yanhong hu, postdoctoral scholar , kai wang, research professor donald brenner, pi
DESCRIPTION
Transferable, Quantum-Based Reactive Potentials for Simulating CHON Species: A Bridge Between ab initio Calculations and Condensed-Phase Reactive Dynamics. Yanhong Hu, Postdoctoral Scholar , Kai Wang, Research Professor Donald Brenner, PI Materials Science and Engineering - PowerPoint PPT PresentationTRANSCRIPT
Transferable, Quantum-Based Reactive Potentials for Simulating CHON Species:
A Bridge Between ab initio Calculations and Condensed-Phase Reactive Dynamics
Yanhong Hu, Postdoctoral Scholar, Kai Wang, Research Professor
Donald Brenner, PI
Materials Science and Engineering
North Carolina State University,
Raleigh, NC, 27695-7907
Program Objectives
Develop an inter-atomic potential for HCNO molecular solids that
• allows reactivity (i.e. bond breaking and forming with rehybridization) within and between molecules
-multiple molecules react under low and high P conditions
• is general and transferable between molecules
-same potential function regardless of molecule
-requires quantum-based functional forms, not ad hoc functions
• reproduces high and low pressure structures
-fit to molecular and solid structures (high & low coordination)
Program Objectives
Continued...
Develop an inter-atomic potential for HCNO molecular solids that
• incorporates intermolecular vdW and Coulombic forces
-must be consistent with reactivity
• is suitable for large-scale simulations (106+ atoms)
• is compatable with existing force fields
-takes advantage of prior work by Rice, Thompson, etc.
Strategy• Bonding Forces: Reactive covalent bonding based on
near-neighbor tight binding theory in the form of a bond order formalism.
• Use screening criterion rather than distance to fullfill near neighbor requirement.
• Non-bonded Forces: Fixed Dispersion (LJ) and Coulomb Interactions.
• Transfer functions to ARL/Thompson
• Variable charge/charge transfer
• Validate, validate, validate
Green: Largely done Yellow: In progress Red: Challenge to be met.
Today
Team Synergies• Richard Martin has provided data for hypothetical high-
coordination oxygen structures needed for effective potential fitting.
• Rod Bartlett is providing data regarding reaction paths for validation (e.g. nitromethane geometries along the C-N rxn coordinate)
• Betsy Rice has been working to incorporate functions into ARL/DoD modeling codes
• Work with Don Truhlar on charge transfer
• Validate, validate, validate
Green: Largely done Yellow: In progress Red: To be initiated.
Today
Bonding FormalismBond Order Potential - pair terms coupled to a bond order
)]ij
(rAVijb)ij
(rR[Vi)j(
Σi
Σb
E
Pair terms model repulsive
core-core interactions and attractive bonding from valence electrons
Bond order modulates attraction depending on•local coordination•bond angles•other environmental effects (e.g. conjugation, rotation about double bonds)
bond energy decreasesbond length increases
Bij (N)-1/2
Bonding FormalismQuantum Basis of the Bond Order Formalism
drrxcV
rVrxcEkk
)(
2
)()(
Self-consistent DFT
scscsc
sc sc
Non-self-consistent Harris functional
in
in
in
in
out Density Functional Energy
Tight Binding Energy
)(rkk
)(||
)(
2ˆ rVxc
Rr
rVH ext 2
Density of statesmomentsdescription
Superposition of atomic orbitals
2nd moment: Eel=(2)1/2=(N)1/2
Bond Order Equations
Multi-step fitting process:
First Step:
• Near-neighbor pair terms (repulsive and attractive) and discrete empirical bond order values for monoelemental structures (molecules, clusters, and solids) fit to bond energies/ lengths/force constants.
• Key feature - same pair potentials used for same elements, only difference being the value of the many-body bond order.
• Produces pair terms and bond order values that are transferable between environments (molecules, solids).
Bond Order EquationsMulti-step fitting process:
First Step (continued):
Assume pair functions:
Nine parameters for the pair terms; one bond order per structure
reAQ/r)(1 (r)(r)RV α cf
rne
1,3nn
BcAVβ
)()( rfr
Bond Energy vs. Bond Distance
-15
-10
-5
0
1 1.5 2 2.5Bond Length (A)
Bo
nd
En
erg
y (
eV
)
Bond Order EquationsFirst Step (continued): Nitrogen
Nitrogen Pair Terms
-2000
-1000
0
1000
2000
0.5 1 1.5 2 2.5
Interatomic Distance (A)En
erg
y (e
V)
Nitrogen Pair Potential
-10
-5
0
5
10
0.5 1 1.5 2 2.5Interatomic Distance (A)
En
erg
y (e
V)
N8
N2
N6 N4
fccbccsccd
solids
molecules
Bond Energy vs. Bond Distance
-6
-4
-2
0
1 1.5 2 2.5
Bond Length (A)
Bo
nd E
nerg
y (e
V)
Bond Order EquationsFirst Step (continued):
fccbccsccd
solids
O2
O3
molecules
Force Constant vs. Bond Distance
0
25
50
75
100
1 1.5 2 2.5
Bond Length (A)
K (
eV
/A2 )
Oxygenfcc oxygen
-432
-430
-428
-426
-424
-422
-420
0 10 20 30 40 50 60
lattice constant
En
erg
y (
eV
) First principles data
From Martin
Bond Order EquationsFirst Step (continued):
Force Constant vs. Bond Distance
0
25
50
75
100
1 1.5 2 2.5
Bond Length (A)
K (
eV
/A2 )
Carbon
Bond Energy vs. Bond Distance
-9
-7
-5
-3
-1
1 1.5 2
Bond Length (A)
Bon
d En
ergy
(eV)
fccsc
cd solids
Double
Single
molecules
Triple
Graphite
C-H Bonds
-5
-4.5
-4
-3.5
1.08 1.1 1.12 1.14
Bond Length (A)
Bo
nd
En
erg
y (
eV
)
CHCH2CH3
molecules
Bond Order EquationsFirst Step (continued):
Force Constant vs. Bond Distance
0
25
50
75
100
1 1.5 2 2.5
Bond Length (A)
K (
eV
/A2 )
CN
C-N Bonds
-10
-8
-6
-4
-2
0
1 1.2 1.4 1.6 1.8
Bond Length (A)
Bon
d En
ergy
(eV) molecules
Solids
Some CN compounds have been predicted to be “super”-hard
materials. The potentials developed here are also applicable
to these systems.
Bond Order Equations
NO Bonds-10
-5
0
1.1 1.2 1.3
Bond Length (A)
Bo
nd
En
erg
y (
eV
)
OH Bonds
-4.8
-4.6
-4.4
-4.2
0.955 0.965 0.975
Bond Length (A)
Bo
nd
En
erg
y (
eV
)
NH Bonds
-5
-4.5
-4
-3.5
-3
1 1.025 1.05
Bond Length (A)
Bo
nd
En
erg
y (
eV
)
CO Bonds
-12
-10
-8
-6
-4
1.1 1.15 1.2 1.25 1.3
Bond Length (A)
Bo
nd
En
erg
y (e
V)
Bond Order EquationsTransferable Effective Pair Potentials
OH Bonds
-4.8
-4.6
-4.4
-4.2
0.955 0.965 0.975
Bond Length (A)
Bo
nd
En
erg
y (
eV
)
NH Bonds
-5
-4.5
-4
-3.5
-3
1 1.025 1.05
Bond Length (A)
Bo
nd
En
erg
y (
eV
)
C-N Bonds
-10
-8
-6
-4
-2
0
1 1.2 1.4 1.6 1.8
O-O Bonds
-6
-4
-2
0
1 1.5 2 2.5
Bon
d E
nerg
y (e
V)
Bond Energy vs. Bond Distance
-9
-7
-5
-3
-1
1 1.5 2
Bond Length (A)
Bond
Ene
rgy
(eV)
C-C Bonds
Bond Energy vs. Bond Distance
-15
-10
-5
0
1 1.5 2 2.5Bond Length (A)B
ond
Ene
rgy
(eV
)
N-N BondsC-H Bonds
-5
-4.5
-4
-3.5
1.08 1.1 1.12 1.14
NO Bonds-10
-5
0
1.1 1.2 1.3
Bond Length (A)
Methyl hydrazine
1,2-dinitrocyclo-
propane
Bond Order EquationsMulti-step fitting process:
Second Step: Fit bond order values to tight-binding-based functional form
Empirical Bond Order Values for Nitrogen
0.96
0.97
0.98
0.99
1
0 2 4 6 8 10 12
Coordination
Bo
nd
Ord
er
Bond Order Equations
i j
k1
k2
k3
i-j bond order
ijk1 ijk3
ijk2
bij = [1+G(cos(ijk1)+G(cos(ijk2))]-1/2
(3)-1/2
bji = [1+G(cos(ijk3)]-1/2
(2)-1/2
Bij = (bij+bji)/2
Tight binding Constant
Tight Binding Result: b (Z) -1/2
Bij = {A-1+[1+Gik(cos(ijk)]-0.5}/A = 1-1/A + {1+ Gik(cos(ijk)]-0.5}/A
New parameter
Bond Order Equations
Nitrogen
1
1.2
1.4
1.6
1.8
2
2.2
60 80 100 120 140 160 180
Angle
G(co
s(an
gle)
)
Oxygen
0.5
1
1.5
2
60 120 180
Angle
G(c
os
())
Oxygen and nitrogen functions have minima around 110o, producing bent structures. Carbon has a minimum at 180o, creating a tendency for open structures.
Example: Ammonia
Carbon
Bond Order EquationsThird Step:
Linear combination of elemental bond order functions and add correction factors for mixed system. Because the tight binding theory is followed (b (Z)-1/2) the corrections are small and the terms are transferable.
Additional Hydrazine Fitting Data Base - bond energies/lengths for:
NH HN2H H2N(NH)2NH2
NH2 H2N2H2 H3N2H3
NH3 (+ inversion barrier)
Bij = (bij+bji)/2 bij = { A - 1+C(N,C,O,H)+[1+Gik(cos(ijk)]-0.5}/A
Screening• The tight binding theory requires that near-neighbors be
defined, which is invaluable for fitting, but…….
• How do you effectively define near neighbors without introducing severe cut-offs and associated non-physical forces?
• Can this definition be used to incorporate intermolecular non-bonded forces?
Screening• We are utilizing an atomic screening function that analytically
distinquishes between covalent and non-bonding forces:
i
k
j
No screening, Sij = 1
ij
Screened, Sij = 0
Screening function:
Potential Energies: Sij x bonded + (1-Sij) x nonbonded
•Significantly smooths potential surface relative to distance dependent cut-off function
•With the exception of O..H hydrogen bonding, the function does remarkably well for energetic molecular solids.
k
CH4 Symmetric Dissociation
CH3-H Dissociation
Screening Function
N N C H H H H H HN X 0.999999 1 1 0.000258 0.000557 0.000204 3.15E-05 0.000115N 0.999999 X 0.000159 8.54E-05 1 1 0.00013 7.09E-05 0C 1 0.000159 X 0.000367 7.41E-09 0 1 1 1H 1 8.54E-05 0.000367 X 0.008738 1.28E-07 0 7.27E-06 0.000268H 0.000258 1 7.41E-09 0.008738 X 0.000529 5.76E-16 0.03176 0H 0.000557 1 0 1.28E-07 0.000529 X 0 0 0H 0.000204 0.00013 1 0 5.76E-16 0 X 0.000549 0.000759H 3.15E-05 7.09E-05 1 7.27E-06 0.03176 0 0.000549 X 0.000455H 0.000115 0 1 0.000268 0 0 0.000759 0.000455 XN 0 7.01E-12 0 4.99E-11 0.981258 0 0 3.16E-09 0N 0 0 0 0 9.48E-08 0 0 0 0C 0 0 0 0 2.43E-06 0 0 1.10E-09 0N 0 0 0 9.39E-11 1.23E-07 0 0 0 0N 0 0 0 0 0 0 0 0 0H 0 0 0 0 0.001617 1.16E-13 0 0 0H 0 6.48E-10 1.07E-13 0 0.204587 0 2.81E-14 0.489794 0H 0 0 0 0 0 0 0 0 0H 0 0 3.19E-12 1.25E-06 0.000172 0 0 0.93376 0
Methyl HydrazineCH3NHNH2
yellow: Intramoleulqr
pink: Intermolecular
Screening Function1,2-dinitrocyclopropane
NO2C3H4NO2
yellow: Intramoleulqr
pink: IntermolecularC C C N N O O O O H H H H
C X 1 0.999988 9.97E-06 1 4.14E-06 0 1.36E-05 4.09E-06 1 2.74E-06 4.56E-06 5.68E-06C 1 X 0.999997 1 1.48E-05 4.35E-06 1.11E-05 0 4.07E-06 1.97E-06 1 8.94E-06 9.32E-07C 0.999988 0.999997 X 5.10E-07 1.69E-06 4.64E-08 0 0 2.01E-07 1.38E-06 1.28E-05 1 1N 9.97E-06 1 5.10E-07 X 0 1 1 0 0 0.000563 5.19E-06 0 1.85E-05N 1 1.48E-05 1.69E-06 0 X 0 0 1 1 1.11E-05 0.001232 0.000549 0O 4.14E-06 4.35E-06 4.64E-08 1 0 X 6.12E-07 0 0 0.600877 0 0 0.11288O 0 1.11E-05 0 1 0 6.12E-07 X 0 0 0 0.002571 0 0O 1.36E-05 0 0 0 1 0 0 X 4.20E-07 0.005761 0 0 0O 4.09E-06 4.07E-06 2.01E-07 0 1 0 0 4.20E-07 X 0 0.725678 0.472852 0H 1 1.97E-06 1.38E-06 0.000563 1.11E-05 0.600877 0 0.005761 0 X 0 0 1.49E-05H 2.74E-06 1 1.28E-05 5.19E-06 0.001232 0 0.002571 0 0.725678 0 X 0.00083 0H 4.56E-06 8.94E-06 1 0 0.000549 0 0 0 0.472852 0 0.00083 X 1.63E-05H 5.68E-06 9.32E-07 1 1.85E-05 0 0.11288 0 0 0 1.49E-05 0 1.63E-05 XC 0 0 0 0 0 0 0 0 0 0 0 0 0C 0 0 0 0 0 0 0 0 0 0 0 0 0C 0 0 0 0 0 0 1.87E-11 0 0 0 0 0 0N 0 0 0 0 0 0 0 0 0 0 0 0 0N 0 0 0 0 0 0 0 0 0 0 0 0 0O 0 0 0 0 0 0 0 0 0 0 0 0 0O 0 0 0 0 0 0 0 0 0 0 0 0 0O 0 0 0 0 0 0 0 9.46E-12 0 0 0 0 0O 0 0 0 0 0 0 0 0 2.95E-16 0 4.43E-14 0 0H 0 0 0 0 0 0 0 0 0 0 0 0 0H 0 0 0 0 0 0 0 0 0 0 0 0 0H 0 0 0 9.99E-16 0 0 0.000819 0 0 0 0.001493 0 0H 0 0 0 3.36E-11 0 0 0.730241 0 0 0 8.06E-17 0 0
Screening Function• How to handle intramolecular electrostatics?
-4
-2
0
2
4
0 1 2 3 4
Distance (A)
En
erg
y (
eV
)
-12
-8
-4
0
4
0 1 2 3 4
Distance (A)
En
erg
y (
eV
)
H…H OK
bonding
Non-bonding
Typical intramolecular 2nd neighbor
N…N too strongbonding
Non-bonding
Topology Function
...)()1( 10
k l k l mmjlmklikljklik
kjkikijij SSSSSSSSSFSNS
2nd 3rd 4th ...
j
i
k l
m j
i
kl
m
Need an analytic function that distiguishes between atom pairs in the same molecule and pairs in different molecules.
Screening Function• Partial charges vary within a molecule:
• How do we compensate in the intramolecular bonding forces? This is where we are today!
PlansShort-Term Plans (6 months): •Incorporate forces from the bond-order potential into our codes •Help with incorporating forces into ARL/Missouri codes•Validate against reaction paths from ab initio/Bartlett data.•Validate against shock/phase data (with Rice/Thompson)•Refine parameters as needed•Incorporate efficient partial charges into simulation codes (with Phillpot/Florida)
Long-Term Plans (6 months - 3 years)
•Incorporate charge-transfer terms into potential (with Truhlar/Stuart(Clemson))•Refit bond order terms terms including charge transfer as needed•Validate against phase and chemistry data