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Accelerated Molecular Dynamics at Surfaces
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1 Accelerated Molecular Dynamics at Surfaces Kristen A. Fichthorn Departments of Chemical Engineering and Physics The Pennsylvania State University University Park, PA 16802 USA Temperature-Programmed Desorption QMS: Intensity θ ν θ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = − T k E dt d B d exp 0 T = T 0 +β t E d from Intensity Maximum….. Goal: To Simulate TPD with MD!!
Transcript of Accelerated Molecular Dynamics at Surfaces
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Accelerated Molecular Dynamics at Surfaces
Kristen A. FichthornDepartments of Chemical Engineering and Physics
The Pennsylvania State UniversityUniversity Park, PA 16802
USA
Temperature-Programmed Desorption
QMS: Intensity
θνθ⎟⎟⎠
⎞⎜⎜⎝
⎛−=−
TkE
dtd
B
dexp0
T = T0 + β t
Ed from IntensityMaximum…..
Goal: To SimulateTPD with MD!!
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n-Alkanes: An Unusual Case
Propane: C3H8
Polyethylene
CH3-[CH2]N-2
-CH3
Methane
CH4
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12 14 16 18
Ru(0001)Au(111)Cu(001)GraphiteAl2O3(0001)Pt(111)
Brand et al., J. Chem. Phys.92, 5136 (1990).
Wetterer et al., J. Phys. Chem. B 102, 9266 (1998).
Teplyakov et al., Surf. Sci.396, 340 (1998).
Paserba and Gellman,PRL 86, 4338 (2001).
Slayton et al., J. Phys.Chem. 99, 2151 (1995).
Bishop et al., J. Phys. Chem.B 104, 754 (2000).
Weaver et al., J. Chem. Phys.110, 10585 (1999).
Number of Carbons
E d(k
J / m
ol)
Binding Energies vs. Chain Length
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Wetterer et al., J. Phys. Chem. B 102, 9266 (1998).
Paserba and Gellman,PRL 86, 4338 (2001).
Tait et al., JCP 125, 234308 (2006).10
12
14
16
18
20
22
0 10 20 30 40 50
Number of Carbons
Log 1
0 (νo
)
Au(111)C(0001)C(0001)
ν0 ≈ 1019.6
ν0 = 1013
ν0 increases
Preexponential Factors vs. Chain Length
Why??
Accelerated MD of an Alkane Chain
OPLS All-Atom Force Field [1]
2eqiib KV )()( θθθ θ −=
( )[ ]∑ +==
3
1jijit j1V2
1V ϕϕ 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)
LJtbintra VVVV ++=
4
∫ −
∫ −−
=→A
TBkVA
TBkV
BATSTkB
)/)(exp(
)/)(exp(*)(
, R
RRRδν
Accelerated Molecular Dynamics(Hyperdynamics) A. Voter, J. Chem. Phys. 106, 11 (1997).
Detailed Balance!
V (R)
**
ABC
**
BA
C
-V (R) -V (R)
-V (R) -V (R)
∫ ∫∫ ∫−
=
⎟⎟⎠
⎞⎜⎜⎝
⎛ −=
∫ −∫ −−
=
)/exp(/)(/)/exp()/exp(/)/exp()(
)(exp)(
)(/)/)(exp()()(/)/)(exp()()(
*
*
TkWTkTkTkk
TkVW
WTkVWWTkVWk
BB
BBBTST
B
B
BBTST
RRR
RR
RRRRRRRR
δν
δν
Accelerated Molecular Dynamics(Hyperdynamics) A. Voter, J. Chem. Phys. 106, 11 (1997).
Detailed Balance!
ABC
**
kTST,A→C / ⟨ 1/W(R)⟩A
=
=
=
→
→
→
→
CATST
BATST
CATST
BATST
kk
k
k
,
,
,
, kTST,A→B / ⟨ 1/W(R)⟩A
kTST,A→BkTST,A→C
MD Time: tMD= NΔt
AMD Time: ( )∑∑==
ΔΔ=Δ
=N
ii
N
i i
kTVtRWtt
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/exp)(
⎟⎠⎞
⎜⎝⎛ Δ=
kTVexpBoost
5
h
bR*
Weighting Functions:Single-Molecule Limit
Temperature AccelerationDesorb at sT, scale back to T
K. Fichthorn and R. Miron, Phys. Rev. Lett. 89, 196103 (2002).
totaliW1
boxiW1
TST
i
i
b1k
⎟⎠⎞
⎜⎝⎛∑
⎟⎠⎞
⎜⎝⎛∑
=ν
1ss
V≥= ,)(RV(R)
Bond Boost PotentialWeaken the Molecule-Surface Interaction
)(exp)( ⎟⎟⎠
⎞⎜⎜⎝
⎛ −=
TkVW
B
RR V (R)
1VVVV LJbts <+++= ααα ,V(R)
n-Alkanes on Au(111)K. Fichthorn and R. Miron, Phys. Rev. Lett. 89, 196103 (2002).
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Arrhenius Plot: Graphite
kTETST ek /−=ν
Simulation Time =100 ps – 5 nsWhat a Boost!!
Activation Energy: Graphite
Paserba, Gellman, JCP 115, 6737, (2001).Tait et al., JCP 125, 234308 (2006).
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Prefactor: Graphite
Paserba, Gellman, JCP 115, 6737, (2001).
Increase forShort Chains
~ Constant forLong Chains
1018.3 vs. 1019.6
in Expt.
Tait et al., JCP 125, 234308 (2006).
K. Becker and K. Fichthorn,JCP 125, 184706 (2006).
Prefactor Analysis BkSoo e
QQ /Δ== ννν
Chain Length
ΔS
Rigid body r
otatio
n incre
ases ν Torsion
decreases ν
vibration
hindered torsion free torsion
Torsion BarrierIndependent ofChain Length
K. Becker and K. Fichthorn,JCP 125, 184706 (2006).
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GaAs Surface ReconstructionsGaAs Surface Reconstructions
L. Daweritz, R. Hey, Surf. Sci. 236, 15 (1990) GaAs(001)β2(2x4)
Molecular Beam Epitaxy
ArsenicGallium
What is the Structure of a Real GaAs(001)β2(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?What Does This Mean forGrowth, Phase Transitions??
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Modified Tersoff Potential for Modified Tersoff Potential for GaAsGaAs
( ) ( ) ( ) ( ) ( )[ ]ijA
ijijijijR
ijiji
ijc
ijpot rVrBrVrfE ⋅−⋅= ∑≠,2
1,..., N1 rr
Pair: Repulsive
Pair: Attractive
( ) ( )( )[ ]( ) ( ) ( ) ( )( )[ ]
( ) ( ) ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−+−+=
⋅⋅=
⋅+=−
≠
−
∑
22
2
2
2
21
cos1
1
ijkikik
ik
ik
ikikijkik
rrijkikik
ijk
cikijij
nnijijijijij
hdc
dc
g
egrfr
rrBikm
ikijik
ijij
θδθ
θχ
χγα
Cutoff
Three Body:
Bond Order
K. Albe, K. Nordlund, A. Nord, A. Kuronen, Phys. Rev. B 66, 035205 (2002)*
*With modified As-As cutoff distance: T. Hammerschmidt et al.
DFTDFTComparisonComparison
As
Ga
PW GGA-II: A. Kley, P. Ruggerone, M. Scheffler, PRL 79, 5278 (1997).
PBE GGA, LDA: P. Kratzer, C. Morgan, M. Scheffler, Prog. Surf. Sci. 59, 135 (1998).
2
5
4
3-1
-3
Binding Preference
(eV)
1
Site Potential PW GGA-II PBE GGA LDA1 -3.20 - -1.9 -2.82 -2.95 -3.2 -2.1 -2.63 -2.91 -2.6 -1.9 -2.54 -2.42 -2.5 -1.5 -2.25 -2.30 -2.2 - -
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Accelerated Molecular DynamicsThe Bond Boost Method
R. Miron & K. Fichthorn, J. Chem. Phys. 119, 6210 (2003)
EmpiricalThreshold
Accelerated Molecular DynamicsDetails of the Bond Boost Method
Channels the Boost intothe Bond that’s Readyto Break
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Adaptive BondAdaptive Bond--Boost Method: Boost Method: Rough Potential SurfacesRough Potential Surfaces
Ai
Af
*
ΔE
kTST
**
Adjust the Magnitudeof the Boost
Use Variable BoostThresholds
M. Mignogna and K. A. Fichthorn(In preparation)
Boost Parameters AreAdjusted On the Fly!
ββ2(2x4)2(2x4) Reconstruction at 300KReconstruction at 300K
Atoms vibrate, but remain in perfect surface positions
After ~3μs
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Bond Boost ValidationBond Boost Validation
-8-6-4-20
0.002 0.003 0.003 0.004
MD
AcceleratedMD
1/T (K-1)
lnra
te (p
s-1 )
Trench Dimer Splitting
Barrier = 0.3 ±0.01 (eV)Prefactor = 3.08x1014 ( s-1)
Boost: 102 – 103
ββ2(2x4)2(2x4) reconstruction at 350Kreconstruction at 350K
Open trench dimerBuried Ga
As atom leaves trench:Newdimer forms
<100ns
570ns
13
250ns
350K
Row dimers zigzag:
Leaves lone As row atoms
New row dimer forms:
Row shifts
Concerted Trench ShiftConcerted Trench ShiftA trench shifted from perfect induces neighboring trenches to shift
T=410K
Movie length: 38 ns
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Strain FieldStrain FieldTotal change in distance from perfect surface positions (Å)
Shifted trench
Strain from moving one trench extends to neighboring trenches
Furthest significant change in position
0.1
0.01
0.001
0.0001
0.00001
Collaborators
FundingNSF ECC-0085604, IGERT DGE-9987598, DMR-0514336,
NIRT CCR-0303976, CBET-0730987ACS PRF, DOE
Kelly BeckerMozhgan AlimohammadiMaria MignognaDerek TriplettYogesh TiwaryDr. Hong-Fei WuDr. Yushan WangDr. Leonidas GergidisJosh Howe
AlumniDr. Radu “Alex” MironDr. Jee-Ching WangDr. Som PalFritz-Haber-InstitutProf.-Dr. Matthias SchefflerDr. Rossitza PentchevaDr. Thomas HammerschmidtDr. Peter Kratzer
