1. Simulations of Physical & Chemical Processes in Gas, Liquid, and Solid Phases Donald L. Thompson University of Missouri-Columbia MURI Review October 27, 2004

2. Collaborators Dr. Paras M. Agrawal (OSU) Prof. Saman Alavi (MU) Prof. Rod Bartlett (U.Fla.) Prof. Carol Deakyne (MU) Prof. Yin Guo (OSU) Dr. Larry Harding (ANL) Mr. Josh McClellan (U.Fla.) Mr. Michael McNatt (MU) Dr. Betsy M. Rice (ARL) Dr. Igor Takmakov (MU) Dr. Gustavo F. Velardez (MU) Dr. Al Wagner (ANL)

3. Overview Physical Properties and Processes Melting Gas-Phase Reactions Using Ab Initio PESs: Fitting Surfaces and Direct Dynamics Chemistry in the Condensed Phases Rate Calculations in Liquids Simulating Impact A report on work in progress…

4. Physical Properties and Processes: Condensed Phases Pre-MURI: Sorescu-Rice-Thompson Crystal Models Liquid Nitromethane MURI: (with Dr. Betsy Rice, ARL) Practical methods for simulating melting  Applications: Rare gases, Nitromethane, TNAZ, RDX, PETN

5. Approaches: Melting Simulations Direct heating of the solid Straightforward to perform Superheating effect due to  G s- interface formation Over-estimation of MP ~ 5%-25%, many cases ~20% Extrapolation of the free energy of solid and liquid phases Accurate determination of melting point (no superheating) Difficult to set up for ionic and complex molecular solids Constant energy two phase solid-liquid simulation Accurate determination of melting point Time consuming, difficult for complex systems Heating of the solid with voids Straightforward to perform Superheating effect eliminated

6. Melting of Nitromethane (molecular solid) Direct heating Void nucleated S- in contact Melting Point: Expt: 244.7 K Calc’d: 255±10 K P. M. Agrawal, B. M. Rice, and D. L. Thompson, J. Chem. Phys. 119, 9617 (2003). Solid Liquid

7. Nitromethane Potential Sorescu, Rice, and Thompson, J. Phys. Chem. B 104, 8406 (2000). Agrawal, Rice, and Thompson, J. Chem. Phys. 119, 9617 (2003).

8. TNAZ, RDX, PETN Melting A work in progress… A paper is being written on the lessons we have learned Force fields are inadequate: All predict too high MP Ultimately, we want to use the MURI potential. But, it would be useful to have simple FF models

9. Gas Phase Chemistry The Challenges:  Develop methods for simulating the sequential, branching decomposition of large molecules to form small stable product molecules.  Predict rates of elementary reactions involving many atoms (e.g., RDX, TNAZ, DMNA …)

10. What we are doing  Reactions  TNAZ dissociation  DMNA dissociation  H 2 CN dissociation  H 2 CN + OH and other small molecules and radicals  Using quantum chemistry to explore potential energy surfaces  TST calculations using the quantum chemistry results  Developing analytical PESs for MD simulations  Developing better fitting methods  Direct dynamics (forces-on-the-fly)

11. Methods for Fitting Ab Initio PESs  Methods that allow facile, accurate local fitting of ab initio points to give global fits and for use in direct dynamics simulations. Partial Support from DOE Collaborator: Larry Harding & Al Wagner * J. Phys. Chem. A 107, 7118 (2003). J. Chem. Phys. 119, 10002 (2003). J. Chem. Phys. 120, 6414 (2004). J. Chem. Phys. 121, 5091 (2004). Approximate –Fits at critical points Real Fitted  Interpolating Moving Least Squares (IMLS) methods*  Application: H 2 CN dissociation and reactions  Methods for coupling PESs for molecules, radicals, & intemediates via TSs** **J. Chem. Phys. 118, 1673-1678 (2003). H 2 CN Dissociation

12. Direct Dynamics Simulations of the Unimolecular Decomposition of CH 3 NO 2 CH 3 NO 2 → CH 3 + NO 2 Objectives: Apply Bartlett’s transfer hamiltonian in simulations Calculate ∂V/∂r on-the-fly using a simple Hamiltonian Potential and Forces NDDO-SRP semi-empirical MO theory Specific Reaction Parameters (SRP) Starting with AM1 values, optimize SRP to reproduce: i)equilibrium bonds ii)UCCSD/TZP forces along the C-N bond fission coordinate Work in Progress Next: SRP for additional reaction channels (e.g., CH 3 NO 2 → CH 3 ONO → CH 3 O + NO) Igor Tokmakov (MU) Josh McClellan (U.Fla.) Rod Bartlett (U.Fla.)

13. What we have done (a work in progress): Performed DFT (B3LYP): 6-31G(d,p) calculations to map out PES Identified and characterized reactants, intermediates, transition states, and products of TNAZ decomposition reactions, providing a general map of the potential energy surface. The geometries, energies and vibrational frequencies of all species are calculated at a uniform level of theory. Sequential, branching decomposition of large molecules TNAZ Good prototype for our purposes Experimental data (although not necessarily definitive) Proposed sequentially branching mechanisms

14. TNAZ Zhang-Bauer Mechanism + + + NO 2 C 3 H 4 + NO 2 + HONO Y.-X. Zhang & S. H. Bauer, J. Phys. Chem. A 102, 5846 (1998).

15. Lee & Coworkers: TNAZ Mechanism N 2 O 2 + C 3 H 4 + NO 2 D. S. Anex, J. C. Allman, and Y. T. Lee, in Chemistry of Energetic Materials, ed. by G. A. Olah and D. R. Squire (Academic Press, New York, 1991), pp.27-54.

16. E – E(TNAZ) (kcal/mol) TNAZ TSs HONO + * + The initial energy barriers to reaction are approximately the same for the different pathways. Initial Steps

17. HONO elimination 38 kcal/mol 44 kcal/mol 45 kcal/mol 41 kcal/mol TNAZ: Barriers to Initial Reactions NO 2 elimination

18. E – E(TNAZ) (kcal/mol) TNAZ ONNO + C 3 H 4 + 2NO 2 Fig. 4 + NO 2 + NO 2 + ONNO + * + NO 2 NO 2 + TS NO 2 + 2NO 2 + + 2NO 2 2NO 2 + NO 2 + Steps following C-NO 2 bond fission triplet ? ? ?

19. TNAZ E – E(TNAZ) (kcal/mol) NO 2 + 2NO 2 + NO 2 + + * TS 2NO 2 + triplet singlet Steps following N-NO 2 bond fission ? ? ?

20. E – E(TNAZ) (kcal/mol) TNAZ TS Fig. 6 HONO + 2NO 2 + HCN + HCCH + HONO + 2NO 2 TS HONO + C≡CNO 2 + C=NNO 2 HONO + * + TS + HCN + HONO + NO 2 + Steps following HONO elimination

21. TNAZ We now have the information needed to compute RRKM rates for unimolecular steps Need to calculate IRCs Develop analytical PESs Higher level calculations desirable, but low-level results sufficient for developing methods

22. DMNA Decomposition Quantum Chemistry Calculations to determine decomposition Pathways: barrier, intermediates Calculate IRCs Calculate rate

23. DMNA N-N Bond Fission (CH 3 ) 2 N NO 2

24.  = 1407i cm -1 DMNA CH 3 CH 2 N + HONO DMNA HONO Elimination

25. DMNA Nitro-Nitrite Isomerization =318.9i cm -1 cis-(CH 3 ) 2 NONO DMNA

26. Bimolecular Reactions Nizamov and Dagdigian: (J. Phys. Chem. A 2003, 107, 2256.) Reported the room-temperature rate constant for the H 2 CN + OH reaction Concluded that H-atom abstraction giving HCN + H 2 O is the predominant reaction channel. We have performed B3LYP/6-31G(d,p) & G2 calculations Identified likely products Eventually – Calculate rate constants

27. Reaction channels considered H 2 CN + OH  HCN + H 2 O(1)  H 2 CNOH(2)  H 2 CONH(3)  H 2 CN(H)O(4)  CH 3 NO(5)  CH 3 ON(6)  HCON + H 2 (7)  HCNO + H 2 (8)  HNCO + H 2 (9)  H 2 CNH + O(10) G2 predicts that (9) is thermodynamically the most favorable. It is more exoergic than reaction (1) by 10 kJ/mol and at least 150 kJ/mol more exoergic than the remaining 8 reactions. Currently – searching for TSs and calculating IRCs for each reaction \

28. Impact Studies: Nitromethane Objectives & Topics –Impact dynamics Study sub-detonation-strength shock simulations of solids, liquids, and gases: –Develop general codes to make and monitor sound, shock, and heat waves through systems –Study sound speeds through various mediums –Study energy transfer rates via sound and supersonic waves (where applicable) –Examine wave front shapes –Study energy transfer mechanisms, i.e. lattice vibrations (phonons) exciting intramolecular bonds (up-pumping), etc. Detonation strength (reactive) shock simulations of molecular systems –Heat Shocks Current Work in Progress –Code development for above objectives –Shock simulations on prototype atomic systems (i.e. Lennard-Jones,...) –Simulations carried out on prototype energetic molecular condensed phase nitromethane

29. Simulates an ~85 Å crystal layer by imposing 2D periodic boundary conditions in the x & y directions. Uses the potential developed by Sorescu, Rice, Agrawal, and Thompson for nonreactive solid, liquid, and gas phases Impacts of varying strengths are initiated by accelerating in the +Z direction a “flyer-plate” of ~1 unit cell (about 80 molecules in the X-Y plane) MD NVE simulations done using DL_POLY ~6.2 Å ~5.2 Å ~85 Å Shock Wave Y Z X Nitromethane 5x4x10 Supercell (800 molecules) Simulations Supercell

30. Time step 0.75 fs This plot gives ~3.3 km/s as the speed of sound through the solid at 50 K. (Å) (Å / ps) Å Shock front

31. Methods for reaction rate calculations in liquids The approach allows for the computation of reaction rates by using a relatively inexpensive stochastic method that is calibrated with the results a few full-dimensional MD simulations.  Application to date: HONO in liquid Kr cis-trans isomerization chemical decomposition  Next: Large molecules e.g., DMNA, TNAZ, RDX Y. Guo and D. L. Thompson, J. Chem. Phys. 120, 898-902 (2004). Y. Guo and D. L. Thompson, “On Combining Molecular Dynamics and Stochastic Dynamics Simulations to Compute Reaction Rates in Liquids: Bond Fission in HONO in Liquid Kr,”J. Chem. Phys., in press.

32. Plans  Continue studies of melting of energetic materials  Studies of RDX, PETN,… with improved force fields  Studies of RDX, PETN,… with MURI potential  Methods for fitting ab initio PESs for reactions  Continue developing IMLS fitting methods.  Apply Bartlett’s transfer hamiltonian approach.  Methods for coupling PESs for molecules, radicals, & intemediates via TSs  Rate calculations and dynamics calculations for decomposition reactions  Perform TST calculations using quantum chemistry results  Develop an analytical PES and perform MD simulations for conditions corresponding to the various gas-phase experiments.

33. Plans, continued  Simulations of shocked solids and liquids  Impact studies of nitromethane  Also: PETN & hydrazine (With Rice & Brenner)  Develop PESs and perform rate calculations for energetic molecules and radicals  We plan to perform quantum chemistry exploratory studies of DMNA decomposition channels.  Develop global PESs and perform MD simulations of the initial steps of nitramine decomposition  Perform direct dynamics  Methods for rate calculations for condensed-phase reactions  Applications to RDX (?)  Methods for simulating evaporation/sublimation

34. Publications & Preprints  Paras M. Agrawal, Betsy M. Rice, and Donald L. Thompson, “Molecular Dynamics Study on the Effects of Voids and Pressure in Defect-Nucleated Melting Simulations,” J. Chem. Phys. 118, 9680-9688 (2003).  Paras M. Agrawal, Betsy M. Rice, and Donald L. Thompson, “Molecular Dynamics Study of the Melting of Nitromethane,” J. Chem. Phys., in press.  Saman Alavi, Lisa M. Reilly, and Donald L. Thompson, “Theoretical Predictions of the Decomposition Pathways of 1,3,3 ‑ Trinitroazetidine (TNAZ)” J. Chem. Phys., in press.  Yin Guo and Donald L. Thompson, “On Combining Molecular Dynamics and Stochastic Dynamics Simulations to Compute Reaction Rates in Liquids,” J. Chem. Phys., in press. Preprints available upon request or at: http://www.chem.missouri.edu/thompson

35. The End http://www.chem.missouri.edu/thompson/MURI