Structure and Density Predictions forStructure and Density Predictions forEnergetic MaterialsEnergetic Materials

Zuyue Du, Sayta Prasad, Ed Wells and Herman L. Ammon

Department of Chemistry & Biochemistry,University of MarylandCollege Park, MD 20742

Picatinny Arsenal, NJOct. 27, 2004

    

computer modeling &

simulations

quantitative estimation

key properties & characteristics... conformation stability/reactivity Hf crystal structure/habit microstructure detonation behavior sensitivity

elemental composition&

molecular structure+

Identification,Design andDevelopment

of new energeticmaterials

Cyclic nitramines, (CH2NNO2)n units

1.810

1.829

“

“

1.847

1.838

VA***

1.750**

1.668**

1.759*

1.902*

1.839*

1.806*

g/cc

C1

~Ci

C2v

Ci

C2

Cs

pt grp

10-ring

4-ring

-HMX

-HMX

-HMX

RDX

*exptl **structure prediction

*** VA = mass / (atom/group volumes)

N

N

NNO2

NO2

O2N

NN

NN NO2

O2N

O2N

NO2

RDX

HMX

NN

NN

N

O2N

NO2

NO2O2N

O2N 10N

N

O2N

NO2

4

DensityDensity --> "primary physical parameter in detonation performance"

problems withproblems with constitutional isomers….constitutional isomers….

O2N NO2 O2N

O2NNO2 NO2

exptl : 1.573 1.569 1.651 g/cc

the solutionsolid state

structure prediction

many variables:atom types,

structure/conformation,packing efficiency

MOLPAKROTPAKMOLPAK-2

Crystal Structure Prediction…Crystal Structure Prediction…

model

MOLPAK

refinement

ab initio geometry optimization;usually G03, b3lyp/631g*

Mimic exptl crystal structures for triclinic -> orthorhombic sp grps;Use exptl coordn geom patterns; Create hypothetical crystal structures for 29 coordination geometries;~6,900 structures/coordn geom

Optimize unit cell parameters, model orientation & position by lattice E minimization;

WMIN: atom-centered charge electrostaticsDMAREL: distributed multipole electrostatics

400-900highest each geom

   0.114C222120

5.2714Pbca [2]6123.23210P212121 [2]19

0.462Pbcn [2]600.457P21212 [3]18

0.335Pccn564.0557C2/c [3]15

0.011Pncn5237.25157P21/c [5]14

0.19Iba2450.112P2/c13

0.110Aba2411.0135Cc [1]9

0.012Pnn2340.346Pc7

1.8253Pna21 [3]330.9125C2 [1]5

1.0137Pca21 [2]2910.91507P21 [2]4

0.012I2222312.61747P-1 [2]2

0.011C222210.458P1 [1]1

MOLPAK coverageMOLPAK coverage… all triclinic to Z = 8 orthorhombic space groups

For C-H-N-O-F molecules, space group frequencies are…

# Sp Grp N % # Sp Grp N %

MOLPAK coordination geometries = [29] ~ 99%

WMIN LE potential…WMIN LE potential…

Optimize crystal structure…Adjust unit cell, model position & orientation

LE = [QiQj*Rij-1 - Aij*Rij

-6 + Bij*exp-(Rij(Ci+Cj))]

A, B, C: empirical coefficients…Aij = (Aatom_type_i * Aatom_type_j)1/2

Currently have 69 atoms types…

Eg, C-NO2, N-NO2, cubane-NO2, N-NO2 R3N, C(=O)NR2

N N

O

Calcd vs. X-ray Density, 352 Crystals

R2 = 0.99

1

1.2

1.4

1.6

1.8

2

2.2

2.4

1 1.5 2

X-ray Density (g/cc)

Cal

cd D

ensi

ty (

g/c

c)

Crystal structure prediction…Crystal structure prediction… successes and problems…successes and problems…

X-ray model

In 80%smallest LE ->exptl structure

Examples..(CH3)2NNO2 *TNAZ *RDX *-CL20 *FOX7 # 2, +0.4

In 20%exptl structurein top 6 lowestLE solutions

MOLPAK+

WMIN

29 coordination geometries +193 = 6,859/geometry ~ 200,000 hypothetical crystal structures

29*400-900/geom -> latticerefinement & LE calcns

# E Space # E Space group group

1 1.996 -43.56 P21/c 16 1.856 -36.46 C2/c 2 1.966 -42.28 P212121 17 1.870 -35.92 P21

3 1.965 -42.20 P212121 18 1.777 -35.85 P21

4 1.898 -39.63 P21/c 19 1.856 -35.56 Cc

5 1.898 -39.63 P21/c 20 1.804 -35.50 Pbcn

6 1.838 -38.07 C2/c 21 1.783 -35.32 Pna21

7 1.851 -37.99 Pbca 22 1.817 -34.63 Pbcn

8 1.875 -37.81 Pca21 23 1.721 -33.68 P21212

9 1.901 -37.68 P21/c 24 1.734 -33.57 C2

10 1.832 -37.34 C2/c 25 1.690 -32.56 Pna21

11 1.802 -37.24 Pbca 26 1.799 -31.96 Pca21

12 1.877 -37.18 P-1 27 1.706 -31.34 P1

13 1.877 -37.18 P-1 28 1.656 -31.04 P21212

14 1.835 -37.11 Pna21 29 1.693 -29.85 P21212

15 1.810 -36.54 P21/c Cell Parameters: a b c X-ray 8.852 Å 12.556 13.386 106.82o

Predicted (%) 1.55 -0.53 0.98 -0.65

obsd = 2.043 g/cc

Structure prediction example, Structure prediction example, -CL20 from B3lyp/631g* model-CL20 from B3lyp/631g* model

-(NO2)8

= 2.008 g/cc

det P = 32.72 gPa

det V = 8.25 km/s

Isp = 229.7 s

-(NO2)8

= 2.105 g/cc

det P = 55.88 gPa

det V = 9.75 km/s

Isp = 266.7 s

-(NO2)12

= 1.981 g/cc, exptl = 1.978

det P = 48.74 gPa

det V = 9.35 km/s

Isp = 267.5 s

= 1.856 g/cc

det P = 32.91 gPa

det V = 8.76 km/s

Isp = 260.7 s

-(NO2)8

= 1.818 g/cc

det P = 35.21 gPa

det V = 9.08 km/s

Isp = 272.1 s

C C NO2O2N

= 1.936 g/cc

det P = 29.56 gPa

det V = 8.00 km/s

Isp = 232.3 s

C C

NO2

O2N NO2

O2N

Structure prediction -> new molecule evaluation…Structure prediction -> new molecule evaluation…

ROTPAKROTPAK……pack & adjust conformation, minimize Etotal…

Criterion: Etotal = Einter + Eintra ~ Ethresh

orientedmolecule at origin

orientedmoving molecule

move togetheruntil

Etotal ~ Ethresh

alter conformationcalc new Etotal

> Ethresh< Ethresh

Ethresh = 0.5

kcal/molfor line

no further improvement in Etotal

new orientation

closest approach

# G03 RPK Xray # G03 RPK Xray # G03 RPK Xray

1 29.4º-> 26.0 20.9 1 -5.4º-> -5.2 -6.0 1 11.6º-> 11.6 9.6 2 0.0 -> 11.4 19.4 2 167.4 -> 173.6 179.3 2 -76.6 -> -1.6 -5.0 3 21.6 -> 10.3 7.2 3 -108.5 -> -30.6 -32.6 4 1.3 -> 1.8 13.5 5 30.0 -> -17.7 -16.4 6 -1.5 -> 30.3 25.4 7 38.3 -> -12.9 -9.2

ROTPAK examples…ROTPAK examples…

O2N NO2

NO2

CUGCOW DUYREU

1

2

3 NCN

NO212

KASBAH

(NO2)7

Model (G03), ROTPAK/WMIN and X-ray torsion angle comparison…

X-ray

B3lyp/631g*model

1

2 3 NH

CH3

O

CH3

O2N

NO2

ROTPAK example…ROTPAK example…

24.6

47.1

0.0o

B3…

22.9

51.9

41.4o

X-ray

3

2

1

29.0

48.6

45.0o

RPK/ WMIN

X-ray G03 + ROTPAK + WMIN

-6.31.53

2.9119.9o

1.819.67c

1.44.85b

6.8%12.57 Åa

1.87 Å1.93 Åa

b

c

X-raymodel

G03B3lyp/631g*model

ROTPAK + WMIN

bend ~20o + N-NO2 twist

ROTPAK example…RDX bond bending…ROTPAK example…RDX bond bending…

RDX X-ray and ROTPAK-modified overlays…RDX X-ray and ROTPAK-modified overlays…

-1.31.806 (g/cc)

-0.610.709c

0.711.574b

1.213.182a (Å)

ROTPAK-

X-ray (%)

X-raydimension

RDX space group: Pbca

unit cellcomparison

Some ROTPAK challenges…Some ROTPAK challenges…

O2NC(NO2)3

O2N

O2N

NO2

N3N3

N3

N3

O

N3N3

N3

NO2

O

O

CH2-N=N=N

CH2-N=N=N

CH2-N=N=N

MOLPAK, the old and the new…MOLPAK, the old and the new…

MOLPAK-1 •Uses pre-established coordn geoms (CN = 14)•Coordn geom sub-programs are hand-coded•Some structures don’t fit the rules•Structures built with repulsion-only potential

MOLPAK-2•Build structures from crystal space group symmetry•One program does all symmetries•Structures built with 3-term potential•Special features more easily handled, eg H-bonding, molecule-solvent complexes, ionic materials

Determine length of an axis ->make line of C1 or Ci images; assume line is a/c or b axis

For each grid, fill unit cell;calculate lattice energy

Lowest LE ->correct structure

Criteria: van der Waals radii repulsion energy total energy

Pre-LE calcn criteria:van der Waals radiicrystal density range

C1/Ci image at origin & each grid point in succession

order surviving unit cells on basis of LE

MOLPAK-2 flowchart for P2MOLPAK-2 flowchart for P211/c…/c…

Symmetry elements: inversion center,2-fold screw axis, glide plane

Make rectangular boxaround origin,0.5 Å spacing

MOLPAK-2 examples…MOLPAK-2 examples…

MOLPAK-1 failed ->no axial repeatmolecules in coodnsphere

NO2

P-1 P21

1

23

7

5

5(NO2)

P21/c

N

O

CH3

NO2

P212121

NH

HNO O

C2/c

Continuing and future work and goals…Continuing and future work and goals…

•Global atom type parameterization for both WMIN and DMAREL -> new atom types potential function cross-terms anisotropic potential coefficients

•Identification of the best/correct structure -> LE’s and ‘s used currently patterns of intermolecular contacts? crystal habits/crystal face E’s?

•ROTPAK & conformational flexibility -> continue development -> focus on intramolecular E evaluation & multi-bond flexibility

•MOLPAK-2 -> continue development -> handle all space groups extensive testing

•Extend to ionics (eg ADN), H-bonding, high N compounds

•New lattice energy refinement code (WMIN replacement) -> modern fortran

analytical derivatives automate use of individual atom types/ cross-terms in LE potential facilitate conformational refinement

•Sensitivity -> density of states impact/shock & friction – weakest bond + lattice E steric hindrance to sheer

•CHSSI: Super parallel MOLPAK/WMIN w/ B. Rice & W. Mattson

thanks

ARL, Picatinny Indian HeadB. ChapmanK. BaumH. ShechterP. EatonJ. Bottaro