PowerPoint Presentation Accelerated Molecular Dynamics Methods

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Temperature Accelerated Dynamics
A web-based presentation Arthur F.
Voter Theoretical Division Los Alamos National
Laboratory Los Alamos, New Mexico USA Work
supported by DOE/BES
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Infrequent-Event System
The system vibrates in 3-N dimensional basin many
times before finding an escape path. In
temperature accelerated dynamics (TAD), we raise
the temperature to quickly find a few escape
events. Using temperature extrapolation, we
determine which event would have happened first
at the low temperature.
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Temperature Accelerated Dynamics (TAD)

• Concept
• Raise temperature of system to make events occur
  more frequently. Filter out the events that
  should not have occurred at the lower
  temperature.
• Assumptions
• - infrequent-event system
• - transition state theory (no correlated events)
  
• - harmonic transition state theory (gives
  Arrhenius behavior)
• k n0 exp-DE/kBT
• - all preexponentials (n0) are greater than nmin

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TAD Procedure

• - Run MD at elevated temperature (Thigh) in state
  A.
• - Intercept each attempted escape from basin A
• - find saddle point (and hence barrier height)
• (e.g., using nudged elastic band method of
  Jonsson et al).
• - extrapolate to predict event time at Tlow.
• - Reflect system back into basin A and continue.
• - When safe, accept transition with shortest time
  at Tlow.
• - Go to new state and repeat.

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• Finding the saddle point

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TAD temperature-extrapolated time
Because each rate is assumed to be
Arrhenius, k n0 exp-DE/kBT , the time
for each particular event at high T can be
extrapolated to low T tlow thigh
expDE(1/kBTlow- 1/kBThigh) . This time is
sampled correctly from the exponential
distribution at low T, mapped from the high T
sample
phigh(t)
thigh
tlow
plow(t)
t
t
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• The Arrhenius view

when can we stop?
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• The confidence line

(or d 1-f)
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• TAD - when we can stop the MD and accept an event

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MDTAD metal deposition simulation

• MD for each deposition event (2 ps)
• TAD for intervening time (1 s)
• Embedded atom method (EAM) for fcc metals
  (e.g., Cu, Ag, LANL fit)

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MDTAD deposition of Cu/Cu(100)
T77K, flux 0.04 ML/s, matching deposition
conditions of Egelhoff and Jacob (1989).
boost factor 107
Tim Germann Francesco Montalenti
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MDTAD deposition of Cu/Cu(100)

• Concerted events observed at T77K and T100K

Tim Germann Francesco Montalenti
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Ag/Ag(100) deposition, MDTAD

• Deposition flux 0.07 ML/s. Embedded-atom
  method potential.
• Perpendicular steering effect gives roughness at
  very low incoming K.E.
• Activated processes reduce this roughness as T is
  raised.

Montalenti, Sorensen and Voter, Phys. Rev. Lett.,
87, 126101 (2001)
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MDTAD deposition of Cu/Ag(100)
T77K, flux 0.04 ML/s, matching deposition
conditions of Egelhoff and Jacob (1989).
1 ML (25 seconds)
Second-layer Cu atoms exhibit novel mobility at
T77K, due to epitaxial strain of Cu on Ag(100).
Sprague, Montalenti, Uberuaga, Kress and Voter,
Phys. Rev. B, in press, 2002.
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Buckyball with a Vacancy using TAD
t0.0 s
t2.2x10-4 s
t1.3x10-4 s
t2.3x10-2 s
t2.3x10-2 s
t2.3x10-2 s
High Temperature 3000K Low Temperature
1000K States Visited 38 Total Time
2.3x10-2 s Boost 1.5x106 B.P. Uberuaga,
S.J. Stuart, and A.F. Voter (2002)
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TAD Nanotube fragment to almost-buckyball
High Temperature 3000K Low Temperature
1500K States Visited 680 CPU Time 297
hours Total Simulation Time 14 ms Boost 127
Equivalent Unboosted CPU Time 1.7 years B.P.
Uberuaga et al (2002)
t0.0 s
t49 ns
t54 ns
t200 ns
t207 ns
t14 ms
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• THE END