Coarse-graining and quantum-classical adaptive coupling in soft matter

Die vorliegende Arbeit untersucht den Zusammenhang zwischen Skalen in Systemen weicher Materie, der für Multiskalen-Simulationen eine wichtige Rolle spielt. Zu diesem Zweck wurde eine Methode entwickelt, die die Approximation der Separierbarkeit von Variablen für die Molekulardynamik und ähnliche Anwendungen bewertet. Der zweite und größere Teil dieser Arbeit beschäftigt sich mit der konzeptionellen und technischen Erweiterung des Adaptive Resolution Scheme'' (AdResS), einer Methode zur gleichzeitigen Simulation von Systemen mit mehreren Auflösungsebenen. Diese Methode wurde auf Systeme erweitert, in denen klassische und quantenmechanische Effekte eine Rolle spielen.rnrnDie oben genannte erste Methode benötigt nur die analytische Form der Potentiale, wie sie die meisten Molekulardynamik-Programme zur Verfügung stellen. Die Anwendung der Methode auf ein spezielles Problem gibt bei erfolgreichem Ausgang einen numerischen Hinweis auf die Gültigkeit der Variablenseparation. Bei nicht erfolgreichem Ausgang garantiert sie, dass keine Separation der Variablen möglich ist. Die Methode wird exemplarisch auf ein zweiatomiges Molekül auf einer Oberfläche und für die zweidimensionale Version des Rotational Isomer State (RIS) Modells einer Polymerkette angewandt.rnrnDer zweite Teil der Arbeit behandelt die Entwicklung eines Algorithmus zur adaptiven Simulation von Systemen, in denen Quanteneffekte berücksichtigt werden. Die Quantennatur von Atomen wird dabei in der Pfadintegral-Methode durch einen klassischen Polymerring repräsentiert. Die adaptive Pfadintegral-Methode wird zunächst für einatomige Flüssigkeiten und tetraedrische Moleküle unter normalen thermodynamischen Bedingungen getestet. Schließlich wird die Stabilität der Methode durch ihre Anwendung auf flüssigen para-Wasserstoff bei niedrigen Temperaturen geprüft.

Electronic properties of liquid ammonia: A sequential molecular dynamics/quantum mechanics approach

The electronic properties of liquid ammonia are investigated by a sequential molecular dynamics/quantum mechanics approach. Quantum mechanics calculations for the liquid phase are based on a reparametrized hybrid exchange-correlation functional that reproduces the electronic properties of ammonia clusters [(NH(3))(n); n=1-5]. For these small clusters, electron binding energies based on Green's function or electron propagator theory, coupled cluster with single, double, and perturbative triple excitations, and density functional theory (DFT) are compared. Reparametrized DFT results for the dipole moment, electron binding energies, and electronic density of states of liquid ammonia are reported. The calculated average dipole moment of liquid ammonia (2.05 +/- 0.09 D) corresponds to an increase of 27% compared to the gas phase value and it is 0.23 D above a prediction based on a polarizable model of liquid ammonia [Deng , J. Chem. Phys. 100, 7590 (1994)]. Our estimate for the ionization potential of liquid ammonia is 9.74 +/- 0.73 eV, which is approximately 1.0 eV below the gas phase value for the isolated molecule. The theoretical vertical electron affinity of liquid ammonia is predicted as 0.16 +/- 0.22 eV, in good agreement with the experimental result for the location of the bottom of the conduction band (-V(0)=0.2 eV). Vertical ionization potentials and electron affinities correlate with the total dipole moment of ammonia aggregates. (c) 2008 American Institute of Physics.

New path integral simulation algorithms and their application to creep in the quantum sine-Gordon chain

A path integral simulation algorithm which includes a higher-order Trotter approximation (HOA)is analyzed and compared to an approach which includes the correct quantum mechanical pair interaction (effective Propagator (EPr)). It is found that the HOA algorithmconverges to the quantum limit with increasing Trotter number P as P^{-4}, while the EPr algorithm converges as P^{-2}.The convergence rate of the HOA algorithm is analyzed for various physical systemssuch as a harmonic chain,a particle in a double-well potential, gaseous argon, gaseous helium and crystalline argon. A new expression for the estimator for the pair correlation function in the HOA algorithm is derived. A new path integral algorithm, the hybrid algorithm, is developed.It combines an exact treatment of the quadratic part of the Hamiltonian and thehigher-order Trotter expansion techniques.For the discrete quantum sine-Gordon chain (DQSGC), it is shown that this algorithm works more efficiently than all other improved path integral algorithms discussed in this work. The new simulation techniques developed in this work allow the analysis of theDQSGC and disordered model systems in the highly quantum mechanical regime using path integral molecular dynamics (PIMD)and adiabatic centroid path integral molecular dynamics (ACPIMD).The ground state phonon dispersion relation is calculated for the DQSGC by the ACPIMD method.It is found that the excitation gap at zero wave vector is reduced by quantum fluctuations. Two different phases exist: One phase with a finite excitation gap at zero wave vector, and a gapless phase where the excitation gap vanishes.The reaction of the DQSGC to an external driving force is analyzed at T=0.In the gapless phase the system creeps if a small force is applied, and in the phase with a gap the system is pinned. At a critical force, the systems undergo a depinning transition in both phases and flow is induced. The analysis of the DQSGC is extended to models with disordered substrate potentials. Three different cases are analyzed: Disordered substrate potentials with roughness exponent H=0, H=1/2,and a model with disordered bond length. For all models, the ground state phonon dispersion relation is calculated.

Ab-initio study of hydrogen technology materials for hydrogen storage and proton conduction

This dissertation deals with two specific aspects of a potential hydrogen-based energy economy, namely the problems of energy storage and energy conversion. In order to contribute to the solution of these problems, the structural and dynamical properties of two promising materials for hydrogen storage (lithium imide/amide) and proton conduction (poly[vinyl phosphonic acid]) are modeled on an atomistic scale by means of first principles molecular dynamics simulation methods.rnrnrnIn the case of the hydrogen storage system lithium amide/imide (LiNH_2/Li_2NH), the focus was on the interplay of structural features and nuclear quantum effects. For these calculations, Path-Integral Molecular Dynamics (PIMD) simulations were used. The structures of these materials at room temperature were elucidated; in collaboration with an experimental group, a very good agreement between calculated and experimental solid-state 1H-NMR chemical shifts was observed. Specifically, the structure of Li_2NH features a disordered arrangement of the Li lattice, which was not reported in previous studies. In addition, a persistent precession of the NH bonds was observed in our simulations. We provide evidence that this precession is the consequence of a toroid-shaped effective potential, in which the protons in the material are immersed. This potential is essentially flat along the torus azimuthal angle, which might lead to important quantum delocalization effects of the protons over the torus.rnrnOn the energy conversion side, the dynamics of protons in a proton conducting polymer (poly[vinyl phosphonic acid], PVPA) was studied by means of a steered ab-initio Molecular Dynamics approach applied on a simplified polymer model. The focus was put on understanding the microscopic proton transport mechanism in polymer membranes, and on characterizing the relevance of the local environment. This covers particularly the effect of water molecules, which participate in the hydrogen bonding network in the material. The results indicate that these water molecules are essential for the effectiveness of proton conduction. A water-mediated Grotthuss mechanism is identified as the main contributor to proton conduction, which agrees with the experimentally observed decay on conductivity for the same material in the absence of water molecules.rnrnThe gain in understanding the microscopic processes and structures present in this materials can help the development of new materials with improved properties, thus contributing to the solution of problems in the implementation of fuel cells.

Selectivity of bis(calix[4]diquinone) ionophores towards metal ions in solvent dimethylsulfoxide: a molecular mechanics and molecular dynamics study

Molecular modelling studies have been carried out on two bis(calix[4]diqu(inone) ionophores, each created from two (calix[4]diquinone)arenes bridged at their bottom rims via alkyl chains (CH2)(n), 1: n = 3, 2; n = 4, in order to understand the reported selectivity of these ligands towards different sized metal ions such as Na+, K+, Rb+, and Cs+ in dmso solution. Conformational. analyses have been carried out which show that in the lowest energy conformations of the two macrocycles, the individual calix[4]diquinones exhibit a combination of partial cone, 1,3-alternate and cone conformations. The interactions of these alkali metals with the macrocycles have been studied in the gas phase and in a periodic box of solvent dmso by molecular mechanics and molecular dynamics calculations. Molecular mechanics calculations have been carried out on the mode of entry of the ions into the macrocycles and suggest that this is likely to occur from the side of the central cavity, rather than through the main axis of the calix[4]diquinones. There are energy barriers of ca. 19 kcal mol(-1) for this entry path in the gas phase, but in solution no energy barrier is found. Molecular dynamics simulations show that in both 1 and 2, though particularly in the latter macrocycle, one or two solvent molecules are bonded to the metal throughout the course of the simulation, often to the exclusion, of one or more of the ether oxygen atoms. By contrast the carbonyl oxygen atoms remain bonded to the metal atoms throughout with bond lengths that remain significantly less than those to the ether oxygen atoms. Free energy perturbation studies have been carried out in dmso and indicate that for 1, the selectivity follows the order Rb+ approximate to K+ > Cs+ >> Na+, which is partially in agreement with the experimental results. The energy differences are small and indeed the ratio between stability constants found for Cs+ and K+ complexes is only 0.60, showing that 1 has only a slight preference for K+. For the larger receptor 2, which is better suited to metal complexation, the binding affinity follows the pattern Cs+ >> Rb+ >> K+ >> Na+, with energy differences of 5.75, 2.61, 2.78 kcal mol(-1) which is perfectly consistent with experimental results.

Statistical mechanics of protein complexed and condensed DNA

In this thesis I treat various biophysical questions arising in the context of complexed / ”protein-packed” DNA and DNA in confined geometries (like in viruses or toroidal DNA condensates). Using diverse theoretical methods I consider the statistical mechanics as well as the dynamics of DNA under these conditions. In the first part of the thesis (chapter 2) I derive for the first time the single molecule ”equation of state”, i.e. the force-extension relation of a looped DNA (Eq. 2.94) by using the path integral formalism. Generalizing these results I show that the presence of elastic substructures like loops or deflections caused by anchoring boundary conditions (e.g. at the AFM tip or the mica substrate) gives rise to a significant renormalization of the apparent persistence length as extracted from single molecule experiments (Eqs. 2.39 and 2.98). As I show the experimentally observed apparent persistence length reduction by a factor of 10 or more is naturally explained by this theory. In chapter 3 I theoretically consider the thermal motion of nucleosomes along a DNA template. After an extensive analysis of available experimental data and theoretical modelling of two possible mechanisms I conclude that the ”corkscrew-motion” mechanism most consistently explains this biologically important process. In chapter 4 I demonstrate that DNA-spools (architectures in which DNA circumferentially winds on a cylindrical surface, or onto itself) show a remarkable ”kinetic inertness” that protects them from tension-induced disruption on experimentally and biologically relevant timescales (cf. Fig. 4.1 and Eq. 4.18). I show that the underlying model establishes a connection between the seemingly unrelated and previously unexplained force peaks in single molecule nucleosome and DNA-toroid stretching experiments. Finally in chapter 5 I show that toroidally confined DNA (found in viruses, DNAcondensates or sperm chromatin) undergoes a transition to a twisted, highly entangled state provided that the aspect ratio of the underlying torus crosses a certain critical value (cf. Eq. 5.6 and the phase diagram in Fig. 5.4). The presented mechanism could rationalize several experimental mysteries, ranging from entangled and supercoiled toroids released from virus capsids to the unexpectedly short cholesteric pitch in the (toroidaly wound) sperm chromatin. I propose that the ”topological encapsulation” resulting from our model may have some practical implications for the gene-therapeutic DNA delivery process.

Computational mechanics reveals nanosecond time correlations in molecular dynamics of liquid systems

Statistical complexity, a measure introduced in computational mechanics has been applied to MD simulated liquid water and other molecular systems. It has been found that statistical complexity does not converge in these systems but grows logarithmically without a limit. The coefficient of the growth has been introduced as a new molecular parameter which is invariant for a given liquid system. Using this new parameter extremely long time correlations in the system undetectable by traditional methods are elucidated. The existence of hundreds of picosecond and even nanosecond long correlations in bulk water has been demonstrated. © 2008 Elsevier B.V. All rights reserved.

Quantum Mechanics of Guiding Center Motion in Strong Magnetic Field (Coherent State Path Integral Approach)

A new approach is proposed for the quantum mechanics of guiding center motion in strong magnetic field. This is achieved by use of the coherent state path integral for the coupled systems of the cyclotron and the guiding center motion. We are specifically concerned with the effective action for the guiding center degree, which can be used to get the Bohr- Sommerfeld quantization scheme. The quantization rule is similar to the one for the vortex motion as a dynamics of point particles.

Path-integral and Coarse-graining Strategies for Complex Molecular Phenomena

Molecular simulation provides a powerful tool for connecting molecular-level processes to physical observables. However, the facility to make those connections relies upon the application and development of theoretical methods that permit appropriate descriptions of the systems or processes to be studied. In this thesis, we utilize molecular simulation to study and predict two phenomena with very different theoretical challenges, beginning with (1) lithium-ion transport behavior in polymers and following with (2) equilibrium isotope effects with relevance to position-specific and clumped isotope studies. In the case of ion transport in polymers, there is motivation to use molecular simulation to provide guidance in polymer electrolyte design, but the length and timescales relevant for ion diffusion in polymers preclude the use of direct molecular dynamics simulation to compute ion diffusivities in more than a handful of candidate systems. In the case of equilibrium isotope effects, the thermodynamic driving forces for isotopic fractionation are often fundamentally quantum mechanical in nature, and the high precision of experimental instruments demands correspondingly accurate theoretical approaches. Herein, we describe respectively coarse-graining and path-integral strategies to address outstanding questions in these two subject areas.

Molecular dynamics computer simulation of scratch resistance testing of polymers: visualization

Experimental scratch resistance testing provides two numbers: the penetration depth Rp and the healing depth Rh. In molecular dynamics computer simulations, we create a material consisting of N statistical chain segments by polymerization; a reinforcing phase can be included. Then we simulate the movement of an indenter and response of the segments during X time steps. Each segment at each time step has three Cartesian coordinates of position and three of momentum. We describe methods of visualization of results based on a record of 6NX coordinates. We obtain a continuous dependence on time t of positions of each of the segments on the path of the indenter. Scratch resistance at a given location can be connected to spatial structures of individual polymeric chains.

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

Molecular dynamics simulations of proteins: can the explicit water model be varied?

In molecular mechanics simulations of biological systems, the solvation water is typically represented by a default water model which is an integral part of the force field. Indeed, protein nonbonding parameters are chosen in order to obtain a balance between water-water and protein-water interactions and hence a reliable description of protein solvation. However, less attention has been paid to the question of whether the water model provides a reliable description of the water properties under the chosen simulation conditions, for which more accurate water models often exist. Here we consider the case of the CHARMM protein force field, which was parametrized for use with a modified TIP3P model. Using quantum mechanical and molecular mechanical calculations, we investigate whether the CHARMM force field can be used with other water models: TIP4P and TIP5P. Solvation properties of N-methylacetamide (NMA), other small solute molecules, and a small protein are examined. The results indicate differences in binding energies and minimum energy geometries, especially for TIP5P, but the overall description of solvation is found to be similar for all models tested. The results provide an indication that molecular mechanics simulations with the CHARMM force field can be performed with water models other than TIP3P, thus enabling an improved description of the solvent water properties.

Mg/Ca partitioning between aqueous solution and aragonite mineral: a molecular dynamics study

We have calculated the concentrations of Mg in the bulk and surfaces of aragonite CaCO3 in equilibrium with aqueous solution, based on molecular dynamics simulations and grand-canonical statistical mechanics. Mg is incorporated in the surfaces, in particular in the (001) terraces, rather than in the bulk of aragonite particles. However, the total Mg content in the bulk and surface of aragonite particles was found to be too small to account for the measured Mg/Ca ratios in corals. We therefore argue that most Mg in corals is either highly metastable in the aragonite lattice, or is located outside the aragonite phase of the coral skeleton, and we discuss the implications of this finding for Mg/Ca paleothermometry.

Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them theta-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing theta-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract theta-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as theta-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The theta-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case.

Dressed coordinates: the path-integral approach

The recently introduced dressed coordinates are studied in the path-integral approach. These coordinates are defined in the context of a harmonic oscillator linearly coupled to massless scalar field and it is shown that in this model the dressed coordinates appear as a coordinate transformation preserving the path-integral functional measure. The analysis also generalizes the sum rules established in a previous work. (c) 2006 Elsevier B.V. All rights reserved.