1 Proton ordering and reactivity of ice Zamaan Raza Department of Chemistry University College London Thesis submitted for the degree of Doctor of Philosophy September 2012 2 I, Zamaan Raza, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. 3 For Chryselle, without whom I would never have made it this far. 4 I would like to thank my supervisors, Dr Ben Slater and Prof Angelos Michaelides for their patient guidance and help, particularly in light of the fact that I was woefully unprepared when I started. I would also like to express my gratitude to Dr Florian Schiffmann for his indispens- able advice on CP2K and quantum chemistry, Dr Alexei Sokol for various discussions on quantum mechanics, Dr Dario Alfé for his incredibly expensive DMC calculations, Drs Jiri Klimeš and Erlend Davidson for advice on VASP, Matt Watkins for help with CP2K, Christoph Salzmann for discussions on ice, Dr Stefan Bromley for allowing me to work with him in Barcelona and Drs Aron Walsh, Stephen Shevlin, Matthew Farrow and David Scanlon for general help, advice and tolerance. Thanks and also apologies to Stephen Cox, with whom I have collaborated, but have been unable to contribute as much as I should have. Doing a PhD is an isolating experience (more so in the Kathleen Lonsdale building), so I would like to thank my fellow students and friends for making it tolerable: Richard, Tiffany, and Chryselle. Finally, I would like to acknowledge UCL for my funding via a DTA and computing time on Legion, the Materials Chemistry Consortium (MCC) for computing time on HECToR and HPC-Europa2 for the opportunity to work in Barcelona. Abstract Cubic ice Ic is a rarely-observed ambient pressure phase of water implicated in the catal- ysis of atmospheric reactions. It forms between 160 K1 and 243 K2, in droplets smaller than 5 µm3 in diameter. It is metastable with respect to hexagonal ice Ih and is poorly characterised both experimentally and theoretically. The proton ordered ground state 4 for cubic ice has I 41 md symmetry and is named ice XIc . We find that the ground state proton ordered configurations of hexagonal and cubic ice, XI and XIc are isoenergetic. The surface energy of ice is strongly dependent on proton ordering. The “striped” configuration5 has the lowest surface energy, and clustering of dangling OH bonds in- creases the surface energy. Cubic ice is has a surface energy approximately 10% higher than hexagonal, and is more reactive. Elementary steps on the ice surface reconstruct to lower the step formation energy; under-coordinated molecules on the step edge relax to form an additional hydrogen bond with the lower terrace. We examine five different steps: the low energy A-and B1-steps and the high energy B1∗-, B2 and B2∗-steps. Different growth rates for these steps combined with a proton disorder are in part responsible for the isotropic bilayer growth of ice observed by Sazaki et al 6. Glycolaldehyde, the simplest sugar, has been observed recently in the interstellar medium7;8 and in a solar-type protostar9. We evaluate two potential mechanisms for its formation on icy dust grains at 10 K, finding that activation barriers are greatly reduced by the ice surface, and that the most likely route is a reaction between H2COH and HCO radicals, which are formed by the sequential hydrogenation of carbon monoxide. 5 Contents Abstract 5 Contents 6 List of Figures 10 Nomenclature 19 1 Introduction 20 1.1 Why study ice? . 20 2 A review of water ice 25 2.1 The crystalline structure of ice . 25 2.2 Cubic ice . 28 2.2.1 Structure: a stacking disordered phase? . 28 2.2.2 Phase transition to hexagonal ice . 28 2.2.3 Cubic ice in nature . 29 2.2.4 Formation conditions . 31 2.2.5 Attempts to prepare pure cubic ice . 32 2.3 Proton ordering in bulk ice . 33 2.4 Modelling ice using empirical potentials . 36 2.5 Ice XI . 40 6 CONTENTS 7 2.6 Generating ice simulation cells . 42 2.7 Proton ordering in ices Ih and Ic . 44 2.8 Proton ordering in the ice surface . 50 3 Theoretical background 54 3.1 Introduction . 54 3.2 General polyelectronic systems . 55 3.3 Hartree-Fock theory (HF) . 57 3.4 Open shell systems: unrestricted Hartree-Fock (UHF) . 62 3.5 Electron correlation and post-Hartree-Fock methods . 65 3.5.1 Configuration interaction (CI) . 67 3.5.2 Møller-Plesset perturbation theory . 71 3.5.3 The coupled cluster method . 75 3.6 Density Functional Theory (DFT) . 78 3.7 Quantum Monte Carlo (QMC) . 86 3.7.1 Variational Monte Carlo . 87 3.7.2 Diffusion Monte Carlo . 87 3.7.3 Some QMC caveats . 88 3.8 A note on nomenclature . 89 3.9 Dispersion corrections in DFT . 89 3.9.1 DFT-D . 90 3.9.2 Van der Waals DFT (vdw-DFT) . 91 3.10 The Gaussian and plane waves (GPW) representation . 92 3.10.1 The Gaussian representation . 92 3.10.2 The plane wave representation . 94 3.10.3 The GPW representation . 95 3.11 Using DFT to model hydrogen bonding in water and ice . 97 CONTENTS 8 4 Proton ordering in bulk ice 100 4.1 Introduction . 100 4.2 Methodology and computational setup . 101 4.2.1 Constructing unit cells . 101 4.2.2 Setup for DFT calculations . 102 4.2.3 Setup for DMC calculations . 104 4.2.4 Setup for empirical forcefield calculations . 104 4.3 Results and discussion . 105 4.3.1 Hexagonal ice . 108 4.3.2 Cubic ice . 111 4.3.3 Estimating the Ic Ih transition energy . 111 ! 4.4 Summary and conclusions . 115 5 The ice surface 120 5.1 Introduction . 120 5.2 Model and methods . 124 5.2.1 Generating proton ordered cubic ice slabs . 124 5.2.2 Surface energy of ices Ih and Ic . 127 5.2.3 Step formation energies of ices Ih and Ic . 130 5.3 Results and discussion . 132 5.3.1 Surface energy of ices Ih and Ic . 132 5.3.2 Steps on striped surfaces . 134 5.3.2.1 A, B1 and B2 steps . 134 5.3.2.2 B1∗ and B2∗ steps.......................... 137 5.3.2.3 Formation energies of different step types . 142 5.3.3 Steps on disordered surfaces . 143 5.3.3.1 Vacancy energies for disordered steps . 146 5.3.3.2 Molecular dipoles of step edge molecules . 147 CONTENTS 9 5.4 Summary and conclusions . 152 6 Formation of interstellar glycolaldehyde 154 6.1 Introduction . 154 6.2 The nature of interstellar dust grains . 155 6.3 Reactions on icy mantles . 158 6.4 The effect of grain surface morphology . 159 6.5 Proposed glycolaldehyde formation mechanisms . 161 6.6 The characteristic (cross-over) temperature . 165 6.7 Gas phase reactions . 166 6.7.1 Choice of density functional for surface reactions . 168 6.7.2 Model and methods . 170 6.7.3 Results and discussion . 174 6.8 Reactions on hydroxylated silicate nanoclusters . 179 6.8.1 Introduction . 179 6.8.2 Model and methods . 180 6.8.3 The nudged elastic band (NEB) method . 182 6.8.4 Results and discussion . 185 6.9 Reactions on icy mantles . 188 6.9.1 Introduction . 188 6.9.2 Model and methods . 189 6.9.3 Results and discussion . 191 6.10 Summary and conclusions . 203 7 Conclusions and future work 204 7.1 Conclusions . 204 7.2 Future work . 206 Bibliography 208 List of Figures 1.1 Photographs of hexagonal ice Ih crystals10, and the crystalline structure of orientationally ordered hexagonal ice. 21 1.2 Stacking of bilayers in hexagonal and cubic ices. The vertical is normal to the (0001) basal surface of hexagonal ice, and the (111) surface of cubic ice. Only oxygen atoms are shown, connected by hydrogen bonds indi- cated by blue lines. The coloured boxes indicate the sequences that have translational symmetry in the z-direction (green: A, pink: B, orange: C). It can be seen that hexagonal ice is characterised by a mirror plane, whereas cubic ice contains straight “channels” that run diagonally from this perspective. 22 1.3 The phase diagram of water11. There is considerable uncertainty in the temperature bounds of the regime of interest for ice Ic, highlighted with aredbox.......................................... 23 2.1 (Taken from Hirsch et al.12) Hydrogen bond types in a tetrahedral ice lattice - h-cis (A), h-trans (B), c-cis (C) c-trans (D). 27 13 2.2 A 22◦ halo around the sun . These are caused by light refracted by large quantities of hexagonal ice crystals in the upper atmosphere. Scheiner’s halo appears at 28◦, has been observed very infrequently and is evidence of octahedral cubic ice crystals. 30 10 LIST OF FIGURES 11 2.3 The six canonical orientations of a water molecule in a tetrahedral ice lattice. ..