Studies in molecular dynamics: new criteria for evaluation of intramolecular force fields

The present thesis deals with some studies in molecular dynamics using spectroscopic data. Two new approximation procedures the variable method and the average bonding energy criterion have been developed for a reliable calculation of molecular force fields and applied to several molecular species belonging to the xy2 type.

Linear viscoelasticity from molecular dynamics simulation of entangled polymers

The linear viscoelastic (LVE) spectrum is one of the primary fingerprints of polymer solutions and melts, carrying information about most relaxation processes in the system. Many single chain theories and models start with predicting the LVE spectrum to validate their assumptions. However, until now, no reliable linear stress relaxation data were available from simulations of multichain systems. In this work, we propose a new efficient way to calculate a wide variety of correlation functions and mean-square displacements during simulations without significant additional CPU cost. Using this method, we calculate stress−stress autocorrelation functions for a simple bead−spring model of polymer melt for a wide range of chain lengths, densities, temperatures, and chain stiffnesses. The obtained stress−stress autocorrelation functions were compared with the single chain slip−spring model in order to obtain entanglement related parameters, such as the plateau modulus or the molecular weight between entanglements. Then, the dependence of the plateau modulus on the packing length is discussed. We have also identified three different contributions to the stress relaxation:  bond length relaxation, colloidal and polymeric. Their dependence on the density and the temperature is demonstrated for short unentangled systems without inertia.

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.

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 simulations of silicate and borate glasses and melts : structure, diffusion dynamics and vibrational properties

Molecular dynamics simulations of silicate and borate glasses and melts: Structure, diffusion dynamics and vibrational properties. In this work computer simulations of the model glass formers SiO2 and B2O3 are presented, using the techniques of classical molecular dynamics (MD) simulations and quantum mechanical calculations, based on density functional theory (DFT). The latter limits the system size to about 100−200 atoms. SiO2 and B2O3 are the two most important network formers for industrial applications of oxide glasses. Glass samples are generated by means of a quench from the melt with classical MD simulations and a subsequent structural relaxation with DFT forces. In addition, full ab initio quenches are carried out with a significantly faster cooling rate. In principle, the structural properties are in good agreement with experimental results from neutron and X-ray scattering, in all cases. A special focus is on the study of vibrational properties, as they give access to low-temperature thermodynamic properties. The vibrational spectra are calculated by the so-called ”frozen phonon” method. In all cases, the DFT curves show an acceptable agreement with experimental results of inelastic neutron scattering. In case of the model glass former B2O3, a new classical interaction potential is parametrized, based on the liquid trajectory of an ab initio MD simulation at 2300 K. In this course, a structural fitting routine is used. The inclusion of 3-body angular interactions leads to a significantly improved agreement of the liquid properties of the classical MD and ab initio MD simulations. However, the generated glass structures, in all cases, show a significantly lower fraction of 3-membered planar boroxol rings as predicted by experimental results (f=60%-80%). The largest boroxol ring fraction of f=15±5% is observed in the full ab initio quenches from 2300 K. In case of SiO2, the glass structures after the quantum mechanical relaxation are the basis for calculations of the linear thermal expansion coefficient αL(T), employing the quasi-harmonic approximation. The striking observation is a change change of sign of αL(T) going along with a temperature range of negative αL(T) at low temperatures, which is in good agreement with experimental results.

Molecular Dynamics Simulations of Couette flow

The first steps towards developing a continuum-molecular coupled simulations techniques are presented, for the purpose of computing macroscopic systems of confined fluids. The idea is to compute the interface wall-fluid by Molecular Dynamics simulations, where Lennard-Jones potential (and others) have been employed for the molecular interactions, so the usual non slip boundary condition is not specified. Instead, a shear rate can be imposed at the wall, which allows to obtain the properties of the wall material by means of an iterative method. The remaining fluid region will be computed by a spectral hp method. We present MD simulations of a Couette flow, and the results of the developed boundary conditions from the wall fluid interaction.

Complex temporal patterns in molecular dynamics:a direct measure of the phase-space exploration by the trajectory at macroscopic time scales

Computer simulated trajectories of bulk water molecules form complex spatiotemporal structures at the picosecond time scale. This intrinsic complexity, which underlies the formation of molecular structures at longer time scales, has been quantified using a measure of statistical complexity. The method estimates the information contained in the molecular trajectory by detecting and quantifying temporal patterns present in the simulated data (velocity time series). Two types of temporal patterns are found. The first, defined by the short-time correlations corresponding to the velocity autocorrelation decay times (â‰0.1â€ps), remains asymptotically stable for time intervals longer than several tens of nanoseconds. The second is caused by previously unknown longer-time correlations (found at longer than the nanoseconds time scales) leading to a value of statistical complexity that slowly increases with time. A direct measure based on the notion of statistical complexity that describes how the trajectory explores the phase space and independent from the particular molecular signal used as the observed time series is introduced. © 2008 The American Physical Society.

Controlling protein molecular dynamics:how to accelerate folding while preserving the native state

The dynamics of peptides and proteins generated by classical molecular dynamics (MD) is described by using a Markov model. The model is built by clustering the trajectory into conformational states and estimating transition probabilities between the states. Assuming that it is possible to influence the dynamics of the system by varying simulation parameters, we show how to use the Markov model to determine the parameter values that preserve the folded state of the protein and at the same time, reduce the folding time in the simulation. We investigate this by applying the method to two systems. The first system is an imaginary peptide described by given transition probabilities with a total folding time of 1 micros. We find that only small changes in the transition probabilities are needed to accelerate (or decelerate) the folding. This implies that folding times for slowly folding peptides and proteins calculated using MD cannot be meaningfully compared to experimental results. The second system is a four residue peptide valine-proline-alanine-leucine in water. We control the dynamics of the transitions by varying the temperature and the atom masses. The simulation results show that it is possible to find the combinations of parameter values that accelerate the dynamics and at the same time preserve the native state of the peptide. A method for accelerating larger systems without performing simulations for the whole folding process is outlined.

Molecular dynamics study of solvent transport in nanoscale osmosis

An ideal of osmotic equilibrium between an ideal solution and pure solvent separated by a semi-permeable membrane is studied numerically using the method of molecular dynamics. The osmotic flow is observed as the inflow of the solvent across the membrane from the dilute to the concentrated side. The validity of van't Hoff's law for osmotic pressure is confirmed over a wide range of concentrations. It is found that the law is established by a balance between non-uniform partial pressures of solute and solvent. Furthermore, the present model permits an understanding of the mechanism of the osmotic flow in the relaxation process as the liquids evolve from the initial state to the equilibrium state. We focus in particular on the interaction between solute and solvent. ©2008 The Physical Society of Japan.

Bridging large and small scales of water models using hybrid Molecular Dynamics/Fluctuating Hydrodynamics framework

This thesis presents a two-dimensional water model investigation and development of a multiscale method for the modelling of large systems, such as virus in water or peptide immersed in the solvent. We have implemented a two-dimensional ‘Mercedes Benz’ (MB) or BN2D water model using Molecular Dynamics. We have studied its dynamical and structural properties dependence on the model’s parameters. For the first time we derived formulas to calculate thermodynamic properties of the MB model in the microcanonical (NVE) ensemble. We also derived equations of motion in the isothermal–isobaric (NPT) ensemble. We have analysed the rotational degree of freedom of the model in both ensembles. We have developed and implemented a self-consistent multiscale method, which is able to communicate micro- and macro- scales. This multiscale method assumes, that matter consists of the two phases. One phase is related to micro- and the other to macroscale. We simulate the macro scale using Landau Lifshitz-Fluctuating Hydrodynamics, while we describe the microscale using Molecular Dynamics. We have demonstrated that the communication between the disparate scales is possible without introduction of fictitious interface or approximations which reduce the accuracy of the information exchange between the scales. We have investigated control parameters, which were introduced to control the contribution of each phases to the matter behaviour. We have shown, that microscales inherit dynamical properties of the macroscales and vice versa, depending on the concentration of each phase. We have shown, that Radial Distribution Function is not altered and velocity autocorrelation functions are gradually transformed, from Molecular Dynamics to Fluctuating Hydrodynamics description, when phase balance is changed. In this work we test our multiscale method for the liquid argon, BN2D and SPC/E water models. For the SPC/E water model we investigate microscale fluctuations which are computed using advanced mapping technique of the small scales to the large scales, which was developed by Voulgarakisand et. al.

Analysis of Molecular Dynamics Simulations of Protein Folding

Microsecond long Molecular Dynamics (MD) trajectories of biomolecular processes are now possible due to advances in computer technology. Soon, trajectories long enough to probe dynamics over many milliseconds will become available. Since these timescales match the physiological timescales over which many small proteins fold, all atom MD simulations of protein folding are now becoming popular. To distill features of such large folding trajectories, we must develop methods that can both compress trajectory data to enable visualization, and that can yield themselves to further analysis, such as the finding of collective coordinates and reduction of the dynamics. Conventionally, clustering has been the most popular MD trajectory analysis technique, followed by principal component analysis (PCA). Simple clustering used in MD trajectory analysis suffers from various serious drawbacks, namely, (i) it is not data driven, (ii) it is unstable to noise and change in cutoff parameters, and (iii) since it does not take into account interrelationships amongst data points, the separation of data into clusters can often be artificial. Usually, partitions generated by clustering techniques are validated visually, but such validation is not possible for MD trajectories of protein folding, as the underlying structural transitions are not well understood. Rigorous cluster validation techniques may be adapted, but it is more crucial to reduce the dimensions in which MD trajectories reside, while still preserving their salient features. PCA has often been used for dimension reduction and while it is computationally inexpensive, being a linear method, it does not achieve good data compression. In this thesis, I propose a different method, a nonmetric multidimensional scaling (nMDS) technique, which achieves superior data compression by virtue of being nonlinear, and also provides a clear insight into the structural processes underlying MD trajectories. I illustrate the capabilities of nMDS by analyzing three complete villin headpiece folding and six norleucine mutant (NLE) folding trajectories simulated by Freddolino and Schulten [1]. Using these trajectories, I make comparisons between nMDS, PCA and clustering to demonstrate the superiority of nMDS. The three villin headpiece trajectories showed great structural heterogeneity. Apart from a few trivial features like early formation of secondary structure, no commonalities between trajectories were found. There were no units of residues or atoms found moving in concert across the trajectories. A flipping transition, corresponding to the flipping of helix 1 relative to the plane formed by helices 2 and 3 was observed towards the end of the folding process in all trajectories, when nearly all native contacts had been formed. However, the transition occurred through a different series of steps in all trajectories, indicating that it may not be a common transition in villin folding. The trajectories showed competition between local structure formation/hydrophobic collapse and global structure formation in all trajectories. Our analysis on the NLE trajectories confirms the notion that a tight hydrophobic core inhibits correct 3-D rearrangement. Only one of the six NLE trajectories folded, and it showed no flipping transition. All the other trajectories get trapped in hydrophobically collapsed states. The NLE residues were found to be buried deeply into the core, compared to the corresponding lysines in the villin headpiece, thereby making the core tighter and harder to undo for 3-D rearrangement. Our results suggest that the NLE may not be a fast folder as experiments suggest. The tightness of the hydrophobic core may be a very important factor in the folding of larger proteins. It is likely that chaperones like GroEL act to undo the tight hydrophobic core of proteins, after most secondary structure elements have been formed, so that global rearrangement is easier. I conclude by presenting facts about chaperone-protein complexes and propose further directions for the study of protein folding.

A coupled meshless technique/molecular dynamics approach for deformation characterization of monocrystalline metal

This paper presents a multiscale study using the coupled Meshless technique/Molecular Dynamics (M2) for exploring the deformation mechanism of mono-crystalline metal (focus on copper) under uniaxial tension. In M2, an advanced transition algorithm using transition particles is employed to ensure the compatibility of both displacements and their gradients, and an effective local quasi-continuum approach is also applied to obtain the equivalent continuum strain energy density based on the atomistic poentials and Cauchy-Born rule. The key parameters used in M2 are firstly investigated using a benchmark problem. Then M2 is applied to the multiscale simulation for a mono-crystalline copper bar. It has found that the mono-crystalline copper has very good elongation property, and the ultimate strength and Young's modulus are much higher than those obtained in macro-scale.

Molecular dynamics studies of the effects of branching characteristics on the crystalline structure of polyethylene

Molecular dynamics simulations were carried out on single chain models of linear low-density polyethylene in vacuum to study the effects of branch length, branch content, and branch distribution on the polymer’s crystalline structure at 300 K. The trans/gauche (t/g) ratios of the backbones of the modeled molecules were calculated and utilized to characterize their degree of crystallinity. The results show that the t/g ratio decreases with increasing branch content regardless of branch length and branch distribution, indicating that branch content is the key molecular parameter that controls the degree of crystallinity. Although t/g ratios of the models with the same branch content vary, they are of secondary importance. However, our data suggests that branch distribution (regular or random) has a significant effect on the degree of crystallinity for models containing 10 hexyl branches/1,000 backbone carbons. The fractions of branches that resided in the equilibrium crystalline structures of the models were also calculated. On average, 9.8% and 2.5% of the branches were found in the crystallites of the molecules with ethyl and hexyl branches while C13 NMR experiments showed that the respective probabilities of branch inclusion for ethyl and hexyl branches are 10% and 6% [Hosoda et al., Polymer 1990, 31, 1999–2005]. However, the degree of branch inclusion seems to be insensitive to the branch content and branch distribution.

Molecular dynamics investigation on edge stress and shape transition in graphene nanoribbons

Graphene nanoribbon (GNR) with free edges demonstrates unique pre-existing edge energy and edge stress, leading to non-flat morphologies. Using molecular dynamics (MD) methods, we evaluated edge energies as well as edge stresses for four different edge types, including regular edges (armchair and zigzag), armchair edge terminated with hydrogen and reconstructed armchair. The results showed that compressive stress exists in the regular and hydrogen-terminated edges along the edge direction. In contrast, the reconstructed armchair edge is generally subject to tension. Furthermore, we also investigated shape transition between flat and rippled configurations of GNRs with different free edges. It was found that the pre-existing stress at free edges can greatly influence the initial energy state and the shape transition.

Molecular dynamics simulation of fracture strength and morphology of defective graphene

Different types of defects can be introduced into graphene during material synthesis, and significantly influence the properties of graphene. In this work, we investigated the effects of structural defects, edge functionalisation and reconstruction on the fracture strength and morphology of graphene by molecular dynamics simulations. The minimum energy path analysis was conducted to investigate the formation of Stone-Wales defects. We also employed out-of-plane perturbation and energy minimization principle to study the possi-ble morphology of graphene nanoribbons with edge-termination. Our numerical results show that the fracture strength of graphene is dependent on defects and environmental temperature. However, pre-existing defects may be healed, resulting in strength recovery. Edge functionalization can induce compressive stress and ripples in the edge areas of gra-phene nanoribbons. On the other hand, edge reconstruction contributed to the tensile stress and curved shape in the graphene nanoribbons.