die RI Näherung zum lokalen Hybridpotential wurde dem numerisch exakten Potential für die Berechnung von Gesamtenergien, isotrope HFCCs und Orbitalenergien für verschiedene Basissätze gegenübergestellt. Wie erwartet ist der Fehler für Gesamtenergien mit der RI-Näherungen vergleichsweise gering, vor allem relativ zu den verbleibenden Abweichungen von experimentellen Energien. Der Vergleich der mittleren absoluten Abweichung von experimentellen Werten für 26 isotrope HFCCs zeigt sogar für mittelgroße und kontrahierte IGLO Basissätze nur geringe Unterschiede zwischen dem RI-Potential und dem numerisch exakten lokalen Hybridpotential. Die Analyse der HFCCs einzelner Moleküle und der Orbitalenergien des CN Moleküls offenbart allerdings, dass Ungenauigkeiten aufgrund der RI-Näherung hier eine größere Rolle spielen, vor allem wenn zu kleine atomare Basissätze verwendet werden. Von den untersuchten lokalen Hybriden stellen sich einige als hervorragende Kandidaten für die Berechnung thermochemischer und kinetischer Eigenschaften heraus. Jeweils unterschiedliche Funktionale erzielen darüber hinaus mit den besten bekannten Funktionalen vergleichbare Ergebnisse für isotrope Hyperfeinkopplungskonstanten und ausgewählte Eigenschaften kleiner Übergangsmetallverbindungen. Die in dieser Arbeit präsentierten lokalen Hybridfunktionale stellen daher einen wichtigen Schritt in der Entwicklung universeller Näherungen zum Austauschkorrelationsfunktional dar. Zur akkuraten Beschreibung molekularer Eigenschaften von Übergangsmetallkomplexen und dem Dissoziationsverhalten von Radikal-Kation-Dimeren neben Thermochemie und Kinetik, werden in Zukunft wohl komplexere LMFs benötigt. Um konkurrenzfähige lokale Hybride mit gradientenkorrigierter Austausch- und Korrelationsenergiedichte zu entwickeln, müssen darüber hinaus weitere Studien zum Einfluss des abweichenden Eichursprungs der miteinander kombinierten Austauschenergiedichten durchgeführt werden. Eine andere Möglichkeit ist die Entwicklung speziell abgestimmter Korrelationsfunktionale für lokale Hybride. Außerdem sollte die Qualität der RI-Näherung zum lokalen Hybridpotential detaillierter untersucht werden. Hierfür könnten zum Beispiel Ionisierungsenergien und Elektronenaffinitäten herangezogen werden. Um zusätzliche Abweichungen oder sogar fälschlicherweise "zu gute" Ergebnisse bei Validierungsrechnungen zu vermeiden, sollten Hilfsbasen für die Entwicklung des nicht-lokalen exakten Austauschpotentials implementiert und optimiert werden. Einer der nächsten Implementierungsschritte sollte auch Gradienten bezüglich der Kernkoordinaten beinhalten, um die Validierung der neuen lokalen Hybridfunktionale auf Strukturoptimierungen auszuweiten.
The spectroscopic properties of molecular aggregates have been investigated by means of quantum dynamical calculations. Thereby both linear and nonlinear spectroscopic techniques have been taken into account. For the simulation of absorption and CD-spectra, coupling effects were regarded as well as the relative orientation of the monomer units in order to determine the parameters by reproducing measured spectra. For a more detailled description, results from quantum chemical calculations have also been included. Furthermore, investigations on nonlinear spectroscopy of molecular dimers have been performed.
Although known about and investigated since the late 1970’s, the picture of the basic principles governing inhibitor strengths and the structure-activity relationships of the cysteine protease inhibition mechanism is still very incomplete. Computational approaches can be a very useful tool for investigating such questions, as they allow the inspection of single, specific effects in isolation from all others, in a manner very difficult to achieve experimentally. The ab initio treatments of such large systems like proteins are still not feasible. However, there is a vast number of computational approaches capable of dealing with protein structures with reasonable accuracy. This work presents a summary of theoretical investigations into cysteine protease cathepsin B using a range of methods. We have concentrated on the investigation of cysteine protease inhibition by epoxide- and aziridine-based inhibitors in order to obtain better insight into these important topics. Various model systems are simulated by means of pure quantum mechanical methods and by hybrid (QM/MM) methods. Both approaches provide a static picture. Dynamical effects are then accounted for by additional molecular dynamics (MD) simulations, using both classical and QM/MM MD approaches. The quantum mechanical approach was used to study very small model systems consisting only of the electrophilic warhead of the inhibitor (both substitituted and not) and molecular moieties simulating a very simplified protein active site (methylthiolate instead of Cys29 and methylimidazolium instead of His199 residue) and solvent surroundings (two waters or two ammonium ions, in combination with a continuum solvent model). Although simple, such a system provides a good description of the most important interactions involved in the inhibition reaction. It also allows investigation of the influence of the properties of the electrophilic warhead on the reaction rate. Beside the properties of the electrophilic warhead, the protein and solvent environment is also an important factor in the irreversible deactivation of the enzyme active site by the inhibitor. The non-covalent interactions of the inhibitor with the oxyanion hole and other subsites of the enzyme, as well as its interaction with the solvent molecules, need to be explicitly taken into account in the calculations, because of their possible impact on the reaction profile. As molecular modeling methods allow the treatment of such large systems, but lack the possibility of describing covalent interactions, our method of choice was the combined quantum mechanics/molecular modeling approach. By splitting the system into a smaller part that undergoes the bond cleavage/formation process and must be treated quantum mechanically, and a larger part, comprised of the rest of the protein, which could be treated using force fields, we managed to simulate the system at the desired precision. Our investigations concentrated on the role of His199 in the inhibition mechanism as well as on the structure-reactivity relationships between cysteine protease and various inhibitors, yielding new insight into the kinetics, regio- and stereospecificity of the inhibition. In particular, our calculations provide the following insights: i.) an explanation for the regioselectivity of the reaction, and original insight into which interactions affect the stereoselectivity; ii.) a clear model which explains the known structure-activity relationships and connects these effects with the pH-dependency of the inhibition; iii.) our computations question the generally accepted two-step model by showing that substituent effects accelerate the irreversible step to such an extent that the achievement of an equilibrium in the first step is doubtful; iv.) by way of theoretical characterizations of aziridine models, the reasons for similarities and differences in the mode of action of epoxide- and aziridine-based inhibitors are elucidated; and finally, v.) combining our results with experimental knowledge will allow rational design of new inhibitors. To account for dynamical effects as well, molecular dynamics (MD) computations were also performed. In these calculations the potential energy was computed at the force field level. The results not only supported and clarified the QM/MM results, but comparison with previous X-ray structures helped correct existing errors in the available geometrical models and resolved inconsistencies in the weighting of various factors governing the inhibition. In the work the first QM/MM MD calculations on the active site of the cysteine proteases are presented. In contrast to the MD simulations, these calculations used potential energies computed at the QM/MM-level. With the help of these computations we sought to address strongly disputed questions about the reasons for the existence of the active site ion pair and its role in the high activity of the enzyme.