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Introduction Monday, January 5, 15 1 Introduction Why to use a simulation Some examples of questions we can address Monday, January 5, 15 2 Molecular Simulations MD Molecular dynamics : solve equations of motion r 1

  1. Introduction Monday, January 5, 15 1

  2. Introduction Why to use a simulation • Some examples of questions we can • address Monday, January 5, 15 2

  3. Molecular Simulations MD • Molecular dynamics : solve equations of motion r 1 • Monte Carlo : r 2 importance sampling r n • Calculate thermodynamic MC and transport properties for a given intermolecular r 1 potential r 2 r n 3 Monday, January 5, 15 3

  4. Uses of Molecular Simulations If one could envision an Exact= in the limit of experimental system of infinitely long simulations these N particles that the error bars can be interact with the potential. made infinitely small The idea for a given intermolecular potential “ exactly” compute the thermodynamic and transport properties of the system Pressure Heat capacity Heat of adsorption We assume the Structure interactions between Diffusion coefficient …. the particles are known! Viscosity … 4 Monday, January 5, 15 4

  5. Why Molecular Simulations Paul Dirac, after completing his formalism of quantum mechanics: “ The rest is chemistry…”. This is a heavy burden the shoulders of “chemistry”: 5 Monday, January 5, 15 5

  6. Intermolecular potential The intermolecular potential can: Mimic the experimental system as • accurate as possible: Replace experiments (dangerous, • impossible to measure, expensive, …) Make a model system: • Test theories that can not directly be • tested with experiment 6 Monday, January 5, 15 6

  7. If we know/guess the “true” intermolecular potential Monday, January 5, 15 7

  8. Example 1: Mimic the “real world” Critical properties of long chain hydrocarbons To predict the thermodynamic properties (boiling points) of the hydrocarbon mixtures it is convenient (=Engineering models use them) to know the critical points of the hydrocarbons. 8 Monday, January 5, 15 8

  9. Critical points of long chain hydrocarbons Heptadecane Pentane 9 Monday, January 5, 15 9

  10. Hydrocarbons: intermolecular potential United-atom model Fixed bond length • CH 2 CH 2 CH 3 Bond-bending • CH 2 CH 3 Torsion • Non-bonded: Lennard-Jones • 10 Monday, January 5, 15 10

  11. OPLS (Jorgensen) Model Monday, January 5, 15 11

  12. Vapour-liquid But my system is Molecular dynamics: press extremely small, is enter and see … equilibria the statistic reliable? Lectures on Free Computational issues: Energies and How to compute • Phase Equilibrium vapour-liquid Lectures on equilibrium? advanced Monte How to deal with • Carlo long chain hydrocarbons? Molecular dynamics: But C48 moves much slower press enter and see … than methane (C1). Do I have enough CPU time 12 Monday, January 5, 15 12

  13. Critical Temperature and Density Nature 365 , 330 (1993). 13 Monday, January 5, 15 13

  14. Example 2 Methane Storage Monday, January 5, 15 14

  15. Methane cars: the technological obstacle Gasoline, 1 liter CH 4 1 liter 34.2 MJ 0.036 MJ Monday, January 5, 15 15

  16. Methane versus gasoline LNG CNG Makal et a l. Chem. Soc. Rev. 2012 41.23, 7761-7779. Monday, January 5, 15 16

  17. 65 bar 5.8 bar Insufficient flow ~1 bar P H = 65 bar P L = 5.8 bar Monday, January 5, 15 17

  18. The deliverable capacity P L P H = 5.8 bar = 65 bar Methane adsorbed Methane adsorbed (v STP/v) (v STP/v) at tank charging at tank discharge pressure pressure ARPA-E (DOE) target: 315 m 3 STP methane/m 3 adsorbent Monday, January 5, 15 18

  19. An optimal heat of adsorption? Goal: maximize deliverable capacity “For methane, an optimal enthalpy change of [16.2] kJ/mol is found.” ( ) opt = H 0 exp − q iso RT H CH 4 Monday, January 5, 15 19

  20. In silico screening of zeolites MFI expt’l data: Sun et al . (1998) J. Phys. Chem. B. 102(8), 1466-1473. Zhu et al. (2000) Phys. Chem. Chem. Phys. 2(9), 1989-1995. Force field: Dubbeldam et al . (2004) Phys. Rev. 93(8), 088302. Monday, January 5, 15 20

  21. In silico screening of zeolites C. Simon et al . (2014) Phys. Chem. Chem. Phys . 16 (12), 5499-5513 Monday, January 5, 15 21

  22. Enthalpy vs. entropy Δ S not the same for all materials • Wide range of Δ H that yields optimal material • Monday, January 5, 15 22

  23. Can we find a material that meets the DOE target? Screening > 100,000 materials zeolites • Metal organic Frameworks, MOFs (Snurr and • co-workers) zeolitic imidazolate frameworks, ZIFs, • (Haranczyk) Polymer Porous Networks, PPNs (Haranczyk) • Monday, January 5, 15 23

  24. Monday, January 5, 15 24

  25. Insight from the model Empty tank Monday, January 5, 15 25

  26. Example 3: make a model system My theory is RIGHT : Question: are attractive interactions needed to but this experimentalist Your theory is WRONG form a solid phase? refuses to use it disagrees with the molecules that do not YES: experiments have any attractive Attractive forces are needed for vapour- • interactions liquid equilibrium Theories predict this .. • BUT: There no molecules with only attractive • interactions How to test the theory? 26 Monday, January 5, 15 26

  27. But we can simulate hard spheres .. Bernie Alder carried out • Molecular Dynamics simulations of the freezing of hard spheres But, …. did the scientific • community accept this computer results as experimental evidence … … during a Gordon conference • it was proposed to vote on it … … and it was voted against the • results of Alder 27 Monday, January 5, 15 27

  28. Experiments are now possible .. But not on molecules but on colloids: From the following article: A colloidal model system with an interaction tunable from hard sphere to soft and dipolar Anand Yethiraj and Alfons van Blaaderen Nature 421, 513-517 (30 January 2003) 28 Monday, January 5, 15 28

  29. Molecular Dynamics MD Theory: • r 1 r 2 r n Compute the forces on the particles • Solve the equations of motion • Sample after some timesteps • 29 Monday, January 5, 15 29

  30. Monte Carlo What is the correct probability? Statistical Thermodynamics Generate a set of configurations with the • correct probability Compute the thermodynamic and transport • properties as averages over all configurations MC How to compute these properties from a simulation? r 1 r 2 30 Monday, January 5, 15 30

  31. Classical and Statistical Thermodynamics Problem: we have a set of coordinates and velocities -what to do with it? Statistical Thermodynamics • The probability to find a particular • configuration Properties are expressed in term of averages • Free energies • Thermodynamics: relation of the free • energies to thermodynamic properties 31 Monday, January 5, 15 31

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