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

DE-FG0 2 0 7 ER4 6 4 1 4 DMR-1 0 0 6 4 5 2

Rare-Event Methods

R* A B

Nudged Elastic Band:

• G. Henkelman, B.Uberuaga, and H. Jonsson,
• J. Chem. Phys. 1 1 3 , 9901 (2000).

Dimer Method:

• G. Henkelman and H. Jonsson, J. Chem.
• Phys. 1 1 1 , 7010 (1999).

Transition Path Sampling:

P . Bolhuis, D. Chandler, et al.

• Ann. Rev. Phys. Chem. 5 3 , 291 (2002).

Forward-Flux Sampling:

• R. J. Allen, D. Frenkel, P

. R. ten Wolde,

• J. Chem. Phys. 1 2 4 , 194111 (2006).

String Method:

• W. E., W. Ren , E. Vanden-Eijnden,
• Phys. Rev. B 6 6 , 052301 (2002).

AND… …

Search and Characterization Molecular Dynamics Simulations Naturally Find Rare Events and Can Simulate Rare-Event Systems… Rare-Event Simulation

Kinetic Monte Carlo:

• K. Fichthorn and W. Weinberg,
• J. Chem. Phys. 9 5 , 1090 (1991).

Kinetic ART:

El-Mallouhi, N. Mousseau, Phys. Rev. B 7 8 ,1532002 (2008).

Master Equation

Accelerated Molecular Dynamics

(Hyperdynamics)

• A. Voter, J. Chem. Phys. 1 0 6 , 11 (1997).

Relative Rates

* *

B

A C A B C * *

Accelerated Molecular Dynamics

(Hyperdynamics)

• A. Voter, J. Chem. Phys. 1 0 6 , 11 (1997).

MD Time: Real Time:

 

 

 

    

N i i N i i

kT V t R W t t

1 1

/ exp ) (

        kT V exp Boost

tMD= Nt A B C * * The Trick is How to Construct

V(R)…

V

Accelerated Molecular Dynamics

The Bond-Boost Method

• R. Miron & K. Fichthorn, J. Chem. Phys. 1 1 9 , 6210 (2003)

Empirical Threshold

Define Local Minima by Bond Lengths Transitions Occur via Bond Breaking Boost the Bonds: Purely Geometric

N i

• i

r

, 1

} {



q

• i

i

r r i





max

) ( } { ~ } {

1

 

 N i i i

r V r A x V 

Envelope Function Boost per Bond

Details of the Bond Boost Method

Boost Potential

       

                                



 2 max max 2 1 max max

1 1 ) ( q f A q V r r V A N V V

i i i i i N i i

          r

Nominal Boost per Bond Envelope: Channels Boost into the Bond Most Ready to Break

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 Vacancy Hop Dimer Hop Dimer Exchange Adatom Exchange

• R. Miron & K. Fichthorn,
• J. Chem. Phys. 1 1 9 , 6210

(2003)

The Bond-Boost Method: Diffusion on Cu(100)

• R. Miron & K. Fichthorn,
• J. Chem. Phys. 1 1 9 , 6210

(2003)

Boost = Physical Time / Simulation Time

exp           T k V Boost

B

The Bond-Boost Method: Diffusion on Cu(100)

log10(Boost) (kBT)-1 (eV-1)

V(R)

• R. Miron & K. Fichthorn,
• J. Chem. Phys. 1 1 9 , 6210 (2003)

Hut Formation in Al(110) Homoepitaxy

• K. Fichthorn and M. Scheffler,

Nature 4 2 9 , 617 (2004). Atoms Hopping (Å, ps) Hut Formation (nm, min) Hut Organization (m, min)

Bautier de Mongeot et al.,

• Phys. Rev. Lett. 91,

016102 (2003).

Accelerated AIMD (VASP): Diffusion on Al/ Al(110)

Climbing-Image Nudged Elastic Band Method Accelerated AIMD

vs. EB = 0.38 eV EB = 0.33 eV

Fichthorn et al., J. Phys. Cond.

• Matt. 2 1 , 084212 (2009).

The Boost in ab initio MD

~ s

        kT V exp Boost

Rare Events and the Small Barrier Problem

Annoyingly Small Barriers

State-Bridging Accelerated MD to Solve the Small-Barrier Problem

Commence With a Low Boost Raise the Boost After A Waiting Time Detect Barriers When Transitions Occur, Compare To Threshold Memorize and Consolidate Pairs of States Connected by Low Barriers

• R. Miron, K. Fichthorn,
• Phys. Rev. Lett. 93, 2004.

Miron, Fichthorn,

• J. Chem. Phys. 115,

2001.

State-Bridging Accelerated MD Regular Accelerated MD

Co on Cu(001): Benefits of State Bridging

Thin Film Growth at 250 K, F = 0.1 ML/ s Note Cluster Mobility

• R. Miron, K. Fichthorn,
• 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

Mechanism of Bilayer Island Formation MD Sim ulations w ere run for 5 .4 s

• R. Miron and K. Fichthorn,
• Phys. Rev. B 72, 115433 (2005).

Temperature-Programmed Desorption

p B d B d p

T k E k E T                   

2

ln ln                T k E dt d

B d

exp

t T T   

• P. A. Redhead, Vacuum

12, 203 (1962).

• K. Becker, M. Mignogna, K. Fichthorn,

PRL 102, 046101 (2009).

Simulation of TPD

Large Molecules Don’t Work in Lattice Models… . vs.

Goal: To Simulate TPD with Accelerated MD!!

Accelerated MD of Adsorbed Alkanes

OPLS All-Atom Force Field [ 1]

2 eq i i b

K V ) ( ) (   



 

 

 

  

 3 1 j i j i t

j 1 V 2 1 V   cos ) (

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) LJ t b intra

V V V V   

Desorption Barrier Diffusion/Torsion Barrier

Many Local Minima, Fast Transitions But Desorption is the Slow Step

…

eq eq i com i i i inter i s i N i i

z z z q A V V V V N A V                            

 , 2 max , 2 , 1 1 max

; 1 1 ; ) 1 ( ) 1 ( ; ) R ( ) ( ) R (        

Funnels Boost into Molecule Farthest from the Surface

Accelerated MD of TPD with the Bond-Boost Method

Weaken Molecule-Molecule + Molecule-Surface Attraction

t ) ( exp            

i B i

T k V t R

• K. Becker, M. Mignogna, K. Fichthorn

PRL 102,046101 (2009).

Accelerated MD of TPD

T = T0 + t;  = Heating Rate

 

          

i j e j

n kT V t t / exp

desorptions

• K. Becker, M. Mignogna, K. Fichthorn,

PRL 102, 046101 (2009).

TPD: Simulation vs. Experiment

Coverage Calibration Defects

• K. Becker, M. Mignogna, K. Fichthorn,

PRL 102, 046101 (2009).

• K. Paserba and A. Gellman, J.
• Chem. Phys. 115, 6737 (2001)

T0 = 120 K 1 ML Initially  = 2 K/s Total Time: 15 s

Desorption Energy And Prefactor

How Can This Happen?

B

k S

• e

Q Q

/ 

    

?

Repulsion??

Large prefactors because of loss in 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

Molecules in Islands Isolated Molecules Second-Layer Molecules Ed = 58.1 kJ/mol 0 = 2.4E+17 Ed = 36.5 kJ/mol 0 = 5.5E+12 Ed = 32.5 kJ/mol 0 = 9.2E+11

• K. Becker, M. Mignogna, K. Fichthorn,

PRL 102, 046101 (2009).

What is the Structure of a Real GaAs(001)2(2x4) Surface?

D.W. Pashley, J.H. Neave, B.A. Joyce,

• Surf. Sci. 582, 189 (2005)

STM Hypothesis: Disordering Involves Shifting of Dimer Rows and Trenches (2x4) Unit Cell 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 Breaking Shifting Shifting (a) (b) (d) (e) (g) 0.67 1.18 1.37 1.59 1.02

• G. Henkelman, B.Uberuaga,

and H. Jonsson, J. Chem.

• Phys. 113, 9901 (2000).

CI-NEB Method (a) (b)

• --- V + Vb

Accelerated MD Simulation at 800 K

• D. W. Pashley, J. H. Neave, and B. A.

Joyce, Surf. Sci. 5 8 2 , 189 (2005)

(c) and (d) c(2× 8) STM (300K, UHV) RHEED (850 K As Over Pressure, 300 K Vacuum) No Difference

Comparison with Experiment

Arrangement based on STM image

Equilibrium Fraction of 2(2x4) and c(2× 8) from 1 s - 4 s Accelerated MD

(a) and (b)

0 .4 1 ; c(2× 8) 0 .5 2 ; Other 0 .0 7

• The Challenge is Dealing with the Small-

Barrier Problem in a General Way

Conclusions: Progress in Accelerated MD

• Consolidating Pools of Shallow States
• R. Miron & K. Fichthorn, Phys. Rev. Lett. 93, 2004;
• Phys. Rev. B7 2 , 035415, 2005.
• The Bond-Boost Method is Useful for Modeling

and/ or Discovering Rare Events

Conclusions: Progress in Accelerated MD

• Bond = Order Parameter
• K. Becker, M. Mignogna, K. Fichthorn, PRL 102, 046101

(2009)

The key to future progress is a general solution to the small barrier problem

• Pathway Boost for GaAs(001)

Y . Lin and K. Fichthorn, in preparation.

Look for our NEW SOLUTI ON to the Small-Barrier Problem Using KMC+ Master Equation!!!!

Collaborators Funding

Shih-Hsien Liu Azar Shahraz Muralikrishna Raju Zifeng Li Lianfei Yan

• Dr. Yangzheng Lin
• Dr. Ya Zhou

Alum ni

• Dr. Yogesh Tiw ary
• Dr. Yushan W ang
• Dr. Kelly Becker
• Dr. Radu “Alex” Miron
• Dr. Jee-Ching Wang
• Dr. Som Pal

Fritz Haber I nstitute Prof.-Dr. Matthias Scheffler Prof.-Dr. Peter Kratzer

• Dr. Thom as Ham m erschm idt

NSF ECC-0085604, IGERT DGE-9987598, DMR-0514336, DMR-1 0 0 6 4 5 2 ACS PRF, DOE DE-FG0207ER46414