@phdthesis{Schmidt2015,
  author    = {Schmidt, Thomas Christian},
  title     = {Theoretical Investigations on the Interactions of Small Compounds with their Molecular Environments},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-127860},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {Im ersten Teil dieser Arbeit wird eine Kombination theoretischer Methoden f{\"u}r die strukturbasierte Entwicklung neuer Wirkstoffe pr{\"a}sentiert. Ausgehend von der Kristallstruktur eines kovalenten Komplexes einer Modellverbindung mit dem Zielprotein wurde mit Hilfe von quantenmechanischen und QM/MM Rechnungen die genaue Geometrie des vorausgehenden nicht-kovalenten Komplexes betimmt. Letztere ist der bestimmende Faktor f{\"u}r die Reaktivit{\"a}t des Inhibitors gegen{\"u}ber der katalytisch aktiven Aminos{\"a}ure und damit f{\"u}r die Ausbildung einer kovalenten Bindung. Aus diesem Grund wurde diese Geometrie auch f{\"u}r die Optimierung der Substitutionsmusters des Ihnibitors verwendet, um dessen Affinit{\"a}t zum Zielenzyme zu verbessern ohne dass dieser seine F{\"a}higkeit kovalent an das aktive Zentrum zu binden verliert. Die Optimierung des Substitutionsmuster wurde doch Methode des Molekularen Dockings unterst{\"u}tzt, das diese optimal dazu geeignet sind, Bindungsaffinit{\"a}ten vorherzusagen, die durch eine Modifikation der chemischen Struktur entstehen. Eine Auswahl der besten Strukturen wurde anschließend verwendet, um zu {\"u}berpr{\"u}fen, ob die ver{\"a}nderten Molek{\"u}le noch gen{\"u}gen Reaktivit{\"a}t gegen{\"u}ber dem Zielprotein aufweisen. Molek{\"u}ldynamik Simulationen der neuen Verbindungen haben jedoch gezeigt, dass die ver{\"a}nderten Verbindungen nur so and das Protein binden, dass die Bilung eine kovalenten Bindung zum Enzym nicht mehr m{\"o}glich ist. Daher wurden in einem weiteren Schritt die Modellverbindungen weiter modifiziert. Neben {\"A}nderungen im Substitutionsmuster wurde auch die chemische Struktur im Kern ver{\"a}ndert. Die Bindungsaffinit{\"a}ten wurde wieder mittels Docking {\"u}berpr{\"u}ft. F{\"u}r die besten Bindungsposen wurden wieder Simulationen zur Molek{\"u}ldynamik durchgef{\"u}hrt, wobei diesmal die Ausbildung einer kovalenten Bindung zum Enzyme m{\"o}glich erscheint. In einer abschließenden Serie von QM/MM Rechnungen unter Ber{\"u}cksichtigung verschiedener Protonierungszust{\"a}nde des Inhibitors und des Proteins konnten Reaktionspfade und zugeh{\"o}rige Reaktionsenergien bestimmt werden. Die Ergebnisse lassen darauf schließen, dass eines der neu entwickelten Molek{\"u}le sowohl eine stark verbesserte Bindungsaffinit{\"a}t wie auch die M{\"o}glichkeit der kovalenten Bindung an Enzyme aufweist. Der zweite Teil der Arbeit konzentriert sich auf die Umgebungseinfl{\"u}sse auf die Elektronenverteilung eines Inhibitormodells. Als Grundlage dient ein vinylsulfon-basiertes Moek{\"u}l, f{\"u}r das eine experimentell bestimmte Kristallstruktur sowie ein theoretisch berechneter Protein Komplex verf{\"u}gbar sind. Ein Referendatensatz f{\"u}r diese Systeme wurde erstellt, indem der Konformationsraum des Inhibitors nach m{\"o}glichen Minimumsstrukturen abgesucht wurde, welche sp{\"a}ter mit den Geometrien des Molek{\"u}ls im Kristall und im Protein verglichen werden konnten. The Geometrie in der Kristallumgebung konnte direkt aus den experimentellen Daten {\"u}bernommen werden. Rechnungen zum nicht-kovalenten Protein Komplex hingegen haben gezeigt, dass f{\"u}r das Modellsystem mehrere Geometrien des Inhibiors sowie zwei Protonierungszust{\"a}nde f{\"u}r die katalytisch aktiven Aminos{\"a}uren m{\"o}glich sind. F{\"u}r die Analyse wurden daher alle m{\"o}glichen Proteinkomplexe mit der Kristallstruktur verglichen. Ebenso wurden Vergleiche mit der Geometrie des isolierten Molek{\"u}ls im Vakuum sowie der Geometrie in w{\"a}ssriger L{\"o}sung angestellt. F{\"u}r die Geometrie des Molek{\"u}ls an sich ergab sich eine gute {\"U}bereinstimmung f{\"u}r alle Modellsysteme, f{\"u}r die Wechselwirkungen mit der Umgebung jedoch nicht. Die Ausbildung von Dimeren in der Kristallumgebung hat einen stark stablisierenden Effekt und ist einer der Gr{\"u}nde, warum dieser Kristall so gut wie keine Fehlordungen aufweist. In den Proteinkomplexen hingegen ergibt sich eine Abstoßung zwischen dem Inhibitor und einer der katalytisch aktiven Aminos{\"a}uren. Als Ursache f{\"u}r diese Abstoßung konnte die Einf{\"u}hrung der Methylaminfunktion ausgemacht werden. Vermutlicherweise f{\"u}hrt diese strukturelle {\"A}nderung auch dazu, dass der Modellinhibitor nicht in der Lage ist, so wie die Leitstruktur K11777 an das aktive Zentrum des Enzyms zu binden.},
  subject      = {Theoretische Chemie},
  language  = {en}
}
@phdthesis{Pfeuffer2009,
  author    = {Pfeuffer, Thomas},
  title     = {Synthese und Testung von Aza-Peptiden als Cystein- und Aspartat-Protease Inhibitoren sowie Kristallisation und Elektronendichtebestimmung von Aziridin-, Epoxid- und Michael-Akzeptor substituierten Bausteinen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-47792},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {Proteasen als Peptid hydrolysierende Enzyme spielen eine essenzielle Rolle im Verlauf verschiedenster Erkrankungen, wie z.B. SARS, Malaria oder Alzheimer. Die irreversible Hemmung dieser Proteasen gilt somit als neues Konzept in der Wirkstoffentwicklung. Dabei ist es von immenser Bedeutung, die Interaktion der beteiligten Proteine zu kennen, um einen geeigneten Wirkstoff zu entwickeln. Ein Ziel dieser Arbeit war es, kleine elektrophile Bausteine wie Aziridine, Epoxide oder Akzetor-substituierte Olefine zu synthetisieren und zu kristallisieren. In Zusammenarbeit mit der Arbeitsgruppe von Prof. Luger (FU Berlin) konnten mittels hochaufl{\"o}sender R{\"o}ntgenstrukturanalyse bei ulta-niedrigen Temperaturen die Elektronendichten von mehreren Protease-Inhibitor-Modell-Verbindungen bestimmt werden. Ein weiteres Ziel dieser Arbeit war ausgehend von bekannten aktiven Aziridinen, Epoxiden oder Michael-Systemen, azapeptidische Analoga darzustellen, welche durch ihre Hydrazid-Verkn{\"u}pfung eine bessere Hydrolysebest{\"a}ndigkeit gegen{\"u}ber enzymatischem Abbau bieten. Alle synthetisierten Verbindungen wurden in fluorimetrischen Enzym-Assays an acht Protesen (Cathepsin B, Cathepsin L, Falcipain 2, Rhodesain, SARS-CoV-Mpro, SARS-COV-plpro, SAP2 and Cathepsin D)getestet und die Hemmkonstanten bestimmt},
  subject      = {Azapeptide},
  language  = {de}
}
@phdthesis{Henn2004,
  author    = {Henn, Julian},
  title     = {The electron density : a bridge between exact quantum mechanics and fuzzy chemical concepts},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-9003},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2004},
  abstract  = {Summary The nature of the chemical bond is a topic under constant debate. What is known about individual molecular properties and functional groups is often taught and rationalized by explaining Lewis structures, which, in turn, make extensive use of the valence concept. The valence concept distinguishes between electrons, which do not participate in chemical interactions (core electrons) and those, which do (single, double, triple bonds, lone-pair electrons, etc.). Additionally, individual electrons are assigned to atomic centers. The valence concept is of paramount success: It allows the successful planning of chemical syntheses and analyses, it explains the behavior of individual functional groups, and, moreover, it provides the "language" to think of and talk about molecular structure and chemical interactions. The resounding success of the valence concept may be misleading to forget its approximative character. On the other hand, quantum mechanics provide in principle a quantitative description of all chemical phenomena, but there is no discrimination between electrons in quantum mechanics. From the quantum mechanical point of view there are only indistinguishable electrons in the field of the nuclei, i.e., it is impossible to assign a given electron to a particular center or to ascribe a particular purpose to individual electrons. The concept of indistinguishability of micro particles is founded on the Heisenberg uncertainty relation, which states, that wavepackets diverge in the 6N dimensional phase space, such that individual trajectories can not be identified. Hence it is a deep-rooted and approved physical concept. As an introduction to the present work density partitioning schemes were discussed, which divide the total molecular density into chemically meaningful areas. These partitioning schemes are intimately related to either the concepts of bound atoms in a molecule (as in the Atoms In Molecules theory (AIM) according to Bader or as in the Hirshfeld partitioning scheme) or to the concept of chemical structure in the sense of Lewis structures, which divide the total molecular density into core and valence density, where the valence density is split up again into bonding and non-bonding electron densities. Examples are early and recent loge theories, the topological analysis by means of the Electron Localization Function (ELF), and the Natural Bond Orbital (NBO) approach. Of these partitioning schemes, the theories according to Bader (AIM), to Becke and Edgecomb (ELF) and according to Weinhold (NBO and Natural Resonance Theory, NRT), respectively, were reviewed in detail critically. Points of criticism were explicated for each of the mentioned theories. Since theoretically derived electron densities are to be compared to experimentally derived densities, a brief introduction into the theory of X-ray di®raction experiments was given and the multipole formalism was introduced. The procedure of density refinement was briefly discussed. Various suggestions for improvements were developed: One strategy would be the employment of model parameters, which are to a maximum degree mutually orthogonal, with the object of minimizing correlations among the model parameters, e.g., to introduce nodal planes into the radial functions of the multipole model. A further suggestion involves the guidance of the iterative refinement procedure by an extremum principle, which states, that when di®erent solutions to the least squares minimization problem are available with about the same statistical measures of quality and with about the same residual density, then the solution is to prefer, which yields a minimum density at the bond critical point (BCP) and a maximum polarity in terms of the ratio of distances between the BCP and the nuclei. This suggestion is based on the well known fact, that the bond polarity (in terms of the ratio of distances between the BCP and the respective nuclei) is underestimated in the experiment. Another suggestion for including physical constraints is the explicit consideration of the virial theorem, e.g., by evaluating the integration of the Laplacian over the entire atomic basins and comparing this value to zero and to the value obtained from the integration of the electron gradient field over the atomic surface. The next suggestion was to explicitly use the electrostatic theorem of Feynman (often also denoted as Hellmann-Feynman theorem), which states, that the forces onto the nuclei can be calculated from the purely classical electrostatic forces of the electron distribution and the nuclei distribution. For a stationary system, these forces must add to zero. This also provides an internal quality criterion of the density model. This can be performed in an iterative way during the refinement procedure or as a test of the final result. The use of the electrostatic theorem is expected to reduce significantly correlations among static density parameters and parameters describing vibrations, since it is a valuable tool to discriminate between physically reasonable and artificial static electron densities. All of these mentioned suggestions can be applied as internal quality criteria. The last suggestion is based on the idea to initiate the experimental refinement with a set of model parameters, which is, as much as possible close to the final solution. This can be achieved by performing periodic boundary conditions calculations, from which theoretically created files are obtained, which contain the Miller indices (h, k, l) and the respective intensity I. This file is used for a model parameter estimation (refinement), which excludes vibrations. The resulting parameters can be used for the experimental refinement, where, in a first step, the density parameters are fixed to determine the parameters describing vibrations. For a fine tuning, again the electrostatic theorem and the other above mentioned suggestions could be applied. Theoretical predictions should not be biased by the method of computation. Therefore the dependence of the density analyzing tools on the level of calculation (method of calculation/basis set) and on the substituents in complex chemical bonding situations were evaluated in the second part of the present work. A number of compounds containing formal single and double sulfur nitrogen bonds was investigated. For these compounds, experimental data were also available. The calculated data were compared internally and with the experimental results. The internal comparison was drawn with regard to questions of convergency as well as with regard to questions of consistency: The resulting molecular properties from NBO/NRT analyses were found to be very stable, when the geometries were optimized at the respective level of theory. This stability is valid for variations in the methods of calculation as well as for variations in the basis set. Only the individual resonance weights of the contributing Natural Lewis Structures differed considerably depending on the level of calculation and depending on the substituents. However, the deviations were in both cases to a large extent within a limit which preserves the descending order of the leading resonance structure weights. The resulting bond orders, i.e., the total, covalent and ionic bond order from NRT calculations, were not affected by the shift in the resonance weights. The analysis of the bond topological parameters resulted in a discrimination between insensitive parameters and sensitive parameters. The stable parameters do neither depend strongly on the method of calculation nor on the basis set. Only minor variation occurs in the numerical values of these parameters, when the level of calculation is changed or even when other functional groups (H, Me, or tBu) are employed, as long as the methods of calculation do not drop considerably below a standard level. The bond descriptors of the sulfur nitrogen bonds were found to be also stable with respect to the functional groups R = H, R = Me, and R = tBu. Stable parameters are the bond distance, the density at the bond critical point (BCP) and the ratio of distances between the BCP and the nuclei A and B, which varies clearly when considering the formal bond type. For very small basis sets like the 3-21G basis set, this characteristic stability collapses. The sensitive parameters are based on the second derivatives of the density with respect to the coordinates. This is in accordance with the well known fact, that the total second derivative of the density with respect to the coordinates is a strongly oscillating function with positive as well as negative values. A profound deviation has to be anticipated as a consequence of strong oscillations. lambda3, which describes the local charge depletion in the direction of the interaction line, is the most varying parameter. A detailed analysis revealed that the position of the BCP in the rampant edge of the Laplacian distribution is responsible for the sensitivity of the numerical value of lambda3 in formal double bonds. Since the slope of the Laplacian assumes very high values in its rampant edge, a tiny displacement of the BCP leads already to a considerable change in lambda3. This instability is not a failure of the underlying theory, but it yields de facto to a considerable dependence of sensitive bond topological properties on the method of calculation and on the applied basis sets. Since the total second derivative is important to judge on the nature of the bond in the AIM theory (closed shell interactions versus shared interactions), the changes in lambda3 can lead to differing chemical interpretations. The comparison of theoretically derived bond topological properties of various sulfur nitrogen bonds provides the possibility to measure the self consistency of this data set. All data sets clearly exhibit a linear correlation between the bond distances and the density at the BCP on one hand and between the bond distances and the Laplacian values at the BCP on the other hand. These correlations were almost independent of the basis set size. In this context, the linear regression has to be regarded exclusively as a descriptive statistics tool. There is no correlation anticipated a priori. The formal bond type was found to be readily deducible from the theoretically obtained bond topological descriptors of the model systems. In this sense, the bond topological properties are self consistent despite of the numerical sensitivity of the derivatives, as exemplified above. Often, calculations are performed with the experimentally derived equilibrium geometries and not with optimized ones. Applying this approach, the computationally costly geometry optimizations are saved. Following this approach the bond topological properties were calculated using very flexible basis sets and employing the fixed experimental geometry (which, of course, includes the application of tBu groups). Regression coe±cients similar to those from optimized geometries were obtained for correlations between bond distances and the densities at the BCP as well as for the correlation between bond distances and the Laplacian at the BCP, i.e. the approach is valid. However, the data points scattered less and the coe±cient of correlation was clearly increased when geometry optimizations were performed beforehand. The comparison between data obtained from theory and experiment revealed fundamental discrepancies: In the data set of bond topological parameters from the experiment, the behavior of only 2 out of 3 insensitive parameters was comparable to the behavior of the theoretically obtained values, i.e. theoretical and experimental bond distances as well as theoretical and experimental densities at the BCP correlate. From the theoretically obtained data it was easy to deduce the formal bond type from the position of the BCP, since it changed in a systematic manner. The respective experimentally obtained values were almost constant and did not change systematically. For the SN bonds containing compounds, the total second derivative assumes exclusively negative values in the experiment. Due to the different internal behavior, experimentally and theoretically sensitive bond topological values could not be compared directly. The qualitative agreement in the Laplacian distribution, however, was excellent. In the third and last part of this work, the application to chemical systems follows. Formal hypervalent molecules, i.e. molecules where some atoms are considered to hold more than 8 electrons in their valence shell, were investigated. These were compounds containing sulfur nitrogen bonds (H(NtBu)2SMe, H2C{S(NtBu)2(NHtBu)}2, S(NtBu)2 and S(NtBu)3) and a highly coordinated silicon compound. The set of sulfur nitrogen compounds also contained a textbook example for valence expansion, the sulfur triimide. For these molecules, experimental reference values were available from high resolution X-ray experiments. The experimental results were in the case of the sulfur triimide not unique. Furthermore, from the experimental bond topological data no definite conclusion about the formal bonding type could be drawn. The situation of sulfur nitrogen bonds in the above mentioned set of molecules was analyzed in terms of a geometry discussion and by means of a topological analysis. The methyl-substituted isolated molecules served as model compounds. For the interpretation of the bonding situation additional NBO/NRT calculations were preformed for the sulfur nitrogen compounds and an ELF calculation and analysis was performed for the silicon compound. The ELF analysis included not only the presentation and discussion of the ELF-isosurfaces (eta = 0.85), but also the investigation of populations of disynaptic valence basins and the percentage contributions to these populations of the individual atoms when the disynaptic valence basins are split into atomic contributions according to Bader's partitioning scheme. The question of chemical interest was whether hypervalency is present in the set of molecules or not. In the first case the octet rule would be violated, in the second case Pauling's verdict would be violated. While the concept of hypervalency is well established in chemistry, the violation of Pauling's verdict is not. The quantitative numbers of the sensitive bond topological values from theory and experiment were not comparable, since no systematic relationship between the experimentally and theoretically determined sensitive bond descriptors was found. However, the insensitive parameters are in good agreement and the qualitative Laplacian distribution is, with few exceptions, in excellent agreement. The formal bonding type was deduced from experimental and theoretical topological data by considering the number and shape of valence shell charge concentrations in proximity to the sulfur and nitrogen centers. The results from NBO/NRT calculations confirmed the findings. All employed density analyzing tools AIM, ELF and NBO/NRT coincided in describing the bonding situation in the formally hypervalent molecules as highly polar. A comparison and analysis of experimentally and theoretically derived electron densities led consistently to the result, that regarding this set of molecules, hypervalency has to be excluded unequivocally.},
  subject      = {Elektronendichtebestimmung},
  language  = {en}
}
@phdthesis{Kocher2003,
  author    = {Kocher, Nikolaus},
  title     = {Experimental charge density studies of highly polar bonds},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-7614},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2003},
  abstract  = {The main aim of this work was the classification of highly polar E-N (E = Al, Si, P) and Li-E' (E' = C, N, O) bonds in terms of ionic (closed-shell) or covalent (shared) interactions. To answer this question the experimentally determined electron density was analyzed using Bader's theory of 'Atoms in Molecules' (AIM). This allows a quantitative evaluation of properties derived from the electron density, such as the Laplacian, the ellipticitiy and the ratio of the highest charge concentration perpendicular to the bond path, to the largest charge depletion along the bonding vector. Most of these properties were monitored along the entire bonding region and not limited to the BCP as in former studies. The analyses are completed by the calculation of the electronic energy densities Hl at the BCPs and the integration of atomic basins also defined within the AIM theory. The electrostatic potential (ESP) was computed from the multipole parameters to reveal preferred reactive sites of the structures under investigation. Apart from that, the multipole formalism was applied to problematic crystal structures in order to open this method for twinned samples or those including disordered groups in the molecule.},
  subject      = {Elektronendichte},
  language  = {en}
}
@phdthesis{Leusser2002,
  author    = {Leußer, Dirk},
  title     = {S=N versus S+-N-},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-3437},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2002},
  abstract  = {The main aim of this thesis was to characterise structurally four sulfur-nitrogen compounds in terms of their experimental electron density distribution: Sulfurdiimide S(NtBu)2 (I), sulfurtriimide S(NtBu)3 (II), methyl(diimido)sulfinic acid H(NtBu)2SMe (III) and methylene-bis(triimido)sulfonic acid CH2{S(NtBu)2(HNtBu)}2 (IV). The electron density was determined by multipole refinements on high-resolution X-ray data at low temperatures. The refined densities were analysed by means of Bader's theory of 'Atoms in Molecules' to get information about the bonding types (shared/ closed shell), bond strengths, and the extent of polarisation. The distributions of the static deformation densities, which already showed the most important electronical features as lone-pairs and bonding densities, were calculated for all compounds. The spatial distributions provided a first impression about the bonding properties. The nitrogen lone-pair densities were found to be inclined towards the electropositive sulfur atoms. In II, III and IV the spatial distributions already suggested sp3 hybridisation of the nitrogen atoms. In I gradual differences between the E/Z and Z/Z oriented NtBu groups were visualised. The charge density distribution was analysed along the bond paths, which showed some of the S,N bonds to be considerably bent. In the central part of the thesis detailed topological analyses of the electron density distributions were performed. All BCPs and the related electronical properties as the electron density, the negative Laplacian, the eigenvalues of the Hessian matrix, and several values, which can be deduced from these, were calculated. Due to the low number of comparable published compounds, internal scaling facilitated by III and IV led to system-specific ranking of the S-N and S-C bonds in terms of bond type (shared vs. closed shell), bond order, and bond strength. To quantify bond polarisation a criterion was developed which relates shifts in the BCPs to electron transfer from the electropositive to the electronegative bonding partner. The distributions of the Laplacian were determined for all S-E (E = N, C) bonds because of their fundamental importance for the classification of atomic interactions. Furthermore, the spatial distribution of the negative Laplacian with respect to all important bonds was determined around the central sulfur and nitrogen atoms. The analyses led to detailed information about the S,N interactions. A calculation of the reactive surfaces where the Laplacian equals zero revealed possible reaction pathways of nucleophilic attacks to the central sulfur atoms. All nitrogen atoms in H(NtBu)2SMe (III) as well as in CH2{S(NtBu)2(HNtBu)}2 (IV) are predominantly sp3 hybridised. The S,N bonds should therefore be formulated as S+-N- single bonds, strengthened and shortened by electrostatic reinforcement. In S(NtBu)2 (I) the sp2 hybridisation of the nitrogen atoms was verified. All topological criteria unearthed the inequality of the formally equivalent S=N double bonds. The differences were assigned to the molecular E/Z conformation in the solid state. Interaction between the in-plane lone-pair density of the nitrogen and the sulfur atom located at the same side causes the non-bonding charge concentration at the sulfur atom to be dislocated into the second S-N bond. The existence of a delocalised 3-centres-2-electrons system within the planar SN2 core was assumed to be formed by non-hybridised p-orbitals. An effective delocalisation was found to be possibly disturbed by a weak intermolecular S...S interaction. The interpretation of the S,N interaction in S(NtBu)3 (II) was not straightforward, since the electron density distribution showed both, indicators for multiple bonding as well as for sp3 hybridisation of the nitrogen atoms, which verifies the formulation of a S+-N- bonding mode. The bonding situation in S(NtBu)3 was identified as an intermediate state between that of a delocalised 4-centres-6-electrons system formed by non-hybridised p-orbitals within the planar SN3 unit and that of a S+-N- system.},
  subject      = {Schwefelverbindungen},
  language  = {en}
}