Between the Scales: Water from Different Perspectives
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Between the Scales: Water from different Perspectives Dissertation zur Erlangung des Grades “Doktor der Naturwissenschaften” am Fachbereich Physik der Johannes Gutenberg-Universit¨at Mainz Christoph Junghans geb. in Merseburg Max-Planck-Institut f¨ur Polymerforschung Mainz, 9. August 2010 Tag der m¨undlichen Pr¨ufung: 29. Okt. 2010 Abstract Water is one of the most frequently studied fluids on earth. In this thesis, water was investigated at two resolutions using multi-scale computer simu- lation techniques. First, the atomistic and coarse-grained resolutions were studied separately. In the atomistic resolution, a water molecule is described chemically by three atoms, while in the coarse-grained case, a molecule is modeled by a sphere. In this work, various coarse-grained models have been developed using different coarse-graining techniques, mainly iterative Boltzmann inversion and iterative inverse Monte Carlo, which are structure-based approaches that aim to reproduce distributions, such as the pair distribution functions, of the atomistic model. In this context the Versatile Object-oriented Toolkit for Coarse-graining Applications (VOTCA) was developed. It was studied to which extent the coarse-grained models can simultane- ously reproduce several properties of the underlying atomistic model, such as thermodynamic properties like pressure and compressibility or structural properties, which have not been used in the coarse-graining process, e. g. the tetrahedral packing behavior, which is responsible for many special properties of water. Subsequently, these two resolutions were combined using the adaptive res- olution scheme, which combines the advantage of atomistic details in a small cavity of high resolution with the computational efficiency of the coarse- grained model in order to access larger time and length scales. In this scheme, the introduced coarse-grained models were used to study the influence of the hydrogen bonds on the hydration of small fullerenes. It was found that the interface structure is more dependent on the nature of the interaction be- tween the solute and water molecules than on the presence of the hydrogen bond network. III IV Zusammenfassung In der vorliegenden Arbeit werden verschiedene Wassermodelle in sogenan- nten Multiskalen-Computersimulationen mit zwei Aufl¨osungen untersucht, in atomistischer Aufl¨osung und in einer vergr¨oberten Aufl¨osung, die als “coarse- grained” bezeichnet wird. In der atomistischen Aufl¨osung wird ein Wasser- molek¨ul, entsprechend seiner chemischen Struktur, durch drei Atome be- schrieben, im Gegensatz dazu wird ein Molek¨ul in der coarse-grained Aufl¨os- ung durch eine Kugel dargestellt. Die coarse-grained Modelle, die in dieser Arbeit vorgestellt werden, wer- den mit verschiedenen coarse-graining Methoden entwickelt. Hierbei kom- men haupts¨achlich die “iterative Boltzmann Inversion” und die “iterative Monte Carlo Inversion” zum Einsatz. Beides sind struktur-basierte Ans¨atze, die darauf abzielen bestimmte strukturelle Eigenschaften, wie etwa die Paar- verteilungsfunktionen, des zugrundeliegenden atomistischen Systems zu re- produzieren. Zur automatisierten Anwendung dieser Methoden wurde das Softwarepaket “Versatile Object-oriented Toolkit for Coarse-Graining Appli- cations” (VOTCA) entwickelt. Es wird untersucht, in welchem Maße coarse-grained Modelle mehrere Eigenschaften des zugrundeliegenden atomistischen Modells gleichzeitig re- produzieren k¨onnen, z.B. thermodynamische Eigenschaften wie Druck und Kompressibilit¨at oder strukturelle Eigenschaften, die nicht zur Modellbil- dung verwendet wurden, z.B. das tetraedrische Packungsverhalten, welches f¨ur viele spezielle Eigenschaft von Wasser verantwortlich ist. Mit Hilfe des “Adaptive Resolution Schemes” werden beide Aufl¨osungen in einer Simulation kombiniert. Dabei profitiert man von den Vorteilen beider Modelle: Von der detaillierten Darstellung eines r¨aumlich kleinen Bereichs in atomistischer Aufl¨osung und von der rechnerischen Effizienz des coarse-grained Modells, die den Bereich simulierbarer Zeit- und L¨angenskalen vergr¨ossert. In diesen Simulationen kann der Einfluss des Wasserstoffbr¨uckenbind- ungsnetzwerks auf die Hydration von Fullerenen untersucht werden. Es zeigt sich, dass die Struktur der Wassermolek¨ule an der Oberfl¨ache haupts¨achlich von der Art der Wechselwirkung zwischen dem Fulleren und Wasser und weniger von dem Wasserstoffbr¨uckenbindungsnetzwerk dominiert wird. V VI Contents Overview 1 Related Publications 3 1 Introduction 5 1.1 Multi-scaletechniques . 6 1.2 AdaptiveResolutionScheme . 7 1.3 Coarse-Graining.......................... 8 2 Theory & Simulation Methods 9 2.1 MolecularDynamics ....................... 9 2.1.1 Newton’s Equation of Motion . 10 2.1.2 Velocity Verlet Algorithm . 10 2.2 Thermostats............................ 11 2.2.1 Fokker-Planck Picture . 12 2.2.1.1 Pawula Theorem . 14 2.2.2 Deterministic Dynamics . 15 2.2.2.1 Velocity Verlet Algorithm . 15 2.2.3 Canonical ensemble . 17 2.2.3.1 Rescaling Thermostats . 17 2.2.4 Langevin Thermostats . 18 2.2.4.1 Deterministic Part . 19 2.2.4.2 Stochastic Part . 19 2.2.4.3 Summary .................... 21 2.2.5 Dissipative Particle Dynamics Thermostat . 22 2.2.5.1 Noise Properties . 23 2.2.5.2 DPD Fokker-Planck operator . 24 2.2.6 Transversal DPD Thermostat . 28 2.2.7 Implementation in ESPResSo . 30 2.2.8 Numerical Validation on Lennard-Jones Particles . 31 2.2.8.1 Diffusion Constant . 32 VII 2.2.8.2 Shear Viscosity . 32 2.2.8.3 Summary .................... 34 2.2.9 Thermostats for Molecules . 34 2.3 Coarse-Graining.......................... 35 2.3.1 Mappings ......................... 35 2.3.2 Coarse-Graining Approaches . 36 2.3.3 Simple Boltzmann Inversion . 37 2.3.4 IterativeMethods. 39 2.3.4.1 Iterative Boltzmann Inversion . 39 2.3.4.2 Pressure Correction . 40 2.3.4.3 Inverse Monte Carlo . 41 2.3.5 ForceMatching . 44 2.3.6 Implementation (VOTCA) . 45 2.3.6.1 Coarse-Graining Engine . 46 2.3.6.2 Iterative Framework . 47 2.3.6.3 Summary .................... 47 2.3.7 Potential of Mean Force using Constraints . 49 2.3.8 Summary ......................... 50 2.4 AdaptiveResolutionScheme . 50 2.4.1 ScaleCoupling ...................... 51 2.4.2 Thermodynamical Equilibrium . 52 2.4.3 Principles behind the Thermodynamical Equilibrium . 53 2.4.3.1 Geometrically induced Phase Transitions . 54 2.4.3.2 Temperature in the Transition Region . 54 2.4.4 Coupling via a Potential Approach . 56 2.4.5 Algorithms of the Implementation . 57 2.4.5.1 Force Fields and Interpolation . 57 2.4.5.2 VirtualSites . 59 2.4.5.3 Interface Pressure Correction . 60 2.4.5.4 Thermodynamic Force . 60 2.4.6 Implementation in ESPResSo . 61 2.4.6.1 General Overview . 61 2.4.6.2 Integrator . 62 2.4.6.3 Parallelization Scheme . 63 2.4.6.4 Thermostat . 64 2.4.6.5 Intramolecular Initialization . 65 2.4.6.6 Bonded Interactions . 65 2.4.6.7 Cut-Offs..................... 65 2.4.6.8 Molecules & Mappings . 66 2.4.6.9 Interface pressure correction . 67 2.4.6.10 Thermodynamic Force . 67 VIII 2.4.7 Summary ......................... 68 3 Coarse-Graining 69 3.1 AtomisticWaterModels . 70 3.2 Coarse-Grained Water Models . 71 3.2.1 Liquid Structure – Geometrical Consideration . 72 3.2.2 Effective Coarse-Grained Potentials . 74 3.2.3 TimeScales ........................ 80 3.2.4 Optimizing the Tetrahedral Packing . 81 3.2.5 Summary ......................... 86 3.3 Other Coarse-Graining Techniques . 88 3.3.1 Comparative coarse-graining of SPC/E Water . 88 3.3.2 Comparative coarse-graining of Methanol . 90 3.3.3 Comparative coarse-graining of Liquid Propane . 93 3.3.4 Angular Potential of a Hexane Molecule . 96 3.3.5 Summary ......................... 97 3.4 Dynamics of Coarse-Grained Water . 98 3.4.1 AtomisticModel ..................... 98 3.4.2 Coarse-grained Model . 98 3.4.3 Results........................... 99 3.4.4 Summary .........................100 4 Adaptive Resolution Simulations 103 4.1 TetrahedralLiquid . .103 4.2 Water ...............................105 4.2.1 SimulationsSetup. .108 4.2.2 Dependence on the Size of the explicit Region . 109 4.2.3 Summary .........................111 4.3 Solvated Fullerenes . 111 4.3.1 Introduction. .111 4.3.2 SimulationSetup . .113 4.3.3 Results...........................117 4.4 Summary .............................120 5 Conclusion & Outlook 121 5.1 Coarse-Graining. .121 5.2 Adaptive Resolution Scheme . 123 5.3 Outlook ..............................124 Bibliography 127 IX Acknowledgment 143 Resume 145 X List of Figures 1.1 Modelingondifferentscales . 6 2.1 Velocity Verlet algorithm . 11 2.2 Decomposition of the relative velocity . 23 2.3 Diffusive dynamics of a LJ system . 32 2.4 Shear viscosity of a LJ system . 33 2.5 Block-scheme of the iterative framework . 48 2.6 IllustrationofAdResS . 50 2.7 AdResS interface pressure correction . 61 3.1 Radial distribution function of all-atom models . 75 3.2 Tetrahedral packing parameter of water . 76 3.3 Radial distribution function of coarse-grained SPC/E water . 77 3.4 Effective coarse-grained potentials . 78 3.5 Potential of extrapolation . 83 3.6 Radial distribution function of the potential of extrapolation . 84 3.7 Tetrahedral packing of the potential of extrapolation . 85 3.8 Coarse-grained SPC/E Water . 88 3.9 Coarse-grainedmethanol . 91 3.10 Coarse-grainedpropane. 94 3.11 Coarse-grained hexane . 96 3.12 Radial distribution functions of the modified TIP3P water . 99 3.13 Diffusion process for different friction constants . 101 4.1 Structureofthetetrahedralliquid . 105 4.2 Density profiles of the tetrahedral liquid . 106 4.3 Thermodynamic force of SPC/E coarse-grained water . 109 4.4 Radial distribution functions for SPC/E water . 110 4.5 Snapshot of a fullerene in an AdResS simulation . 112 4.6 Water distribution near the surface of a fullerene . 116 4.7 Radial distribution function of water near the fullerene surface 117 4.8 Tetrahedral packing of water near the fullerene surface . 119 XI XII List of Tables 3.1 Parameters of all-atom water models . 71 3.2 Structural properties of different water models . 73 3.3 Thermodynamic properties of different water models .