Ch121a Atomic Level Simulations of Materials
and Molecules
Room BI 115
Lecture: Monday, Wednesday Friday 2-3pm
Lecture 7, April 21, 2013
Reactive Force Fields – 1: ReaxFF
William A. Goddard III, wag@wag.caltech.edu
Charles and Mary Ferkel Professor of Chemistry,
Materials Science, and Applied Physics,
California Institute of Technology
TA’s Jason Crowley and Jialiu Wang
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1
Homework and Research Project
First 5 weeks: The homework each week uses generally available computer software
implementing the basic methods on applications aimed at exposing the students to
understanding how to use atomistic simulations to solve problems.
Each calculation requires making decisions on the specific approaches and parameters
relevant and how to analyze the results.
Midterm: each student submits proposal for a project using the methods of Ch121a to
solve a research problem that can be completed in the final 5 weeks.
The homework for the last 5 weeks is to turn in a one page report on progress with the
project
The final is a research report describing the calculations and conclusions
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2
ReaxFF: first principles force field
Bridging the Gap between QM and MD to
describe reactive processes ranging from
combustion to catalysis, fuel cells,
nanoelectronics, and shock induced chemistry
471. ReaxFF: A Reactive Force Field for Hydrocarbons
A.C.T. van Duin, S. Dasgupta, F. Lorant and W. A. Goddard III
J. Phys. Chem. A, 105: (41) 9396-9409 (2001)
514. ReaxFF sio Reactive Force Field for Silicon and Silicon Oxide Systems
Adri C. T. van Duin, Alehandro Strachan, Shannon Stewman, Qingsong Zhang,
Xin Xu, and William A. Goddard, III
J. Phys. Chem. A, 107, 3803 (2003)
533. Shock waves in high-energy materials: The initial chemical events in
nitramine RDX
Strachan A, van Duin ACT, Chakraborty D, Dasgupta S, Goddard WA
Physical Review Letters,
91 (9): art. no. 098301 (2003)
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Motivation: Design Materials, Catalysts, Pharma from 1st
Principles so can do design prior to experiment
To connect 1st Principles (QM) to Macro work use an overlapping hierarchy of
methods (paradigms)
Need accurate force fields (potentials) with parameters
derived from first-principles QM
time
ELECTRONS ATOMS
GRAINS
GRIDS
hours
Continuum
(FEM)
millisec
Micromechanical modeling
Protein clusters
MESO
nanosec
MD
picosec
Deformation and Failure
Protein Structure and Function
QM
femtosec
simulations real devices and
full cell (systems biology)
distance
Å
nm
micron
mm
Big breakthrough making FC simulations
yards practical:
Accurate calculations for bulk phases
reactive force fields based on QM
and molecules (EOS, bond dissociation)
Describes: chemistry,charge transfer, etc. For
Chemical
Reactions (P-450© oxidation)
metals,
oxides,
organics.
L10-2013-Ch121A-Goddard
copyright 2013 William
A. Goddard
III, all
rights reserved
Ordinary Force Fields
Bonds, angles, torsions described as elastic springs
r
A
E = kA(A-A0)
E = kr(r-r0)
Fixed charges, Empirical vdw nonbond terms,
Bonds cannot be broken, making the model unsuitable for modeling
reactions.
Examples: MM3, Dreiding, Amber, Charmm, Gromos, UFF
ReaxFF:
Allow bonds to break and form and describe barriers for reactions.
All parameters from quantum mechanics, no empirical data
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ReaxFF reactive force field for Reactive Dynamics
(RD)
Allow bonds to break and form, describe barriers for reactions.
All parameters from quantum mechanics (no empirical data)
ReaxFF describes reactive processes (from oxidation to
combustion to catalysis to shock induced chemistry) for 1000s
to millions atoms
We use ReaxFF to prepare the structures of complex
heterogeneous systems by processes similar to experimental
synthesis (DLC, SiO2/Si)
Adri van
Duin
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First Principles Reactive force fields: strategy
• Describe Chemistry (i.e., reactions) of molecules
-Fit QM Bond dissociation curves for breaking every type of bond
(XnA-BYm), (XnA=BYm), (XnA≡BYm)
-Fit angle bending and torsional potentials from QM
-Fit QM Surfaces for Chemical reactions (uni- and bi-molecular)
-Fit Ab initio charges and polarizabilities of molecules
•Pauli Principle: Fit to QM for all coordinations (2,4,6,8,12)
•Metals: fcc, hcp, bcc, a15, sc, diamond
•Defects (vacancies, dislocations, surfaces)
•cover high pressure (to 50% compression or 500GPa)
•Generic: use same parameters for all systems (same O in O3, SiO2,
H2CO, HbO2, BaTiO3)
Require that One FF reproduces all the ab-initio data (ReaxFF)
Most theorists (including me) thought that this would not be possible,
but
we claim to have achieved
it for
many
systems
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© copyrightand
2013 validated
William A. Goddard
III, all
rights reserved
Many Chemical processes: bond breaking for
5000millions atoms. This is far too large for DFT
Solution: ReaxFF first principles reactive force field
EE
Val
Valence energy
E
Coul
E
VdW
Electrostatic energy
short distance Pauli Repulsion
+ long range dispersion
(pairwise Morse function)
•Based completely on First Principles QM (no empirical parameters)
•Valence Terms (EVal) based on Bond Order: dissociates smoothly
• Bond distance  Bond order  Bond energy
•Forces depend only on geometry (no assigned bond types)
•Allows angle, torsion, and inversion terms (where needed)
•Describes resonance (benzene, allyl)
•Describes forbidden (2s + 2s) and allowed (Diels-Alder) reactions
•Atomic Valence Term (sum of Bond Orders gives valency)
•Pair-wise Nonbond Terms between all atoms (no “bond” exclusions)
•Short range Pauli Repulsion plus Dispersion (EvdW)
•QEq Electrostatics allows charges to flow depending on
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2013 William A. Goddard III, all rights reserved
environment and external
fields
Charge Equilibration for Molecular
Charge Equilibration (QEq) Dynamics Simulations
A. K. Rappé and W. A. Goddard III
•Self-consistent Charge Equilibration (QEq) J. Phys. Chem. 95, 3358 (1991)
•Describe charges as distributed (Gaussian)
•Thus charges on adjacent atoms shielded
(interactions  constant as R0) and include
interactions over ALL atoms, even if bonded (no
exclusions)
•Allow charge transfer (QEq method)
atomic
interactions
I
1 2

E {qi }J ij (qi ,q j ,rij )  i qi  J i qi 
2

i j
i 


E int rij , Qik , Q lj 

Erf 

ij kl
ij kl
rij

rij 

Qik Qkl
Keeping:
q Q
i
i
Hardness (IP-EA)
Jij
1/rij
Electronegativity (IP+EA)/2
rij
r i0 + r j0
Three universal parameters for each element:  io , J io , Ric , Ris & qic
1991:
use experimental©IP,
EA,2013
Ri; William
ReaxFF
getIII, from
fitting QM
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copyright
A. Goddard
all rights reserved
Bond distance
Bond distance
bond order
bond energy
bond order

 ro

BO ij exp  p bo,1 
r

 ij





pbo, 2 

 exp  p  ro ,

 bo,3  rij







p bo, 4 

 exp  p  ro ,

 bo,5  rij







pbo, 6 



4
3
Bond order
C-C bond


s
2
Use general functional form.
Determine parameters from
fitting QM bond breaking for
many single, double, and triple
bonded systems. Bond distance (Å)
100
1
0
1
1.5
2
2.5
Bond distance (Å)
Bond order
bond energy
3
Bond energy (kcal/mol)
0
 1  BO 
E
bond   De  BOij  exp p
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1
1.5
2
2.5
-100
-200
Sigma energy
Pi energy
-300
pbe, 2
,1 William A. Goddard
ij
© copyrightbe
2013
III, -400
all rights reserved
Double pi energy
Total bond energy
f7
vdW Energy
6.4
f7(r_ij)
5.4
4.4
3.4
2.4
1.4
0.50
1.50
2.50
3.50
4.50
5.50
6.50
r_ij
E_vdW
200
E (kcal/mol)
150
100
50
0
1.4
2.4
3.4
4.4
-50
f(r_ij)
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5.4
Key features of ReaxFF
-To get a smooth transition from nonbonded to single, double and
triple bonded systems ReaxFF employs a bond length/bond order
relationship1,2. Bond orders are updated every iteration.
- Nonbonded interactions (van der Waals, Coulomb) are
calculated between every atom pair, irrespective of connectivity.
Excessive close-range nonbonded interactions are avoided by
shielding.
- All connectivity-dependent interactions (i.e. valence and torsion
angles) are made bond-order dependent, ensuring that their
energy contributions disappear upon bond dissociation.
- ReaxFF uses a geometry-dependent charge calculation scheme
(EEM) that accounts for polarization effects.
1:Tersoff,
2:
PRB 1988;
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Brenner
PRB
© copyright
20131990
William A. Goddard III, all rights reserved
General rules ReaxFF
MD-force field; no discontinuities in energy or forces even during
reactions.
User does not pre-define reactive sites or reaction
pathways; ReaxFF automatically handles
coordination changes associated with reactions.
Each element is represented by only 1 atom type in the force field;
force field determine equilibrium bond lengths,
valence angles etc. from chemical environment.
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ReaxFF uses generic rules
for all parameters and functional forms
ReaxFF automatically handles coordination changes and
oxidation states associated with reactions, thus no discontinuities
in energy or forces.
User does not pre-define reactive sites or reaction pathways
(ReaxFF figures it out as the reaction proceeds)
Each element leads to only 1 atom type in the force field. (same O
in O3, SiO2, H2CO, HbO2, BaTiO3) (we do not pre-designate the
CO bond in H2CO as double and the CO bond in H3COH as single
or in CO as triple, ReaxFF figures this out)
ReaxFF determines equilibrium bond lengths, angles, and
charges solely from the chemical environment.
Require that One FF reproduces all the ab-initio data (ReaxFF)
Most theorists (including me) thought that this would be impossible,
hence it would never have been funded by NSF, DOE, or NIH since it
was
far too risky. (DARPA
came2013
through,
then ONR,
then
ARO).
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© copyright
William A. Goddard
III, all rights
reserved
Current applications of ReaxFF
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Catalysts: Pt-Co Fuel cell cathode, Pt-Ru FC anode
VOx catalyzed oxidative dehydrogenation: propane to propene
MoVNbTaTeOx ammoxidation catalysts (propaneacrylonitrile)
Ni,Co,Mo catalyzed growth of bucky tubes
Metal alloy phase transformations (crystal-amorphous)
Si-Al-Mg oxides: Zeolites, clays, mica, intercalated polymers
Gate oxides (Si-HfO2, Si-ZrO2, Si-SiOxNy interfaces)
Ferroelectric oxides (BaTiO3) domain structure,
Pz/Ez Hysteresis Loop of BaTiO3 at 300K, 25GHz by MD
Decomposition of High Energy (HE) Density Materials (HEDM)
MD simulations of shock decomposition and of cook-off
MD elucidation of the origins of sensitivity in HE materials
Reaction Kinetics from MD simulations (oxidations)
ADP-ATP hydrolysis
Enzyme Proteolysis
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Coulomb interacions
Include Coulomb for 1-2 and 1-3 interactions since bonded atoms
may dissociate and nonbonded atoms may bond during the
dynamics
1
ECoulomb  C 
qi  q j
f 7 rij 
3 3


3  1 
f 7 rij   rij   

  w  
This f7 function provides shielding so that the Coulomb potential
goes to a constant, Cqiqj w at small R, where w is related to the
size of the atoms.
ReaxFF uses the Electron






2

Equilibration Method (EEM) of Mortier
i
i qi
to determine charges rather than
rather than QEq
Electronegativity
Mortier, W. J.; Ghosh, S. K.; Shankar, S. J. Am. Chem. Soc. 1986,108,
Hardness
4315; Janssens, G. O. A.; Baekelandt, B. G.; Toufar, H.; Mortier, W.
J.;Schoonheydt,
R. A. J. Phys. Chem.
1995,
99,William
3251. A. Goddard III, all rights reserved
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© copyright
2013

j i
qj
Rij
Discussion about charges in ReaxFF
I believe that the use of a shielding denominator in the Coulomb
energy and the use of EEM in ReaxFF are inconsistent and a
fundamental mistake.
We should use QEq. In QEq the shielding of charges on different
centers is built in both in calculating the Coulomb energy and in
calculating the charges.
Separating them leads to potential problems for small R, where
the charges may be affected by the 1/R form in the potential.
In QEq this shielding is based on the covalent radius of the atom
and hence need not be optimized.
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Bond Order Dependence on r (CC)
Bond Order
BO-sigma
3.0
Value
2.5
BO-pi1

2.0
BO-pi2

Total
1.5
s
1.0
0.5
0.0
0.50
1.00
1.50
2.00
2.50
r
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3.00
Bond Order Dependent Potentials
pbo, 2


 rij
 rij  
BO ij  exp  pbo,1     exp  pbo,3   


 r0  
 r0




pbo, 4



 rij
 exp  pbo,5   


 r0

Ebond   De  BOij  exp pbe,1  1  BO
pbe, 2
ij
• Sigma Bond 1.5Å - 2.3Å
• First Pi Bond 1.2Å - 1.75Å
• Second Pi Bond 1.0Å - 1.4Å
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




pbo, 6



Bond Energy
CC Bond Dissociation Energy
200
E (kcal/mol)
100
Experiment
0
-100
E_vdW
-300
-400
0.50
Mol. Eb
E_bond
-200
C2H6 90.4 - 1.533
C3H8 85.8 - 1.526
C4H10 86.5 - 1.532
Total E_bond
1.00
1.50
2.00
2.50
3.00
r
In ReaxFF the BO-BE
term is monotonic and
attractive, becoming a
constant at small R
Bond Energy
0
E (kcal/mol)
This is balance by the
vdW term which is large
and repulsive at small R
re
-50
-100
-150
-200
-250
1.00
1.10 1.20
1.30 1.40
1.50 1.60
r
1.70 1.80
To finally give the normal
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bonding
function.
1.90 2.00
Van der Waals
Include vdW for 1-2 and 1-3 interactions since bonded
atoms may dissociate and nonbonded atoms may bond
during the dynamics
We use a Morse function rather than LJ12-6 (which is too
stiff in the inner wall region
Or exponential-6 which has problems for small R
EvdW


f 7 rij  
f 7 rij  


 
  2  exp 0.5  ij  1 

 Dij  exp  ij  1 
rvdW 
rvdW 




 
Here f7 was introduced to modify interactions for small R
This was a mistake and should be eliminated
1
L10-2013-Ch121A-Goddard
3 3


3  1 
f 7 rij   rij   
w  


 III, all rights reserved
© copyright2013 William A. Goddard
Coordination
• Deviation of bond orders from saturation
i  Vali 
nbond
 BO ;Val  C  4; H  1
j 1
ij
i


1
• Over-coordination

Eover   pover   i  
 1  exp i  i  
Penalty Energy
E_penalty (kcal/mol)
120
100
80
60
40
20
0
-3
-2.5
-2
-1.5
-1
-0.5
0
Over coordination (4-BO)
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Under-coordination
Eunder


1

  BOij,  f1 i ,  j 
  punder  1  exp  2   i  
 1  exp  1  i  


f1  i ,  j   exp  3   i   j

2
f1(delta_i,delta_j)
1.0
value
0.8
0.6
0.4
E_under
0.2
0
0.2
0.4
0.6
delta(delta)
0.8
E_under (kcal/mol)
0.0
0.0
-1.0
1
-2.0
-3.0
-4.0
-5.0
-6.0
0
0.2
0.4
0.6
delta_i
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0.8
1
Angle


Eval  f 2 BOij  f 2 BO jk  ka  ka  exp  kb  0  ijk 
2

f 2 BOij   1  exp  5  BOij 
f2(BO_ij)
1.0
0.8
f2(BO_ij)
0.6
0.4
1.0
0.2
0.8
3.0
2.5
2.0
1.5
BO_ij
1.0
0.5
f2
0.0
0.6
0.0
0.4
0.2
0.0
1.0
1.5
2.0
2.5
r_ij
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3.0
Calculation of 0
 0     0, 0 1  exp  7  2  SBO 2

 62 j  nbon( j )
 
SBO   j  2  2  exp 
BOj
 64  


 n 1
SBO2 = 2; SBO>2
SBO2 = 2-(2-SBO)5; 1<SBO<2
SBO2 = SBO 5; 0<SBO<1
2j = j; j < 0
SBO2 = 0; SBO  0
2j = 0; j  0
Theta_0 (degrees)
Equilibrium CCC angle
180
170
160
150
140
130
120
110
100
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Sum of Pi Bond Order
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Eangle
E (kcal/mol)
E_angle CCC
7.0
E_angle
6.0
E_vdw
5.0
Sum
4.0
E_harmonic
3.0
2.0
1.0
0.0
-1.0100
105
110
115
C-C-C angle
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120
Torsion
Etors  f 3 BOij , BO jk , BOkl  f 4  j ,  k *
Sin  ijk  Sin  jkl 


0.5  V2  exp pt ,1  BO jk  2 2  1  Cos 2  ijkl   


0.5  V3  1  Cos3  ijkl 

•V2 diminishes rapidly when central bond deviates from BO=2
•Sin terms ensure this terms goes to 0 when the angles approach 180
•f4 accounts for over-coordinated central C-C atoms
•f3 allows for proper dissociation behavior
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f3


f 3 BOij , BO jk , BOkl   1  exp  8  BOij  
1  exp    BO  1  exp    BO 
8
jk
8
kl
f3
1.0
0.6
F3
0.8
0.4
0.2
3.00
2.50
2.00
1.50
1.00
0.50
0.0
0.00
BO
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
f4
1
f 4  j ,  k  
1  exp  9   j   k   10 
f4
1.0
1.0
f4
0.9
0.9
0.8
0.8
0.7
0
0.5
1
1.5
delta_j+delta_k
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
2
V2
V2 (kcal/mol)
V2_effective
40
35
30
25
20
15
10
5
0
V2_eff CCCC
V2_eff CCCH
V2_eff HCCH
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
BO_jk
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Etors
E_tors
E_tors CCCC
E_tors CCCH
E_tors (kcal/mol)
1.0
E_tors HCCH
0.8
0.6
0.4
0.2
0.0
0
50
100
150
w_ijkl (degrees)
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Conjugation
Econj  f 5 BOij , BO jk , BOkl  f 6 BOij , BO jk , BOkl 
f 7 i ,  j ,  k , l  11  1  Sinijk  Sin jkl * Cos2  ijkl 
E_conj
0.0
0
50
100
150
E (kcal/mol)
-0.4
-0.8
-1.2
-1.6
-2.0
w_ijkl
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Heats of Formation for 40 compounds/radicals
Heats of Formation
Experimental
80
y = 0.972x - 0.7557
R2 = 0.9892
50
20
-10
-40
-70
-70
-50
-30
-10
10
30
50
70
90
Calculated
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Bond dissociation energies
Well Depths
300
250
200
150
100
50
0
N:::N N=N
L10-2013-Ch121A-Goddard
N-N
N=O
N-O N:::C N=C
N-C C:::O C=O
© copyright 2013 William A. Goddard III, all rights reserved
C-O
Bond lengths and r0
Bonds
R_o
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.0
N:::N N=N N-N N=O N-O N:::C N=C N-C C:::O C=O C-O
L10-2013-Ch121A-Goddard
1.5
1.45
1.4
1.35
1.3
1.25
1.2
1.15
1.1
1.05
1
r0
ro,pi
ro,pi,pi
C-N
C-O
C-C
N-N
© copyright 2013 William A. Goddard III, all rights reserved
N-O
O-O
RDX concerted ring breaking
Concerted RDX-dissociation
Energy (kcal/mol)
75
64.6
64.37
50
DFT
25
ReaFF
0
1
2
3
4
C-N distance (Angstrom)
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
5
RDX N-N dissociation
NO2-dissociation from RDX
Energy (kcal/mol)
50
39.00
40
34.00
30
20
ReaFF
DFT
10
0
1
2
3
4
N-N distance (Angstrom)
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
5
HONO elimination
Successive HONO-dissociation from RDX
75
DFT
Energy (kcal/mol)
50
ReaFF
25
0
RDX
-25
RDXHONO+HONO
RDX-2 HONO
+ 2 HONO
TAZ+3 HONO
-50
Reaction Coordinate
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
3 HCN + 3
HONO
DFT Calculation
E (kcal/mol)
TS 14
51.7
TS10
39.2
TS13
52.2
TS11
32.0
MN(74) + 2HCN(27) +
2HONO(47)
24.8
TS12
20.1
RDX
0.0
3HCN(27) + 3HONO(47)
14.2
INT175+HONO
-8.5
INT128+2HONO
-13.0
TAZ +3HONO
-36.4
HONO-Elimination Pathway
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
EoS
Pressure (GPa)
Pressure vs. compression
55 44
ReaFF
40
rdx.ff
18.3
25
7.2
10
-5
0.5
0.6
0.7
2.4
0.6
-0.2
0.8
0.9
1
V/V_0
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
1.1
EoS
Energy vs. compression
2500
ReaFF
E (kcal/mol)
2000
rdx.ff
1500
1000
500
0
-500 0.5
0.6
0.7
0.8
0.9
1
V/V_0
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
1.1
Over-coordination energy and van der Waals
Shielded van der Waals
E vdW
  
rij*
  ij  exp  ij 1 

   rvdW
1 

rij*
  2 exp   ij 1 

 2  rvdW


1 
r   rij3  3 
w 

*
ij
L10-2013-Ch121A-Goddard
1
3
Over-coordination energy
30
20
10
0
3
3.5
-10
4
4.5
5
Total bond order
250
 
 

 
Energy (kcal/mol)
Eover


1


 pover  i 



1

exp


1
i


40
Energy (kcal/mol)
Over-coordination penalty
200
Unshielded van der Waals
150
Unshi
Shield
100
Shielded vdW (w= 0.8)
50
0
-50
1
2
3
C-C distance (Å)
© copyright 2013 William A. Goddard III, all rights reserved
4
Applications to energetic materials
Sergey Zybin, Peng Xu, Yi Liu, Qing Zhang,
Luzheng Zhang, Adri van Duin and William A. Goddard III
- Force field development
- Training sets for HE-materials
- Treating organic crystals
- Overview of past and ongoing applications
- Predicting chemistry : cookoff of RDX, HMX and
TATB and carbon cluster analysis
- Prediction of sensitivity for HE materials
- Energy release: ISP prediction for RDX/Al and
hydrazine materials
- New HE-materials: all-Nitrogen
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Training set for nitramine potential
Bond and angle distortion
Reaction barriers
C-N bond dissociation in
H2C=NH
Nitromethane C-N-O
angle bending
Charge distributions
QM
Mulliken charges
DFT; 6-31G**
ReaxFF charges
+0.35
QM:PETN-I
QM:PETN-II
+0.26
+0.54
+0.12
+0.15
-0.31
+0.14
-0.05
+0.61
-0.49
+0.12
+0.12
-0.31
+0.12
Energy (kcal/mol)
-0.49
+0.26
-0.01
ReaxFF: PETN_I
ReaxFF:PETN-II
200
-0.64 +0.26
+0.14
Condensed
PETN equations of statephase
+0.34
-0.62
-0.57 +0.26
+0.14
First-row elements
150
100
50
-0.47
0
150
200
250
300
3
L10-2013-Ch121A-Goddard
Volume ( /mol)
© copyright 2013 William A. Goddard III, all rights reserved
350
ReaxFF gives accurate description of complex chemical
reactions: Decomposition Mechanism RDX (gas-phase)
NO2 dissociation
100
INT149+
HCN+NO2
80
concerted
60
INT176+
NO2
MN+MNH+
HCN+NO2
RDRo+
NO2
O2N
N
N
N
O
N
RDR+
NO2
NO2
O
H
2MN
+LM2
O
N
40
Energy (kcal/mol)
QM
ReaxFF
New mechanism
O
+N2O
N
O
N
3MN
N
O
HO
H C N
20
MN+LM2+
N2O+H2CO
2MN+N2O+
0
O
-20
RDX
RDX''+2HONO
TAZ+3HONO
-80
N
O
N
O
N
HONO elimination
H2C=O
+N2O
+2 HCN
+2 HONO
O
N
O
N
N
HO
-40
3N2O+3H2CO
O
O
O
N
2H2CO MN+2N2O+
-60
O
N
RDX'+HONO
2H2CO
O
N N
N
H2CO
LM2+2N2O+
+N2O
+HONO
O
+N2O
+HONO
8 membered
ring
N
O
N
NO2
+N2O
+HONO
N
O
N
+N2O
+2 HONO
Concerted, NO2 and HONOReaxFF MD simulation found New
dissociation pathways
unimolecular reaction, confirmed by QM,
(part of the original training set)
More important than concerted pathway
Strachan,
L10-2013-Ch121A-Goddard
Kober, van Duin, Oxgaard ©
and
copyright
Goddard,
2013
J.Chem.Phys
William A. Goddard
2005
III, all rights reserved
RDX shock simulations: MD with ReaxFF
•Simulate High impact shock chemistry using MD simulations
•1st step: thermalize two semi-infinite slabs of RDX (1344 atoms/cell)
•Add the shock velocity on top of the thermal velocities
•Constant NVE molecular dynamics (adiabatic)
∞ Slab: 32 RDX molecules/cell on ∞ Slab: 32 RDX molecules/cell
1 vimpact
2
 1 vimpact
2
Full-physics, full-chemistry simulations of shock induced chemistry
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Hydrocarbon combustion and metaloxide catalyzed hydrocarbon oxidation
Adri, Kimberly Chenoweth, Sanja Pudar, Mu-Jeng Cheng, and wag
cat.
O
+
2 H2O
Selective oxidation of
propene using multiMixed metal oxide catalyst (BixMoyVzTeaOb)
metal oxide (MMO)
catalysts
Develop ReaxFF based
on QM-data , use
ReaxFF to perform
high-temperature
simulations on
catalyst/hydrocarbon
reactions
First, establish that
ReaxFF can describe
non-catalytic
hydrocarbon
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all combustion
rights reserved
+
O2 (air)
Force field development: hydrocarbon oxidation
ReaxFF
QM
QM
Oxidation reactions
ReaxFF
75
75
Energy (kcal/mol)
Cp+O2 singlet
Cp+O2 triplet
25
Benzene+O2 singlet
Benzene+O2 triplet
0
Energy (kcal/mol)
50
50
25
Cp+O2
Benzene+O
Butadiene+
0
Butadiene+O2 singlet
Butadiene+O2 triplet
-25
-25
-50
-50
1
1
1.5
2
2.5
3
3.5
1.5
4
2
2.5
3
3.5
4
C-O distance (
)
C-O distance (
)
QM: Jaguar/DFT/B3LYP/6-311G**
Radical rearrangements
75
Rotational barriers
QM
ReaxFF
H3C• + CO
0
1
2
15
10
5
-180
3
C-C bond distance (angstroms)
L10-2013-Ch121A-Goddard
4
5
45
30
15
0
0
•
H3C-C=O
ReaxFF
60
Energy (kcal/mol)
50
25
QM
ReaxFF
20
Energy (kcal/mol)
Relative Energy (kcal/mol)
QM
Angle strain
-120
-60
0
60
Torsion angle
120
180
50
75
100
O-C-O angle
- total training set contains about 1700 compounds
© copyright 2013 William A. Goddard III, all rights reserved
125
Test ReaxFF CHO-description: oxidation of o-xylene
- Oxidation initiates
with OOH-formation
- Final products
dominated by CO,
CO2 and H2O
Consumed O2
CO2
H2O
CO
o-Xylene
OOH
2 o-Xylene; 70 O2 in 20x20x20 Angstrom box
ReaxFF NVT/MD at T=2500K
L10-2013-Ch121A-Goddard
-Exothermic reaction
-Exothermic events
are related to H2O
and CO2 formation
© copyright 2013 William A. Goddard III, all rights reserved
OH
o-Xylene oxidation: Detailed reaction mechanism
O2
H 2COOH
CH 2
CH 3
HO 2
frame 128
CH 3
O2
O
OH
H 2C=O
OH
CH 3
CH 3
frame 176
CH 2
frame 179
HC=O
OH H O
2
H
OH
H
CO
H 2O
H
H
H
H
H
OH
H 2O
O2
H 2O
frame 209
H
H
CO 2 H 2O
CO
H 2O
O 2H
O
H
CH 2
CO 2 HO 2
H 2O
OH
HO 2
O2
CO
O
H
H
O
O
H
H
H
H
frame 180
frame 193
CO 2
H 2O
H
H
frame 232
OH
CH 2 H O
2
O
frame 205
CO 2
H
O
frame 182
H
H
H
O
O
CH 2
H
H
O
O
H 2C=O
OH
CH 3
O2
O
OH
Kimberly
Chenoweth
- Reaction initiation with HO2formation
- Dehydrogenation occurs at
methyl-groups, not at benzylhydrogens
- Only after H2C=O is formed and
dissociated the benzene ring gets
oxidized
- Ring opens shortly after
destruction of aromatic system
- Ring-opened structure reacts
quickly with oxygen, forming CO2,
H2O and CO
- ReaxFF gives sensible
predictions that can be directly
© copyright 2013 William A. Goddard
all rights reserved
testedIII,
against
QM
H 2CO
frame 176
frame 177
OH
CH 3
frame 175
O
H 2C=O
frame 174
CH 3
H
CO 2
H 2O
CO
H 2O
H
O 2H
O
H
frame 232
O
H
H
H
H
H
H
O
L10-2013-Ch121A-Goddard
O
H 2O
H 2O
frame 234
H
O 2H
CO 2
CO 2 CO
H
H
HC=O
O 2H
H 2O
H 2O
Determining the parameters for ReaxFF:
MoOx
Mo17O47-crystal
(kcal/mol)
Energy
Energy (kcal/mol)
Need to describe the complicated
bonding in MoxOy polymorphs
Step 1: get ReaxFF for MoQCmetal
QM
100
diamond
Simple cubic
fcc
A15
bcc
50
0
5
10
15
20
Volume/Atom
ReaxFF
Energy
(kcal/mol)
(kcal/mol)
Energy
ReaxFF
Simple cubic
50
fcc
A15
bcc
0
5
L10-2013-Ch121A-Goddard
diamond
100
10
© copyright 2013 William A. Goddard III, all rights
reserved
Volume/Atom
15
20
Oxidation of MoO2 slab by O3
Epot (kcal/mol)
-45000
-47500
-50000
-52500
-55000
0
10
20
30
40
50
60
Time (ps)
Initial reaction is fast
Reaction slows down as MoO2
surface gets oxidized
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Analysis MoO2 + O3 simulation
g(r)
Mo-Mo
Mo-O
O -O
Start: Mo64O128 [MoO2]
1
2
3
4
5
6
7
8
r (Å)
Mo=O
g(r)
Mo-Mo
Mo-O
O -O
End: Mo64O175 [MoO2.7]
1
2
3
4
5
r (Å)
6
7
8
ReaxFF predicts correctly the formation of Mo=O surface double bonds
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
ReaxFF for reactions on Pt catalysts
Energy (eV)
4
3
2
Pt crystals
DFT
FCC
HCP
diamond
BCC
Simple cubic
1
0
10
hcp A15
fcc
SC
Dia
A15
bcc
15
20
25
Energy (eV)
4
3
2
ReaxFF
diamond
FCC
HCP
Simple cubic
BCC
SC
1
ReaxFF gives a good description
to the EOS of the stable phases
(FCC, BCC, A15)
ReaxFF properly predicts the
instability of the lowcoordination phases (SC,
Diamond)
Dia
0
10
hcp A15
fcc
A15
bcc
15
20
25
Volume/atom (Å3)
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Test of ReaxFF for Pt metal clusters
Energy (kcal/Pt)
0
QC
-60
ReaxFF
-120
9_10_9
5_10_5
12_7
8_4
6_3
12
8
6
3
1
Cluster description
ReaxFF gives a good description for undercoordinated Pt-systems
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
QC
ReaxFF
HCCH3
CCH2
Hydrocarbon interaction with
35-atom Pt-cluster
Binding energy (kcal/mol)
150
100
50
- ReaxFF can describe different C-Pt bonding modes
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
H2CCH2(II)
H2CCH2(I)
HCCH
H2CCH3
CH3
CHCH2
CH2
CCH
CCH3
C2
CH
C
0
Equation of State for Pt bulk metal oxides
(kcal/mol)
Energy
Ef/Pt (kcal/mol)
QM
PtO (P342mmc)
PtO2 (P3barm1) in ab
PtO2 (P3barm1) in c
PtO2 (Pnnm)
Pt3O4
350
300
250
200
150
100
50
0
-50
10
15
20
25
30
35
40
45
50
55
equations of state for Ptbulk oxides from ReaxFF
are in good agreement
with QM-data
V/Pt ( 3)
Ef/Pt (kcal/mol)
Energy (kcal/mol)
ReaxFF
PtO(P342mmc)
PtO2 (P3barm1) in ab
PtO2 (P3barm1) in c
PtO2 (Pnmm)
Pt3O4
350
300
250
200
150
100
50
0
-50
10
15
20
25
L10-2013-Ch121A-Goddard
30
35
40
45
50
55
V/Pt
( 3)
© copyright
2013 William A. Goddard III, all rights reserved
Also do Equation of State for Bulk metal oxide
phases
(kcal/mol)
Energy
Energy (kcal/mol)
60
ReaxFF MD-NVT
simulation at T=300K
MoO3
40
DFT
ReaxFF
ReaxFF
20
DFT
0
30
40
50
60
70
Volume (Angstrom3)
Do similar calculations on:
MoO2 equation of state
Equilibrium structures of MoO2, Mo8O24, Mo5O8
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Bond dissociation, valence distortions
750
HO-Mo=O angle bending in
cluster (HO)2MoO250
500
DFT singlet
DFT triplet
ReaxFF
DFT S=0
250
ReaxFF DFT S=1
0
1
2
3
4
5
6
Mo-O distance (Angstrom)
Also break Mo-OH bonds,
Mo-CH3 bonds
Mo-H bonds
L10-2013-Ch121A-Goddard
40
(kcal/mol)
Energy
Energy (kcal/mol)
(kcal/mol)
Energy
Energy
(kcal/mol)
Mo=O bond dissociation in MoO3-cluster
30
ReaxFF
20
10
DFT
0
125
Other angle50cases: 75Angle 100
(de gre e s)
Mo-O-Mo
O=Mo=O
HO-Mo-OH
Mo-O-O
Mo-O-H
Mo-O-C
© copyright 2013 William A. Goddard III, all rights reserved
150
Reactions in training set for ReaxFF
Example test:
Oxidation of
MoO2 rutile
using ozone
Energy
(kcal/mol)
(kcal/mol)
Energy
200
150
ReaxF
F
100
DF
T
QM
ReaxFF
50
Mo3O9
3 MoO3
0
1
2
3
4
5
Mo-O distances (Angstrom)
Other reactions considered:
MoO4  MoO3 +O  MoO2 + 2O
 MoO+3O
MoO3 + 0.5 O2  (O-O)MoO2
L10-2013-Ch121A-Goddard
Periodic (a=b=20.69 Å, c=55 Å)
192-atom MoO2-slab + 50 O3
62.5 ps. NVT MD at T = 1000K.
Analyze
final
oxidation state
© copyright 2013 William A. Goddard
III, all
rightsMo
reserved
Reactions of H2 and O2
over Pt(111) surfaces
8 H2 + 4 O 2
8 H2 + 4 O2
Pt(111) perfect
Pt (111) stepped
96 atoms
84 atoms
MD simulation at 1000K
Energy release
perfect
stepped
Perfect surface generates H2O
stepped surface gets oxidized
Energy profile for perfect surface shows
H2O generation events
Have not yet done QM with stepped
surface to compare with ReaxFF
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Vanadium oxide based catalysts
O
Selective oxidation catalyst:
• selective oxidation of o-xylene to phthalic anhydride
• ammoxidation of alkyl aromatics (i.e. toluene, picolines)
• oxidation of benzene, olefins, n-butane (poor selectivity)
• oxidation of butane or hexane to maleic anhydride
Selective catalytic reduction:
• SCR of NOx with NH3
• controlling oxidation of SO2 to SO3 during SCR
Oxidative dehydrogenation(ODH):
• convert alkane to olefin (i.e. propane to propene)
• selective oxidation of methanol to formaldehyde H C OH
3
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
O
O
O
O
O
N
H2C
O
ReaxFF – Vanadium Force Field Development
Bond Dissociations
Angle
Dihedral
Charge
Distributions
• Include bond dissociations, angle and dihedral
distortion energies, charge distributions in
training set for small clusters
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
ReaxFF Development for Bi, Te, V, Nb, Mo oxides
Double Bond Dissociation
ReaxFF
DFT - Singlet
Te(OH)n  Te(OH)n-1 + OH
DFT - Triplet
8080
180
O
7070
O
Bi
140
O
O
O
O
Bi
Bi
O Bi O
120
H
Bi
O
O
O
O
Bi
Bi
O Bi O
5050
100
40
V
O
OH
V
O
O O
O V
O
O
H
H
O
O
V
2020
V
1010
0
00
O-Nb-O Angle Bending
60
V
O
O
O V
H
O
O V
O
H
O
O V
O
V
O
O
O
O
H
H
O
H
O
H
O
H
O
V
O
V
V
O
O V
V
O
O
O
H
QM
H
ReaxFF
O
O
O
Reactioncoordinate
coordinate
Reaction
Mo-O-V Angle Bending
Charge Distributions (VO2OH)
50
40
30
20
10
0
60
80
O
O
O
O
V O
H
O
O
V
H
H
O
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Bi=O Bond Length (angstroms)
O
O
V
H
V
H
O
3030
60
H
V
O
4040
80
20
Relative energy (kcal/mol)
O
6060
O
Energy (kcal/mol)
Energy (kcal/mol)
Relative Energy (kcal/mol)
160
Hydrogen shift in V4O10H
100 120 140 160 180
O-Nb-O Angle (degrees)
Caltech
L10-2013-Ch121A-GoddardMSC, ©
copyright 2013 William A. Goddard III, all rights reserved
H
Derive one FF for V to describe all coordinations in
the metal and oxide and all oxidation states
Metal
FCC,
BCC,HCP,
A15, SC,
Diamond
VO
V2O3
V2O5
V:bcc
VO2
Metal
oxides
Heat of formation (kcal/unit)
100
V(bcc)
0
VO
V2O3
V2O5
V:bcc
100
QM:
SeqQuest
(SNL
Gaussianbased
periodic DFT)
VO2
V(bcc)
0
VO
-100
VO2
VO2
-200
4, 6, 8
Oxygen -300
coordination -400
VO
-100
-200
V2O3
V2O3
-300
-400
V2O5
V2O5
QM
-500
ReaxFF
-500
2
3
4
5
6
7
8
9
10
2
3
4
5
6
7
8
9
10
• Energy difference for oxidation changes is in good agreement with QM data
• Indicates
that ReaxFF is©able
to capture
energetics
ofallredox
reactions
L10-2013-Ch121A-Goddard
copyright
2013 William
A. Goddard III,
rights reserved
ReaxFF Development: Bulk oxides
Heat of formation (kcal/mol)
TeO2
ReaxFF
QM
Density (kg/dm3)
Same ReaxFF describes: Te0, TeII, TeIV, TeVI, Bi0, BiIII, BiV
V0, VIII, VIV, VV, Mo0, MoII,MoIV, MoV, MoVI,
Energy
difference for oxidation changes is in good agreement with QM-data
ReaxFF
able to capture the energetics of redox-reactions at metal oxide surfaces
ReaxFF
slight systematic tendency to overestimate stability of metal oxide phases
PBE GGA exchange-correlation
functional
with
Gaussian
basisIII,
sets
as implemented
in SeqQuest
L10-2013-Ch121A-Goddard
© copyright
2013
William
A. Goddard
all rights
reserved
ReaxFF Development: Propanepropene on V4O10
ReaxFF
QM
V4O10 + O2
+ 2 propane
Binding of O2 displaces
propene product
QM (B3LYP/LACVP**): Cheng, Chenoweth, Oxgaard, van Duin, Goddard JPC-C 2007, 111, 5115.
V4O10 + 2 H2O
+ 2 propene
MSC,QM
Caltech
Kimberly
Chenoweth
L10-2013-Ch121A-Goddard
©
copyright
2013 William
Goddard
III, all rights
reserved pathway
ReaxFF
reproduces
energies
forA.the
entire
reaction
ReaxFF MD Simulation Conditions
Started from a minimized structure
30 methanol molecules
3-layer V2O5 (001) periodic slab
Total number of atoms = 684
Slab Temp = 650K
CH3OH Temp = 2000K
Time step = 0.25 fs
Temperature damping = 100 fs
Total simulation time = 250ps
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
ReaxFF NVT-MD Simulation: Methanol
Oxidative DeHydrogenation (ODH)
30
Methanol
Formaldehyde
H2COH Radical
Water
Others
30
20
Methanol
Formaldehyde
H2COH Radical
Water
Others
25
15
Number of Molecules
Number of Molecules
25
10
5
0
0
50
20
15
10
100
5
150
200
250
Time (ps)
0
0
50
100
150
200
Time (ps)
• methanol converts to formaldehyde with production of water
• Others include the number of hydrocarbons bound to the surface
• Expt.:
Major product is©formaldehyde
(also
H2O,III,CO
x)
L10-2013-Ch121A-Goddard
copyright 2013 William
A. Goddard
all rights
reserved
250
ReaxFF Mechanistic Details
Formation
of H2C-OH
radical
3.45ps
8.80ps
H-abstraction by surface vanadyl groups
L10-2013-Ch121A-Goddard
Formation of
formaldehyde
© copyright 2013 William A. Goddard III, all rights reserved
ReaxFF Validation: H3COH H2C=O on V2O5 (001)
H2O desorption induced by
interlayer binding to convert
VIII … O=VV pair to VIV-O-VIV
NVT-MD simulation at 650K
with 30 CH3OH (at 2000K)
Observe conversion of CH3OH
to CH2O in dynamics
Observe
CH3OH 
CH2O + H2O
Longer
simulation also
leads to COx
Agrees
with Experiment
3.425ps
3.450ps
8.800ps
Chenoweth, van Duin,
Cheng,2013
Persson,
Oxgaard,
Goddard,
in preparation.
L10-2013-Ch121A-Goddard
© copyright
William
A. Goddard
III, all rights
reserved
Desorption of Water from catalyst
Snapshots from simulation showing atoms within 5.5Å of V bound to H2O
1
Water bound
to VIII, bond
very strong,
will not desorb
2
3
2nd layer has
VV=O pointing
at VIII of top
layer
L10-2013-Ch121A-Goddard
2nd layer O
bonds to top V
get VIV-O-VIV
4
5
H2O bonds
weakly to VIV
now desorbs
© copyright 2013 William A. Goddard III, all rights reserved
ReaxFF Validation:
Reaction of Propene on Bi2O3 and MoO3
Propene + Bi2O3 Slab
Propene + MoO3 Slab
1100K
Get abstraction of allylic
hydrogen by bridging oxygen on
amorphous Bi2O3 surface
No formation of oxide products
Agree with experiment
L10-2013-Ch121A-Goddard
No abstraction of allylic hydrogen by MoO3.
No formation of oxide products
Agree
with
experiment
© copyright 2013
William
A. Goddard
III, all rights reserved
ReaxFF Validation:
Oxidation of Propene on Bi2Mo3O12 (010)
H abstracted by Mo=O bond next to Mo-O-Bi
Had expected Bi=O bond to be involved
Allyl subsequently is trapped on a different Mo=O bond
Much Longer times required to observe oxidation of allyl radical
to form acrolein
Goddard, van Duin, Chenoweth, Cheng, Pudar, Oxgaard, Merinov,
Jang, Persson
Topics
Catal.A.38,
2006,III,93.
L10-2013-Ch121A-Goddard
© copyright
2013 in
William
Goddard
all rights reserved
Grasselli et al. 1984
Validation of ReaxFF for Ni and NiC
crystals
Ni Crystals
350
fcc
bcc
diamond
a15
sc
Energy of Formation
(kcal/mol)
Energy of Formation
(kcal/mol)
90
80
70
60
50
40
30
20
10
0
-10 7
300
NiC: B3
NiC: B4
250
Ni2C
Ni3C
200
150
100
50
5
25
45
Volume per Unit Cell (cubic Angstroms)
ReaxFF: NiC Inverse Density vs Energy
a15
sc
350
Energy of Formation
(kcal/mol)
Energy of Formation
(kcal/mol)
50
NiC: B2
12
17
22
Volume per Nickel Atom (cubic angstroms)
fcc
bcc
diamond
60
NiC: B1
0
ReaxFF: Ni Crystal EOS
70
NixC Crystals
QM: NiC Inverse Density vs Energy
QM: Ni Crystal EOS
40
30
20
10
NiC: B1
NiC: B3
Ni2C
300
250
NiC: B2
NiC: B4
Ni3C
200
150
100
50
0
0
7
12
17
Volume per Ni (cubic Angstroms)
L10-2013-Ch121A-Goddard
22
5
25
45
Unit Cell (cubic Angstroms)
© copyright 2013 William A. GoddardVolume
III, all per
rights
reserved
Validation of ReaxFF for binding of C to Ni
surface and Bulk
C Migration in Bulk Ni
Binding Energy (kcal/mol)
160
155
ReaxFF
150
QM
145
140
135
130
125
C oct-subsurf
C oct-bulk
L10-2013-Ch121A-Goddard
C tet-bulk
Reaction Energy (kcal/mol)
C Binding to Ni 111 Subsurface & Bulk
25
ReaxFF
20
QM
15
10
5
0
0
1
2
Reaction Coordinate (Angstroms)
© copyright 2013 William A. Goddard III, all rights reserved
3
50
H Binding to Ni111
Subsurface & Bulk
H Migration in Bulk Ni
ReaxFF
QM
48
Relative Energy
(kcal/mol)
binding energy per nickel
(kcal/mol)
Validation of ReaxFF for binding of H to Ni
surface and Bulk
46
44
42
40
38
3
ReaxFF
2
QM
1
0
-1 0.5
1
1.5
2
2.5
-2
-3
36
H octH tetH tet2subsurf subsurf subsurf
L10-2013-Ch121A-Goddard
H octbulk
H tetbulk
-4
Relaction Coordinate (Angstroms)
© copyright 2013 William A. Goddard III, all rights reserved
3
Validation of ReaxFF for H, C, CHx
binding to Ni(111)
100
ReaxFF
80
QM
60
40
20
0
-20
hc
p
H
2f
H
to
C p
hc
p
C
fc
c
C
2f
C
t
C op
H
h
C cp
H
fc
C c
H
C 2f
H
C top
H
2
C fc c
H
2
h
C cp
H
2
C 2f
H
2
C top
H
3
C fc c
H
3
h
C cp
H
3
C 2f
H
3
to
p
H
fc
c
-40
H
Energy of Formation (kcal/mol)
H, C & CH x Binding to 4 Layer Ni111 Slab
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
50
40
30
ReaxFF
QM
20
10
0
-10
-20
fc
chc
C
p
C
H
fc
chc
p
C
C
H
fc
ct
C
op
C
H
2
fc
cC
to
H
p
C
H
fc
cC
hc
H
p
C
H
2
C
2f
H
-to
2C
p
H
2
fc
C
cH
to
2C
p
H
2
to
pto
p
-30
C
C
Energy of Formation (kcal/mol)
C2Hy Binding to 4 Layer Ni111 Slab
L10-2013-Ch121A-Goddard
Enegy of Formation Relative to
Graphene on Ni111 (kcal/mol)
Validation of ReaxFF for CC bonded species
on Ni(111)
C-C Bond Formation
40
30
ReaxFF
20
QM
10
0
-10
C fcc
CC
fcchcp
C chain
CH
chain
© copyright 2013 William A. Goddard III, all rights reserved
CHCH
fcchcp
CH
Force field development: CxHy-clusters on Ni[111]
QM: SeqQuest (SNL Gaussianbased periodic DFT)
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Reactions of hydrocarbons on Ni468
nanoparticle
Jan. 20, 2010
New paper on ReaxFF
6 cases:
120 methane,
60 ethene,
60 ethyne,
40 propene,
20 benzene,
20 Cylclohexane
Initial and Final structures for ReaxFF RD simulation of 40 propene
molecules adsorbing and decomposing on a Ni468 cluster
L10-2013-Ch121A-Goddard
Ni ©468
particle, 21A diameter
copyright 2013 William A. Goddard III, all rights reserved
Jonathan
Mueller
ReaxFF: Acetylene Adsorption &
Decomposition on Ni468 nanoparticle
T(K)
C2H2,gas
2300
Cad
50
2100
C2H2(g)
C2H2(s)
H2(g)
H
C2H
C2
C
CH
C2H3
T(K)
30
20
TA
1900
H
ad
1700
1500
1300
TC
1100
TH
HCCHad
C2
H2
900
temperature (K)
# of molecules
40
10
10
2500
# of molecules
60
8
6
C2H2(s)
C2H3
C2
CCH
H2(g)
C2H
CH
H2
C2
4
2
0
1300
1500
1700
1900
2100
target temperature (K)
Critical Temperatures
•1st adsorbs at 550 K
•1st H produced at 1050 K
•1st C produced at 1450 K.
700
CCH
0
500
1000
1500
2000
target temperature (K)
L10-2013-Ch121A-Goddard
2300
500
2500
© copyright 2013 William A. Goddard III, all rights reserved
2500
ReaxFF: Acetylene Adsorption &
Decomposition on Ni468 nanoparticle
Start: 60 C2H2
end:
52 Cad + 2 C2H3 gas + 2 C2H2ad + C2Had+C2ad
L10-2013-Ch121A-Goddard
Conclusions
1. Both C-H bonds
break before the C-C
bond breaks
2. Formation of
subsurface C helps
break C-C bonds.
© copyright 2013 William A. Goddard III, all rights reserved
Ethyne detail
Reaction of C with 2nd
layer Ni very important
Build up surface NixCx in
first few rows
Dynamics of surface
Ni plays important
role in dissociating C2
Get some carbon into
interior
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
ReaxFF: CH4 Adsorption, Decomposition
on Ni468
120
60
2300
CH4,gas
Had
2100
T(K)
1900
1700
1500
1300
TC
40
Cad
1100
TA=TH
900
20
8
# of molecules
# of molecules
80
CH4(g)
CH4(s)
CH3(g)
CH3(s)
CH2
CH
C
H
C2
H2(g)
CH5(g)
T(K)
temperature (K)
100
10
2500
6
CH4(s)
CH3(g)
CH3(s)
CH2
CH
C2
CH5(g)
4
2
0
1500
1700
1900
2100
target temperature (K)
2300
700
0
500
1000
1500
2000
target temperature (K)
L10-2013-Ch121A-Goddard
500
2500
Critical Temperatures
•1st adsorbs at 1300 K
•1st H produced at 1300 K
•1st C produced at 1850 K.
© copyright 2013 William A. Goddard III, all rights reserved
2500
ReaxFF: CH4 Adsorption, Decomposition
on Ni468
44 CHx Reactions out of 120
CH4,gas44
[76]
CH3,ad34 CH2,ad31 CHa 28 Cad
d
[3]
[3]
[26]
[3]
5
1
1
1 CH
CH
C
CH3,gas
[5]
2 6,g
as
2 5,g
as
[0]
[1]
2,ad
[1]
Conclusions
1. Chemisorption is the rate limiting step for CH4 decomposition (as
previously known). No C-C pi bond available to provide electrons to
bond with surface.
2. Must break C-H bond to chemisorb.
3. Formation of subsurface C helps break the final C-H bond to form Cad
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
ReaxFF: Benzene
Adsorption &
Decomposition on Ni
Particle
C 6 Hx
H2
C2
C6H6ad
Simplified sequence
C6H6C6H5C6H4C6H3C5H3
C5H2C4H2C4HC3HC3
C2C
At the end
7
6
46 2013 William A. Goddard III, all rights reserved
L10-2013-Ch121A-Goddard
© copyright
Benzene detail
Benzene chemisorbs
horizontally on the Ni
C6H6 chemisorbed
C6H3-allyl
particle surface
chemisorbed
through pi electrons.
As H removed, get
strong C-Ni sigma
bonds, reorienting
benzene vertically.
C atoms denuded of H
are “swallowed” by
the particle by PacC6H3-allyl tail in surface
C3H with bare C in
Man mechanism, for
subsurface
cleaving C-C bonds.
C-H bonds far from the
surface are
protected until the C
atoms separating
them from the
surface are “eaten”
away.
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Early Stages of CNT Growth from Acetylene
Feedstock at 1500K
400 ps NVT-RD
1500 K
Start with 100 gas phase
C2H2 molecules, add an
additional molecules every
100 ps.
L10-2013-Ch121A-Goddard
After 400 ps the following multicarbon surface species have formed:
C6H4, C5H4, C4H3, C4H2 (4), C3H3,
C3H2.
© copyright 2013 William A. Goddard III, all rights reserved
Experimental Confirmation of a Yarmulke Mechanism
Atomic-scale, video-rate environmental transmission
microscopy was used to monitor the nucleation and
growth of single walled nanotubes.
L10-2013-Ch121A-Goddard
Hofmann,
S.2013
et al.William
NanoA. Lett.
2007,
602.reserved
© copyright
Goddard
III, all7,
rights
Stopped May 3, 2013
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Hydrogen diffusion in Y-doped BaZrO3 (FC membrane)
Use QM on Ba, BaO, Zr, ZrO2, Y, Y2O3 etc plus H migration barriers in Ba8Zr7Y1O24
crystal to develop ReaxFF
70
60
40
2
D*10 (cm /s)
50
(nanocrystalline,
>100nm)H hopping
UsedIS
ReaxFF
to
follow
IS (nanocrystalline, ~10 nm)
as function
of Temperature
QENS (polycrystalline,
>100 nm) long
QENS (nanocrystalline, ~10 nm)
enough
to get D
Our simulation
6
30
20
Experiment
(QENS)
10
Theory - squares
0
600
800
1000
1200
1400
1600
1800
2000
Temperature (K)
Used ReaxFF to construct grain boundary
interfaces and to calculate H diffusion for
composite system. Get effect of grain size
Note: H moves along
Good agreement with experiment
edges of octahedra
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
ReaxFF MD simulation at T=1000 K, 328 atoms,
8 hydrogen atoms, ~700 ps
Proton diffusion coefficients in
Ba(Zr0.875Y0.125)O3
with grain boundaries
70
50
In both of grain and grain boundary
-10
-11
ln D (cm /sec)
60
2
40
2
D*10 (cm /s)
Activation energy for H+ diffusion
IS (nanocrystalline, >100nm)
IS (nanocrystalline, ~10 nm)
QENS (polycrystalline, >100 nm)
QENS (nanocrystalline, ~10 nm)
Our simulation
30
-12
slope=-7.33
-13
-14
slope=-13.04
Only in grain boundary core
6
-15
-16
20
10
simulation
-17
0.5
Experiment
QENS
0
600
1000
1200
0.7
0.8
0.9
-1
1000/T (K )
IS
800
0.6
1400
1600
1800
2000
Temperature (K)
Activation energy (eV)
G
0.38
G+GB 0.63
GB
1.13
Grain boundaries severely
reduce proton mobility
L10-2013-Ch121A-Goddard
copyrightspectroscopy
2013 William A. Goddard III, all rights reserved
QENS:
Quasi-elastic neutron scattering, IS:©Impedance
For BaZr0.85Y0.15O2.925, (Groβ et al., Solid State Ionics v.145, pp.325, 2001)
1.0
Restrained dynamics
MD(300K)
5Si(OH)4+OH-
Si5O15H9+6H2O
Zeolite growth
ZnO/H2O
Partially hydroxyl
covered surface
With Thuat Trinh (Eindhoven)
Cu/Zn oxides
With David Raymand (Uppsala)
ReaxFF for water
Dendrimers/metal
cations
Pt/Ni fuel cells
Nafion fuel cell
Enzymes/
Amines/
DNA/
carboxylate pKa organic
Phosphates/sulfonates
With Peter Fristrup
With
Ram
Devanathan (PNNL))
catalysis
Jahn-Teller distorted
Cu(H2O)62+-cluster
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Aqueous phase chemistry: Need to describe bulk
water while describing proton hopping
Water dimer
5
QM
2.5
Binding energy (kcal/mol)
Binding energy (kcal/mol)
5
ReaxFF
2.5
Cs
0
0
Ci
C2
-2.5
C2v
-2.5
-5
-7.5
-5
-7.5
2
3
4
5
6
2
O--O distance (Å)
3
4
5
O--O distance (Å)
Water clusters
14
6
Other training data
H-O-H bond energy
Cs
H-O-H
angle change
Ci
Ice(cmc)
equation of
C2
C2v
state
QM charges for water
clusters
Water vibrational
frequencies
H-H, O=O and HOOH bond dissociation
12
10
8
6
4
QM
ReaxFF
TTM2
QM-data from Julius Su
(X3LYP/6-311G**)
0
TTM2: Burnham and
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
(JCP 2002)
L10-2013-Ch121A-Goddard Cluster size
© copyright 2013 William A. Goddard III, Xantheas
all rights reserved
2
Hydrogen transfer barriers
ReaxFF
70
60
60
50
water 2
30
water 3
water 4
water 5
20
water 6
40
10
Neutral
0
Energy (kcal/mol)
Energy (kcal/mol)
QM
70
50
water
30
water
water
water
20
water
40
10
0
Reaction coordinate
Reaction coordinate
QM
QM
ReaxFF
ReaxFF
40
30
O--O=2.4
O--O=2.8
20
O--O=3.2
O--O=3.4
10
Enery (kcal/mol)
Enery (kcal/mol)
40
30
O--O=2.4
O--O=2.8
O--O=3.2
20
O--O=3.4
10
H3O+/H2O
0
-1
-0.5
0
0.5
H distance from O--O-centre (Å)
1
0
-1
-0.5
0
0.5
H distance from O--O-centre (Å)
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
1
Molecular dynamics tests of ReaxFF for bulk
water
Excellent fit to experimental
Density, data
cohesive energy
box with 800 water
NIST: Hvap=10.5 kcal/mol
ReaxFF: Hvap=10.9 kcal/mol
Radial distribution
Diffusion constant
45
y = 1.2635x + 2.3366
40
35
MSD
30
25
20
Lit : d=0.2272 Å2/ps
Reax:d=0.2106 Å2/ps
15
10
5
0
0
5
10
15
20
25
30
35
Time(ps)
Eisenberg and Kauzman, Oxford Univ. Press 1969
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Experimental
data from
Chem. Phys.
Special Issue
vol. 258, pp.
121-137
(2000)
Proton diffusion simulation in bulk water
31 H2O/ 1 H3O+ ; MD/NVT at 300K, density 1.00 kg/dm3
O in H2O
O in H3O+
- Proton hops frequently from oxygen to oxygen
- No changes in atom type during simulation
- ReaxFF
agree with QM/MD-simulations
forGoddard
proton
migration
rate
L10-2013-Ch121A-Goddard
© copyright 2013 William A.
III, all
rights reserved
Development of the ReaxFF potential for Cu/O/H
Water binding energies to Cu(OH)x(H2O)y-clusters
Cu(H2O)x2+-clusters
125
CuOH(H2O)x1+-clusters
75
QM
Binding energy (kcal/mol)
50
ReaxFF
50
25
QM-level: DFT/LACV3P/6-311G**++
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
CuOHw10_4c14
CuOHw10_5c8
CuOHw10_5c4
CuOHw10_5c1
- Includes 2,3,4,5,6-coordinated Cu-ions
- ReaxFF reproduces QM-preference for 4-coordinated Cu2+-ions
CuOHw9_5c10
CuOHw9_4c7
CuOHw8_4c3
CuOHw8_6c1
CuOHw6_5c4
CuOHw6_4c2
CuOHw5_3
CuOHw3_2
w
16
_b
b
w
10
w
9_
b
w
8_
c
w
6_
a
w
6_
w
5_
a
0
w
3
w
1
0
25
CuOHw2
Binding energy (kcal/mol)
75
100
Proton transfer energy between Cu(H2O)n
complexes
E(QM)= 13.7 kcal/mol
E(ReaxFF)= 15.8 kcal/mol
Cu(H2O)52+
[H3O--HOCu(H2O)3]2+
(constrained O-H bonds in H3O)
Similar reaction in [H2O]8 is uphill about 25 kcal/mol;
Cu facilitates the formation of OH-/H3O+ ion pairs
L10-2013-Ch121A-Goddard
2013 Williamwith
A. Goddard
III, allsolvation
rights reserved
Reaction
become less© copyright
endothermic
more
Jahn-Teller distortion in [Cu(H2O)6]2+
Energy difference (kcal/mol)
ReaxFF: Symmetric distortion
ReaxFF: Inversion path
QM: Symmetric distortion
QM: Inversion path
8
6
r3
r3
4
r1
r2
2
0
1.95
r2
r1
r2
r1
r1
r2
r3
r3
2
2.05
2.1
2.15
2.2
2.25
2.3
Cu-O distance r1 (Å)
ReaxFF predicts a non-symmetric ground state for the
[Cu(H2O)6]2+-complex, in agreement with QM.
ReaxFF finds a barrier of 1.1 kcal/mol for axial/equatorial
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
inversion.
Copper metal/metal oxide/metal hydroxide bulk
phases
QM/experiment
ReaxFF
100
Heat of formation (kcal/mol)
Heat of formation (kcal/mol)
100
50
50
C
C
C
C
C
C
Cu(fcc)
0
CuO(mncl)
CuO(spha)
CuO(NaCl)
Cu2O(cuprite) -50
Cu(OH)2 (spert.)
0
-50
-100
-150
-100
-150
0
20
40
Volume/unit (Angstrom
60
3
)
0
20
40
Volume/unit (Angstrom
ReaxFF describes both Cu2+-ions and CuOx bulk phases.
This allows simulation of aqueous phase crystal growth,
L10-2013-Ch121A-Goddard
dissolution,
failure © copyright 2013 William A. Goddard III, all rights reserved
60
3
)
Molecular dynamics simulation on a Cu2+/water
mixture
Cu2+/100 H2O
Oxygen in H2O initially
associated with Cu2+
Oxygen in H2O initially not
associated with Cu2+
All oxygens described with
the same force field atom
type
Jahn-Teller distortions
change with time
Collaboration
L10-2013-Ch121A-Goddard
with
Obaidur
Rahaman
and Doug
Doren
(U.Del)
© copyright
2013
William A. Goddard
III, all rights
reserved
Molecular dynamics simulation on a Cu2+/water mixture
Radial distributions over dynamics
1 Cu2+/100 H2O, T=300K, 25 picosecond trajectory
Axial
Equatorial
Solvation shell
Radial distribution analysis shows distorted clusters with on average 4 waters
at short Cu-O distances (equatorial) and 2 water at long Cu-O distance (axial).
Total coordination: 6
g(r) close to zero between first and second solvation shell, indicating no
exchange
of water ligands
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Cu-H2O system: Cluster inversion rate
O5
4.65
O1---O2
O1
4.4
O4
O3
4.15
O6
O2
O---O distance (Å)
3.9
3.65
0
25
50
75
O3---O4
4.65
4.4
4.15
3.9
3.65
0
25
50
75
ReaxFF predicts 14
inversions in 75 ps. at
T=300K; 1 inversion
per 5.4 ps.
Always 4 equatorial/2
axial waters
4.65
4.4
4.15
3.9
O5---O6
3.65
0
25
L10-2013-Ch121A-Goddard
50
75
NMR-experiment by
Merback et al. gives
an inversion time of
5.1 ps.
Time
(ps) 2013 William A. Goddard III, all rights reserved
© copyright
Temperature effect
T=300K
T=500K
T=700K
- At T=500 and T=700K we begin to see H2O exchange between the
complex and the solvent
(non-zero
rdf between
axial
andreserved
solvation)
L10-2013-Ch121A-Goddard
© copyright
2013 William
A. Goddard III,
all rights
Water ligand exchange at T=700K
t=0 ps.
t=25 ps.
- We observe 2 ligand exchange events in 25 ps. at T=700K; need longer
dynamics to improve statistics
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Water dissociation on ZnO-surface
Collaboration with David Raymand and Kersti Hermannsson (Uppsala)
See: Raymand, van Duin, Baudin and Hermannsson, accepted in Surface Science
Key step in water-gas shift reaction (ZnO/Cu catalyst)
ReaxFF properly predicts the formation of a 50% OH-covered
ZnO-surface
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
Pt-catalyzed water formation
O2-bridge path
OOH path
O2-bridge path
ReaxFF
OOH path
OOH-path
Agrees with QM-energies and barriers
Enables simulation of reactions on fuel
QM Jacob et al., CPC 2007
cell
cathodes under realistic
conditions
L10-2013-Ch121A-Goddard
© copyright 2013 William A. Goddard III, all rights reserved
QM