Accelerated Molecular Dynamics with the Bond Boost Methodwith the Bond Boost Method

(mostly of thin-film growth)Kristen A FichthornKristen A. Fichthorn

The Pennsylvania State UniversityUniversity Park, PA 16802

USA

DE-FG0207ER46414DMR-1006452

Multi-Scale Simulation of Interfacesfrom First Principleso st c p es

Solid-State Systems Molec les on S faces

Well Understood

Solid State SystemsThin-Film GrowthAssembly at SurfacesENERGY DOMINATES

Molecules on SurfacesDiffusionThermal Desorptiony ENERGY DOMINATES

DFT IS GREAT!Thermal DesorptionAdsorptionENTROPY PLAYS A ROLEDFT IS LIMITEDm

plex

ity

DFT IS LIMITED

Nanoparticles in SolutionInterparticle Forces

Com

W. Al-Saidi,, and KFIn preparation.Interparticle Forces

Assembly in SolutionENTROPY PLAYS A BIG ROLEDFT IS LIMITED

HELP!

DFT IS LIMITED

R. Sathiyanarayanan,, and KFSubmitted to J. Phys. Chem. C

Surface Phenomena Involve MultipleLength and Time ScalesLength and Time Scales

Bautier de Mongeot et al Phys Rev Lett 91al., Phys. Rev. Lett. 91,016102 (2003).Thin-Film

Growthe g fcc(110) Atoms Hopping (, ps)e.g. fcc(110) homoepitaxy

Also Catalysis at Hut FormationHut Organization(m, min)y

Surfaces, CVD, and More

(nm, min)

K. Fichthorn and M. Scheffler,Nature 429, 617 (2004).

Challenge: Reactor DesignFrom First PrinciplesFrom First PrinciplesExample: Growth of GaAs Thin Films

Continuum Equations forFluid Flow, Heat Transfer,Mass Transfer, Kinetics in

Kinetic Monte CarloSimulation of Growthof GaAs(001) (nm s)

Charge-Density Contoursfor GaAs(001) fromDensity-FunctionalTheory ( ,

a Rotating Disk Reactor (m,h)of GaAs(001) (nm, s)Theory (

Rare-Event MethodsThis Link Needs Work!

Kratzer and Scheffler, Comp. Sci. Eng. 2001.

This Link ReallyNeeds Work!!!!!

Rare-Event Methods[e.g.,Transition-State Theory (TST)][e g , a s t o State eo y ( S )]

)(

)/)(exp(*)(k

TkV

BATSTA B

RRR

R*

)/exp(*

)/)(exp(,

TkEq

TkVBATSTA B

RB

)/exp( 00 TkEq BA

A

TST Search Sampling Methods

Nudged Elastic Band Method: Henkelman and JonssonDimer Method: Henkelman and Jonsson

TST Search, Sampling Methods

Step and Slide Method: Miron and FichthornTransition Path Sampling: Dellago, Bolhuis, Geissler, ChandlerString Method: E, Ren, Vanden-Eijnden

Molecular Dynamics SimulationsNaturally Find Rate Processes

Accelerated Molecular Dynamics(Hyperdynamics)

A. Voter, J. Chem. Phys. 106, 11 (1997).**

BC

Relative Rates*

BA

C

**

ABC A

Accelerated Molecular Dynamics(Hyperdynamics)( yp y )

A. Voter, J. Chem. Phys. 106, 11 (1997).

**

V

ABC

MD Time: Real Time:

NN tN

i

ii i

kTVtRWtt

11/exp

)(

V

tMD= Nt

Th T i k i H t C t t

kTVexpBoost The Trick is How to Construct

V(R) and Where to Apply it

Accelerated Molecular DynamicsThe Bond-Boost Method

R. Miron & K. Fichthorn, J. Chem. Phys. 119, 6210 (2003)

Define Local Minima by Bond Lengths

Nio

ir ,1}{

Empirical

Transitions Occur via Bond Breaking

ir EmpiricalThreshold

Boost the Bonds: Purely Geometric

qoi

i

rr

i max

Boost the Bonds: Purely Geometric

)(}{~}{1

N

iii rVrAxV

1i

Envelope Function Boost per Bond

Details of the Bond Boost MethodBoost PotentialBoost Potential

0maxmax )( rrVA

NVV ii

N

ir

1 rN ii

Nominal Boost per Bond

2

1q

V ii

Envelope: Channels Boost into the Bond Most Ready to Break

2max

max 1fA

to Break

q

Overview of the Bond Boost MethodR. Miron & K. Fichthorn, J. Chem. Phys. 119, 6210 (2003)

Diffusion on Cu(100): Elementary Processes

Adatom Hop Dimer ExchangeAdatom Exchange

R Mi & K Fi hth

Vacancy HopDimer Hop

R. Miron & K. Fichthorn,J. Chem. Phys. 119, 6210(2003)

The Bond-Boost Method: Diffusion on Cu(100)R. Miron & K. Fichthorn,J. Chem. Phys. 119, 6210(2003)

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

Boost = Physical Time / Simulation Time

10(Boost)

V(R)

log 1

V

(kBT)-1 (eV-1)

& h h exp

TkVBoost

B

R. Miron & K. Fichthorn,J. Chem. Phys. 119, 6210 (2003)

Rare Events and the Small Barrier Problem

Annoyingly Small Barriers

State-Bridging Accelerated MD toSolve the Small-Barrier Problem R i thSolve the Small Barrier Problem

Commence

Raise theBoost AfterA WaitingTimeWith a Low

BoostTime

Miron, Fichthorn, J. Chem. Phys. 115,

Memorize and

J. Chem. Phys. 115,2001.

Memorize andConsolidatePairs of StatesConnected by Low

Detect BarriersWhen TransitionsOccur, CompareT Th h ld

Connected by LowBarriers

To ThresholdR. Miron, K. Fichthorn,Phys. Rev. Lett. 93, 2004.

Co on Cu(001): Benefits of State Bridging

State-Bridging RegularState BridgingAccelerated MD

gAccelerated MD

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

Note Cluster MobilityR. 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 MD Simulations were run for 5.4 s

Mechanism of Bila eMechanism of BilayerIsland Formation

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

Hut Formation in Al(110) Homoepitaxy

Bautier de Mongeot et al., Phys. Rev. Lett. 91,016102 (2003).

Atoms Hopping ( ps)

016102 (2003).

Atoms Hopping (, ps)

Hut FormationHut Organization(m, min)Hut Formation

(nm, min)(m, min)

K. Fichthorn and M. Scheffler,Nature 429, 617 (2004).

Exchange of Al on Al(110): The CI-NEB Method in First-Principles DFT (VASP)

In-Channel Cross-Channel

Method in First Principles DFT (VASP)

vs.

E = 0.39 E = 0.38E = 0.33 and E = 0.49

W. Zhu et al., PRL 92, 106102 (2004).

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

Climbing-ImageNudged ElasticNudged ElasticBand Method

vs

AcceleratedAIMD

vs.

AIMD

Fichthorn et al., J. Phys. Cond.Matt. 21, 084212 (2009).

EB = 0.38 eV EB = 0.33 eV

The Boost in ab initio MD

s~ s

VexpBoost

kT

pBoost

Temperature-Programmed DesorptionK. Becker, M. Mignogna, K. Fichthorn,

pB

d

B

d

p TkE

kE

T

02

lnln

Ed d

, g g , ,PRL 102, 046101 (2009).

pp

Tkdt Bdexp0

tTT 0 P. A. Redhead, Vacuum12, 203 (1962).

Simulation of TPD

vs.

Large Molecules DontWork in Lattice Models.

Goal: To SimulateGoal: To SimulateTPD with MD!!

Accelerated MD of Adsorbed Alkanes

OPLS All-Atom Force Field [1]

2eqiib KV )()(

LJtbintra VVVV

3

1jijit j1V2

1V cos)(

Constrained Bond Stretching: RATTLE [2]Steeles Potential for Molecule-Surface Interaction [3]

[1] J l J A Ch S 118 11225 (1996)[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 TransitionsBut Desorption is the Slow Step

Desorption Barrier

Diffusion/Torsion Barrier

Accelerated MD of TPD withthe Bond Boost Method

NVVVVAV max 1;)1()1(;)R(

)()R(

the Bond-Boost Method

iiinterisii

i VVVVNV

,2,1

11 ;)1()1( ; )R()R(

Weaken Molecule-Molecule +Molecule-Surface Attraction

eqicomi

zzA

,

2

max ;1

Molecule Surface Attraction

eqzq

Funnels Boost into Molecule Farthest from the Surface )(

iV RFarthest from the Surface t )(exp

i B

i

TkVt

K. Becker, M. Mignogna, K. FichthornPRL 102,046101 (2009).

Accelerated MD of TPD

T = T0 + t; = Heating Rate

i jej nkTVtt /expi j

desorptionsK. Becker, M. Mignogna, K. Fichthorn, PRL 102, 046101 (2009).

TPD: Simulation vs. Experiment

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

T0 = 120 KDefects

T0 120 K1 ML Initially = 2 K/s

Total Time: 15 s

CoverageCoverageCalibration K. Becker, M. Mignogna, K. Fichthorn,

PRL 102, 046101 (2009).

A Total Differential Analysis

exp1 Ed d

Constant

),(

exp0

TkTkdt B

)(J. Taylor and W. Weinberg,Surf. Sci. 78, 259 (1978).

J. B. Miller, et al., J. Chem.Phys. 87, 6725 (1987).

This is DifficultThis is DifficultExperimentallyK. Becker, M. Mignogna, K. Fichthorn, PRL 102, 046101 (2009).

Desorption EnergyAnd Prefactor

Repulsion??

And Prefactor

kSQ / BkSoo eQ

Q /

?

How Can This Happen?Large prefactors because of loss in rotational entropy.K Fichthorn and R Miron Phys RevK. Fichthorn and R. Miron, Phys. Rev. Lett. 89, 196103 (2002).

Multi-Exponential Time Distribution

tki ieatP )(

Fast, Second-Layer

i

i eatP )(

Fast, Second LayerDesorption

+Slow, First-LayerDesorption

+

= 1 ML

Desorption

1 ML160 K

Second-Layer Desorption Can OccurAt (S b) Monola e Co e ageAt (Sub) Monolayer Coverage

S d L D tiSecond-Layer Desorptionat = 0.75

Multiple Time Scales at All Coverages

8

10

Fast Desorption of

6

8 Fast Desorption ofIsolated Molecules

+4

LnP

t +

Slow Desorption ofMolecules in Islands

0

2L Molecules in Islands

-2 = 0.25T 160 K0 10 20 30 40 50 60

t sT = 160 K

Rate Processes in Pentane Desorption

Second-Layer Molecules Ed = 32.5 kJ/mol0 = 9.2E+11

Ed = 36.5 kJ/mol

0 9

Isolated Molecules 0 = 5.5E+12

Molecules in Islands

Ed = 58.1 kJ/mol0 = 2.4E+17

K. Becker, M. Mignogna, K. Fichthorn, PRL 102, 046101 (2009).

Coverage Dependence of KineticsIsland Desorption

IncreasingSecond-LayerFewer

EntropyEntropy GainyDesorption

Isolated Molecule

IsolatedMoleculesEntropy

LossIsolated Molecule

Second-Layer

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

(2x4) Unit Cell

STMUnit Cell

Hypothesis: Disordering Involves Shifting of DimerD.W. Pashley, J.H. Neave, B.A. Joyce,

Surf. Sci. 582, 189 (2005)Involves Shifting of Dimer Rows and Trenches

How Does this Surface Disorder?How Does this Surface Disorder?What Does This Mean forDiffusion and Growth??

ArsenicGallium

Modified Tersoff Potential for GaAs

ARc VBVfE 1C ff ijAijijijijRijiji

ijc

ijpot rVrBrVrfE ,2

,..., N1 rr

Pair: Pair:

Cutoff

Three Body:Pair: Repulsive

Pair: AttractiveBond Order

K. Fichthorn et al., Phys. Rev. B 83, 195328 (2011)

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

Barrier Energy for As Dimer Breaking

Regular MD of GaAs (001)

T =600K

24 084 24 09024 0890.0 ns 24.084 ns 24.090 ns24.089 ns

24.216 ns 24.217 ns 24.224 ns

n-Bond-Boost MethodAchieve Systematic TemporalCoarse-Graining by Increasing n

n = 3 lose information about kineticsof two transitions

n = 2 lose information about kineticsf i l i i

n=1 lose information about vibrationin minima

of single transitions

N

njjj

nn

iiii rVL

AArVA

LnNLV

1

1

1

r

Nnn AAAA ,,min,, 11 n N, L > 0 (e.g., L = nN)

n-Bond-Boost Method in a Model 3-Bond System

n-Bond-Boost Method: 3-Bond System

n-Bond-Boost Method: 2 As Trench Dimers Breaking

Th bl t b t dThe blue atoms were boosted

2-Bond Boost, T = 600 KTotal Time 26 sTotal Time = 26 s

4-Bond Boost, T = 600 KTotal Time 14 msTotal Time = 14 ms

Conclusions: Progress in Accelerated MDThe Big Problem is Multiple Time-Scale

PhenomenaC lid ti P l f Sh ll St t Consolidating Pools of Shallow StatesR. Miron & K. Fichthorn, Phys. Rev. Lett. 93, 2004;

Phys. Rev. B72, 035415, 2005.

Focusing on Only One Transition TypeK. Becker, M. Mignogna, K. Fichthorn, PRL 102, 046101 (2009)

n-Bond BoostLin and Fichthorn, In Progress.

CollaboratorsMozhgan Alimohammadi

AlumniDr Yogesh TiwaryMozhgan Alimohammadi

Azar ShahrazHaijun Feng

Dr. Yogesh TiwaryDr. Yushan WangDr. Kelly Becker

d l iJin HongDr. Yangzheng LinDr. Ya Zhou

Dr. Radu Alex MironDr. Jee-Ching WangDr. Som PalDr. Ya ZhouFritz Haber InstituteProf.-Dr. Matthias SchefflerProf -Dr Peter KratzerProf.-Dr. Peter KratzerDr. Thomas Hammerschmidt

FundingNSF ECC-0085604, IGERT DGE-9987598, DMR-0514336,

DMR-1006452ACS PRF, DOE DE-FG0207ER46414