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Parameterization of a reactive force field using a MonteCarlo algorithm
Eldhose Iype
Asst. Prof.Department of Chemical Engineering,
BITS Pilani Dubai Campus
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 1 / 18
Who am I?
Asst. Prof. (Currently)
Department of Chemical Engineering,
BITS Pilani Dubai Campus
Post-doc (2014-2016)
Simulation of self-replenishing hydrophilic polyurethane coatings.
Eindhoven University of Technology
PhD (2014)
Computational modelling of hydration/dehydration behaviour ofenergy storage materials.
Eindhoven University of Technology
Masters in Chemical Engineering (2008)
Indian Institute of Technology, Madras
Bachelors in Chemical Engineering (2006)
Kerala University
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 2 / 18
Molecular dynamics
Force Field
Energy ,E = E (r1, r2, · · · rN)
Force,F = −∇E (r1, r2, · · · rN)Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 3 / 18
Reax force field
Esystem =EvdWaals + ECoulomb + Ebond + Eval + Etors
+ Eover + Eunder + EH−bond + Elp
+ Econj + Epen + Ecoa + EC2 + Etriple
Characteristics of ReaxFF
Dynamic charges are calculated using EEM
van Der Waal’s interaction is calculated using a Morse-type potential
Energy surface is made continuous
Connected interactions include
Bonded interaction (two body)Valence angle interaction (three body)Torsion interaction (four body)Hydrogen bond interaction
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 4 / 18
Reax force field
Esystem =EvdWaals + ECoulomb + Ebond + Eval + Etors
+ Eover + Eunder + EH−bond + Elp
+ Econj + Epen + Ecoa + EC2 + Etriple
Characteristics of ReaxFF
Dynamic charges are calculated using EEM
van Der Waal’s interaction is calculated using a Morse-type potential
Energy surface is made continuous
Connected interactions include
Bonded interaction (two body)Valence angle interaction (three body)Torsion interaction (four body)Hydrogen bond interaction
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 4 / 18
What makes ReaxFF reactive?
ReaxFF calculates bond order between every pair of atoms
Bond order is a function of distance of separation
Every connected interaction is made a function of this bond order
Thus all the bonds become dynamic
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 5 / 18
Parameterization of ReaxFF force field
Quantum Chemical (DFT) data is used to parameterize the force field
A training data set is prepared which contains the followinginformations
Atomic charges (Mulliken)Equilibrium bond lengthsEquilibrium bond anglesTorsion anglesEnergies of the DFT optimized geometriesHeat of formation
Error in the force field is then calculated
Err(p1, p2, · · · pn) =n∑
i=1
[xi ,QM − xi ,ReaxFF
σi
]2
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 6 / 18
Parameterization of ReaxFF force field
Quantum Chemical (DFT) data is used to parameterize the force field
A training data set is prepared which contains the followinginformations
Atomic charges (Mulliken)Equilibrium bond lengthsEquilibrium bond anglesTorsion anglesEnergies of the DFT optimized geometriesHeat of formation
Error in the force field is then calculated
Err(p1, p2, · · · pn) =n∑
i=1
[xi ,QM − xi ,ReaxFF
σi
]2
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 6 / 18
Parameterization of ReaxFF force field
Quantum Chemical (DFT) data is used to parameterize the force field
A training data set is prepared which contains the followinginformations
Atomic charges (Mulliken)Equilibrium bond lengthsEquilibrium bond anglesTorsion anglesEnergies of the DFT optimized geometriesHeat of formation
Error in the force field is then calculated
Err(p1, p2, · · · pn) =n∑
i=1
[xi ,QM − xi ,ReaxFF
σi
]2
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 6 / 18
Challenges with parametrization of ReaxFF
Multiple parameters need to be optimized simultaneouslyShould not be computationally expensiveShould not get stuck in any local minimaWe do not know a good starting point
Shapes of typical ReaxFF Error surface
20000
40000
60000
80000
100000
120000
140000
160000
2.4 2.5 2.6 2.7 2.8 2.9 3 3.1
Err
or
σ-bond radius of S-atom
Error vs σ-bond radius
24500
24600
24700
24800
24900
25000
25100
25200
25300
25400
25500
25600
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Err
or
EEM hardness for Mg-atom
Error vs EEM hardness
0
1e+06
2e+06
3e+06
4e+06
5e+06
6e+06
7e+06
8e+06
9e+06
1e+07
2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3
Err
or
vdw parameter for S-O interaction
Error vs vdw parameter
23000
24000
25000
26000
27000
28000
29000
30000
31000
32000
2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2
Err
or
vdw radius of Mg-atom (rvdw)
Error vs rvdw
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 7 / 18
Metropolis Monte Carlo algorithm
Start from any random point in space and calculate the initial energy,Eold
Propose a new move in any direction (random(−1.0, 1.0) ∗ dmax ),here dmax is the step size.
Calculate the new energy of the particle, Enew
Calculate the difference in the Energies, ∆E = Enew − Eold
Accept the move with a probability given by,P = min [1, exp (−β∆E )], where β = 1
kB T
Repeat the algorithm
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 8 / 18
Monte Carlo sampling in a double well potential
U(x) = x4 − 0.75x2 + 0.01x
The distribution has a global maximum near the left well.
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
0.25
−2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.50
100
200
300
400
500
600
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 9 / 18
MCFF-Optmizer
Calculate the error of the starting force field, Errold
Make a new proposition (move) for the parameters
Calculate the error of the new force field, Errnew
Calculate the difference in the Error, i.e.
∆Err = Errnew − Errold
Accept the move with a probability given by,
P = min [1, exp (−β∆Error)] ,where, β =1
kBT
Repeat the algorithm
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 10 / 18
Error vs β for a Simulated Annealing run
0
1e+06
2e+06
3e+06
4e+06
5e+06
6e+06
7e+06
1e-05 0.0001 0.001
Err
or
β
Error vs β =1/(KBT)
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 11 / 18
Comparison between MMC and ParSearch
For five random starting force fields
0
0.2
0.4
0.6
0.8
1
1.2
0 200 400 600 800 1000
Err
or r
atio
(E
rror
MM
C/E
rror
ParS
earc
h)
Iteration
Trial 1Trial 2Trial 3Trial 4Trial 5
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 11 / 18
Comparison of the error values
Initial and final errors of the five simulations. The average < Error > and the
coefficient of variation, std(sigma)<Error> , of the final errors are shown.
Trial Errorinitial × 1E − 6 Errorfinal × 1E − 6
ParSearch MMC1 4.3 0.9 0.312 1.1 0.4 0.443 8.1 2.5 0.314 2.0 1.4 0.265 4.3 1.3 0.42
< Error > 1.3 0.35std(Error)<Error> 0.6 0.21
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 12 / 18
Technical details
Maximum step size (dmax )
Maximum change in parameter value at every stepIt is different for each parameter in a force fieldSmaller step size results in more acceptance and vice versa, for a giventemperature
Acceptance rate
The ratio of accepted moves to the total number of movesSet an acceptance rate of your choice (typically, I use around 20%)Lower, the better (but computationally expensive)
Cooling rate
Slow cooling rate is goodAt any temperature, the acceptance rate is maintained by scaling up ordown dmax valueSo ideally, one would like to have a slow cooling rate and lowacceptance rate. But this come at a cost.
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 13 / 18
Challenges
Bounds for the parameters
Taken from the values of each parameter from a set of 11 force fieldsThis would mean, two different elements have same bounds for a givenparameterNo way to monitor if the optimized value for the parameter isphysically meaningful
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 14 / 18
Energies of the hydrates of MgSO4.xH2O
x ranging from 0 to 6
-3000
-2500
-2000
-1500
-1000
-500
0 1 2 3 4 5 6 7 8 9
Energy (kca
l/mol)
Geometry number
Errrms : 9.8 kcal/mol
DFT
ReaxFF
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 15 / 18
Equation of state for MgSO4
-3450
-3440
-3430
-3420
-3410
-3400
-3390
-3380
230 240 250 260 270 280 290 300 310
Energy (kcal/mol)
Volume
ErrrmsReaxFF: 4.8 kcal/mol
ErrrmsReaxFF (100 * σi): 4.5 kcal/mol
DFT
ReaxFFReaxFF (100 * σi)
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 15 / 18
Equation of state for MgSO4.7H2O
-13140
-13130
-13120
-13110
-13100
-13090
-13080
860 880 900 920 940 960 980 1000
Ener
gy (
kca
l/m
ol)
Volume
ErrrmsReaxFF: 3.4 kcal/mol
ErrrmsReaxFF (100 * σi) : 7.0 kcal/mol
DFT
ReaxFFReaxFF (100 * σi)
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 15 / 18
Binding energy
Binding energy of one water molecule on the (100) surface of MgSO4
-3400
-3350
-3300
-3250
-3200
2 2.5 3 3.5 4 4.5 5 5.5
Energy (kcal/mol)
Distance
Binding Energy with one water molecule MgSO4
ErrrmsReaxFF: 18.0 kcal/mol
ErrrmsReaxFF (100 * σi): 10.7 kcal/mol
DFT
ReaxFFReaxFF (100 * σi)
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 15 / 18
Examples of works based on MCFF-optimizer
J. Phys. Chem. C. 2014. 118. 6882-6886
ACS Catal. 2015. 5. 596601
PCCP 2016. 18. 15838
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 16 / 18
Conclusion
Metropolis MC algorithm is used to parameterize the ReaxFF forcefield.
The method shows good improvement over the traditionaloptimization scheme.
The stochastic nature of the method allows one to arrive at the globalminima in the parameter space.
The method is efficient and cheaper
One does not need a good starting point
Acknowledgement
dr. M. (Markus) Hutter, dr. A.P.J. (Tonek) Jansen, dr. Adri van Duin
SCM, NCF-SARA, EGS, NSCCS
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 17 / 18
Conclusion
Metropolis MC algorithm is used to parameterize the ReaxFF forcefield.
The method shows good improvement over the traditionaloptimization scheme.
The stochastic nature of the method allows one to arrive at the globalminima in the parameter space.
The method is efficient and cheaper
One does not need a good starting point
Acknowledgement
dr. M. (Markus) Hutter, dr. A.P.J. (Tonek) Jansen, dr. Adri van Duin
SCM, NCF-SARA, EGS, NSCCS
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 17 / 18
Thank You!!
Eldhose Iype (BITS Pilani Dubai Campus) Parameterization of a reactive force field using a Monte Carlo algorithm 18 / 18