Spectroscopic properties from hybrid QM, MM molecular dynamics simulation

The central aim of this thesis work is the application and further development of a hybrid quantum mechanical/molecular mechanics (QM/MM) based approach to compute spectroscopic properties of molecules in complex chemical environments from electronic structure theory. In the framework of this thesis, an existing density functional theory implementation of the QM/MM approach is first used to calculate the nuclear magnetic resonance (NMR) solvent shifts of an adenine molecule in aqueous solution. The findings show that the aqueous solvation with its strongly fluctuating hydrogen bond network leads to specific changes in the NMR resonance lines. Besides the absolute values, also the ordering of the NMR lines changes under the influence of the solvating water molecules. Without the QM/MM scheme, a quantum chemical calculation could have led to an incorrect assignment of these lines. The second part of this thesis describes a methodological improvement of the QM/MM method that is designed for cases in which a covalent chemical bond crosses the QM/MM boundary. The development consists in an automatized protocol to optimize a so-called capping potential that saturates the electronic subsystem in the QM region. The optimization scheme is capable of tuning the parameters in such a way that the deviations of the electronic orbitals between the regular and the truncated (and "capped") molecule are minimized. This in turn results in a considerable improvement of the structural and spectroscopic parameters when computed with the new optimized capping potential within the QM/MM technique. This optimization scheme is applied and benchmarked on the example of truncated carbon-carbon bonds in a set of small test molecules. It turns out that the optimized capping potentials yield an excellent agreement of NMR chemical shifts and protonation energies with respect to the corresponding full molecules. These results are very promising, so that the application to larger biological complexes will significantly improve the reliability of the prediction of the related spectroscopic properties.

Ab-initio determination of x-ray absorption near edge structure (xanes) spectra in an ultrasoft and norm conserving pseudopotentials scheme

X-ray absorption spectroscopy (XAS) is a powerful means of investigation of structural and electronic properties in condensed -matter physics. Analysis of the near edge part of the XAS spectrum, the so – called X-ray Absorption Near Edge Structure (XANES), can typically provide the following information on the photoexcited atom: - Oxidation state and coordination environment. - Speciation of transition metal compounds. - Conduction band DOS projected on the excited atomic species (PDOS). Analysis of XANES spectra is greatly aided by simulations; in the most common scheme the multiple scattering framework is used with the muffin tin approximation for the scattering potential and the spectral simulation is based on a hypothetical, reference structure. This approach has the advantage of requiring relatively little computing power but in many cases the assumed structure is quite different from the actual system measured and the muffin tin approximation is not adequate for low symmetry structures or highly directional bonds. It is therefore very interesting and justified to develop alternative methods. In one approach, the spectral simulation is based on atomic coordinates obtained from a DFT (Density Functional Theory) optimized structure. In another approach, which is the object of this thesis, the XANES spectrum is calculated directly based on an ab – initio DFT calculation of the atomic and electronic structure. This method takes full advantage of the real many-electron final wavefunction that can be computed with DFT algorithms that include a core-hole in the absorbing atom to compute the final cross section. To calculate the many-electron final wavefunction the Projector Augmented Wave method (PAW) is used. In this scheme, the absorption cross section is written in function of several contributions as the many-electrons function of the finale state; it is calculated starting from pseudo-wavefunction and performing a reconstruction of the real-wavefunction by using a transform operator which contains some parameters, called partial waves and projector waves. The aim of my thesis is to apply and test the PAW methodology to the calculation of the XANES cross section. I have focused on iron and silicon structures and on some biological molecules target (myoglobin and cytochrome c). Finally other inorganic and biological systems could be taken into account for future applications of this methodology, which could become an important improvement with respect to the multiscattering approach.

Molecular dynamics simulations of sheared brush-like systems

Mit Hilfe von Molekulardynamik-Simulationen untersuchen wir bürstenartige Systeme unter guten Lösungsmittelbedingungen. Diese Systeme sind, dank ihren vielfältigen Beschaffenheiten, die von Molekularparametern und äußeren Bedingungen abhängig sind, wichtig für viele industrielle Anwendungen. Man vermutet, dass die Polymerbürsten eine entscheidende Rolle in der Natur wegen ihrer einzigartigen Gleiteigenschaften spielen. Ein vergröbertes Modell wird verwendet, um die strukturellen und dynamischen Eigenschaften zweier hochkomprimierter Polymerbürsten, die eine niedrige Reibung aufweisen, zu untersuchen. Allerdings sind die Lubrikationseigenschaften dieser Systeme, die in vielen biologischen Systemen vorhanden sind, beeinflußt. Wir untersuchen so-genannte "weiche Kolloide", die zwischen den beiden Polymerbürsten eingebettet sind, und wie diese Makroobjekte auf die Polymerbürsten wirken.rnrnNicht-Gleichgewichts-Molekulardynamik-Simulationen werden durchgeführt, in denen die hydrodynamischen Wechselwirkungen durch die Anwendung des DPD-Thermostaten mit expliziten Lösungsmittelmolekülen berücksichtigt werden. Wir zeigen, dass die Kenntnis der Gleichgewichtseigenschaften des Systems erlaubt, dynamische Nichtgleichgewichtsigenschaften der Doppelschicht vorherzusagen.rnrnWir untersuchen, wie die effektive Wechselwirkung zwischen kolloidalen Einschlüßen durch die Anwesenheit der Bürsten (in Abhängigkeit der Weichheit der Kolloide und der Pfropfdichte der Bürsten) beeinflußt wird. Als nächsten Schritt untersuchen wir die rheologische Antwort von solchen komplexen Doppelschichten auf Scherung. Wir entwickeln eine Skalen-Theorie, die die Abhängigkeit der makroskopischen Transporteigenschaften und der lateralen Ausdehnung der verankerten Ketten von der Weissenberg Zahl oberhalb des Bereichs, in dem die lineare Antwort-Theorie gilt, voraussagt. Die Vorhersagen der Theorie stimmen gut mit unseren und früheren numerischen Ergebnissen und neuen Experimenten überein. Unsere Theorie bietet die Möglichkeit, die Relaxationszeit der Doppelschicht zu berechnen. Wenn diese Zeit mit einer charakteristischen Längenskala kombiniert wird, kann auch das ''transiente'' (nicht-stationäre) Verhalten beschrieben werden.rnrnrnWir untersuchen die Antwort des Drucktensors und die Deformation der Bürsten während der Scherinvertierung für grosse Weissenberg Zahlen. Wir entwickeln eine Vorhersage für die charakteristische Zeit, nach der das System wieder den stationären Zustand erreicht.rnrnrnElektrostatik spielt eine bedeutende Rolle in vielen biologischen Prozessen. Die Lubrikationseigenschaften der Polymerbürsten werden durch die Anwesenheit langreichweitiger Wechselwirkungen stark beeinflusst. Für unterschiedliche Stärken der elektrostatischen Wechselwirkungen untersuchen wir rheologische Eigenschaften der Doppelschicht und vergleichen mit neutralen Systemen. Wir studieren den kontinuierlichen Übergang der Systemeigenschaften von neutralen zu stark geladenen Bürsten durch Variation der Bjerrumlänge und der Ladungsdichte.

Ab initio quantum mechanical investigation of structural and chemical-physical properties of selected minerals for minero-petrological, structural ceramic and biomaterial applications

The purpose of this thesis is the atomic-scale simulation of the crystal-chemical and physical (phonon, energetic) properties of some strategically important minerals for structural ceramics, biomedical and petrological applications. These properties affect the thermodynamic stability and rule the mineral-environment interface phenomena, with important economical, (bio)technological, petrological and environmental implications. The minerals of interest belong to the family of phyllosilicates (talc, pyrophyllite and muscovite) and apatite (OHAp), chosen for their importance in industrial and biomedical applications (structural ceramics) and petrophysics. In this thesis work we have applicated quantum mechanics methods, formulas and knowledge to the resolution of mineralogical problems ("Quantum Mineralogy”). The chosen theoretical approach is the Density Functional Theory (DFT), along with periodic boundary conditions to limit the portion of the mineral in analysis to the crystallographic cell and the hybrid functional B3LYP. The crystalline orbitals were simulated by linear combination of Gaussian functions (GTO). The dispersive forces, which are important for the structural determination of phyllosilicates and not properly con-sidered in pure DFT method, have been included by means of a semi-empirical correction. The phonon and the mechanical properties were also calculated. The equation of state, both in athermal conditions and in a wide temperature range, has been obtained by means of variations in the volume of the cell and quasi-harmonic approximation. Some thermo-chemical properties of the minerals (isochoric and isobaric thermal capacity) were calculated, because of their considerable applicative importance. For the first time three-dimensional charts related to these properties at different pressures and temperatures were provided. The hydroxylapatite has been studied from the standpoint of structural and phonon properties for its biotechnological role. In fact, biological apatite represents the inorganic phase of vertebrate hard tissues. Numerous carbonated (hydroxyl)apatite structures were modelled by QM to cover the broadest spectrum of possible biological structural variations to fulfil bioceramics applications.

Novel algorithms for electronic structure based molecular dynamics with linear system-size scaling

Die vorliegende Arbeit behandelt die Entwicklung und Verbesserung von linear skalierenden Algorithmen für Elektronenstruktur basierte Molekulardynamik. Molekulardynamik ist eine Methode zur Computersimulation des komplexen Zusammenspiels zwischen Atomen und Molekülen bei endlicher Temperatur. Ein entscheidender Vorteil dieser Methode ist ihre hohe Genauigkeit und Vorhersagekraft. Allerdings verhindert der Rechenaufwand, welcher grundsätzlich kubisch mit der Anzahl der Atome skaliert, die Anwendung auf große Systeme und lange Zeitskalen. Ausgehend von einem neuen Formalismus, basierend auf dem großkanonischen Potential und einer Faktorisierung der Dichtematrix, wird die Diagonalisierung der entsprechenden Hamiltonmatrix vermieden. Dieser nutzt aus, dass die Hamilton- und die Dichtematrix aufgrund von Lokalisierung dünn besetzt sind. Das reduziert den Rechenaufwand so, dass er linear mit der Systemgröße skaliert. Um seine Effizienz zu demonstrieren, wird der daraus entstehende Algorithmus auf ein System mit flüssigem Methan angewandt, das extremem Druck (etwa 100 GPa) und extremer Temperatur (2000 - 8000 K) ausgesetzt ist. In der Simulation dissoziiert Methan bei Temperaturen oberhalb von 4000 K. Die Bildung von sp²-gebundenem polymerischen Kohlenstoff wird beobachtet. Die Simulationen liefern keinen Hinweis auf die Entstehung von Diamant und wirken sich daher auf die bisherigen Planetenmodelle von Neptun und Uranus aus. Da das Umgehen der Diagonalisierung der Hamiltonmatrix die Inversion von Matrizen mit sich bringt, wird zusätzlich das Problem behandelt, eine (inverse) p-te Wurzel einer gegebenen Matrix zu berechnen. Dies resultiert in einer neuen Formel für symmetrisch positiv definite Matrizen. Sie verallgemeinert die Newton-Schulz Iteration, Altmans Formel für beschränkte und nicht singuläre Operatoren und Newtons Methode zur Berechnung von Nullstellen von Funktionen. Der Nachweis wird erbracht, dass die Konvergenzordnung immer mindestens quadratisch ist und adaptives Anpassen eines Parameters q in allen Fällen zu besseren Ergebnissen führt.

Molecular Dynamics Simulation of a PNA·DNA·PNA Triple Helix in Aqueous Solution

Molecular dynamics simulations have been used to explore the conformational flexibility of a PNA·DNA·PNA triple helix in aqueous solution. Three 1.05 ns trajectories starting from different but reasonable conformations have been generated and analyzed in detail. All three trajectories converge within about 300 ps to produce stable and very similar conformational ensembles, which resemble the crystal structure conformation in many details. However, in contrast to the crystal structure, there is a tendency for the direct hydrogen-bonds observed between the amide hydrogens of the Hoogsteen-binding PNA strand and the phosphate oxygens of the DNA strand to be replaced by water-mediated hydrogen bonds, which also involve pyrimidine O2 atoms. This structural transition does not appear to weaken the triplex structure but alters groove widths and so may relate to the potential for recognition of such structures by other ligands (small molecules or proteins). Energetic analysis leads us to conclude that the reason that the hybrid PNA/DNA triplex has quite different helical characteristics from the all-DNA triplex is not because the additional flexibility imparted by the replacement of sugar−phosphate by PNA backbones allows motions to improve base-stacking but rather that base-stacking interactions are very similar in both types of triplex and the driving force comes from weak but definate conformational preferences of the PNA strands.

Molecular Dynamics Simulations of the d(TAT) Triple Helix

Molecular dynamics (MD) simulations have been used to study the dynamical and time-averaged characteristics of the DNA triple helix d(T)10âd(A)10âd(T)10. The structures sampled during the trajectory resemble closely the B-type model for the DNA triplex proposed on the basis of NMR data, although there are some subtle differences. Alternative P- and A-type conformations for the triplex, suggested from X-ray experiments, are not predicted to contribute significantly to the structure of the DNA triplex in solution. Comparison with the best available experimental data supports the correctnes of the MD-generated structures. The analysis of the collected data gives a detailed picture of the characteristics of triple-helix DNA. A new and interesting pattern of hydration, specific for triplex DNA, is an important observation. The results suggest that molecular dynamics can be useful for the study of novel nucleic acid structures.

Ramachandran-type Plots for Glycosidic Linkages: Examples from Molecular Dynamics Simulations using the Glycam06 Force Field

The goals of this article are to (1) provide further validation of the Glycam06 force field, specifically for its use in implicit solvent molecular dynamic (MD) simulations, and (2) to present the extension of G.N. Ramachandran's idea of plotting amino acid phi and psi angles to the glycosidic phi, psi, and omega angles formed between carbohydrates. As in traditional Ramachandran plots, these carbohydrate Ramachandran-type (carb-Rama) plots reveal the coupling between the glycosidic angles by displaying the allowed and disallowed conformational space. Considering two-bond glycosidic linkages, there are 18 possible conformational regions that can be defined by (α, ϕ, ψ) and (β, ϕ, ψ), whereas for three-bond linkages, there are 54 possible regions that can be defined by (α, ϕ, ψ, ω) and (β, ϕ, ψ, ω). Illustrating these ideas are molecular dynamic simulations on an implicitly hydrated oligosaccharide (700 ns) and its eight constituent disaccharides (50 ns/disaccharide). For each linkage, we compare and contrast the oligosaccharide and respective disaccharide carb-Rama plots, validate the simulations and the Glycam06 force field through comparison to experimental data, and discuss the general trends observed in the plots.