Simulations ofPhysical & Chemical Processes in

Gas, Liquid, and Solid Phases

Donald L. ThompsonUniversity of Missouri-Columbia

MURI ReviewOctober 27, 2004

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)

Overview

Physical Properties and Processes Melting

Gas-Phase ReactionsUsing 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…

Physical Properties and Processes: Condensed Phases

Pre-MURI: Sorescu-Rice-Thompson

Crystal ModelsLiquid Nitromethane

MURI: (with Dr. Betsy Rice, ARL)Practical methods for simulating melting Applications: Rare gases, Nitromethane, TNAZ, RDX, PETN

Approaches: Melting SimulationsDirect heating of the solid

Straightforward to performSuperheating effect due to G s- interface formationOver-estimation of MP ~ 5%-25%, many cases ~20%

Extrapolation of the free energy of solid and liquid phasesAccurate determination of melting point (no superheating)Difficult to set up for ionic and complex molecular solids

Constant energy two phase solid-liquid simulationAccurate determination of melting pointTime consuming, difficult for complex systems

Heating of the solid with voidsStraightforward to performSuperheating effect eliminated

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

Nitromethane Potential

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

intrainter VVV

r

qq

r

C – e A ii

6ijrB-

ijinterij V

torsionbendstretchintra VVVV

112

)(stretch

0

iii rri eDV 20

21

bend )( iiikV

)cos(1torsion iiimVVi

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

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 …)

What we are doing

Reactions TNAZ dissociation DMNA dissociationH2CN dissociationH2CN + 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)

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 DOECollaborator: 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: H2CN dissociation and reactions Methods for coupling PESs for molecules, radicals, & intemediates via TSs**

**J. Chem. Phys. 118, 1673-1678 (2003).

H2CN Dissociation

Direct Dynamics Simulations of theUnimolecular Decomposition of CH3NO2

CH3- NO2 → CH 3 + NO2

(UCCSD/ TZP)

-80

-40

0

40

80

120

160

200

0.5 1.5 2.5 3.5 4.5

r(C-N), Ǻ

V(r

), k

cal/m

ol

CH3NO2 → CH3 + NO2

• Objectives: • Apply Bartlett’s transfer hamiltonian in simulations• Calculate ∂V/∂r on-the-fly using a simple

HamiltonianPotential and ForcesNDDO-SRP semi-empirical MO theory• Specific Reaction Parameters (SRP)Starting with AM1 values, optimize SRP to reproduce:i) equilibrium bondsii) UCCSD/TZP forces along the C-N bond fission

coordinate• Work in ProgressNext: SRP for additional reaction channels (e.g., CH3NO2 → CH3ONO → CH3O + NO) Igor Tokmakov (MU)

Josh McClellan (U.Fla.)Rod Bartlett (U.Fla.)

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 decompositionof large molecules

TNAZGood prototype for our purposesExperimental data (although not necessarily definitive)Proposed sequentially branching mechanisms

TNAZZhang-Bauer Mechanism

++

+ NO2+ NO2

C3H4 + NO2+ HONO + HONO

Y.-X. Zhang & S. H. Bauer,J. Phys. Chem. A102, 5846 (1998).

Lee & Coworkers: TNAZ Mechanism

N2O2 + C3H4

+ NO2 + NO2

+ NO2

+ NO2

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.

E –

E(T

NA

Z)

(kc

al/m

ol)

TNAZ

TSs

HONO +

*

+

The initial energy barriers to reaction are approximately the same for the different pathways.

Initial Steps

HONO elimination

38 kcal/mol

44 kcal/mol

45 kcal/mol

41 kcal/mol

TNAZ: Barriers toInitial Reactions

NO2 elimination

E –

E(T

NA

Z)

(kc

al/m

ol)

TNAZ

ONNO + C3H4

+ 2NO2

Fig. 4

+ NO2 +

NO2 + ONNO +

*

+ NO2

NO2 +

TS

NO2 +

2NO2 +

2NO2 +

+ 2NO2

2NO2 +

NO2 +

Steps following C-NO2 bond fission

triplet

?

?

?

TNAZ

E –

E(T

NA

Z)

(kc

al/m

ol)

NO2 +

NO2 +

2NO2 +

NO2 +

+NO2 +

*

TS

2NO2 + triplet

singlet

Steps following N-NO2 bond fission

?

?

?

E –

E(T

NA

Z)

(kc

al/m

ol)

TNAZ

TS

Fig. 6

HONO + 2NO2 +

HCN + HCCH +HONO +2NO2TS

HONO +C≡CNO2 +C=NNO2

HONO +

*

+

TS

+

HCN + HONO +

HONO + NO2 +

Steps following HONO elimination

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

DMNA Decomposition

Quantum Chemistry Calculations to determine decompositionPathways: barrier, intermediates

Calculate IRCs

Calculate rate

DMNA N-N Bond Fission

(CH3)2N NO2

Reaction Coordinate

-12 -10 -8 -6 -4 -2 0 2 4 6 8

Ene

rgy

(kca

l/m

ol)

0

10

20

30

40

50

60

= 1407i cm-1

DMNA

CH3CH2N + HONO

DMNAHONO Elimination

DMNA Nitro-Nitrite Isomerization

=318.9i cm-1

cis-(CH3)2NONO

DMNA

Bimolecular Reactions

Nizamov and Dagdigian: (J. Phys. Chem. A 2003, 107, 2256.) • Reported the room-temperature rate constant for the H2CN + OH reaction

• Concluded that H-atom abstraction giving HCN + H2O is

the predominant reaction channel.

• We have performed B3LYP/6-31G(d,p) & G2 calculations • Identified likely products • Eventually – Calculate rate constants

Reaction channels considered

H2CN + OH HCN + H2O (1)

H2CNOH (2)

H2CONH (3)

H2CN(H)O (4)

CH3NO (5)

CH3ON (6)

HCON + H2 (7)

HCNO + H2 (8)

HNCO + H2 (9)

H2CNH + 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 \

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

• 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 YZ

X

Nitromethane 5x4x10 Supercell (800 molecules)

Simulations Supercell

-2

-1

0

1

2

0.5000

1.0000

1.5000

2.0000

2.5000

-40 -30 -20 -10 0 10 20 30 40

Velocity Shock Wave Through a Thin Layer (~86 ang.) of Nitromethane Perfect Crystal

-200 m /s

-100 m /s 0 m /s 100 m /s 200 m /s • 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

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 isomerizationchemical decomposition

Next: Large moleculese.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.

Plans Continue studies of melting of energetic materials Studies of RDX, PETN,… with improved force fieldsStudies of RDX, PETN,… with MURI potential

Methods for fitting ab initio PESs for reactionsContinue 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 resultsDevelop an analytical PES and perform MD simulations for conditions corresponding to the various gas-phase experiments.

Plans, continued Simulations of shocked solids and liquidsImpact studies of nitromethaneAlso: PETN & hydrazine (With Rice & Brenner)

Develop PESs and perform rate calculations for energetic molecules and radicalsWe plan to perform quantum chemistry exploratory studies of DMNA decomposition channels.Develop global PESs and perform MD simulations of the initial steps of nitramine decompositionPerform direct dynamics

Methods for rate calculations for condensed-phase reactionsApplications to RDX (?)

Methods for simulating evaporation/sublimation

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

The End

http://www.chem.missouri.edu/thompson/MURI