Accelerated Molecular Dynam ics w ith the Bond Boost Method Kristen - PowerPoint PPT Presentation

Accelerated Molecular Dynam ics w ith the Bond Boost Method Kristen A. Fichthorn The Pennsylvania State University University Park, PA 16802 USA DMR-1 0 0 6 4 5 2 DE-FG0 2 0 7 ER4 6 4 1 4

Rare-Event Methods Search and Characterization R * Nudged Elastic Band: G. Henkelman, B.Uberuaga, and H. Jonsson, B J. Chem. Phys. 1 1 3 , 9901 (2000). Dimer Method: G. Henkelman and H. Jonsson, J. Chem. Phys. 1 1 1 , 7010 (1999). A Transition Path Sampling: P . Bolhuis, D. Chandler, et al. Rare-Event Simulation Ann. Rev. Phys. Chem. 5 3 , 291 (2002). Forward-Flux Sampling: Kinetic Monte Carlo: R. J. Allen, D. Frenkel, P . R. ten Wolde, K. Fichthorn and W. Weinberg, J. Chem. Phys. 1 2 4 , 194111 (2006). J. Chem. Phys. 9 5 , 1090 (1991). String Method: Kinetic ART: W. E., W. Ren , E. Vanden-Eijnden, El-Mallouhi, N. Mousseau, Phys. Rev. Phys. Rev. B 6 6 , 052301 (2002). B 7 8 ,1532002 (2008). AND… … Master Equation Molecular Dynamics Simulations Naturally Find Rare Events and Can Simulate Rare-Event Systems…

Accelerated Molecular Dynamics (Hyperdynamics) * A. Voter, J. Chem. Phys. 1 0 6 , 11 (1997). * B C A Relative Rates * * B C A

Accelerated Molecular Dynamics (Hyperdynamics) A. Voter, J. Chem. Phys. 1 0 6 , 11 (1997). * *  V B C A Real Time: MD Time:  N N   t   t MD = N  t     t t exp V / kT i W ( R )   i 1 i 1 i    V    The Trick is How to Construct exp Boost    V(R) … kT

Accelerated Molecular Dynamics The Bond-Boost Method R. Miron & K. Fichthorn, J. Chem. Phys. 1 1 9 , 6210 (2003) Define Local Minima by Bond Lengths o { r }  1 , i i N Transitions Occur via Bond Breaking   r Empirical max q i Threshold i o r i Boost the Bonds: Purely Geometric N    V { x } ~ A { r } V ( r ) i i  i 1 Envelope Function Boost per Bond

Details of the Bond Boost Method Boost Potential N        V r        max i V ( r ) A V max i i 0 N r  i i 1 Nominal Boost per Bond 2            i V 1   i   q Envelope: Channels Boost into the Bond Most Ready to Break   2              max A f 1   max     q  

Overview of the Bond Boost Method R. Miron & K. Fichthorn, J. Chem. Phys. 1 1 9 , 6210 (2003)

Diffusion on Cu(100): Elementary Processes Adatom Hop Dimer Exchange Adatom Exchange R. Miron & K. Fichthorn, J. Chem. Phys. 1 1 9 , 6210 (2003) Dimer Hop Vacancy Hop

The Bond-Boost Method: Diffusion on Cu(100) R. Miron & K. Fichthorn, J. Chem. Phys. 1 1 9 , 6210 (2003)

The Bond-Boost Method: Diffusion on Cu(100) Boost = Physical Time / Simulation Time log 10 (Boost)  V(R) ( k B T ) -1 (eV -1 )    V    R. Miron & K. Fichthorn, Boost exp   J. Chem. Phys. 1 1 9 , 6210 (2003)   k T B

Hut Formation in Al(110) Homoepitaxy Bautier de Mongeot et al., Phys. Rev. Lett. 91 , 016102 (2003). Atoms Hopping ( Å, ps) Hut Organization (  m, min) Hut Formation (nm, min) K. Fichthorn and M. Scheffler, Nature 4 2 9 , 617 (2004).

Accelerated AIMD (VASP): Diffusion on Al/ Al(110) Climbing-Image Nudged Elastic Band Method vs. Accelerated AIMD Fichthorn et al., J. Phys. Cond. Matt. 2 1 , 084212 (2009). E B = 0.38 eV E B = 0.33 eV

The Boost in ab initio MD ~  s    V    exp Boost   kT

Rare Events and the Small Barrier Problem Annoyingly Small Barriers

State-Bridging Accelerated MD to Solve the Small-Barrier Problem Raise the Boost After A Waiting Commence Time With a Low Boost Miron, Fichthorn, J. Chem. Phys. 115, 2001. Memorize and Consolidate Pairs of States Connected by Low Detect Barriers Barriers When Transitions Occur, Compare To Threshold R. Miron, K. Fichthorn, Phys. Rev. Lett. 93, 2004.

Co on Cu(001): Benefits of State Bridging Regular State-Bridging Accelerated MD Accelerated MD

Thin Film Growth at 250 K, F = 0.1 ML/ s R. Miron, K. Fichthorn, Note Cluster Mobility Phys. Rev. Lett. 93, 2004.

State-Bridging Accelerated MD of Co/ Cu(001) Heteroepitaxy: T = 250 K, F = 0.1 ML/ s,  = 0.54 ML MD Sim ulations w ere run for 5 .4 s Mechanism of Bilayer R. Miron and K. Fichthorn, Island Formation Phys. Rev. B 72 , 115433 (2005).

Temperature-Programmed Desorption K. Becker, M. Mignogna, K. Fichthorn,      PRL 102 , 046101 (2009). E E        d d ln ln        2    T k k T   d E       p B 0 B p d exp   0   dt k T B    T T t P. A. Redhead, Vacuum 0 12 , 203 (1962).

Simulation of TPD vs. Large Molecules Don’t Work in Lattice Models… . Goal: To Simulate TPD with Accelerated MD!!

Accelerated MD of Adsorbed Alkanes OPLS All-Atom Force Field [ 1]    V V V V intra b t LJ      2 V ( ) K ( )  b i i eq     3 1      V ( ) V 1 cos j t i j i 2  j 1 Constrained Bond Stretching: RATTLE [ 2] Steele’s Potential for Molecule- Surface Interaction [ 3] [1] Jorgensen et al., J. Am. Chem. Soc. 118 , 11225 (1996) [2] H.C. Andersen, J. Comput. Phys. 52 , 24 (1983) [3] W. A. Steele, Surf. Sci. 36 , 317 (1973)

Many Local Minima, Fast Transitions But Desorption is the Slow Step Desorption Barrier Diffusion/Torsion Barrier …

Accelerated MD of TPD with the Bond-Boost Method  A ( ) N              max V ( R ) V ( R ) ; V ( 1 ) V ( 1 ) V ; 1 i i 1 s , i 2 inter , i i N  i 1 Weaken Molecule-Molecule + Molecule-Surface Attraction   2     z z         com , i eq max A 1   ; i     q z   eq Funnels Boost into Molecule    V ( R )     Farthest from the Surface  i t exp t     k T i B K. Becker, M. Mignogna, K. Fichthorn PRL 102 ,046101 (2009).

Accelerated MD of TPD T = T 0 +  t;             = Heating Rate exp / t t V kT n  j e  i j K. Becker, M. Mignogna, K. Fichthorn, desorptions PRL 102 , 046101 (2009).

TPD: Simulation vs. Experiment K. Paserba and A. Gellman, J. Chem. Phys. 115 , 6737 (2001) T 0 = 120 K 1 ML Initially Defects  = 2 K/s Total Time: 15 s Coverage Calibration K. Becker, M. Mignogna, K. Fichthorn, PRL 102 , 046101 (2009).

Desorption Energy Repulsion?? And Prefactor Q       S / k e B o o Q ? Large prefactors because of loss in How Can This Happen? rotational entropy on adsorption. K. Fichthorn and R. Miron, Phys. Rev. Lett. 89 , 196103 (2002). K. Becker and K. Fichthorn, JCP 125 , 184706 (2006).

Second-Layer Desorption Can Occur At (Sub) Monolayer Coverage Second-Layer Desorption at  = 0.75

Rate Processes in Pentane Desorption E d = 32.5 kJ/mol Second-Layer Molecules  0 = 9.2E+11 E d = 36.5 kJ/mol  0 = 5.5E+12 Isolated Molecules E d = 58.1 kJ/mol  0 = 2.4E+17 Molecules in Islands K. Becker, M. Mignogna, K. Fichthorn, PRL 102 , 046101 (2009).

What is the Structure of a Real GaAs(001)  2(2x4) Surface? (2x4) Unit Cell STM Hypothesis: Disordering Involves Shifting of Dimer D.W. Pashley, J.H. Neave, B.A. Joyce, Rows and Trenches Surf. Sci. 582, 189 (2005) How Does this Surface Disorder? W hat Does This Mean for Diffusion and Grow th?? K. A. Fichthorn, et al ., Phys. Rev. B, 83 , 195328 (2011)

Regular MD of GaAs (001): T = 600 K

Minimum-Energy Path for Row Shift: Another Form of the Small-Barrier Problem (a) (b) (d) (e) (g) Breaking Shifting Breaking Shifting 1.59 1.37 1.18 1.02 (e) (g) CI-NEB Method 0.67 (d) (b) ---- V +  V b G. Henkelman, B.Uberuaga, (b) and H. Jonsson, J. Chem. Phys. 113, 9901 (2000). (a) (a)

Accelerated MD Simulation at 800 K

Equilibrium Fraction of  2(2x4) and c(2× 8) from 1  s - 4 s Accelerated MD (c) and (d) c(2× 8) (a) and (b) Comparison with Experiment STM (300K, UHV) 0 .4 1 ; c(2× 8) 0 .5 2 ; Other 0 .0 7 RHEED (850 K As Over Pressure, 300 K Vacuum) No Difference D. W. Pashley, J. H. Neave, and B. A. Joyce, Surf. Sci. 5 8 2 , 189 (2005) Arrangement based on STM image

Conclusions: Progress in Accelerated MD ● The Bond-Boost Method is Useful for Modeling and/ or Discovering Rare Events ● The Challenge is Dealing with the Small- Barrier Problem in a General Way ● Consolidating Pools of Shallow States R. Miron & K. Fichthorn, Phys. Rev. Lett. 93, 2004; Phys. Rev. B 7 2 , 035415, 2005.