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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
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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
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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).
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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!!!!!
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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
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Accelerated Molecular Dynamics(Hyperdynamics)
A. Voter, J. Chem. Phys. 106, 11 (1997).**
BC
Relative Rates*
BA
C
**
ABC A
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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
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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
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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
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Overview of the Bond Boost MethodR. Miron & K. Fichthorn, J. Chem. Phys. 119, 6210 (2003)
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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)
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The Bond-Boost Method: Diffusion on Cu(100)R. Miron & K. Fichthorn,J. Chem. Phys. 119, 6210(2003)
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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)
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Rare Events and the Small Barrier Problem
Annoyingly Small Barriers
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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.
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Co on Cu(001): Benefits of State Bridging
State-Bridging RegularState BridgingAccelerated MD
gAccelerated MD
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Thin Film Growth at 250 K, F = 0.1 ML/s
Note Cluster MobilityR. Miron, K. Fichthorn,Phys. Rev. Lett. 93, 2004.
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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).
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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).
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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).
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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
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The Boost in ab initio MD
s~ s
VexpBoost
kT
pBoost
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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).
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Simulation of TPD
vs.
Large Molecules DontWork in Lattice Models.
Goal: To SimulateGoal: To SimulateTPD with MD!!
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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)
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Many Local Minima, Fast TransitionsBut Desorption is the Slow Step
Desorption Barrier
Diffusion/Torsion Barrier
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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).
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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).
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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).
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Multi-Exponential Time Distribution
tki ieatP )(
Fast, Second-Layer
i
i eatP )(
Fast, Second LayerDesorption
+Slow, First-LayerDesorption
+
= 1 ML
Desorption
1 ML160 K
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Second-Layer Desorption Can OccurAt (S b) Monola e Co e ageAt (Sub) Monolayer Coverage
S d L D tiSecond-Layer Desorptionat = 0.75
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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)
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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
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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.
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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