The End of Simulation?

1. The End of Simulation? Mike Payne

2. If we are honest about the usefulness of simulations they should be: Genuinely predictive Free of adjustable parameters Computationally tractable and affordable ..... and if you want lots of people to use them then running the simulations should be as simple as possible – ideally nothing beyond specifying the system.

3. ONETEPLinear scaling quantum mechanical calculations Peter Haynes Arash Mostofi Imperial College, London Chris Kriton Skylaris University of Southampton

4. Application to DNA £20 Total energy calculations with ONETEP on pieces of DNA. The total time taken by each DNA piece is plotted as a function of the number of atoms. Also shown are times for calculations of equivalent quality with CASTEP.

5. Hierarchies of atomistic modelling Accuracy topological qualitative empirical 0.01 eV Tight binding 0.0001 eV DFT 0 QMC CI Atoms 1 10 100 1000 1,000,000 Time 0 0 ps ns ms

6. Empirical atomistic DFT Continuum Multiscale Modelling Schemes Correlated QM

7. Scheme to couple continuum simulations to empirical simulations developed by Peter Gumbsch and co-workers in 1991. Many similar examples: electrostatics, solvation,... What about coupling DFT (or cheap QM) atomistic and empirical atomistic simulations.? Many so-called QM/MM schemes - few of them suitable for dynamicalyl evolving systems – let alone being parameter-free, predictive and usable.

8. Gábor Csányi Engineering, Cambridge Alessandro De Vita King’s College, London “Learn on the fly” - Hybrid classical/quantum molecular dynamics simulation

9. Learn on the Fly Scheme (LOTF) Continuum Empirical Atomistic Atoms represented by empirical potentials with parameters fit to a quantum mechanical calculation

10. Learning the environment

11. Crack Propagation in Silicon J.R. Kermode1, T. Albaret2, D. Sherman3, N. Bernstein4, P. Gumbsch5,6, MCP, G. Csányi7 & A. De Vita8,9 1. TCM Group, Cavendish Laboratory 2. Université de Lyon 1, 3. Department of Materials Engineering, Technion–Israel Institute of Technology, 4. Center for Computational Materials Science, NRL, 5. Institut für Zuverlässigkeit von Bauteilen und Systemen, Universitat Karlsruhe 6. Fraunhofer–Institut für Werkstoffmechanik Freiburg 7. Engineering Laboratory, University of Cambridge. 8. Dept. of Physics, King’s College London, 9. INFM–DEMOCRITOS CENMAT, University of Trieste

12. Propagation of [1-10] (111) crack in silicon Kermode et al., Nature 455, 1224 (2008) This gives detailed description of stress fields around the crack tip

13. Propagation of [1-10] (111) crack in silicon

14. Multiscale modelling

15. BUT

16. Albert Bartok-Partay & Gabor Csanyi, Engineering, Cambridge Imre Risi Kondor, Caltech

17. ‘An art rather than a science’

20. Surface energies • MEAM error ≈ 20-30%

21. Considerable recent progress by empirically correcting the limitations of DFT – DFT-D, LDA+U,.... What about when you do need properly correlated QM methods coupled to DFT simpler QM? Simple in the case of, say CI, region within Hartree-Fock calculation. Alternative approach – DMFT (Cedric Weber).

22. Empirical atomistic DFT Continuum Hybrid Modelling Schemes (QM/MM) Correlated QM

23. BUT

24. Hierarchies of atomistic modelling Accuracy topological qualitative empirical 0.01 eV Tight binding 0.0001 eV DFT 0 QMC CI But larger systems have longer timescales Atoms 1 10 100 1000 1,000,000 Time 0 0 ps ns ms

25. The timescale problem Some sampling based approaches: Simulated annealing Random sampling – Needs and Pickard Generic algorithms – Nested sampling – Csanyi and Bartok-Partay Mark Buchanan, New Scientist, p42 Vol. 2157 magazine, 24 October 1998

26. The ‘known unknowns’ The long timescales are usually associated with getting over energy barriers between minima. IF the end points are known then many techniques exist for finding the transition state and its energy or free energy: Nudged elastic band, LST, QST, Blue Moon, OPTIM - Wales Mark Buchanan, New Scientist, p42 Vol. 2157 magazine, 24 October 1998

27. So the problem is the ‘unknown unknowns’ Speeding up dynamics: Parallelise time ie do multiple uncorrelated dynamical simulations (perfect for Exaflops computers) Hyperdynamics – Voter Metadynamics – Parrinello Mark Buchanan, New Scientist, p42 Vol. 2157 magazine, 24 October 1998

28. The efficient solution to the unknown unknowns Metadynamics with machine learning Parrinello So is everything in place to be able to perform predictive, parameter free simulations for any system – ie the end of simulation as an intellectual challenge ? Not quite – need to retain data for re-use. Mark Buchanan, New Scientist, p42 Vol. 2157 magazine, 24 October 1998