ReaxFF force fields. Development of a transferable empirical method for atomic-scale simulations of chemical reactions

Transcription

1 ReaxFF force fields Development of a transferable empirical method for atomic-scale simulations of chemical reactions Adri van Duin, Kimberley Chenoweth 2 and Bill Goddard 2 : Department of Mechanical ngineering, Penn State 2: Materials and Process Simulation Center, California Institute of Technology Interatomic Potentials Workshop, Oxford July 2008

2 Contents - ReaxFF background - Key features and development rules - Current status - ReaxFF energy terms - ReaxFF flow diagram - Bond orders - Angle terms - Non-bonded interactions - Force field development for Si/SiO systems - Summary 2

3 ReaxFF: background and rules Time years 0-5 ierarchy of computational chemical methods lectrons Bond formation QM ab initio, DFT, F Atoms Molecular conformations FF ReaxFF mpirical force fields MSO Grains FA Grids Design FF methods: - Allow large systems - Rigid connectivity - Dynamics QM methods: - Allow reactions - xpensive, only small systems - Mostly static Simulate reactions in large, dynamical systems Ångstrom Distance Kilometres 3

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 relationship,2. Bond orders are updated every iteration. -All connectivity-dependent interactions (i.e. valence and torsion angles) are made bond-order dependent, ensuring that their energy contributions disappear upon bond dissociation. - Nonbonded interactions (van der Waals, Coulomb) are calculated between every atom pair, irrespective of connectivity. xcessive close-range nonbonded interactions are avoided by shielding. - ReaxFF uses a geometry-dependent charge calculation scheme that accounts for polarization effects. :Tersoff, PRB 988; 2 : Brenner PRB 990 4

5 General rules - MD-force field; no discontinuities in energy or forces even during reactions. - User should not have to pre-define reactive sites or reaction pathways; potential functions should be able to automatically handle coordination changes associated with reactions. - ach element is represented by only atom type in the force field; force field should be able to determine equilibrium bond lengths, valence angles etc. from chemical environment. 5

6 Current status of ReaxFF not currently described by ReaxFF - Code has been distributed to over 70 research groups - Parallel ReaxFF (GRASP/Reax, USC/Reax, Purdue/Reax, incorporation into LAMMPS ongoing) YSZ/Ni/butane interface simulation at T=750K Snapshot from a 6,000 atom 6 parallel ReaxFF simulation (Nomura, USC) on shock impact chemistry

7 Selection of published ReaxFF parameters and applications - /C/O - van Duin, Dasgupta, Lorant and Goddard, JPC-A 200, 05, van Duin and Sinninghe Damste, Org. Geochem.2003, 34, 55 - Chen, Lusk, van Duin and Goddard PRB 2005, 72, an, Kang, Lee, van Duin and Goddard Appl. Phys. Lett. 2005, 86, 20308) - Chenoweth, van Duin and Goddard, JPC-A Si/SiO 2 /SiC - van Duin, Strachan, Stewman, Zhang, Xu and Goddard, JPC-A 2003, 07, Chenoweth, Cheung, van Duin, Goddard and Kober, JACS 2005, 27, Buehler, van Duin and Goddard, PRL 2006, 96, Buehler, Tang, van Duin and Goddard, PRL 2007, 90, igh energy -Strachan, van Duin, Chakraborty, Dasgupta and Goddard, PRL 2003,9, Strachan, van Duin, Kober and Goddard, JCP 2005,22,054502; - van Duin, Dubnikova, Zeiri, Kosloff and Goddard, JACS 2005, 27, 053, 58 - Nomora, Kalia, Nakano, Vashista, van Duin and Goddard PRL , Parallel ReaxFF - Al/Al 2 O 3 - Zhang, Cagin, van Duin, Goddard, Qi and ector, PRB 2004,69, Ni/Cu/Co/C - Nielson, van Duin, Oxgaard, Deng and Goddard, JPC-A 2005, 09, Su, Nielsen, van Duin and Goddard, PRB 75, Pt/Pt/PtC - Ludwig, Vlachos, van Duin and Goddard, JPC-B Sanz-Navarro, Astrand, Chen, Ronning, van Duin, Jacob and Goddard, JPC-A 2008 Fuel cell anode - Na/Al/Mg/ - Cheung, Deng, van Duin and Goddard, JPC-A 2005, 09, 85 - Ojwang, van Santen, Kramer, van Duin and Goddard, JCP B/N - an, Kang, Lee, van Duin and Goddard, JCP 2005, 23, an, Kang, Lee, van Duin and Goddard, JCP 2005, 23, Li/LiC - an, van Duin and Goddard, JPC-A 2005, 09, Mo/V/Bi/O/C/ - Goddard et al Topics in Catalysis 2006, 38 (-3) Chenoweth, van Duin, Oxgaard, Cheng and Goddard, accepted in JPC-A. - Cu/Zn/O/ - Raymand, van Duin, Baudin and ermannsson, Surface Science van Duin et al., in preparation. - Y/Zr/Ba/O/ - van Duin,, Merinov, Jang. and Goddard, W.A. JPC-A van Duin, Merinov, an, Dorso, Goddard, W.A. accepted in JPC-A Original ReaxFF Combustion; Appendix contains current equations Siloxane polymers Crack propagation Nanotube growth -storage C-oxidation catalysis Fuel cell membrane 7

8 ReaxFF energy terms system = bond lp over under val pen coa C 2 tors conj! bond vdwaals Coulomb - bond : bond energy; attractive term, directly derived from bond orders - lp : Lone pair energy; penalty for breaking up lone pairs in O, N - over : Overcoordination energy: penalty for overcoordinating atoms - under : Undercoordination energy: stabilizes undercoordinated atoms - val : Angle strain; equilibrium angle depends on bond order central atom - pen : Penalty for allene -type molecules ( 2 C=C=C 2 ) - coa : Angle conjugation; stabilizes NO 2 groups General - C2 : C 2 correction: destabilizes C=C - tors : Torsion energy: bond-order dependent V 2 -term Special case - conj : Torsion conjugation: general conjugation stability - -bond : ydrogen bond - vdwaals : van der Waals: calculated between every atom - Coulomb : Coulomb interaction: calculated between every atom; polarizable charges get updated every iteration 8

9 ReaxFF general energy terms = system bond over val tors vdwaals Coulomb Covalent materials - bond : bond energy; attractive term, directly derived from bond orders - over : Overcoordination energy: penalty for overcoordinating atoms - val : Angle strain; equilibrium angle depends on bond order central atom - tors : Torsion energy: bond-order dependent V 2 -term - vdwaals : van der Waals: calculated between every atom - Coulomb : Coulomb interaction: calculated between every atom = system system bond = vdwaals system = vdwaals over = system bond over Coulomb vdwaals vdwaals Coulomb Metal alloys Metals Ionic materials Noble gases 9

10 ReaxFF flow diagram Covalent interactions Find angles and torsions angle, tors Atom positions Determine bond orders BO Correct BO for local overcoordination bond, over Charges and polarization energies Coulomb system vdwaals Non-bonded interactions 0

11 Calculation of bond orders from interatomic distances BO ij & = exp $ p $ % bo, & exp $ p $ % & exp $ p $ % p bo, 2, r # ij ) - *! / Sigma bond r o (!" bo,3 bo,5, r ij - * r o., r - * r o ij.. Double pi bond ) ( p ) ( bo,4 p #!! " bo,6 #!!" Pi bond Bond order Bond order (uncorrected) Sigma bond Pi bond Double pi bond Interatomic distance (Å)

12 Bond order correction Uncorrected bond orders in ethane C 0.95 C ΣBO C =4.6 ΣBO =.7 - Unphysical; normally coordinated atoms should not have binding interactions with next-neighbours - Puts strain on angle and overcoordination potentials - Short-range bond orders will not capture transition states 2

13 Corrected bond orders BO " ij = BO " ij # f ($ i BO % ij = BO % ij # f ($ i " i boc = #Val i boc,$ j,$ j BO %% ij = BO %% ij # f ($ i neighbours(i ) BO ij $ j = )# f 4 ($ i,$ j )# f ($ i BO ij = BO ij " BO ij % BO ij %% f (" i," j ) = 2 # $ & % f 2 (" i f 3 (" i f 4 (" i," j )# f ($ i,bo ij,$ j,$ j )# f 5 ($ j )# f 4 ($ i Val i f 2 (" i," j ) Val i f 2 (" i ) = exp(# p boc $ " i %," j ) = #,BO ij ) = 0.0 C ," j 0.95 Uncorrected bond orders 0.0 ) f 3 (" i 0.0 )# f 4 ($ i," j,bo ij ),BO ij,bo ij ) exp(# p boc $ " j ) $ ln p boc2 2 $ exp # p $ " & boc 2 i )# f 5 ($ j )# f 5 ($ j,bo ij ),BO ij ) ) Val j f 2 (" i," j ) Val j f 2 (" i," j ) f 3 (" i [ ( ) exp (# p boc 2 $ " j )] exp(# p boc 3 $( p boc 4 $ BO ij C $ BO ij ( ) * # " boc i ) p boc 5 ) Corrected bond order ," j 0 ) )( undercoorinated systems (radicals) Uncorrected bond order - Normally coordinated carbon will not make weak bonds, under-coordinated carbon (radical) can make weak bonds (no correction) Sum of bond orders on! BO carbon

14 Uncorrected bond orders Corrected bond orders C C 0.94 C C ΣBO C =4.6 ΣBO C =3.88 ΣBO =.7 ΣBO = Correction removes unrealistic weak bonds but leaves strong bonds intact - Increases computational expense as bond orders become multibody interactions - Correction only applied for covalent-systems, not for metals 4

15 Overcoordination Avoid unrealistically high amounts of bond orders on atoms nbonds BO (C)=3 i= i, j nbonds BO (C)=4 i= i, j nbonds BO (C)=5 i= i, j # over i = f ( BO = Valency i ij ) $ # " i $ exp( % $# neighbours! j= BO ij i ) Atom energy nbonds BO i, j i= 5

16 ReaxFF flow diagram Covalent interactions Find angles and torsions angle, tors Atom positions Determine bond orders BO Correct BO for local overcoordination bond, over Charges and polarization energies Coulomb system vdwaals Non-bonded interactions 6

17 Valence and torsion angles non-reactive force field φ >φ ο Bond orders: φ ( ) angle = ka! # "# 2 o Bond orders: 0.4 Angle energy ReaxFF Non-reactive: = k!( " ) Reactive: # # 2 angle a o [ ( )] $ " exp # 3 $ BO 3 [ ( b) ] $ k a " k a exp "k b $ % "% o angle = " exp # 3 $ BO a 3 φ ο φ Angle [ ( ) 2 ] { } Bond-order dependent part - quilibrium angle is bond-order dependent - Stronger pi-bond character increases equilbrium angle 0 ( BO) =! # " $ { # exp[ # pval $ ( 2 # f ( ))] } " BO 0,0 0! BO BO a b = Bond order a = Bond order b! = Angle! o = quilibrium angle

18 ReaxFF flow diagram Covalent interactions Find angles and torsions angle, tors Atom positions Determine bond orders BO Correct BO for local overcoordination bond, over Charges and polarization energies Coulomb system vdwaals Non-bonded interactions 8

19 Nonbonded interactions j l i k m Non-reactive force field: ignore vdwaals and Coulomb interactions between atoms sharing a bond (I-j, j-k, k-l and l-m) or a valence angle (I-k, j-l and k-m). These exception rules are very awkward when trying to describe reactions. ReaxFF: calculate nonbonded interactions between all atom pairs, regardless of connectivity. To avoid excessive repulsive/attractive nonbonded interactions at short distances both Coulomb and van der Waals interactions are shielded in ReaxFF. 9

20 000 nergy (kcal/mol) Shielded vdwaals and Coulomb interactions Unshielded Coulomb Shielded Coulomb Unshielded vdwaals Shielded vdwaals q i " q j Coulomb = C " $ % r 3 ij /# & ij ( ) 3 Shielded Coulomb potential ( ) / Interatomic distance (Å) vdwaals: Shielded Morse potential - For metals ReaxFF only uses bond energy, overcoordination, vdwaals and Coulomb-terms (no angle or dihedrals) - vdwaals and overcoordination terms serve as a densitydependent repulsive term (as used in AM-potentials [Daw and Baskes, PRB 984] ), allowing ReaxFF to describe bulk metals - We have recently added an additional, repulsive Morse at very short distances and removed the vdwaals shielding to avoid Coulomb-collapse at high energy and density 20

21 , 3, 3 2, 3 2, , 3, =!! " # $ $ % &!! " # $ $ % & = ( (!! " # $ $ % &!! " # $ $ % & = ( (!! " # $ $ % &!! " # $ $ % & = ( ( ) ) ) ) = = = = n i i n j j n j n j n n n n n j j j j n j j j j q r q C q q r q C q q r q C q q *, *, *, Charge polarization - Assign one electronegativity and hardness to each element; optimize these parameters against QM-charge distributions - Use system geometry in solving electronegativity equilibration equations in every iteration M-method (Mortier et al., JACS 986); shielding: Janssens et al. J.Phys.Chem Similar to Qeq-method (Rappe and Goddard, J. Phys. Chem. 99) with empirical shielding correction. χ: atom electronegativity η: atom hardness γ: shielding parameter r: interatomic distances q:atom charge

22 0.26 ReaxFF charges QM Mulliken charges DFT; 6-3G ** Good reproduction of Mulliken charges (similar concepts) - Combined with -2 Coulomb-interactions, this enables ReaxFF to simulate polarization effects on local chemistry - M/Qeq methods work well around equilibrium; incorrect description of charge flow at high compression and dissociation (Chen and Martinez, Chem.Phys.Lett. 2006) - Most expensive part of the reactive force field; needs to be 22 updated every MD-step and forces sub-femtosecond steps

23 Force field development for Si/SiO systems = Covalent system bond over val vdwaals Coulomb - bond : bond energy; attractive term, directly derived from bond orders - over : Overcoordination energy: penalty for overcoordinating atoms - val : Angle strain; equilibrium angle depends on bond order central atom - tors : Torsion energy: bond-order dependent V 2 -term - vdwaals : van der Waals: calculated between every atom - Coulomb : Coulomb interaction: calculated between every atom - Concept: build a QM-based database (training set) that describes reactive and non-reactive aspects of the material and optimize ReaxFF to reproduce these QM-data. - Bigger (more extensive) training sets yield more transferable force fields (but longer development time!) - Things to include in training sets: charges, bond dissociation, angle bending, under/overcoordination, key reactions with transition states, equations of state tors materials 23 Adri van Duin, Alejandro Strachan, Shannon Stewman, Qingsong Zhang, Xin Xu and Bill Goddard, Journal of Physical Chemistry-A 2003

24 Charges - Fit atom electronegativities and hardnesses to QM-based charge distributions QM/Mulliken charge ReaxFF charge = system bond over val vdwaals Coulomb 24

25 Bond energy O-Si(O) 3 bond 300 nergy (kcal/mol) Si-O distance (Angstrom) DFT Singlet DFT Triplet ReaxFF Other SiO bonds: - Si-Si - Si=Si - Si=O - Si- - O-O - O=O - O- = system bond over val vdwaals Coulomb 25

26 Valence angle bending. Individual valence angles 3 Si-Si 2 -O angle nergy (kcal/mol) Angle (degrees) DFT ReaxFF Other SiO angles: - Si-Si-Si - Si-Si- - Si-O-Si - -Si- - Si-Si- - -O- - Si-O- - O-O-O - O-Si- - Si-O-O - O-O- 26

27 Valence angle bending 2. Ring deformation 50 nergy (kcal/mol) r DFT ReaxFF r (Angstrom) 27

28 Valence angle bending 3. Ring size/ring strain Δ/SiO 2 (kcal/mol) QC ReaxFF 0 Monomer system 4-ring 6-ring 8-ring 0-ring 2-ring = bond over val vdwaals 4-ring Coulomb alfa- Quartz 28

29 Over/undercoordination Δ (DFT) Δ(ReaxFF) Si(O) 4 O-O 3 Si-O-Si 3 3 Si-Si 3 Si(O) kcal/mol 48.2 kcal/mol O(Si 3 ) kcal/mol 87.4 kcal/mol O 2 Si Si 2 2 Si O Si kcal/mol 35. kcal/mol O 2 Si Si 2 2 Si Si O 67.8 kcal/mol 75.5 kcal/mol = system bond over val vdwaals Coulomb 29

30 Reactions. 2 Si=O 2 Si=O 4-ring 50 nergy (kcal/mol) DFT ReaxFF Si-Si distance (Å) 30

31 Reactions 2. 2 O- incorporation in a Si-cluster 20 DFT 0 ReaxFF nergy (kcal/mol) Reactive force field can be used to simulate the entire reaction pathway 3

32 nergy/si (ev) ReaxFF quations of state crystals. All-Si crystals Si(a) Si(b) Si(sc) Force field recognizes high-pressure transition from 4-coordinated (α) to 6-coordinated (β) phase QC Si(a) Si(sc) Si(b) Volume/Si (Å 3 )

33 Compression/expansion crystals 2. Silicon oxide crystals nergy/sio 2 (kcal) ReaxFF QC Volume/SiO 2 (Å 3 ) - ReaxFF reproduces the QC-data for both the clusters as well as the condensed phases. = system bond over val vdwaals Coulomb 33

34 Correcting a finished ReaxFF force field MD-anneal run on bulk phase Si-α with original ReaxFF - Original ReaxFF overstabilizes 5-coordination for silicon bulk phase 5-coordinate 34 Si-phase

35 Re-optimize ReaxFF with equation of state for 5-coordinate Si-phase ReaxFF QC nergy/atom (kcal) Si(alfa) Si(beta) Si(cubic) Si(5-coor) nergy/atom (kcal) Si(alfa) Si(beta) Si(cubic) Si(5-coor) Volume/atom (Å 3 ) Volume/atom (Å 3 ) - Re-optimized ReaxFF gets proper stability for 5-coordinate Si-phase - 5-coordinate phase is more stable than 6-coordinate Si(β)! - 5-coordinate Si might be important in amorphous Si 35

36 MD-anneal run on bulk phase Si-α with ReaxFF Amorphous 36

37 - ReaxFF describes proper, brittle behaviour of crack propagation in silicon - ReaxFF can be used to simulate effects of corrosive reactants ( 2 O, 3 O, O 2 ) on crack propagation speed ydrogen-terminated Si-slab ReaxFF NVT (00K) MD-simulation 37

38 ReaxFF/CMDF application to crack propagation in silicon (0) crack surface, 0 % strain Crack Speed vs. Loading () (00) crack surface, 0 % strain Crack Speed (m/s) ReaxxFF and Tersoff potentials auch et al. (experimental) Stillinger Weber DIP force field G/Gc ReaxFF Tersoff - xcellent agreement with experiment - ReaxFF can predict material properties not covered specifically by its QM-training set Buehler, van Duin and Goddard, PRL 2006, 96, Buehler, Tang, van Duin and Goddard, PRL 2007, 90,

39 Restrained dynamics ZnO/ 2 O MD(300K) Cu/Zn oxides With David Raymand (Uppsala) Partially hydroxyl covered surface 5Si(O) 4 O - Si 5 O O With Thuat Trinh (indhoven) Zeolite growth Dendrimers/metal cations ReaxFF for water Pt/Ni fuel cells Nafion fuel cell MP2/6-3G(**) ReaxFF Jahn-Teller distorted Cu( 2 O) 6 2 -cluster Amines/ carboxylate pka With Peter Fristrup nzymes/ DNA/ organic catalysis Phosphates/sulfonates With Ram Devanathan (PNNL)) 39

40 Conclusions - We have developed a ReaxFF potentials for a large section of the periodic table. These force fields all use the same set of potential functions, making the method highly transferable - The low computational cost of ReaxFF (compared to QM) makes the method suitable for simulating reaction dynamics for large (>> 000 atoms) systems (single processor). ReaxFF has been parallelized, allowing reactive simulations on >>000,000 atoms. - The low computational cost and high transferability of the ReaxFF method opens up new areas for simulations of chemistry at the atomic scale : not currently described by ReaxFF 40

41 Acknowledgements -This work was sponsored by NSF, ONR/MURI-SOFC and Dogrants - Additional funding for ReaxFF development at MSC was provided by ONR, DARPA/PROM, ARL, ASC, Seiko-pson, Nissan, Intel and Dow-Corning - Initial funding for ReaxFF development was provided by the British Royal Society More information on ReaxFF: -Website: --mail: duin@wag.caltech.edu 4