Introduction to ReaxFF: Reactive Molecular Dynamics

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1 Introduction to ReaxFF: Reactive Molecular Dynamics Ole Carstensen TCCM ADF Tutorial April 21 Amsterdam

2 Outline ReaxFF - general aspects Molecular Dynamics Intro 200 DFT 100 ReaxFF Harmonic 0 1 Selected ReaxFF studies

3 Molecular Dynamics (MD) What? Simulate physical movement of atoms and molecules. How? by numerically solving Newton's equation of motion, e.g. via the simple Verlet algorithm future position Δ t2 x i+1=2 x i x i 1+ Fi m ( ) current position previous position timestep dv dx ( ) current force F i = x= x i Repeated application: positions and momenta as a function of time, x(t) p(t), termed the Trajectory. -3-

4 Molecular Dynamics (MD) What? Simulate physical movement of atoms and molecules. How? by numerically solving Newton's equation of motion, e.g. via the simple Verlet algorithm future position Δ t2 x i+1=2 x i x i 1+ Fi m ( ) current position previous position timestep dv dx ( ) current force F i = x=x i Repeated application: positions and momenta as a function of time, x(t) p(t), termed the Trajectory. Important consequence: Δ t : discretization of time, from finite differences approach good timestep -4- dx Δ x dt Δ t

via the simple Verlet algorithm future position Δ t2 x i+1=2 x i x i 1+ Fi m ( ) current position previous position timestep dv dx ( ) current force F i

5 Molecular Dynamics (MD) What? Simulate physical movement of atoms and molecules. How? by numerically solving Newton's equation of motion, e.g. via the simple Verlet algorithm future position Δ t2 x i+1=2 x i x i 1+ Fi m ( ) current position previous position timestep dv dx ( ) current force F i = x=x i Repeated application: positions and momenta as a function of time, x(t) p(t), termed the Trajectory. Important consequence: Δ t : discretization of time The length of Δ t - and therefore ttotal is limited by the fastest movement in your system. Typically: Δ t t total bad timestep -5- ~ 1 fs ~ nanosecond(s)

- conceptually simple and efficient (huge systems) - study dynamic properties of systems, e.g. diffusion, etc.

6 Molecular Dynamics (MD) What? Simulate physical movement of atoms and molecules. How? by numerically solving Newton's equation of motion Why? - conceptually simple and efficient (huge systems) - study dynamic properties of systems, e.g. diffusion, etc... - elegant link to macroscopic properties of materials through statistical mechanics/thermodynamics linked atomistic macroscopic Source: -6-

7 Force fields (FF) de dx ( ) MD requires forces: F i = x= xi Force fields: E(x) for a given mol. structure via parametrized, analytic functions EFF =E bond+ E angle+e dihedral + Eelectrostatic +E v.d.waals bonded + non-bonded Example: Harmonic potentials Ebond = k (r-req.)2 Parameters: k, req per atomtype Atomtypes: (CCsingle, CCdouble, COsingle, COdouble, etc...) -7-

8 ReaxFF The concept... Standard forcefields vs ReaxFF Fixed atomtypes and harmonic potentials: bond breaking impossible, e.g. Non-harmonic potentials based on bond orders: bond breaking/forming possible, e.g. Ebond (distance) 2 Ebond -(bond order) exp[ (1 bond order) ] dynamic bond orders: depending on distance (no atomtypes) -a triple bond will always stay a triple bond - a Ctriple atom will always be a Ctriple atom (Ebond ) (Ebond 0) -8- A.C.T. van Duin et al,j. Phys. Chem. A 2001, 105,

Non-harmonic potentials based on bond orders: bond breaking/

9 ReaxFF The concept... Standard forcefields vs ReaxFF Fixed atomtypes and harmonic potentials: bond breaking impossible, e.g. Non-harmonic potentials based on bond orders: bond breaking/forming possible, e.g. Ebond (distance) 2 Ebond -(bond order) exp[ (1 bond order) ] dynamic bond orders: depending on distance (no atomtypes) -a triple bond will always stay a triple bond - a Ctriple atom will always be a Ctriple atom (Ebond ) (Ebond 0) Speed: (scaling) non-reactive MD (N 2) ~10-50 ReaxFF times faster (NlogN) -9- A.C.T. van Duin et al,j. Phys. Chem. A 2001, 105, ~ times faster QM (conventional DFT) (N 3 or worse)

ReaxFF Parameters Parametersets included in ADF: ADF 2013: 17 sets,

elements Note: Bonded terms for each pair are needed. e. g. FeOCHCl.

Sources for new ReaxFF parameters: - Academic research groups: CH4

Carlo force-field parameter optimizer (included in the ADF-molecular

10 ReaxFF Parameters Parametersets included in ADF: ADF 2013: 17 sets, 19 elements ADF 2014: 38 sets, 29 elements ADF 2016: 58 sets, 39 elements Note: Bonded terms for each pair are needed. e. g. FeOCHCl.ff A.C.T. van Duin et al npj Computational Materials 2016, Sources for new ReaxFF parameters: - Academic research groups: CH4 van Duin, Goddard, Hartke and others CH3Cl - MCFFOptimizer Monte Carlo force-field parameter optimizer (included in the ADF-molecular modelling suite)

ReaxFF Concept ReaxFF development A.C.T.

Initial and ongoing development: Prof. Dr.

Non-harmonic potentials based on bond orders, bond

Adri Ebond -(bond order) exp[ (1 bond order) ] ReaxFF

11 ReaxFF Concept ReaxFF development A.C.T. van Duin et al,j. Phys. Chem. A 2001, 105, Initial and ongoing development: Prof. Dr. Adri van Duin (Penn State University). Non-harmonic potentials based on bond orders, bond breaking/forming possible, e.g. Adri Ebond -(bond order) exp[ (1 bond order) ] SCM - optimization & parallelization of the original code. - many parameters included (e.g. transition metals) - GUI support - automatic reaction event detection, rate constants - analysis tools - force-bias and grand canonical Monte Carlo - internal parameter optimization via Monte Carlo Alexei Olivier Hans Anna Ole -11- (ReaxFF-Parameters)

12 Outline ReaxFF - general aspects Molecular Dynamics Intro 200 DFT 100 ReaxFF Harmonic 0 1 Selected ReaxFF studies

13 ReaxFF Selected Research Highlights L. Zhang, S. V. Zybin, A. C. T. Van Duin & W. A. Goddard III, J. Energ. Mat. 28, (2010). -13-

14 ReaxFF Selected Research Highlights L. Zhang, S. V. Zybin, A. C. T. Van Duin & W. A. Goddard III, J. Energ. Mat. 28, (2010). RDX: Research Department Formula X - widely used commercial explosive - approx. 1.5 x the explosive power of TNT - very stable at ambient conditions Simulate impact sensitivity? -14-

15 ReaxFF Selected Research Highlights L. Zhang, S. V. Zybin, A. C. T. Van Duin & W. A. Goddard III, J. Energ. Mat. 28, (2010). Modeling of the high rate impact sensitivity 1. compression of volume 8.76 km/s for ps (100-40)% V0) RDX: Research Department Formula X - widely used commercial explosive 2. NVE dynamics for 1ps - approx. 1.5 x the explosive power of TNT 3. expansion - very stable at ambient conditions (@ 8.76 km/s for ps 140% V0) Simulate impact sensitivity! 4. NVE dynamics for 4ps -15-

Modeling of the high rate impact sensitivity RDX: Research Department Formula X - widely

16 ReaxFF Selected Research Highlights L. Zhang, S. V. Zybin, A. C. T. Van Duin & W. A. Goddard III, J. Energ. Mat. 28, (2010). Modeling of the high rate impact sensitivity RDX: Research Department Formula X - widely used commercial explosive - approx. 1.5 x the explosive power of TNT - very stable at ambient conditions Simulate impact sensitivity! -16-

ReaxFF Selected Research Highlights M. M. Islam, V. S. Bryantsev, and A. C. T.

Lithium-Sulfur Batteries - high energy density (500 W h/kg vs.

Problems - unwanted reactions between Li and electrolyte - during charging Li can

17 ReaxFF Selected Research Highlights M. M. Islam, V. S. Bryantsev, and A. C. T. van Duin, J. Electrochem. Soc. 161, E3009-E3014 (2014). Lithium-Sulfur Batteries - high energy density (500 W h/kg vs W h/kg in Li-ion) - environmental friendliness - abundance and lowcost Problems - unwanted reactions between Li and electrolyte - during charging Li can deposit as metallic phase on the anode surface - dissolved polysulfides anions migrate through electrolyte insoluble sulfides passivate the anode

18 ReaxFF Selected Research Highlights M. M. Islam, V. S. Bryantsev, and A. C. T. van Duin, J. Electrochem. Soc. 161, E3009-E3014 (2014). Lithium-Sulfur Batteries Modeling with ReaxFF: Li/SWCNT anode - high energy density single-walled carbon nanotube (SWCNT) composite electrode (500 W h/kg vs W h/kg in Li-ion) - environmental friendliness - abundance and lowcost Problems - unwanted reactions between Li and electrolyte - during charging Li can deposit as metallic phase on the anode surface - dissolved polysulfides anions migrate through electrolyte insoluble sulfides passivate the anode PEGDME Electrolyte α-sulfur poly(ethylene glycol) dimethyl ether NVT-MD simulations at 300 K -18-

Lithium-Sulfur Batteries modeling with ReaxFF: Li/SWCNT anode single-walled carbon nanotube (SWCNT) composite

19 ReaxFF Selected Research Highlights M. M. Islam, V. S. Bryantsev, and A. C. T. van Duin, J. Electrochem. Soc. 161, E3009-E3014 (2014). Lithium-Sulfur Batteries modeling with ReaxFF: Li/SWCNT anode single-walled carbon nanotube (SWCNT) composite electrode Anode Electrolyte 2D-Temp. Distr. hot Li-ions PEGDME Electrolyte α-sulfur poly(ethylene glycol) dimethyl ether Electrolyte dissociation, build up of ethylene NVT-MD simulations at 300 K -19-

Lithium-Sulfur Batteries modeling with ReaxFF: Anode Li/SWCNT anode Electrolyte single-walled carbon nanotube (SWCNT)

20 ReaxFF Selected Research Highlights M. M. Islam, V. S. Bryantsev, and A. C. T. van Duin, J. Electrochem. Soc. 161, E3009-E3014 (2014). Lithium-Sulfur Batteries modeling with ReaxFF: Anode Li/SWCNT anode Electrolyte single-walled carbon nanotube (SWCNT) composite electrode 2D-Temp. Distr. Anode Teflon coating Electrolyte 2D-Temp. Distr. with Teflon α-sulfur PEGDME Electrolyte poly(ethylene glycol) dimethyl ether Electrolyte is protected, ethylene reduced by 90% -20-

21 ReaxFF Research Highlights

22 The End. -contactlicenses General information User support -22-

23 -23-

24 Appendix -24-

25 Inside ReaxFF Parameters Example: Bond orders from atom distance... [ () ] [ ( ) ] [ ( ) ] BOij (r ij) = exp pbo,1 r ij ro pbo,2 + exp pbo,3 π r ij r o,π In: distance between atoms, rij Out: 1, 2, 1.42, etc... pbo, 4 + exp pbo,5 ππ r ij r o,ππ pbo,6 4 3 Parameters = 9 pbo,1,pbo,2,pbo,3,pbo,4,pbo,5,pbo,6,r0, r0,π, r0,ππ BO (r ij) ij r ij -25-

between atoms, rij Out: 1, 2, 1.42, etc.

26 Inside ReaxFF Parameters Example: Bond orders from atom distance... [ () ] [ ( ) ] [ ( ) ] BOij (r ij) = exp pbo,1 r ij ro pbo,2 + exp pbo,3 π r ij pbo, 4 + exp pbo,5 r o,π In: distance between atoms, rij Out: 1, 2, 1.42, etc... ππ r ij r o,ππ pbo,6 4 3 Parameters = 9 pbo,1,pbo,2,pbo,3,pbo,4,pbo,5,pbo,6,r0, r0,π, r0,ππ BO (r ij) ij Problems: Resulting bond orders not correct... residual 1-3 bonding overbonding r ij A.C.T. van Duin et al,j. Phys. Chem. A 2001, 105,

Inside ReaxFF Parameters Example term: Bond orders from atom distance.

distance between atoms, rij Out: 1, 2, 1.42, etc.

pbo,1,pbo,2,pbo,3,pbo,4,pbo,5,pbo,6,r0, r0,π, r0,ππ val1, val λ1ij),λ2,λ3,λ4,λ5 BO2,ij (r

27 Inside ReaxFF Parameters Example term: Bond orders from atom distance... [ () ] [ ( ) ] [ ( ) ] BOij (r ij) = exp pbo,1 r ij ro pbo,2 + exp pbo,3 π r ij r o,π In: distance between atoms, rij Out: 1, 2, 1.42, etc... pbo, 4 + exp pbo,5 ππ r ij r o,ππ pbo,6 4 3 Parameters = 16 pbo,1,pbo,2,pbo,3,pbo,4,pbo,5,pbo,6,r0, r0,π, r0,ππ val1, val λ1ij),λ2,λ3,λ4,λ5 BO2,ij (r Correction terms f 1, f 2, f 3: BOij (r ij) = BOij (r ij) f 1(BO ij) f 2(BO ij) f 3(BO ij) residual 1-3 bonding overbonding r ij A.C.T. van Duin et al,j. Phys. Chem. A 2001, 105,

28 Inside ReaxFF Parameters Example term: Bond orders from atom distance... CHO.ff: BO-Parameters: 16 Reactive MD-force field c/h/o combustion force field: p bo,1,p bo,2,p bo,3,p bo,4,p bo,5,p bo,6,r 0, Chenoweth, K.; van Duin, A.C.T.; Goddard, W.A. J. Phys. Chem. A 2008, 112, val 1, val 2, λ1,λ2,λ3,λ4,λ5 39! Number of general parameters !p(boc1) !p(boc2) !p(coa2) !p(trip4) [...SNIP...] 3! Nr of atoms; atomid;ro(sigma); Val;atom mass;rvdw;dij;gamma;ro(pi);val(e) alfa;gamma(w);val(angle);p(ovun5);n.u.;chieem;etaeem;n.u. ro(pipi);p(lp2);heat increment;p(boc4);p(boc3);p(boc5),n.u.;n.u. p(ovun2);p(val3);n.u.;val(boc);p(val5);n.u.;n.u.;n.u. C H [...SNIP...] 6! Nr of bonds; at1;at2;de(sigma);de(pi);de(pipi);p(be1);p(bo5);13corr;n.u.;p(bo6),p(ovun1) p(be2);p(bo3);p(bo4);n.u.;p(bo1);p(bo2) [...SNIP...] -28- r 0,π, r 0,ππ

Charge equilibration

Charge equilibration Taylor expansion of energy of atom A @E E A (Q) =E A0 + Q A + 1 @Q A 0 2 Q2 A @ 2 E @Q 2 A 0 +... The corresponding energy of cation/anion and neutral atom E A (+1) = E A0 + @E @Q