Adaptive Resolution Simulations: Towards Open Systems Molecular Dynamics Simulations. K. Kremer Max Planck Institute for Polymer Research, Mainz

Transcription

1 Adaptive Resolution Simulations: Towards Open Systems Molecular Dynamics Simulations K. Kremer Max Planck Institute for Polymer Research, Mainz ACMAC Crete * June, 30, 2011

2 COWORKERS: Luigi Delle Site Matej Praprotnik R. Delgado Buscalioni (Ljubljana) (Madrid) Christoph Junghans Simon Poblete Han Wang Adolfo Poma Sebastian Fritsch (Beijing) C. Clementi and her group (Rice), G. Ciccotti (Rome) Support: MMM Initiative of the MPG, Volkswagen Foundation, DAAD

3 Outline Motivation: Soft and Nanostructured Matter AdResS: Adaptive Resolution MD Simulation Method, first Applications Recent developments Particle-Continuum: AdResS + Hybrid MD Conclusions/Outlook

4 Soft Matter?? Thermal energy of particles/ per degree of freedom E=kT Room temperature 300K: E = J 23 = J / kt K 300K Chemical Bond Hydrogen Bond E 3 10 E 6kT 19 J 80kT 10kT Soft Matter: Thermal Energy dominates properties

5 Soft Matter: Energy Density Normal crystal: NN Energy E 1..2 kt to 100kT noble gas covalent x-tal # of Neighbors 10 < 1 2 Å > E/V kt/å 3 Polymer Glas (Plastics,Rubber): E/V kt/å strand-strand distance 3-6 Å 100 to times softer than normal crystals

6 Soft Matter: Elastic Constant E Normal crystal E 100GPa = kT / Nm / m o A 3 3 < 1 2 Å > Polymer Glas (Plastics,Rubber): E MPa = Nm / m 3 ο kT / Α 100 to times softer than normal crystals

7 Soft Matter II h 5nm Bending stiffness κ 20k B T stable sheet, but κ not much bigger than thermal energy Cellular processes can deform membranes (ATP hydrolysis 12k B T) κ 1 Y h 12 3 κ 20k B T, h 5nm Y 8MPa (rubber)

8 Why soft matter? κ 1 Y h 12 But modern nano-engineers could take much better materials to work with, such as steel? κ 20k B T, Y 100GPa 3 h o 2A falls apart!

9 Soft Matter Soft means: - low energy density - nanoscopic length scales ( 10Å 1000Å) - large fluctuations - thermal energy k B T relevant energy scale

10 Energy Scale k B T fort=300k E = J / K 300K kt J kt ev Electronic structure, CPMD kt E H Quantum Chemistry kt 4.1pNnm Biophysics Membranes, AFM kt 200cm 1 Spectroscopy kt 0.6kcal / mol kt 2.5kJ / mol 19 E 3 10 J 80kT E 4kT 10kT Chemical Bond Hydrogen Bond

11 Energy Scale k B T fort=300k E = J / K 300K kt J kt ev Electronic structure, CPMD kt E H Quantum Chemistry kt 4.1pNnm Biophysics Membranes, AFM kt 200cm 1 Spectroscopy kt 0.6kcal / mol kt 2.5kJ / mol 19 E 3 10 J 80kT E 4kT 10kT Chemical Bond Hydrogen Bond

12 Soft Matter Nanostructured Matter Volume V= L 3 A: Surface and Interface Area Nanoscopically Structured Material: V/A << 1μm => Distinction Bulk vs Surface/Interface not usefull Definition of A usually depends on the question studied!

13 Characteristic Time and Length Scales Time ESPResSo, ESPResSo++ VOTCA, CPMD, Gaussian GROMACS Length Local Chemical Properties --- Scaling Behavior of Nanostructures Energy Dominance --- Entropy Dominance of Properties

14 ESPResSo/ESPResSo++ Extensible Software Package for Research on Soft matter Highly extensible C/C++ core Highly flexible TCL/Python user interface Free open source Fully parallelized, runs on all modern HPC architectures (Linux clusters, BlueGene, ) Joint collaboration

15 Software Package II Versatile Object-oriented Toolkit for Coarse-graining Applications V. Ruehle, C. Junghans, A. Lukyanov, K. Kremer, D. Andrienko, J. Chem. Theor. Comp., 5, , 2009 votca.org apache license C++, scripting test suite hg, google code wiki pages bug tracker

16 Coarse Graining of Macromolecules: Examples Azo Benzene C. Peter, L. Delle Site, D. Marx BPA-PC L. Delle Site, C. Abrams K. Johnston Polystyrene V. Harmandaris, D. Fritz N. Van der Vegt Peptides C. Peter

17 Application: Diffusion Constant of PS (two step approach AA->UA->CG) Simulation: NO adjustable parameter M W 50kD V. Harmandaris, KK, Soft Matt Experiment: Raw FRS data, Sillescu

18 Standard Approach: Run whole system on one level of resolution. Do we need/want to do that? Andrienko et al, PRL 98, (2007) C. Peter et al, 2008ff M. Deserno et al., Nature, 2007

19 Outline Motivation: Soft and Nanostructured Matter AdResS: Adaptive Resolution MD Simulation Method, first Applications Recent developments Particle-Continuum: AdResS + Hybrid MD Conclusions/Outlook

20 Aim at: Adsorption Desorption, Flux of Chains, Additives Structure Formation Relevant Levels of Resolution Example:Polymer/Nanotube Composites C. F. Abrams, Drexel

21 Adaptive Inhomogenous Coarse-Graining Specific atomic-scale energetics dominant at surface Molecule-scale entropy O(M) dominant in bulk Coarsened fragments provide equilibrated boundary conditions for full-blown embedded atomistic simulation

22 AdResS: Adaptive Resolution Simulations M. Praprotnik, L. Delle Site, KK, Ann. Rev. Phys. Chem. 2008, 59: Free exchange of molecules/particles between regimes with different levels of resolution: equilibrium between both regimes, no kinetic barrier

23 Adaptive Methods: Changing degrees of freedom on the fly Adaptive multiscale method: Simple test case Tetrahedron, repulsive LJ Particles, Hybrids Softer Sphere FENE bonds Explicit Atom Transition Coarse Grained regime regime regime M. Praprotnik, L. DelleSite, KK, JCP 2005

24 Adaptive Methods: Changing degrees of freedom (DOFs) on the fly Requirements Same mass density Same Pressure (=>Eq. of state) Same temperature Free exchange between regimes Same center-center g(r) Simple two body potential Some similarities to 1 st order phase transition Phase equilibrium Thermostat has to provide/take out latent heat due to change in degrees of freedom VW Foundation Project M. Praprotnik, L. DelleSite, KK, JCP 2005, PRE (2006)

25 Coarse Grained Model Study explicite atom and CG system seperately => fit CG Interaction Potential: U cm ( r) = γ{1 exp[ κ ( r r0)]} 2 μ ex = μ cg, p ex =p cg, T ex =T cg

26 Initial General Considerations µ ex = µ, p = p, T = cg ex cg ex T cg Pressure p Molecular Density ρ

27 Transition Regime: Changing Degrees of Freedom (DOF): switching function w(x) for DOFs

28 Transition Temperature: Regime: Changing Degrees of of Freedom (DOF): switching function w(x) for DOFs w=1... w=0 Definition of Temperature in transition regime: Fractional degrees of freedom, switching function w(x) => generalization of equipartition theorem => Defines thermostat to take out/in latent heat of the DOFs dv w = d w H ( q) = qγ( w / 2) / 2π q n H ( q) w/ 2 w Γ( w) = = w n k B q T w 1 dq / Γ( w) = dq w / wγ( w) w is the fractional dimension of DOF q, w=1 and n=2 standard case PRE 2007

29 Theoretical Basis: Temperature Change resolution, Latent heat of fading/emerging degrees of freedom (DOFs) Generalized Equipartition Theorem for DOFs with fractional dimension w(x) Well defined temperature T in Δ, well defined thermostat - Smooth switching region Δ with switching function w(x) Practical Implementation?

30 Langevin DPD Thermostats Langevin: m i dv i dt = F i m i Γ i (x)v i + R(x,t) R(t 1 )R(t 2 ) = 2Γ i (x)m i ktδ(t 1 t 2 ) R(t) = 0 DPD: replace v i by relative velocity v ij, use as thermostat in MD (Soddeman, Dunweg, KK, PRE 2003) Local temperature and hydrodynamics preserved

31 New DPD Thermostat Junghans, Praprotnik, KK, Soft Matter 2007 Thermalize transverse velocities define local temperature preserve hydrodynamics adjust viscosities, diffusion constants

32 New DPD Thermostats Junghans, Praprotnik, KK, Soft Matter 2007

33 AdResS: Transition Regime - Force Interpolation F αβ = atom αβ w( X ) w( X ) F + [1 α β w( X α ) W ( X β )] F cg αβ Full atomistic force Full coarse grained force Interactions explicit-explicit CG-CG hybrid-hybrid CG- hybrid: CG-CG explicit-hybrid: explicit-explicit

34 AdResS: Transition Regime - Force Interpolation F αβ = atom αβ w( X ) w( X ) F + [1 α β w( X α ) W ( X β )] F cg αβ Full atomistic force Full coarse grained force Transition regime: Force interpolation Interactions (Newtons 3rd law fulfilled, no drift forces) explicit-explicit CG-CG hybrid-hybrid No transition energy function defined! CG- hybrid: CG-CG explicit-hybrid: explicit-explicit

35 Particle Exchange Particle Numbers, Density cg aa

36 M. Praprotnik, L. Delle Site, KK, JCP (2007) 1 st Application: Chain in solvent Explicit resolution regime moves with the polymer

37 2 nd Application TIP3P Water coarse-grained model, effective interactions adaptive, hybrid scheme to switch from one to the other on-the-fly all-atom model, physical force-field

38 Single-site model Pressure, temperature are also in excellent agreement, 4 nearest neighbors in first shell, tetrahedral order in 2 nd shell for cg model almost completely lost

39 coarse grained hybrid explicit coarse grained hybrid explicit

40 Adaptive Resolution Simulations of Water Explicit resolution regime moves with the polymer

41 Hydrophobic Solutes: Surface vs Bulk CG regime Transition layer All atom layer, d ex Water cg water reproduces g(r) but NOT tetrahedral packing!

42 Hydrophobic Solutes C 60 Influence of bulk H-bond structure on surface layer # two surface potentials - standard (weak) Lennard Jones (ε CO 0.2k B T, σ CO 0.34nm) - purely repulsive (r -12 ) # variable width of explicit layer C 2160

43 # of Water Molecules around Solute, variable all atom water layer d ex ( 1 st, 2 nd shell, ) C 2160 C 60 LJ interaction dominated by surface Interaction Repulsive # of waters close to surface strongly depleted

44 Tetrahedral Order LJ: Surface layer not signifcantly influenced by bulk surrounding for all molecules. Repulsive: Density near surface needs Structural support from bulk, order parameter seems independent of density (Compensation of effects?). LJ Repulsive

45 Transition Regime, Generalizations Density wiggles in transition regime => thermodynamic force to level off pressure Generalization => Open System MD Particle Numbers, Density Equation of state in transition regime not the same!

46 Pressure Equation of state in transition regime not the same! (not surprising) No potential energy function in whole system, but well defined forces and thus well defined pressures Calculate pressure in a plane x (Todd, Evans, Davies) S. Poblete, S. Fritsch, G. Ciccotti, KK, L. Delle Site, in prep.2011

47 Pressure Well defined constant pressure ensemble If density fixed to constant value Pressure bump in hybrid zone Thermodynamic force, iterate Calculate pressure in a plane x (Todd, Evans, Davies)

48 Effective Chemical Potential S. Poblete, M. Praprotnik, KK, L. Delle Site, JCP, 132, (2010)

49 Latent Heat Effective Chemical Potential

50 Latent Heat Effective Chemical Potential

51 Latent Heat Effective Chemical Potential Allows to couple almost any system! No need to have same μ in both regimes! S. Poblete, M. Praprotnik, KK, L. Delle Site, JCP, 132, (2010)

52 Extensions : Mixtures

53 Extensions AdResS: Continuum QM Description

54 Extension I: R. Delgado Buscalioni, KK, M. Praprotnik, JCP 128, (2008)

55 AdResS-HybridMD: Water 2 nd Scheme R. Delgado Buscalioni, KK, M. Praprotnik, JCP 131, (2009)

56 Simple shear Oscillatory shear ( exact solution)

57 QM-AdResS A. Poma, L. Delle Site PRL 2010

58 QM-AdResS A. Poma, L. Delle Site PRL 2010

59 Conclusion / Challenges Dual-Triple Scale Simulations/Theory Adaptive quantum force field coarse grained Grand Canonical i.e. salt etc Thermodynamic Force: couple rather different systems Nonbonded Interactions: NEMD, Structure Formation, Morphology Conformations Electronic Properties Structure Formation, Aggregation Online Experiments: Nanoscale Experiments, long Times

60 KITP UCSB Program 2012 Physical Principles of Multiscale Modeling, Analysis and Simulation in Soft Condensed Matter Apr 2, Jun 29, 2012 Application deadline: August 15, 2011 Coordinators: Paul Atzberger, Kurt Kremer, Mark Robbins