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ReaxFF parameterizationusing Metropolis MonteCarlo algorithm

Eldhose Iype (e.iype@tue.nl)

S.V.NedeaEnergy Technology Group

December 2, 2014

2/5

/department of mechanical engineering

Parameterization of Reax force field

◮ Quantum Chemical (DFT) data is used to parameterize the forcefield

◮ A training data set is prepared which contains the followinginformations

• Atomic charges (Mulliken)• Equilibrium bond lengths• Equilibrium bond angles• Torsion angles• Energies of the DFT optimized geometries• Heat of formation

◮ Error in the force field is then calculated

Err(p1, p2, · · · pn) =

n∑

i=1

[

xi ,QM − xi ,ReaxFF

σi

]2

2/5

/department of mechanical engineering

Parameterization of Reax force field

◮ Quantum Chemical (DFT) data is used to parameterize the forcefield

◮ A training data set is prepared which contains the followinginformations

• Atomic charges (Mulliken)• Equilibrium bond lengths• Equilibrium bond angles• Torsion angles• Energies of the DFT optimized geometries• Heat of formation

◮ Error in the force field is then calculated

Err(p1, p2, · · · pn) =

n∑

i=1

[

xi ,QM − xi ,ReaxFF

σi

]2

2/5

/department of mechanical engineering

Parameterization of Reax force field

◮ Quantum Chemical (DFT) data is used to parameterize the forcefield

◮ A training data set is prepared which contains the followinginformations

• Atomic charges (Mulliken)• Equilibrium bond lengths• Equilibrium bond angles• Torsion angles• Energies of the DFT optimized geometries• Heat of formation

◮ Error in the force field is then calculated

Err(p1, p2, · · · pn) =

n∑

i=1

[

xi ,QM − xi ,ReaxFF

σi

]2

3/5

/department of mechanical engineering

Metropolis Monte Carlo (MMC) method

◮ 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∆Err)] ,where, β =1

kBT

◮ Repeat the algorithm

4/5

/department of mechanical engineering

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)

5/5

/department of mechanical engineering

Overview

◮ How to set-up input files (geo,trainset.in)?

◮ Optimizing water force field, MMC at low temperature

◮ Simulated annealing

5/5

/department of mechanical engineering

Overview

◮ How to set-up input files (geo,trainset.in)?

◮ Optimizing water force field, MMC at low temperature

◮ Simulated annealing

5/5

/department of mechanical engineering

Overview

◮ How to set-up input files (geo,trainset.in)?

◮ Optimizing water force field, MMC at low temperature

◮ Simulated annealing