Quantum effects and dynamics in hydrogen-bonded systems: a first-principles approach to spectroscopic experiments

Computer simulations have become an important tool in physics. Especially systems in the solid state have been investigated extensively with the help of modern computational methods. This thesis focuses on the simulation of hydrogen-bonded systems, using quantum chemical methods combined with molecular dynamics (MD) simulations. MD simulations are carried out for investigating the energetics and structure of a system under conditions that include physical parameters such as temperature and pressure. Ab initio quantum chemical methods have proven to be capable of predicting spectroscopic quantities. The combination of these two features still represents a methodological challenge. Furthermore, conventional MD simulations consider the nuclei as classical particles. Not only motional effects, but also the quantum nature of the nuclei are expected to influence the properties of a molecular system. This work aims at a more realistic description of properties that are accessible via NMR experiments. With the help of the path integral formalism the quantum nature of the nuclei has been incorporated and its influence on the NMR parameters explored. The effect on both the NMR chemical shift and the Nuclear Quadrupole Coupling Constants (NQCC) is presented for intra- and intermolecular hydrogen bonds. The second part of this thesis presents the computation of electric field gradients within the Gaussian and Augmented Plane Waves (GAPW) framework, that allows for all-electron calculations in periodic systems. This recent development improves the accuracy of many calculations compared to the pseudopotential approximation, which treats the core electrons as part of an effective potential. In combination with MD simulations of water, the NMR longitudinal relaxation times for 17O and 2H have been obtained. The results show a considerable agreement with the experiment. Finally, an implementation of the calculation of the stress tensor into the quantum chemical program suite CP2K is presented. This enables MD simulations under constant pressure conditions, which is demonstrated with a series of liquid water simulations, that sheds light on the influence of the exchange-correlation functional used on the density of the simulated liquid.

Dynamics, rheology and critical properties of colloidal fluid mixtures

Liquids under the influence of external fields exhibit a wide range of intriguing phenomena that can be markedly different from the behaviour of a quiescent system. This work considers two different systems — a glassforming Yukawa system and a colloid-polymer mixture — by Molecular Dynamics (MD) computer simulations coupled to dissipative particle dynamics. The former consists of a 50-50 binary mixture of differently-sized, like-charged colloids interacting via a screened Coulomb (Yukawa) potential. Near the glass transition the influence of an external shear field is studied. In particular, the transition from elastic response to plastic flow is of interest. At first, this model is characterised in equilibrium. Upon decreasing temperature it exhibits the typical dynamics of glassforming liquids, i.e. the structural relaxation time τα grows strongly in a rather small temperature range. This is discussed with respect to the mode-coupling theory of the glass transition (MCT). For the simulation of bulk systems under shear, Lees-Edwards boundary conditions are applied. At constant shear rates γ˙ ≫ 1/τα the relevant time scale is given by 1/γ˙ and the system shows shear thinning behaviour. In order to understand the pronounced differences between a quiescent system and a system under shear, the response to a suddenly commencing or terminating shear flow is studied. After the switch-on of the shear field the shear stress shows an overshoot, marking the transition from elastic to plastic deformation, which is connected to a super-diffusive increase of the mean squared displacement. Since the average static structure only depends on the value of the shear stress, it does not discriminate between those two regimes. The distribution of local stresses, in contrast, becomes broader as soon as the system starts flowing. After a switch-off of the shear field, these additional fluctuations are responsible for the fast decay of stresses, which occurs on a time scale 1/γ˙ . The stress decay after a switch-off in the elastic regime, on the other hand, happens on the much larger time scale of structural relaxation τα. While stresses decrease to zero after a switch-off for temperatures above the glass transition, they decay to a finite value for lower temperatures. The obtained results are important for advancing new theoretical approaches in the framework of mode-coupling theory. Furthermore, they suggest new experimental investigations on colloidal systems. The colloid-polymer mixture is studied in the context of the behaviour near the critical point of phase separation. For the MD simulations a new effective model with soft interaction potentials is introduced and its phase diagram is presented. Here, mainly the equilibrium properties of this model are characterised. While the self-diffusion constants of colloids and polymers do not change strongly when the critical point is approached, critical slowing down of interdiffusion is observed. The order parameter fluctuations can be determined through the long-wavelength limit of static structure factors. For this strongly asymmetric mixture it is shown how the relevant structure factor can be extracted by a diagonalisation of a matrix that contains the partial static structure factors. By presenting first results of this model under shear it is demonstrated that it is suitable for non-equilibrium simulations as well.

Crystal phases and glassy dynamics in monodisperse hard ellipsoids

We have performed Monte Carlo and molecular dynamics simulations of suspensions of monodisperse, hard ellipsoids of revolution. Hard-particle models play a key role in statistical mechanics. They are conceptually and computationally simple, and they offer insight into systems in which particle shape is important, including atomic, molecular, colloidal, and granular systems. In the high density phase diagram of prolate hard ellipsoids we have found a new crystal, which is more stable than the stretched FCC structure proposed previously . The new phase, SM2, has a simple monoclinic unit cell containing a basis of two ellipsoids with unequal orientations. The angle of inclination is very soft for length-to-width (aspect) ratio l/w=3, while the other angles are not. A symmetric state of the unit cell exists, related to the densest-known packings of ellipsoids; it is not always the stable one. Our results remove the stretched FCC structure for aspect ratio l/w=3 from the phase diagram of hard, uni-axial ellipsoids. We provide evidence that this holds between aspect ratios 3 and 6, and possibly beyond. Finally, ellipsoids in SM2 at l/w=1.55 exhibit end-over-end flipping, warranting studies of the cross-over to where this dynamics is not possible. Secondly, we studied the dynamics of nearly spherical ellipsoids. In equilibrium, they show a first-order transition from an isotropic phase to a rotator phase, where positions are crystalline but orientations are free. When over-compressing the isotropic phase into the rotator regime, we observed super-Arrhenius slowing down of diffusion and relaxation, and signatures of the cage effect. These features of glassy dynamics are sufficiently strong that asymptotic scaling laws of the Mode-Coupling Theory of the glass transition (MCT) could be tested, and were found to apply. We found strong coupling of positional and orientational degrees of freedom, leading to a common value for the MCT glass-transition volume fraction. Flipping modes were not slowed down significantly. We demonstrated that the results are independent of simulation method, as predicted by MCT. Further, we determined that even intra-cage motion is cooperative. We confirmed the presence of dynamical heterogeneities associated with the cage effect. The transit between cages was seen to occur on short time scales, compared to the time spent in cages; but the transit was shown not to involve displacements distinguishable in character from intra-cage motion. The presence of glassy dynamics was predicted by molecular MCT (MMCT). However, as MMCT disregards crystallization, a test by simulation was required. Glassy dynamics is unusual in monodisperse systems. Crystallization typically intervenes unless polydispersity, network-forming bonds or other asymmetries are introduced. We argue that particle anisometry acts as a sufficient source of disorder to prevent crystallization. This sheds new light on the question of which ingredients are required for glass formation.

Coarse-graining methods and polymer dynamics

This thesis studies molecular dynamics simulations on two levels of resolution: the detailed level of atomistic simulations, where the motion of explicit atoms in a many-particle system is considered, and the coarse-grained level, where the motion of superatoms composed of up to 10 atoms is modeled. While atomistic models are capable of describing material specific effects on small scales, the time and length scales they can cover are limited due to their computational costs. Polymer systems are typically characterized by effects on a broad range of length and time scales. Therefore it is often impossible to atomistically simulate processes, which determine macroscopic properties in polymer systems. Coarse-grained (CG) simulations extend the range of accessible time and length scales by three to four orders of magnitude. However, no standardized coarse-graining procedure has been established yet. Following the ideas of structure-based coarse-graining, a coarse-grained model for polystyrene is presented. Structure-based methods parameterize CG models to reproduce static properties of atomistic melts such as radial distribution functions between superatoms or other probability distributions for coarse-grained degrees of freedom. Two enhancements of the coarse-graining methodology are suggested. Correlations between local degrees of freedom are implicitly taken into account by additional potentials acting between neighboring superatoms in the polymer chain. This improves the reproduction of local chain conformations and allows the study of different tacticities of polystyrene. It also gives better control of the chain stiffness, which agrees perfectly with the atomistic model, and leads to a reproduction of experimental results for overall chain dimensions, such as the characteristic ratio, for all different tacticities. The second new aspect is the computationally cheap development of nonbonded CG potentials based on the sampling of pairs of oligomers in vacuum. Static properties of polymer melts are obtained as predictions of the CG model in contrast to other structure-based CG models, which are iteratively refined to reproduce reference melt structures. The dynamics of simulations at the two levels of resolution are compared. The time scales of dynamical processes in atomistic and coarse-grained simulations can be connected by a time scaling factor, which depends on several specific system properties as molecular weight, density, temperature, and other components in mixtures. In this thesis the influence of molecular weight in systems of oligomers and the situation in two-component mixtures is studied. For a system of small additives in a melt of long polymer chains the temperature dependence of the additive diffusion is predicted and compared to experiments.

A mesoscopic simulation method for electrolyte solutions

This thesis deals with the development of a novel simulation technique for macromolecules in electrolyte solutions, with the aim of a performance improvement over current molecular-dynamics based simulation methods. In solutions containing charged macromolecules and salt ions, it is the complex interplay of electrostatic interactions and hydrodynamics that determines the equilibrium and non-equilibrium behavior. However, the treatment of the solvent and dissolved ions makes up the major part of the computational effort. Thus an efficient modeling of both components is essential for the performance of a method. With the novel method we approach the solvent in a coarse-grained fashion and replace the explicit-ion description by a dynamic mean-field treatment. Hence we combine particle- and field-based descriptions in a hybrid method and thereby effectively solve the electrokinetic equations. The developed algorithm is tested extensively in terms of accuracy and performance, and suitable parameter sets are determined. As a first application we study charged polymer solutions (polyelectrolytes) in shear flow with focus on their viscoelastic properties. Here we also include semidilute solutions, which are computationally demanding. Secondly we study the electro-osmotic flow on superhydrophobic surfaces, where we perform a detailed comparison to theoretical predictions.

Pi release from myosin: a simulation analysis of possible pathways

The release of phosphate (Pi) is an important element in actomyosin function and has been shown to be accelerated by the binding of myosin to actin. To provide information about the structural elements important for Pi release, possible escape pathways from various isolated myosin II structures have been determined by molecular dynamics simulations designed for studying such slow processes. The residues forming the pathways were identified and their role was evaluated by mutant simulations. Pi release is slow in the pre-powerstroke structure, an important element in preventing the powerstroke prior to actin binding, and is much more rapid for Pi modeled into the post-rigor and rigor-like structures. The previously proposed backdoor route is dominant in the pre-powerstroke and post-rigor states, whereas a different path is most important in the rigor-like state. This finding suggests a mechanism for the actin-activated acceleration of Pi release.

Molecular Mechanics of Water Monomer

Simulation of the classical molecular dynamics of a water molecule can be useful in explaining normal modes of motion, Fourier Transforms, and fundamental frequencies of vibration, as illustrated herein.

Characterization of residual structure in the thermally denatured state of barnase by simulation and experiment: Description of the folding pathway

Residual structure in the denatured state of a protein may contain clues about the early events in folding. We have simulated by molecular dynamics the denatured state of barnase, which has been studied by NMR spectroscopy. An ensemble of 104 structures was generated after 2 ns of unfolding and following for a further 2 ns. The ensemble was heterogeneous, but there was nonrandom, residual structure with persistent interactions. Helical structure in the C-terminal portion of helix α1 (residues 13–17) and in helix α2 as well as a turn and nonnative hydrophobic clustering between β3 and β4 were observed, consistent with NMR data. In addition, there were tertiary contacts between residues in α1 and the C-terminal portion of the β-sheet. The simulated structures allow the rudimentary NMR data to be fleshed out. The consistency between simulation and experiment inspires confidence in the methods. A description of the folding pathway of barnase from the denatured to the native state can be constructed by combining the simulation with experimental data from φ value analysis and NMR.

Comportamento tribo-mecânico e desgaste adesivo de materiais em nanoescala: análises por dinâmica molecular e mecânica do contínuo.

As formulações baseadas na mecânica do contínuo, embora precisas até certo ponto, por vezes não podem ser utilizadas, ou não são conceitualmente corretas para o entendimento de fenômenos em escalas reduzidas. Estas limitações podem aparecer no estudo dos fenômenos tribológicos em escala nanométrica, que passam a necessitar de novos métodos experimentais, teóricos e computacionais que permitam explorar estes fenômenos com a resolução necessária. Simulações atomísticas são capazes de descrever fenômenos em pequena escala, porém, o número necessário de átomos modelados e, portanto, o custo computacional - geralmente torna-se bastante elevado. Por outro lado, os métodos de simulação associados à mecânica do contínuo são mais interessantes em relação ao custo computacional, mas não são precisos na escala atômica. A combinação entre essas duas abordagens pode, então, permitir uma compreensão mais realista dos fenômenos da tribologia. Neste trabalho, discutem-se os conceitos básicos e modelos de atrito em escala atômica e apresentam-se estudos, por meio de simulação numérica, para a análise e compreensão dos mecanismos de atrito e desgaste no contato entre materiais. O problema é abordado em diferentes escalas, e propõe-se uma abordagem conjunta entre a Mecânica do Contínuo e a Dinâmica Molecular. Para tanto, foram executadas simulações numéricas, com complexidade crescente, do contato entre superfícies, partindo-se de um primeiro modelo que simula o efeito de defeitos cristalinos no fenômeno de escorregamento puro, considerando a Dinâmica Molecular. Posteriormente, inseriu-se, nos modelos da mecânica do contínuo, considerações sobre o fenômeno de adesão. A validação dos resultados é feita pela comparação entre as duas abordagens e com a literatura.

Modeling molecular transport in slit pores

We examine the transport of methane in microporous carbon by performing equilibrium and nonequilibrium molecular dynamics simulations over a range of pore sizes, densities, and temperatures. We interpret these simulation results using two models of the transport process. At low densities, we consider a molecular flow model, in which intermolecular interactions are neglected, and find excellent agreement between transport diffusion coefficients determined from simulation, and those predicted by the model. Simulation results indicate that the model can be applied up to fluid densities of the order to 0.1-1 nm(-3). Above these densities, we consider a slip flow model, combining hydrodynamic theory with a slip condition at the solid-fluid interface. As the diffusion coefficient at low densities can be accurately determined by the molecular flow model, we also consider a model where the slip condition is supplied by the molecular flow model. We find that both density-dependent models provide a useful means of estimating the transport coefficient that compares well with simulation. (C) 2004 American Institute of Physics.

The interlayer swelling and molecular packing in organoclays

Understanding the interlayer swelling and molecular packing in organoclays is important to the formation and design of polymer nanocomposites. This paper presents recent experimental and molecular simulation studies on a variety of organoclays that show a linear relationship between the increase of d-spacing and the mass ratio between organic and clay. A denser molecular packing is observed in organoclays containing surfactants with hydroxyl-ethyl units. Moreover, our simulation results show that the head (nitrogen) groups are essentially tethered to the clay surface while the long hydrocarbon chains tend to adopt a layering structure with disordered conformation, which contrasts with the previous assumptions of either the chains lying parallel to the clay surface or being tilted at rather precise angles. (c) 2005 Elsevier Inc. All rights reserved.

Transport of simple fluids in nanopores: Theory and simulation

A theory is discussed of single-component transport in nanopores, recently developed by Bhatia and coworkers. The theory considers the oscillatory motion of molecules between diffuse wall collisions, arising from the fluid-wall interaction, along with superimposed viscous flow due to fluid-fluid interaction. The theory is tested against molecular dynamics simulations for hydrogen, methane, and carbon tetrafluoride flow in cylindrical nanopores in silica. Although exact at low densities, the theory performs well even at high densities, with the density dependency of the transport coefficient arising from viscous effects. Such viscous effects are reduced at high densities because of the large increase in viscosity, which explains the maximum in the transport coefficient with increase in density. Further, it is seen that in narrow pore sizes of less than two molecular diameters, where a complete monolayer cannot form on the surface, the mutual interference of molecules on opposite sides of the cross section can reduce the transport coefficient, and lead to a maximum in the transport coefficient with increasing density. The theory is also tested for the case of partially diffuse reflection and shows the viscous contribution to be negligible when the reflection is nearly specular. (c) 2005 American Institute of Chemical Engineers AIChE J, 52: 29-38, 2006.

Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem.

Complexity of classical dynamics of molecular systems. II. Finite statistical complexity of a water-Na+ system

The computational mechanics approach has been applied to the orientational behavior of water molecules in a molecular dynamics simulated water–Na + system. The distinctively different statistical complexity of water molecules in the bulk and in the first solvation shell of the ion is demonstrated. It is shown that the molecules undergo more complex orientational motion when surrounded by other water molecules compared to those constrained by the electric field of the ion. However the spatial coordinates of the oxygen atom shows the opposite complexity behavior in that complexity is higher for the solvation shell molecules. New information about the dynamics of water molecules in the solvation shell is provided that is additional to that given by traditional methods of analysis.

Molecular mechanisms of salt effects on carbon nanotube dispersions in an organic solvent (N-methyl-2-pyrrolidone)

We consider the effects of salt (sodium iodide) on pristine carbon nanotube (CNT) dispersions in an organic solvent, N-methyl-2-pyrrolidone (NMP). We investigate the molecular-scale mechanisms of ion interactions with the nanotube surface and we show how the microscopic ion-surface interactions affect the stability of CNT dispersions in NMP. In our study we use a combination of fully atomistic Molecular Dynamics simulations of sodium and iodide ions at the CNT-NMP interface with direct experiments on the CNT dispersions. In the experiments we analyze the effects of salt on the stability of the dispersions by photoluminescence (PL) and optical absorption spectroscopy of the samples as well as by visual inspection. By fully atomistic Molecular Dynamics simulations we investigate the molecular-scale mechanisms of sodium and iodide ion interactions with the nanotube surface. Our simulations reveal that both ions are depleted from the CNT surface in the CNT-NMP dispersions mainly due to the two reasons: (1) there is a high energy penalty for the ion partial desolvation at the CNT surface; (2) NMP molecules form a dense solvation layer at the CNT surface that prevents ions to come close to the CNT surface. As a result, an increase of the salt concentration increases the "osmotic" stress in the CNT-NMP system and, thus, decreases the stability of the CNT dispersions in NMP. Direct experiments confirm the simulation results: addition of NaI salt into the NMP dispersions of pristine CNTs leads to precipitation of CNTs (bundle formation) even at very small salt concentration (∼10 -3 mol L -1). In line with the simulation predictions, the effect increases with the increase of the salt concentration. Overall, our results show that dissolved salt ions have strong effects on the stability of CNT dispersions. Therefore, it is possible to stimulate the bundle formation in the CNT-NMP dispersions and regulate the overall concentration of nanotubes in the dispersions by changing the NaI concentration in the solvent. © 2012 The Royal Society of Chemistry.