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1、Reactive Empirical Force Fields,Jason Quennevillejasonqlanl.govX-1: Solid Mechanics, EOS and Materials PropertiesApplied Physics DivisionLos Alamos National LaboratoryTimothy C. Germann, Los AlamosAlejandro Strachan, PurdueAdri C. T. van Duin, Caltech William A. Goddard III, CaltechAlexei A. Stucheb
2、rukhov, UC Davis,2019 Summer School on Computational Materials ScienceJuly 31 - August 11, 2019 University of Illinois,Reactive Empirical Force Field,Motivation,Empirical force fields are used in biology, chemistry, physics and materials science to calculate the potential energy surface and atomic f
3、orces.Most, like CHARMM and AMBER, assume the same atomic connectivity (molecular composition) throughout simulation.No Chemistry! Straightforward solution: ab initio or QM/MM (up to 300 atoms for QM system)For materials simulation, we may want 10s of 1000s to millions of atoms and as much as a nano
4、second of simulation time. Need a more efficient method!,MotivationEmpirical force fiel,Empirical Force Fields,Empirical force fields contain potential energy functions for each atomic interaction in a molecular system.Bond Stretch:Bond Bending:Bond Torsion:Parameters can be taken from experiment (e
5、.g., vibrational spectroscopy) or from ab initio quantum chemistry calculations.,Empirical Force FieldsEmpirica,Non-Bonded potentials give the intermolecular interactions:Coulomb:van der Waals: Parameters obtained through ab initio quantum chemistry and liquid simulations.e.g. OPLS (optimized potent
6、ials for liquid simulations, W. L. Jorgensen and J. Tirado-Rives, J. Am. Chem. Soc. 110, 1657 (1988). ),Empirical Force Fields,Non-Bonded potentials give the,Empirical Valence Bond (EVB),EVB attempts to combine empirical potential energy functions with valence bond ideas to describe chemical reactio
7、ns efficiently and accurately.EVB Applications Proton transport in aqueous acid (CPL, 284, 71 (98); JPCB, 102, 5547 (98) Aqueous acid-base reactions (JPCA, 105, 2814 (01) Enzyme catalysis (Warshel) Nucleophilic substitution reactions Good Introduction:Computer Modeling of Chemical Reactions in Enzym
8、es and Solutions, A. Warshel Wiley-Interscience (02/01/2019),Empirical Valence Bond (EVB)EV,EVB: introduction,EVB starts with a NN potential energy matrix: N diabatic states (diagonal) N(N-1) couplings (off-diagonal)Each diabatic state looks like a configuration in a standard non-reactive force fiel
9、d.Off-diagonal coupling elements: interaction between each diabatic state and the N-1 remaining states.Diagonalize V adiabatic states. The minimal value is the ground state.,coupling term,adiabatic ground state,diabatic states,EVB: introductionEVB starts wi,Calculation of Forces,Diagonalizing the NN
10、 EVB matrix yields the ground state as a linear combination of diabatic states. If an is the set of corresponding coefficients, the forces can be calculated using the Hellman-Feynman theorem:,Calculation of ForcesDiagonali,EVB: diagonal matrix elements,Because we need to treat bond breaking and form
11、ation, the Bond Stretch should be anharmonic:Bending and Torsional potentials can be as before:System-environment interactions treated with standard non-bonding potentials:,EVB: diagonal matrix elementsB,Interaction between EVB States,System-system non-bonding interactions more complicated due to th
12、e potential for chemical reaction.A functional form more flexible than Coulomb + Lennard-Jones is required.The intermolecular interactions (part of the diagonal element) and the coupling terms (off-diagonal) must be parametrized together in order to describe the reaction correctly.In the activated c
13、omplex, the favorable interaction between the two states is controlled by the intermolecular interaction. It is normally written in terms of the distance between the two reactant centers.The reaction barrier is controlled by coupling term. This term is generally a function of the reaction coordinate
14、.,Interaction between EVB States,Optimized geometries of the H2OHOH2+ (left) and HOHOH (right) complexes, obtained from first principles (MP2/aug-cc-pVTZ).,Application: Proton Transfer in Water,1.2 1.2 0.97 0.97 0.97 0.,H,H,O,O,H,H,H,H,H,O,O,H,H,H,H,H,O,O,H,H,H,Diabatic States:,Adiabatic State:,EVB
15、of H3O+H2O Proton Transfer,HHOOHHHHHOOHHHHHOOHHHDiabatic,H3O+H2O Proton Transfer:Diagonal Elements,H3O+H2O Proton Transfer:Diag,H3O+H2O Proton Transfer:Coupling Elements,H3O+H2O Proton Transfer:Coup,EVB vs Ab Initio for H3O+/H2O,EVB vs Ab Initio for H3O+/H2O2,EVB Summary,Very good for systems with s
16、mall number of possible reactionsReaction barriers are treated explicitlyOffers an empirical description of chemical reactionsGives mixing of diabatic states during reactionCan be difficult to parametrize intermolecular potentials and couplingsLimitation on number of states due to diagonalization (c
17、ubic scaling),EVB SummaryVery good for syste,ReaxFF,Bond-Order potential, developed at CalTech by Adri van Duin and Bill GoddardPotential parametrized using ab initio calculations (B3LYP/6-31G*) on a “training set” of reactionsWhy bond-order based? non-reactive potentials have atom-types that define
18、 connectivity Applications:High Explosives, Propellants, Catalysis, Fuel Cells, Corrosion, Friction, etc.,HN NH,N N,+ H2,ReaxFFBond-Order potential, de,Background References,Bond Order/Bond Length relationship Pauling, J. Am. Chem. Soc., 69, 542 (1947).Reactive Empirical Bond Order (REBO) Johnston,
19、Adv. Chem. Phys., 3, 131 (1960). Johnston, Parr, J. Am. Chem. Soc., 85, 2544 (1963).Other Bond-Order Potentials Tersoff, Phys. Rev. Lett., 56, 632 (1986); Tersoff, Phys. Rev. Lett., 61, 2879 (1988). Brenner, Phys. Rev. B, 42, 9458 (1990). Brenner, et al, J. Phys.: Condens. Matter, 14, 783 (2019).Rea
20、xFF van Duin, Dasgupta, Lorant, Goddard, J. Phys. Chem. A, 105, 9396 (2019). Strachan, Kober, van Duin, Oxgaard, Goddard, J. Chem. Phys., 122, 054502 (2019). User Manual: wag.caltech.edu/home/duin/reax_um.pdf,Background ReferencesBond Orde,ReaxFF allows for computationally efficient simulation of ma
21、terials under realistic conditions, i.e. bond breaking and formation with accurate chemical energies.Due to the chemistry, ReaxFF has a complicated potential energy function:,ReaxFF Potential Energy Function,Charge equilibration: EEM (Mortier, et al, JACS, 108, 4315, (86).),ReaxFF allows for computa
22、tiona,Example: Acetylene Bond Order goes smoothly from 0 1 2 3 as C-C Bond Length shortens from large distance to 1.0 ,Bond Order, Bond Energy,not explicitly a function of bond distance,Bond Order,C-C Distance / ,Example: Acetylene Bond Order,Bond orders adjusted to get rid of unphysical bonds.,Bond
23、 Order Corrections,Over- and under-coordination of atoms must be avoided.Energy penalty added to the potential energy function for the case where an atom has more bonds than its valence allows.e.g., Carbon cant have more than 4 bonds; Hydrogen no more than 1If an atom is under-coordinated, the stabi
24、lization of p bonding should be used if possible.,Bond orders adjusted to get ri,Bond Angles, Bond Torsion,Bond Angles and Torsions are intimately tied to the bond types.With a bond order potential, angles and torsions must be written in terms of the bond order.Angle and torsion energy terms must 0
25、as B.O. 0.,See J. Phys. Chem. A, 105, 9396 (2019) for full potential form.,CCH 120,CCH = 180,Bond Angles, Bond TorsionBond,Lone Pair Electrons, Conjugation,The creation or reaction of lone-pair electrons should be assigned an energy term. Elone pair corresponds to an energy penalty for having too ma
26、ny lone pairs on an atom (i.e., overcoordination)Conjugated systems should have added stabilization.Econj has maximum contribution when successive bonds have bond-order values of 1.5.,implicit in AMBER/CHARMM-like potentialsthrough atom type,Lone Pair Electrons, Conjugati,Hydrogen bonding extremely
27、important in biological systems but also in many organic solids. X H YHydrogen bonds are calculated between group X-H and Y, where X and Y are atoms known to form H-bonds (e.g., N, O)The H-bond energy term is written in terms of the bond-order of X-H, the distance between H and Y, as well as the X-H
28、-Y angle.Can be an expensive part of the calculation because many acceptor (Y) atoms could be available for any given X-H group. All interactions must be calculated out to a cutoff distance (10 ) in order to remain consistent from timestep to timestep.,Hydrogen Bonding,Hydrogen bonding extremely imp
29、,- Short-range Pauli Repulsion- Long-range attraction (dispersion)- Coulomb forcesvan der Waals and Coulomb terms are included for all atom pairs (whether bonded or non-bonded)!This avoids changing the potential when chemistry occurs. Such alterations, which are natural in the EVB formalism, would b
30、e awkward in ReaxFF.Shielding included for both Coulomb and van der Waals in order to avoid excessive interaction between atoms sharing bond and/or bond angle.,Non-Bonded Interactions,Energy / kcal mol-1,Interatomic Distance / ,- Short-range Pauli RepulsionN,Charge Equilibration,The charge on an ato
31、m depends on the molecular species:Atomic charges are adjusted with respect to connectivity and geometry.Many QEq methods available. ReaxFF uses Electronegativity Equalization Method (EEM: Mortier, et al, JACS, 108, 4315, (86).)The desired charge distribution is that which minimizes,Final Coulomb en
32、ergy from screened potential all atom-pairs calculated,HN NH,N N,+ H2,Charge EquilibrationThe charge,ReaxFF/Ab Initio Comparison,ReaxFF can decribe a wide variety of chemical reactions.,Strachan, et al, JCP, 122, 054502 (05).,e.g., unimolecular decomposition of RDX,ReaxFF/Ab Initio ComparisonRea,103
33、,680 atoms(4320 molecules,121215 unit cells)256 processors,TATB,768 atoms(32 molecules,224 unit cells),Interested in chemical reaction dynamics of high explosives (HE) under shock conditions Want as big a system (105 to 106 atoms) as possible in order to study the spread of reactions, temperature di
34、stribution, carbon-clustering, etc.,Application: HE at High T, P,103,680 atomsTATB768 atoms Int,TATB,N2,H2O,CO2,Tinitial = 1700 K Tfinal = 3200 K,Decomposition of TATB at High T,TATBN2H2OCO2Tinitial = 1700 KD,GRASP (General Reactive Atomistic Simulation Program) developed at Sandia National Lab by A
35、idan P. Thompson. Objective: Parallel scalable MD code (C+) which enables implementation of a wide range of force field types, particularly reactive force fields, including ReaxFF.,CPU Time per timestep: serial code: 2.8 seconds parallel code: 0.6 seconds (32 CPUs) System size limits: serial code: 5
36、000 atoms parallel code: 500,000 atoms (510 CPUs),ASC Flash: 2.0-GHz procs 8 GB memory per node,ReaxFF in Parallel,CPU Time per timestep:ASC Fla,ReaxFF Summary,Can simulate chemistry for a wide range of materials significantly faster than ab initio and semi-empirical methodsAccuracy similar to semi-empirical methodsHydrocarbons, CHNO explosives, silicon oxides, etc.Main limitation is governed by the size of reaction training setUsed extensively for explosives under extreme conditions - many possible reactionsSimulation sizes up to a half million atoms,ReaxFF SummaryCan simulate che,
