1. Methane hydrate: interfacial nucleation Crystal Melted under vacuum (300 K), then pressurised under methane (30 atm)

2. Time Evolution Potential Energy (rolling average over 10 ps) (n.b. should divide by 1654 to quote per mole of water Density profile across interfaces I = 0–0.3 ns II = 9–10 ns

3. Hydrate Formation: Analysis upper half of water film (0 – 20 Å) lower half of water film(- 20 – 0 Å) Methane-Methane radial distribution functions, g(r)

4. Order parameters: 3-body Fluctuations from tetrahedral network Average over all triplets, based on central oxygen and “bonding” radius

5. Order parameters: “4-body” Locate a three H-bond chain Calculate torsion angle and triple product from “bond” vectors Mimic by two-molecules Average over coordination shell

6. Local Phase of Water Molecules Define local order parameters that distinguish between bulk phases Determine standard deviations, , within stable bulk phases (hydrate/ice) Assign individual molecule as hydrate/ice if all its order parameters agree with bulk values to within 2  H-bond network angles H-bond network torsions

7. Order parameters & melting Analysis of melting crystal shows order parameters are consistent Analysis of covariance matrix (bulk) shows they are independent

8. Characterising Molecular Order Define vector of three order parameters (f) Calculate covariance matrix for each molecule (C –1 ) for stable phases Eigenvalue analysis to de- correlate (y)

9. Local Phase Assignment Calculate f for each molecule in arbitrary system Project onto eigenvectors (components of y) Compare with  : assign “local phase” if all three components within 2(?) standard deviation of  for that phase

10. Water in Hydrate Environment

11. Distribution of order parameters 1 ns Difference: 22 ns - 1 ns

12. Animated Nucleation

13. Simulated Nucleation [ hydrate-waters ) 3.3ns2.4ns4.2ns5.1ns 6.9ns6.0ns 1.5ns 7.8ns20ns40ns 0.6ns 10.5ns

14. Which hydrate structure? type II Best signature is arrangement of dodecahedra type I

15. Which hydrate structure? Early appearance of face- sharing dodecahedra  type II Oswald’s step rule: form the unstable polymorph first Experimental verification: time resolved X-ray powder study (Kuhs, 2002)