1. Theoretical Chemistry: Applications in Energetic Materials Research
Betsy M. Rice
U. S. Army Research Laboratory
Aberdeen Proving Ground, Maryland

2. Acknowledgements Donald L. Thompson, Oklahoma State University
Samuel F. Trevino, ARL
William Mattson, U. Illinois Urbana Champaign and ARL
Dan C. Sorescu, National Energy Technology Laboratory
John Grosh and Jen Hare, formerly of ARL
Herman Ammon, University of Maryland

3. OBJECTIVE Use standard theoretical chemical approaches to
Screen proposed materials—eliminate poor candidates before expending resources on synthesis, formulation and tests
Identify and understand the individual fundamental chemical and physical steps that control the conversion of the material to final products

4. METHODS Quantum Mechanics – First principles
Solution of HY=EY for collection of atoms - characterizes system
Provides information for parameterization of classical models
Molecular Dynamics – A classical simulation method
Integration in time of F=ma for every atom – requires model
Provides molecular-level details of chemical and physical processes through computer simulation of dynamic events
How a material responds to set of initial conditions at the atomic level.
What mechanisms control the response—will provide guidance on how to manipulate system such that desired response obtained.
Molecular Packing – A classical simulation method for “ab initio” crystal prediction
Evaluates lattice energy of molecule in a variety of possible crystalline environments – requires model
Ranks possible crystal structures (usually in order of increasing energy)
Provides density and details of structure of crystal (size, shape and position of atoms in it)
What we will learn from 2:
How a material responds to set of initial conditions at the atomic level.
What mechanisms control the response
Benefit of the information used:
Provides guidance on how to manipulate system such that desired response is obtained.

5. Prediction of Energetic Materials Properties
from correlations with charge distribution
Mapping out e- Density
Electrostatic Potential +
Electrostatic Potential: Helps analyze how the electrons are distributed in a molecule. The electrostatic potential represents the net electronic response of the electron cloud and the nuclei due to the probe at that point on the isosurface.
1 Nanometer
(electron poor)
CL20
(electron rich)

6. Correlations of Quantum mechanical predictions with bulk properties
B. M. Rice, S. V. Pai and Jennifer Hare, “Predicting Heats of Formation of Energetic Materials Using Quantum Mechanical Calculations”, Combustion and Flame, Vol. 118, p. 445 (1999).
Condensed Phase Heats of Formation:
COMPLETELY PREDICTED!
DHGas from quantum mechanics
DHSub and DH Vap estimated from correlation between bulk properties and electrostatic potential of a molecule.
J. S. Murray and P. Politzer, “A General Interaction Property Function (GIPF): An Approach to Understanding and Predicting Molecular Interactions” in “Quantitative Treatments of Solute/Solvent Interactions”, ed. P. Politzer and J. S. Murray, (Elsevier Pub. Co., New York, 1994).
B. M. Rice, S. V. Pai and J. Hare, “Predicting Heats of Detonation Using Quantum Mechanical Calculations”, Thermochemica Acta, Vol. 38, p. 377 (2002).

7. Impact machine
Weight
Measured Impact Sensitivity
Explosive
Sample
Drop
Height
(cm)
Explosives (in mg) placed in between on flat tool steel anvil and flat surface of tool striker.
2.5 kg drop weight is dropped from predetermined height onto the striker plate.
Result of the event (explosion or otherwise) is determined by sound, smell and visual inspection of the sample.
Drop height is varied, with height increased or decreased depending on result of previous event.
Sequence of tests carried out, with result quoted at h50, the height at which 50% of tests result in explosions.

8. B. M. Rice and J. J. Hare, “A Quantum Mechanical Investigation of the Relation Between Impact Sensitivity and the Charge Distribution in Energetic Molecules”, B. M. Rice and J. J. Hare, Journal of Physical Chemistry, Vol. 106, 1770 (2002).
11 cm
11 cm
28 cm
71 cm
22 cm
47 cm
141 cm
320 cm
490 cm

9. Evaluating the Model: Predicting Crystal Structures using molecular packing
b-HMX
a-HMX
d-HMX
Place single molecule in variety of crystalline environments
Using classical force field, minimize energy with respect to crystal parameters
Rank various crystal structures (usually lattice energy)

10. 8 Papers published in J. Physical Chemistry
Potential Energy Functions for classical molecular simulation of energetic molecular crystals
8 Papers published in J. Physical Chemistry
Transferability (4)
Limitations of Rigid Body Approximation (1)
Inclusion of Flexible Motion (1)
Behavior in Liquid State(1)
Current investigation: prediction of crystal structure using molecule packing
RDX; Minimum criteria for a good model
Correct no. of molecules in unit cell
Correct size and shape of unit cell
(cell dimension to within 2% of experiment)
Correct relative orientation (tilt) of molecules
(within 2º)
Correct spatial distribution of molecules
(Translation of centers-of-mass < 0.1Å)
D. C. Sorescu, B. M. Rice and D. L. Thompson, “Intermolecular Potential for the Hexahydro-1,3,5-trinitro-1,3,5-triazine Crystal (RDX): A Crystal Packing, Monte Carlo and Molecular Dynamics Study,” the Journal of Physical Chemistry B, vol. 101, pp , 1997.

11. MOLPAK (MOLecular PAcKing) J. R. Holden, Z. Du and H. L. Ammon, J. Comp. Chem. 14, 422 (1993)
Uses rigid-body molecular structure to provide packing arrangements in 13 space groups.
Triniclinic: P1, P-1
Monoclinic: P21, P21/c, Cc, C2, C2/c
Z=4 Orthorhombic: P21212, P212121, Pca21, Pna21
Z=8 Orthorhombic: Pbcn, Pbca
MOLPAK search produces “initial guesses” --- needed to energy refinement. For each space group ~7000 “Possible structures” are generated.
25 most dense structures are further refined using WMIN

12. How good is the force field?
Applied to 39 nitramine and non-nitramines
From Nitramine and non-Nitramine paper, nitrocubane series
Predicted experimental structure for 38 of 39 (1 catastrosphic failure, believed numeric) – max. deviation no more than 4% in edge length, largest deviation of cell angle is 7º.
Low-energy structure is experimental structure for 28
For remaining 10 cases, all within 1.5 kcal/mol of low-energy structure; 7 were within 0.4 kcal/mol.

13. Tetradecanitrobicubane
Modeling Results for candidate materials from ARDEC
Rapid Assessment N O 2
Heat of Formation (solid): kcal/mol
Heat of Detonation: 1.41 (kcal/g)
h50%: 9 cm
Density of low-energy structure:
1.77 g/cc
Tetradecanitrobicubane
Heat of Formation (solid): 242 kcal/mol
Heat of Detonation: 1.81 (kcal/g)
h50%: 68 cm
Density of low-energy structure:
1.81 g/cc

14. Ab initio crystal prediction of chemical families of explosives:
What now?
Ab initio crystal prediction of chemical families of explosives:
Nitrocubane series (6 have been resolved)
Nitramines (71)
Nitrate Esters (32)
Notified October 4 that team consisting of Rice, Mattson, (ARL), Ammon (U MD), Singh (NRL) and Kim (U Miss) awarded 2003 DOD High Performance Computing Modernization Plan CHSSI grant to parallelize MOLPAK and incorporate DOD Planewave

15. MOLECULAR DYNAMICS SIMULATION OF DETONATION
Model Explosive: A-B. Reactions that can occur:
2 A-B  A2 + B2
A-B  A + B
Initial crystal at 10 K, molecules arranged in equilibrium configuration
Left side of plate hit with flyer plate of molecules moving at a very high speed. The impact compresses the quiescent crystal, and a shock wave propagates through the material.
Reactions begin, and heat released from the reaction drives the shock-wave, resulting in a self-sustained detonation

16. The frame at the top of the figure shows the solid explosive, and the lower frame is a zoom window that will be centered on a shock wave that traverses the crystal. A shock is initiated by a flyer plate, and rapidly proceeds through the crystal. Behind the shock front are product molecules, formed with extreme energy release that drives the shock wave forward. The properties of the reaction wave are consistent with those associated with a detonation; however, the chemical model is highly idealized due to computational limtitations. (Go back, discuss limitations)

17. MOLECULAR SIMULATION OF DETONATION
B. M. Rice, W. Mattson, J. Grosh and S. F. Trevino, “A Molecular Dynamics Study of Detonation: II. The Reaction Mechanism”, Physical Review E, Vol. 53, 623 (1996).
B. M. Rice, W. Mattson, J. Grosh and S. F. Trevino, “A Molecular Dynamics Study of Detonation: I. A Comparison with Hydrodynamic Predictions”, Physical Review E, Vol. 53, 611 (1996).
Reaction Mechanism: Pressure-induced atomization, little thermal excitation

18. Intramolecular bonds (covalent)
REBO Potentials
The Bij term is a short-range function that introduces many-body effects into the interaction between two atoms that are within a range typically associated with a covalent bond.
Bij = 1 corresponds to isolated molecule
Intramolecular bonds (covalent)
Intermolecular
bonds
Bij + 

19. DESENSITIZATION OF DETONABLE MATERIAL
B. M. Rice, W. Mattson and S. F. Trevino, “Molecular Dynamics Investigation of the Desensitization of Detonable Material”, Physical Review E, Vol. 57, (1998).

20. Reactive Potentials
Reactive Force Fields (ReaxFF) (Goddard et al., Center for Simulation of Dynamic Response of Materials, California Institute of Technology)
Uses QM calculations to parameterize a function
Applied to RDX and HMX
Flyer-plate shock simulations show:
Initiation threshold exists
Large fraction of products have been observed in experiment
Some unlikely fragments
Improvements will include products of secondary reaction channels
Uses QM (isolated molecule) calculations to parameterize a function
Applied to RDX and HMX
Preliminary results of flyer-plate shock simulations show:
Initiation threshold exists
Large fraction of products have been observed in experiment
Some unlikely fragments
Improvements will include products of secondary reaction channels
Chakraborty, D.; Muller, R. P.; Dasgupta, S.; Goddard, W. A., J. Phys. Chem. A 2000, 104, 226.

21. SUMMARY
Theoretical chemistry calculations will provide information necessary to tailor explosives – BUT OFTEN RESULTS ARE COMPLETELY DEPENDENT ON QUALITY OF THE MODEL
Realistic classical molecules exist for non-reactive events for CHNO explosives -- are not bad
Reactive potentials—basic concepts there, but need additional and better information for parameterization
Direct Ab initio MD simulations progressing, not quite there, but extremely promising