Homogeneous ice nucleation

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Table of contents

1 Résumé en français 
2 Introduction 
2.1 Context
2.2 Thermodynamics and phase transitions
2.3 Numerical study of transformations of matter
2.3.1 Enhanced sampling methods
2.3.2 Reaction coordinates
2.4 Complexity of water
2.4.1 The “liquid-liquid transition”
2.4.2 Homogeneous ice nucleation
2.5 Open challenges
I Methods 
3 Simulations of Condensed Matter 
3.1 Classical molecular dynamics
3.1.1 Short introduction to statistical principle
3.1.2 Time evolution
3.1.3 Temperature coupling
3.1.4 Pressure coupling
3.1.5 Periodic boundary conditions
3.2 Force fields
3.2.1 The mW model
3.2.2 The ST2 model
3.2.3 The TIP4P family
3.3 About the choice of water model
4 Describing our systems with collective variables 
4.1 Local collective variables
4.1.1 Coordination number
4.1.2 The Steinhardt parameters
4.1.3 The Chill+ algorithm
4.2 Global collective variable
4.2.1 The largest nucleus size
4.2.2 Cubicity
4.2.3 Permutation Invariant Vector (PIV) and PIV distance
4.2.4 Path collective variables
4.2.5 Commitment probability
4.3 Quality of reaction coordinates
4.3.1 Maximum likelihood optimization
4.4 Development of PIV in plumed
4.4.1 User interface
4.4.2 Counting sort algorithm
4.4.3 Computing the derivatives
5 Enhanced sampling methods 
5.1 Free energy exploration and reconstruction
5.1.1 Umbrella sampling
5.1.2 Metadynamics
5.2 Transition path sampling
5.2.1 Seeding
5.2.2 Aimless shooting algorithm
5.2.3 Shooting range algorithm
II Results 
6 Study of the Liquid-Liquid Phase Transition 
6.1 Introduction
6.1.1 The two-states model
6.1.2 Experimental studies of the liquid-liquid transition
6.1.3 Numerical studies of the liquid-liquid transition
6.2 Simulation methods
6.2.1 Molecular dynamics parameters
6.2.2 States preparation
6.2.3 Order parameter definition
6.2.4 Free energy calculations
6.3 Exploration of the (P, T) diagram
6.3.1 First exploration using Berendsen barostat
6.3.2 Proper exploration with ensemble consistent barostat
6.3.3 Convergence assessment and error estimation
6.3.4 Schematic no man’s land phase diagram
6.4 Kinetic properties of the explored (P, T) conditions
6.5 Structural properties
6.5.1 Coordination number
6.5.2 Cluster analysis
6.6 Discussion
6.7 Conclusions and outlook
7 Study of the Homogeneous Ice Nucleation 
7.1 Introduction
7.1.1 Classical nucleation theory
7.1.2 The ice I polymorphs
7.1.3 A bit of crystallography
7.1.4 Numerical study of nucleation of ice I
7.2 Generation of initial reactive trajectories
7.2.1 Freezing and melting with metadynamics
7.2.2 Exploration of the transition state with seeding
7.3 Order parameter quality
7.3.1 Choice of the order parameter
7.3.2 committor analysis
7.3.3 Maximum likelihood optimization
7.4 Sampling of the transition path ensemble
7.4.1 Standard aimless shooting
7.4.2 Aimless shooting within a range
7.4.3 Difference of efficiency between the two techniques
7.4.4 Critical nuclei evolution
7.5 Conclusions and outlook
8 Conclusion 
References