Yanhong Hu, Postdoctoral Scholar , Kai Wang, Research Professor Donald Brenner, PI

1. Transferable, Quantum-Based Reactive Potentials for Simulating CHON Species: A Bridge Between ab initio Calculations and Condensed-Phase Reactive Dynamics Yanhong Hu, Postdoctoral Scholar, Kai Wang, Research Professor Donald Brenner, PI Materials Science and Engineering North Carolina State University, Raleigh, NC, 27695-7907

2. Program Objectives Develop an inter-atomic potential for HCNO molecular solids that • allows reactivity (i.e. bond breaking and forming with rehybridization) within and between molecules -multiple molecules react under low and high P conditions • is general and transferable between molecules -same potential function regardless of molecule -requires quantum-based functional forms, not ad hoc functions • reproduces high and low pressure structures -fit to molecular and solid structures (high & low coordination)

3. Program Objectives Continued... Develop an inter-atomic potential for HCNO molecular solids that • incorporates intermolecular vdW and Coulombic forces -must be consistent with reactivity • is suitable for large-scale simulations (106+ atoms) • is compatable with existing force fields -takes advantage of prior work by Rice, Thompson, etc.

4. Today Strategy • Bonding Forces: Reactive covalent bonding based on near-neighbor tight binding theory in the form of a bond order formalism. • Use screening criterion rather than distance to fullfill near neighbor requirement. • Non-bonded Forces: Fixed Dispersion (LJ) and Coulomb Interactions. • Transfer functions to ARL/Thompson • Variable charge/charge transfer • Validate, validate, validate Green: Largely doneYellow: In progressRed: Challenge to be met.

5. Today Team Synergies • Richard Martin has provided data for hypothetical high-coordination oxygen structures needed for effective potential fitting. • Rod Bartlett is providing data regarding reaction paths for validation (e.g. nitromethane geometries along the C-N rxn coordinate) • Betsy Rice has been working to incorporate functions into ARL/DoD modeling codes • Work with Don Truhlar on charge transfer • Validate, validate, validate Green: Largely doneYellow: In progressRed: To be initiated.

6. Bond ordermodulates attraction depending on • local coordination • bond angles • other environmental effects (e.g. p conjugation, rotation about double bonds) Pair terms model repulsive core-core interactions and attractive bonding from valence electrons bond energy decreases bond length increases Bonding Formalism Bond Order Potential - pair terms coupled to a bond order Bija (N)-1/2

7. 2 out in in sc sc sc Density of states moments description sc in sc Superposition of atomic orbitals in Self-consistent DFT Non-self-consistent Harris functional Bonding Formalism Density Functional Energy Tight Binding Energy Quantum Basis of the Bond Order Formalism 2nd moment: Eel=(m2)1/2=(N)1/2

8. Bond Order Equations Multi-step fitting process: First Step: • Near-neighbor pair terms (repulsive and attractive) and discrete empirical bond order values for monoelemental structures (molecules, clusters, and solids) fit to bond energies/ lengths/force constants. • Key feature - same pair potentials used for same elements, only difference being the value of the many-body bond order. • Produces pair terms and bond order values that are transferable between environments (molecules, solids).

9. Bond Order Equations Multi-step fitting process: First Step (continued): Assume pair functions: Nine parameters for the pair terms; one bond order per structure

10. sc bcc cd fcc N8 N4 N6 solids N2 Bond Order Equations First Step (continued): Nitrogen molecules

11. sc bcc cd fcc solids Bond Order Equations Oxygen First principles data First Step (continued): From Martin O3 O2 molecules

12. Bond Order Equations Carbon CH First Step (continued): CH2 CH3 fcc molecules sc molecules Single cd solids Graphite Double Triple

13. molecules Solids Bond Order Equations CN Some CN compounds have been predicted to be “super”-hard materials. The potentials developed here are also applicable to these systems. First Step (continued):

14. Bond Order Equations

15. Methyl hydrazine 1,2-dinitro cyclo- propane N-N Bonds C-C Bonds Bond Order Equations Transferable Effective Pair Potentials

16. Bond Order Equations Second Step: Fit bond order values to tight-binding-based functional form Multi-step fitting process:

17. bij = [1+G(cos(qijk1)+G(cos(qijk2))]-1/2 i-j bond order k3 k1 qijk1 qijk3 (3)-1/2 i j bji = [1+G(cos(qijk3)]-1/2 k2 qijk2 (2)-1/2 Bond Order Equations Tight Binding Result: ba(Z) -1/2 Bij = (bij+bji)/2 Bij = {A-1+[1+SGik(cos(Qijk)]-0.5}/A = 1-1/A + {1+ SGik(cos(Qijk)]-0.5}/A Constant Tight binding New parameter

18. Bond Order Equations Oxygen and nitrogen functions have minima around 110o, producing bent structures. Carbon has a minimum at 180o, creating a tendency for open structures. Example: Ammonia Carbon

19. Bond Order Equations Third Step: Linear combination of elemental bond order functions and add correction factors for mixed system. Because the tight binding theory is followed (b a (Z)-1/2) the corrections are small and the terms are transferable. Bij = (bij+bji)/2 bij ={ A - 1+C(N,C,O,H)+[1+SGik(cos(Qijk)]-0.5}/A Additional Hydrazine Fitting Data Base - bond energies/lengths for: NH HN2H H2N(NH)2NH2 NH2 H2N2H2 H3N2H3 NH3 (+ inversion barrier)

20. Screening • The tight binding theory requires that near-neighbors be defined, which is invaluable for fitting, but……. • How do you effectively define near neighbors without introducing severe cut-offs and associated non-physical forces? • Can this definition be used to incorporate intermolecular non-bonded forces?

21. Screening • We are utilizing an atomic screening function that analytically distinquishes between covalent and non-bonding forces: j j Screening function: i k i k No screening, Sij = 1 Screened, Sij = 0 • Potential Energies: Sij x bonded + (1-Sij) x nonbonded • Significantly smooths potential surface relative to distance dependent cut-off function • With the exception of O..H hydrogen bonding, the function does remarkably well for energetic molecular solids.

22. CH4 Symmetric Dissociation

23. CH3-H Dissociation

24. Screening Function Methyl Hydrazine CH3NHNH2 yellow: Intramoleulqr pink: Intermolecular

25. Screening Function 1,2-dinitrocyclopropane NO2C3H4NO2 yellow: Intramoleulqr pink: Intermolecular

26. Non- bonding H…H OK Typical intramolecular 2nd neighbor bonding Non- bonding bonding N…N too strong Screening Function • How to handle intramolecular electrostatics?

27. j m l k i Topology Function Need an analytic function that distiguishes between atom pairs in the same molecule and pairs in different molecules. j m k l i 2nd 3rd 4th ...

28. Screening Function • Partial charges vary within a molecule: • How do we compensate in the intramolecular bonding forces? This is where we are today!

29. Plans • Short-Term Plans (6 months): • Incorporate forces from the bond-order potential into our codes • Help with incorporating forces into ARL/Missouri codes • Validate against reaction paths from ab initio/Bartlett data. • Validate against shock/phase data (with Rice/Thompson) • Refine parameters as needed • Incorporate efficient partial charges into simulation codes (with Phillpot/Florida) • Long-Term Plans (6 months - 3 years) • Incorporate charge-transfer terms into potential (with Truhlar/Stuart(Clemson)) • Refit bond order terms terms including charge transfer as needed • Validate against phase and chemistry data