Structure, Dynamics and Thermodynamics of Liquid Water Insights from Molecular Simulations Kjartan Thor Wikfeldt Thesis for the Degree of Doctor of Philosophy in Theoretical Physics Department of Physics Stockholm University Stockholm 2011 c Kjartan Thor Wikfeldt ISBN 978–91–7447–287–5 Printed by Universitetsservice US-AB, Stockholm It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature... Niels Bohr Abstract Water is a complex liquid with many unusual properties. Our understanding of its physical, chemical and biological properties is greatly advanced after a century of dedicated research but there are still many unresolved questions. If answered, they could have important long-term consequences for practical applications ranging from drug design to water purification. This thesis presents results on the structure, dynamics and thermodynamics of liquid water. The focus is on theoretical simulations applied to interpret experimental data from mainly x-ray and neutron scattering and spectroscopy techniques. The structural sensitivity of x-ray and neutron diffraction is investigated using reverse Monte Carlo simulations and information on the pair-correlation functions of water is derived. A new method for structure modeling of computationally demanding data sets is presented and used to resolve an inconsistency between experimental extended x-ray absorption fine-structure and diffraction data regarding oxygen-oxygen pair-correlations. Small-angle x-ray scattering data are modeled using large-scale classical molecular dynamics simulations, and the observed enhanced scattering at supercooled temperatures is connected to the presence of a Widom line emanating from a liquid-liquid critical point in the deeply supercooled high pressure regime. An investigation of inherent structures reveals an underlying structural bimodality in the simulations connected to disordered high-density and ordered low-density molecules, providing a clearer interpretation of experimental small-angle scattering data. Dynamical anomalies in supercooled water observed in inelastic neutron scattering experiments, manifested by low-frequency collective excitations resembling a boson peak, are investigated and found to be connected to the thermodynamically defined Widom line. Finally, x-ray absorption spectra are calculated for simulated water structures using density functional theory. An approximation of intra-molecular zero-point vibrational effects is found to significantly improve the relative spectral intensities but a structural investigation indicates that the classical simulations underestimate the amount of broken hydrogen bonds. i Kjartan Thor Wikfeldt Stockholm May 2011 ii List of Papers I. Diffraction and IR/Raman Data Do Not Prove Tetrahedral Water M. Leetmaa, K.T. Wikfeldt, M.P. Ljungberg, M. Odelius, J. Swenson, A. Nilsson and L.G.M. Pettersson J. Chem. Phys. 129, 084502 (2008) II. On the Range of Water Structure Models Compatible with X-ray and Neutron Diffraction Data K.T. Wikfeldt, M. Leetmaa, M.P. Ljungberg, A. Nilsson and L.G.M. Pettersson J. Phys. Chem. B 113, 6246 (2009) III. The inhomogeneous structure of water at ambient conditions C. Huang, K.T. Wikfeldt, T. Tokushima, D. Nordlund, Y. Harada, U. Bergmann, M. Niebuhr, T.M. Weiss, Y. Horikawa, M. Leetmaa, M.P. Ljungberg, O. Takahashi, A. Lenz, L. Ojamäe, A.P. Lyubartsev, S. Shin, L.G.M. Pettersson and A. Nilsson Proc. Natl. Acad. Sci. (USA) 106, 15214 (2009) IV. SpecSwap-RMC: a novel reverse Monte Carlo approach using a discrete set of local configurations and pre-computed properties M. Leetmaa, K.T. Wikfeldt and L.G.M Pettersson J. Phys.: Cond. Matter 22, 135001 (2010) V. Oxygen-oxygen correlations in liquid water: Addressing the discrepancy between diffraction and extended x-ray absorption fine-structure using a novel multiple-data set fitting technique K.T. Wikfeldt, M. Leetmaa, A. Mace, A. Nilsson and L.G.M. Pettersson J. Chem. Phys. 132, 104513 (2010) VI. Enhanced small-angle scattering connected to the Widom line in simulations of supercooled water K.T. Wikfeldt, C. Huang, A. Nilsson and L.G.M. Pettersson Submitted to J. Chem. Phys. (2011) VII. X-ray diffraction study of temperature dependent structure of liquid water C. Huang, K.T. Wikfeldt, D. Nordlund, U. Bergmann, T. McQueen, J. Sellberg, L.G.M. Pettersson and A. Nilsson Submitted to VIII. Possible origin of low-frequency excitations in supercooled bulk and protein-hydration water iii P. Kumar, K.T. Wikfeldt, D. Schlesinger, L.G.M. Pettersson and H.E. Stanley Manuscript IX. Bimodal inherent structure in simulated liquid water from 200 to 360 K K.T. Wikfeldt, A. Nilsson and L.G.M. Pettersson Submitted to Nature (2011) Papers not included in this thesis X. Reply to Soper et al.: Fluctuations in water around a bimodal distribution of local hydrogen-bonded structural motifs C. Huang, K.T. Wikfeldt, T. Tokushima, D. Nordlund, Y. Harada, U. Bergmann, M. Niebuhr, T.M. Weiss, Y. Horikawa, M. Leetmaa, M.P. Ljungberg, O. Takahashi, A. Lenz, L. Ojamäe, A.P. Lyubartsev, S. Shin, L.G.M. Pettersson and A. Nilsson Proc. Natl. Acad. Sci. (USA) 107, E45 (2010) XI. Complementarity between high-energy photoelectron and L-edge spectroscopy for probing the electronic structure of 5d transition metal catalysts T. Anniyev, H. Ogasawara, M.P. Ljungberg, K.T. Wikfeldt, J.B. MacNaughton, L.Å. Näslund, U. Bergmann, S. Koh, P. Strasser, L.G.M. Pettersson and A. Nilsson Phys. Chem. Chem. Phys. 12, 5694 (2010) XII. In situ X-ray probing reveals fingerprints of surface platinum oxide D. Friebel, D.J. Miller, C.P. O’Grady, T. Anniyev, J. Bargar, U. Bergmann, H. Ogasawara, K.T. Wikfeldt, L.G.M. Pettersson and A. Nilsson Phys. Chem. Chem. Phys. 13, 262 (2010) XIII. Increasing correlation length in bulk supercooled H2O, D2O, and NaCl solution determined from small angle x-ray scattering C. Huang, T.M. Weiss, D. Nordlund, K.T. Wikfeldt, L.G.M. Pettersson and A. Nilsson J. Chem. Phys 133, 134504 (2010) XIV. Ab initio van der Waals interactions in simulations of water alter structure from mainly tetrahedral to high-density-like A. Møgelhøj, A. Kelkkanen, K.T. Wikfeldt, J. Schiøtz, J.J. Mortensen, L.G.M. Pettersson, B.I. Lundqvist, K.W. Jacobsen, A. Nilsson and J.K. Nørskov Submitted to J. Phys. Chem. B (2011) iv List of Abbreviations AFF – atomic form factor AIMD – ab initio molecular dynamics CPF – critical point free EPSR – empirical potential structure refinement EXAFS – extended x-ray absorption fine-structure FS – fragile-to-strong DD – double donor ∆KS – delta Kohn-Sham DFT – density functional theory DW – Debye-Waller FMS – full multiple scattering GGA – generalized gradient approximation H-bond – hydrogen bond HDA – high-density amorphous ice HDL – high-density liquid HH – hydrogen-hydrogen INS – inelastic neutron scattering IS – inherent structure ISF – intermediate scattering function IXS – inelastic x-ray scattering LDA – local density approximation LDA – low-density amorphous ice LDL – low-density liquid LFE – low-frequency excitation LLCP – liquid-liquid critical point LSI – local structure index MAFF – modified atomic form factor MD – molecular dynamics MS – multiple scattering ND – neutron diffraction OH – oxygen-hydrogen OO – oxygen-oxygen OZ – Ornstein-Zernike v PCF – pair-correlation function PES – potential energy surface QENS – quasi-elastic neutron scattering RMC – reverse Monte Carlo SAXS – small-angle x-ray scattering SD – single donor SF – singularity-free SL – stability-limit SPC/E – extended simple-point charge TIP4P – transferable interaction potential with 4 points TMD – temperature of maximum density TP – transition potential vdW – van der Waals VDOS – vibrational density of states XAS – x-ray absorption spectroscopy XD – x-ray diffraction XES – x-ray emission spectroscopy ZP – zero-point vi Contents Abstract i List of Papers iii List of Abbreviations v 1 Introduction 1 2 Structure of water 5 2.1 Introduction . 5 2.2 Time-independent correlation functions . 6 2.2.1 Pair-correlation functions and structure factors . 6 2.2.2 The Ornstein-Zernike equation . 8 2.2.3 Experimental methods: elastic scattering . 10 2.3 Structure modeling . 15 2.3.1 Reverse Monte Carlo (RMC) . 15 2.3.2 SpecSwap-RMC . 16 2.4 Many-body correlation functions . 17 2.4.1 Bond angles . 17 2.4.2 Voronoi polyhedra . 18 2.4.3 Local structure index . 19 2.4.4 Experimental methods: EXAFS, XAS . 20 2.5 Pair correlation functions of water . 20 2.6 Tetrahedrality and local structure index of simulated water . 24 2.7 Long-range correlations . 25 3 Dynamics of water 31 3.1 Introduction . 31 3.2 Time-dependent correlation functions . 32 3.2.1 van Hove correlation functions . 32 3.2.2 Velocity and current autocorrelation functions . 34 3.2.3 Experimental methods: inelastic scattering . 35 3.3 Molecular dynamics . 35 vii CONTENTS 3.4 Low-frequency excitations in supercooled water . 37 3.4.1 Finite-size effects in simulations . 38 3.4.2 Dynamic correlation functions . 40 4 Thermodynamics of water 43 4.1 Introduction . 43 4.2 Theoretical scenarios . 44 4.3 Thermodynamic response functions from molecular simulations . 46 4.4 Enhanced small-angle scattering and the Widom line . 47 4.5 Bimodality in inherent structures . 50 5 Electronic structure of water 55 5.1 Theoretical background . 55 5.1.1 Density functional theory . 57 5.1.2 Theoretical spectrum calculations . 59 5.2 Extended x-ray absorption fine-structure . 63 5.2.1 Experimental results . 63 5.2.2 Theoretical calculations and structural information . 64 5.3 X-ray absorption spectroscopy . 66 5.3.1 Experimental results . 66 5.3.2 Importance of zero-point vibrational effects . 67 5.3.3 Structural sensitivity of XAS . 68 6 Summary of main results 71 6.1 Water, tetrahedral or not - Paper I . 71 6.2 Bounds on liquid water structure from diffraction - Paper II . 73 6.3 Inhomogeneous structure of water - Paper III . 75 6.4 SpecSwap-RMC: a new multiple-data set structure modeling technique - Paper IV .