DFTB-based QM/MD simulations of nanostructure formation processes far from thermodynamic equilibrium Stephan Irle, Zhi Wang, Guishan Zheng,

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DFTB-based QM/MD simulations of nanostructure
formation processes far from thermodynamic
equilibrium Stephan Irle, Zhi Wang, Guishan
Zheng, Keiji Morokuma ACS Natl.
Fall Meeting SF, COMP 159, 9/12/2006
Now PD at UIUC
Morokuma Group Computational Nanomaterials
Research Team Kyoto University Emory University
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Ignis mutat res - Fire transmutes
everything Alchimistic maxim
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The maintenance of organization in nature is not
- and cannot be - achieved by central management
order can only be maintained by
self-organzation. Briebacher, Nicolis, Schuster
Report EUR 16546 (1995)
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Overview

1. General features and properties of systems far
   from thermodynamic equilibrium
2. The Shrinking Hot Giant road of fullerene
   formation Simulations and indirect evidence
3. Sc-metallofullerene formation following the
   Shrinking Hot Giant road
4. Catalyst-free CNT growth from SiC with chirality
   preference as consequence of surface patterning
5. TM-catalyzed nucleation of carbon nanotubes
   overview and perliminary simulations
6. Summary

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1. General features and properties of systems far
   from thermodynamic equilibrium
2. The Shrinking Hot Giant road of fullerene
   formation Simulations and indirect evidence
3. Sc-metallofullerene formation following the
   Shrinking Hot Giant road
4. Catalyst-free CNT growth from SiC with chirality
   preference as consequence of surface patterning
5. TM-catalyzed nucleation of carbon nanotubes
   overview and perliminary simulations
6. Summary

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Centrally managed C60 formation models
Hypothetical mechanisms relying on more or less
sound assumptions no intermediate species
experimentally confirmed so far. Underlying
assumption of structural order Systematic
construction from smaller fragments or collapse
of highly pre-organized structures. No
experimental or theoretical verification !
(Cn)x
C60
Scheme from Yamaguchi, T. Maruyama, S. JSME
1997, 63-611B 2398
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Dissipative structures vs the arrow of time
Examples for order created dynamically out of
chaos in open systems Dissipative structures
without associated single potential energy
function
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System bifurcations, irreversible processes, and
symmetry breaking
Ilya Prigogine et al., George M. Whitesides et al.
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Order out of chaos List of ingredients
Ilya Prigogine et al., George M. Whitesides et al.

• Open systems far from thermodynamic equilibrium
  which can exchange matter and energy with
  environment

• Non-linearity through turbulent behavior and/or
  auto-catalysis, giving rise to bifurcation and
  symmetry breaking

• Irreversible processes manifesting (freezing)
  ordered spontaneous structures (irreversibility
  resulting from random processes as a consequence
  of the 2nd law)

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1. General features and properties of systems far
   from thermodynamic equilibrium
2. The Shrinking Hot Giant road of fullerene
   formation Simulations and indirect evidence
3. Sc-metallofullerene formation following the
   Shrinking Hot Giant road
4. Catalyst-free CNT growth from SiC with chirality
   preference as consequence of surface patterning
5. TM-catalyzed nucleation of carbon nanotubes
   overview and perliminary simulations
6. Summary

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Carbon-based nanostructured systems All sp2
carbon networks Need for full quantum chemical
treatment of electronic wavefunctions
Example 2 QM/MM is bad for SWNT
functionalization studies (Kar et al. CPL 392,
176 (2004) Bauschlicher et al. PRB 68, 035433
(2003))
COMP 396 (Th)
Patch models, ONIOM(QMMM)
Example 3 MM/MD (REBO) is much slower than
QM/MD, predicts more sp3 defects!
Maruyama et al.
REBO MDs Timescale 10 ns
Ding et al. JPCB, 108, 17369 (2004).
DFTB-based QM/MDs Timescale 100 ps
REBO MDs Timescale 10 ns
Raty et al. PRL 96, 096193 (2005)
Raty et al. PRL 96, 096193 (2005)
DFT CPMD, Timescale 10 ps
Morokuma et al.
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DFTB/MD simulation of high-T carbon chemistry

• DFTB calculates the force on the fly during MD
• (roughly speaking, 103 slower than MM 103
  faster than DFT)
• Velocity Verlet Integrator (step size 50 au
  1.2 fs)
• Isokinetic ensemble Velocity is universally
  scaled at averagely every five steps (10 scaling
  after every ten steps randomly 10 scaling)
  (currently)
• Code is parallelized on EMSLs MPP2 but scales
  well only from 400 atoms

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Fullerene Isomer Geometries and EnergeticsG.
Zheng, S. Irle, K. Morokuma, TACC04 Symposium
Proceedings
What about non-cage carbon cluster structures?
Some C28 isomers as example (from Scuseria, CPL
301, 98 (1999))
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Fullerene Isomer Geometries and EnergeticsG.
Zheng, S. Irle, K. Morokuma, TACC04 Symposium
Proceedings
Wrong minimum structures!
AM1 and PM3 are performing very bad! DFTB
includes effects of polarization functions
through parameterization
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C60 The Beginning
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The Shrinking Hot Giant road of C60 fullerene
formation
IZM Nano Lett. 3, 1657 (2003), ZIM JCP 122, 14708
(2005) IZWM JCPB 110, 14531 (2006), ZWIM JNN, in
press IZWM Carbon, submitted
octopus on a rock
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Linear polyyne chains are highly reactive and
auto-catalytic

• Wakabayashi flashing carbon
• initial nucleus formation statistic event,
  amplified
• sp--gtsp2 hybridization highly exothermic,
  because of high backward barrier irreversible
• gt sp2-graphene growth irreversible, larger
  surface area increases catching rate of C2 and
  other Cn fragments (autocatalysis)
• larger ??system is synergistically stabilized
  (autocatalysis)
• autocatalytic self-healing with carbon adatoms
  (Heggie et al., Science 2002)

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Schematics of Size Up approach - self-assembly
through a sequence of irreversible processes
IZWM JPCB 110, 14531 (2006)
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Analysis of Size-Up PES, comparison w/ first
principles DFT
Approach followed here DFTB opt, PBE//DFTB MD
snapshot (i.e., PBE should follow QM/MD profile)
T3000 K
T2000 K
S3

• Observations
• Energy increases when high-energetic C2 units
  are added, driving force of reaction
• PBE energetic follows nicely DFTB energetic
• DFTB opt. energetic is largely smoothed out but
  all the way downhill!

IZWM Carbon, submitted
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Typical unsuccessful (unfinished) trajectories
- Junk in soot (70 S, 95 W trajectories)
U7z sideview
U7z frontview
5MR6MR 0.42

bold successful, plain unfinished
SWZM, Carbon, submitted
High pentagon/hexagon ratio not necessarily
important for successful cage formation! Initial
entanglement more important!
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Continued heating of successful S-type (high
density) Size-Down trajectories (old) -
Smalleys shrink-wrap-like
G. Zheng, S. Irle, K. Morokuma, JCP 122, 014708
(2004)
C1440C

S1
C1450C
198.0
C14617C
8.1
15.1
33.5
3.5
20/34/11
23/39/8
19/37/11
T 3000 K
C1820C
1.2

C1860C
S2
21/54/13
24/52/14
C1857C
3.7
20.6
196.0
23/50/12
C1190C



S3

19/36/7

44.1
14/42/2
C14729C
11.5
19.9
C1310C
196.0
2.8
20/32/11
C2000C
C2080C

S4
25/57/15
26/52/18
29/54/15
16.5
15.4
C2080C
196.0
C12439C

0/0/0
S5




t ps
7.2
46.8
23.0
14.5
0.6
17/32/8
10.0
10.0
5.0
15.0
0.0
20.0
200.0
45.0
Very expensive calculations!
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C2 pop-out on kinks of giant fullerenes W53
MANY OTHERS
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Experimental evidence for carrier-gas assisted
giant fullerene shrinking
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Cooling carbon vapor and our modeling of
non-equilibrium
Temporal photo emission profiles of
laser-generated carbon vapor
1C 2C2 3C3
0 mm
2.5 mm
5 mm
Monchicourt, PRL 66, 1430 (1990)
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Experimental MS distributions of carbon cluster
products
W53 C67 Size-Down
Fuel combustion flame, conditions optimized for
largest C60 yield jumps in steps of C2
S3 C147 Size-Up
S4 C208 Size-Up
Johnson et al., Carbon 40, 189 (2002)
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C60 The End
C60 is the smallest IPR-obeying carbon
cage Carbon soccerball!!
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Speculative state diagram for carbon in
dependence of distance from thermodynamic
equilibrium
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Summary of the Shrinking Hot Giant Road

• Open system far from thermodynamic equilibrium
  which can exchange matter and energy with
  environment by means of intermolecular collisions

• Irreversible processes manifesting (freezing)
  ordered spontaneous structures Csp?Csp2 cage
  closing C2 evaporation

• Fullerene formation is first case of
  intramolecular dynamic self-assembly as
  dissipative structure!

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1. General features and properties of systems far
   from thermodynamic equilibrium
2. The Shrinking Hot Giant road of fullerene
   formation Simulations and indirect evidence
3. Sc-metallofullerene formation following the
   Shrinking Hot Giant road
4. Catalyst-free CNT growth from SiC with chirality
   preference as consequence of surface patterning
5. TM-catalyzed nucleation of carbon nanotubes
   overview and perliminary simulations
6. Summary

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DFTB-based QM/MD simulation of metallo-GF
formation following the SHG Road
M-X (XC,H,O,N) Parameterization model systems
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DFTB-based QM/MD simulation of metallo-GF
formation following the SHG Road
Sc-C Parameterization large model systems
B3LYP data from Redondo et al., JPCA 109, 8504
(2005)
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Benjamin Finck
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Sc-entrapment in S3 trajectory at 2000 K
0 ps
1.3 ps
0.7 ps
12.1 ps
36.5 ps
27.8 ps
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(No Transcript)
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Mechanism of Sc entrapment in metallo-GFs

• metal entrapment is an even rarer event than C60
  formation yields are 5 of empty cages
• gt starting from S3 at 40 ps
• T 2000 K and 3000 K, at 3000 K no Sc entrapment
  observed
• Sc seems to like attachment to polyyne chains
  to make Sc-C ??bonds, but not always
• Maruyama et al. already noted preference of Sc
  for location at the opening
• Out of 10 trajectories at 2000 K, only one
  successful entrapment process observed!

Maruyama et al. Eur. Phys. J. D 9, 385 (1999)
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1. General features and properties of systems far
   from thermodynamic equilibrium
2. The Shrinking Hot Giant road of fullerene
   formation Simulations and indirect evidence
3. Sc-metallofullerene formation following the
   Shrinking Hot Giant road
4. Catalyst-free CNT growth from SiC with chirality
   preference as consequence of surface patterning
5. TM-catalyzed nucleation of carbon nanotubes
   overview and perliminary simulations
6. Summary

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CNT nucleation on SiC (000-1) surface
Si-face/C-face DFTB-based QM/MDs
High energy species!
High energy species!
Si-face
C-face
S. Irle, Z. Wang, G. Zheng, K. Morokuma, M.
Kusunoki, ACS Division of Fuel Chemistry (2006),
51(1), 264-265 S. Irle, Z. Wang, G. Zheng, K.
Morokuma, M. Kusunoki, JCP, 125, 044702/1-5 (2006)
Kusunoki et al. APL 77, 531 (2000)
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Origin of Cap Formation and Chirality Preference

1. Easy Cap formation on C face due to strong C-C
   ?-bond formation
2. Repulsion from Si face due to stronger C-C
   ?-conjugation, weaker Si-C bond --gt Roll up,
   parallel CNT growth or large diameter caps

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Remove the whole Si layer suddenly at 2000 K on C
face magic carpet
COMP 126, Mo
0ps, cap
6 ps, remove Si
18 ps, end of 1 cycle
24 ps, remove Si
36 ps, end of 2 cycle
18 ps, add 1 layer SiC
54 ps, 3 cycle
72 ps, 4cycle
90 ps, 5 cycle
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1. General features and properties of systems far
   from thermodynamic equilibrium
2. The Shrinking Hot Giant road of fullerene
   formation Simulations and indirect evidence
3. Sc-metallofullerene formation following the
   Shrinking Hot Giant road
4. Catalyst-free CNT growth from SiC with chirality
   preference as consequence of surface patterning
5. TM-catalyzed nucleation of carbon nanotubes
   overview and perliminary simulations
6. Summary

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New Parameter Performance (Fe) Scooter-like
benchmark
DFTB very often overbinding, but trends OK!
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New Parameter Performance (Co) Scooter-like
benchmark
DFTB very often overbinding, but trends OK!
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New Parameter Performance (Ni) Scooter-like
benchmark
DFTB very often overbinding, but trends OK!
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SWNT Nucleation Studied on Fe, Ni and Co TM38
Clusters 24 C2

• Target Temperatures 1100 K, 1200 K, 1400 K,
  1500 K
• Periodic boundary conditions
• Runtime of simulations 9 ps only (so far)

Co38
1200 K, 9.6 ps
9.6 ps
1100 K
Ni38
VLS Model valid for Co or Ni or Co/Ni?
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SWNT Nucleation Studied on Fe, Co and Ni

• Temperatures around 1200 K seem to be OK, higher
  T damages carbon network
• Fe does not show signs of C to diffuse inside, Co
  does, Ni maybe
• C30 cap partially destroyed and dissolved in Co
  case
• Additional C2 molecules are needed to observe
  further growth.
• Substrate may be needed to prevent encapsulation
  of metal particle (catalyst death).

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Summary

• Introduction of temperature gradient (NE
  conditions) by means of shock-cooling of
  high-energy species fast process, structures
  self-assemble rapidly, perhaps too fast

• DFTB ideal quantum chemical potential for ns
  and perhaps longer simulations of C-C and Si-C
  systems, the best we got for TM-C

• If things occur predominantly in nature, there
  is a good chance that they can be observed in
  relatively short QM/MD simulations

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Das Einfache ist das Siegel des Wahren -
Simplicity is the seal of approval for truth
Inscription in Göttingens Physics Auditorium
Pulchritudo splendor veritatis - Beauty is the
splendor of truth
Chemistry is a madmans passion G.-F. Venel in D.
Diderots LEncyclopédie, (1750-1765)
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Acknowledgements
Mitsubishi Chemical Corporation ACS Petroleum
Research Funds AFOSR DURIP EMSL Grand Challenge
GC3564 Pacific Northwest National
Laboratory ORNL NTI CNMS
Morokuma Computational Nanomaterials Research
Team Website http//euch4m.chem.emory.edu/nano
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How good is DFT or MP2?C20 as problematic example
lowest isomer lt higher isomer lt highest isomer
Ring
Bowl
Cage