correlation between sensitivity and approximated heats of detonation of several nitroamines using...

Correlation between Sensitivity andApproximated Heats of Detonation ofSeveral Nitroamines Using QuantumMechanical Methods

JESSE EDWARDS,1 CLAUDIA EYBL,2 BRIAN JOHNSON3

1Department of Chemistry/AHPCRC, Florida A&M University, Tallahassee, FL 323072College of Pharmacy and Pharmaceutical Sciences/AHPCRC, Florida A&M University,Tallahassee, FL 323073Computer Information Systems/AHPCRC, Florida A&M University, Tallahassee, FL 32307

Received 12 May 2004; accepted 12 May 2004Published online 15 September 2004 in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/qua.20235

ABSTRACT: Storage, synthesis, and application of energetic materials is significantlyimpacted by the fundamental property of sensitivity. The method of storage andhandling is affected by the sensitive nature of the explosive. Possessing the ability topredict the sensitivity of energetic material candidates before expensive synthesis isbegun would be an asset. Also, predicting the applications of various energeticcompounds before synthesis and testing can be made possible with the aid of sensitivitypredictions. Quantum mechanical methods are applied to approximating the heat ofdetonation. Correlation between heat of detonation and impact sensitivity is examined.© 2004 Wiley Periodicals, Inc. Int J Quantum Chem 100: 713–719, 2004

Key words: energetic materials; sensitivity; heat of detonation; nitroamines; quantummechanics

Introduction

T he possibility of predicting the explosive en-ergy, sensitivity, and related structure of po-

tential energetic materials would provide signifi-cant cost savings, increase the safety of storage andtesting of these compounds, and provide for greater

control of the performance of these explosives. Pos-sessing the ability to predict potential explosivesusing computational methods would be helpfulduring and before the synthetic process.

One of the experimental measures of energeticmaterials is the sensitivity. Using quantum mechan-ical methods as a predictive tool for assessing mo-lecular properties of various molecules including orwith emphasis on explosives has been suggested inseveral previous works [1–15]. In these works,properties of these energetic materials were pre-

Correspondence to: J. Edwards; e-mail: [email protected]

International Journal of Quantum Chemistry, Vol 100, 713–719 (2004)© 2004 Wiley Periodicals, Inc.

dicted using quantum mechanical methods. Theseproperties included bond dissociation processesand the heat of detonation. The heat of detonationis the property examined in this work. Differentmethods have been used to calculate the heat ofdetonation using quantum mechanical techniques.One methodology used by Rice and coworkers [1,16] was to assume that the heats of detonation ofthe explosive compound can be approximated asthe difference between the heats of formation of thedetonation products and that of the explosive, di-vided by the formula weight of the explosive. Ricepoints out that the �Hf (solid) is equal to the dif-ference between the heat of formation of the gasand the heat of sublimation. We neglect the heat ofsublimation in our calculations and report the gas-phase results. This is the approximation that will be

used in this work. Rice et al. furthered this effort bypredicting the solid state heats of formation of sev-eral energetic materials using statistical analysis ofthe charge distribution and electrostatic potential[1, 16]. This type of theory was first introduced byPolitzer et al. [3].

In several of these works, the sensitivity of theenergetic materials was correlated with the calcu-lated property. The sensitivity was determined ex-perimentally using the drop weight impact test,h50% [17]. The h50% test determines the height atwhich milligrams of the material will detonate 50%of the time. The sensitivity of these moleculesshould correlate with their explosive power. In fact,this correlation was described in other theoreticalworks on a large assortment of explosive com-pounds. This work will further display the correla-

FIGURE 1. Heat of detonation PM3 level of theory nocarbon path vs. sensitivity (experimental h50, dropweight test) (cm�1) fit to a power and exponential.

FIGURE 2. Heat of detonation PM3 level of theory nocarbon monoxide path vs. sensitivity (experimental h50,drop weight test) (cm�1) fit to a power and exponential.

FIGURE 3. Heat of detonation PM3 level of theory nocarbon path vs. natural log of sensitivity (experimentalh50, drop weight test) (cm�1) fit to a line.

FIGURE 4. Heat of detonation PM3 level of theory nocarbon monoxide path vs. natural log of sensitivity (ex-perimental h50, drop weight test) (cm�1) fit to a line.

EDWARDS, EYBL, AND JOHNSON

714 VOL. 100, NO. 5

tion between sensitivity and the heat of detonationof using the semiempirical, PM3 [18–20], techniqueand density functional theory [20, 21]. Figures 1–6show the correlation plots using the methods dis-cussed in the next section.

Methods

In this work we will use the quantum mechanicallydetermined �Hf (explosive), �Hf (detonation prod-ucts) both in the gas phase, and the formula weight ofthe explosive. The heat of detonation is indeed ap-

proximated in this way by Rice et al. [1] with a subtledifference mentioned in the Introduction.

Q ��Hf�detonationproducts� � ��Hf�explosive��

formulaweightof explosive .

(1)

This can be seen in Eq. (1) where Q is the heat ofdetonation. In this approximation the ��f (detona-tion products) and ��f (explosives) are also ap-proximated. These two quantities are calculated ingas phase. The heat of sublimation contribution isconsiderably small for most molecules; therefore,the gas-phase heat of formation gives a good ap-proximation to the �Hf (solid). Thus, using �Hf(solid) � �Hf (gas) � �Hf (sublimation) and ap-proximating the equation to �Hf (solid) � �Hf (gas)will give a fair approximation. Using Kamlett andAdolph’s [22] Eqs. (2) and (3) for the detonation

FIGURE 5. Heat of detonation B3LYP/6-31G* level oftheory no carbon path vs. natural log of sensitivity (ex-perimental h50, drop weight test) (cm�1) with a linearcorrelation.

FIGURE 6. Heat of detonation B3LYP/6-31G* level oftheory no carbon monoxide path vs. natural log of sen-sitivity (experimental h50, drop weight test) (cm�1) witha linear correlation.

FIGURE 7. Highest occupied molecular orbital energy(PM3) vs. sensitivity (experimental h50, drop weight test)(cm�1) with a slight correlation.

FIGURE 8. Lowest unoccupied molecular orbital energy(B3LYP/6-31G*) vs. sensitivity (experimental h50, dropweight test) (cm�1) with a slight exponential decay.

CORRELATING SENSITIVITY AND HEAT OF DETONATION OF NITROAMINES

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 715

properties of explosives containing C-H-N-O atomswith high crystal densities, the detonation productsand their heat of formation can be determinedkeeping in mind the approximation that was justmentioned. The predicted paths consist of one withno carbon monoxide (2) and the other with nocarbon (3).

• If no trace of carbon residues exist, then

CaHbNcOd 3 �c/2�N2 � �b/2�H2O

� �d � a � b/2�CO2 � �2a � b/2 � d�CO (2)

• If no trace of CO residues exist, then

CaHbNcOd 3 �c/2�N2 � �b/2�H2O

� �d/2 � b/4�CO2 � �a � b4 � d/2�C* (3)

The optimized geometries and heats of forma-tion of the explosives and the detonation productswere determined using the semiempirical, PM3,method and the B3LYP [23, 24] functional with a6-31G* basis set [25]. The calculations were con-ducted using the G98 suite of quantum chemistrycodes [26]. The optimized structures were not de-termined to be the global minimum due to the largesize and flexibility of the molecules studied. How-ever, we assumed that the optimized structures areclose to the global minima structures in energy.

In this way, 30 (24 at the B3LYP/6-31G* level)optimized nitroamine structures and their corre-sponding calculated heats of formations weredetermined. Using Eq. (1) and the heats of forma-tion of the detonation products and the explo-

FIGURE 9. Lowest unoccupied molecular orbital en-ergy (B3LYP/6-31G*) vs. sensitivity (experimental h50,drop weight test) (cm�1) with a slight correlation.

FIGURE 10. Highest occupied molecular orbital en-ergy (B3LYP/6-31G*) vs. Sensitivity (experimental h50,drop weight test) (cm�1) with a slight correlation.

FIGURE 11. Sensitivity (cm�1) vs. number of O atomsshows strong correlation that breaks down about 6NO2 groups.

FIGURE 12. Sensitivity (cm�1) vs. number of NO2

groups shows strong correlation that breaks downabout 6 NO2 groups.


716 VOL. 100, NO. 5

sives at both levels of theory the approximateheat of detonation was determined andcorrelated with experimentally determined sensi-tivity measurements, drop weight test measure-ments.

Results

The optimized energies, corresponding heatsof formations and experimentally determinedsensitivities and calculated heats of detonation

are reported in Tables I (PM3 level of theory) andII (B3LYP level of theory). The calculated heat offormation of the detonation products used in Eq.(1) are reported in Table III.

The optimized energy, �Hf, for N2 is calculatedreported to be zero at the DFT level; however, itis reported as �109.5 au at the PM3 level, other-wise there appeared to be no apparent correla-tion. This is probably due to the lack of accuracyof the lower level semiempirical method. The109.5 au of energy is the optimized energy of N2

at the PM3 level.

TABLE I ______________________________________________________________________________________________Formula weights, experimental h50 values, calculated heats of detonation (PM3 level) with no carbon and nocarbon monoxide products of 30 nitroamines.

Name C H N OMwt(amu)

h50

(cm)Hdet(C)

(kcal/g)Hdet(CO)

(kcal/g)

N,N�-Dinitromethanediamine 1 4 4 4 136 13 1.678552 1.678552N-Nitro-N-methylformamide 2 4 2 3 104 320 0.675978 1.271651N,N�-Dinitro-1,2-ethanidiamine 2 6 4 4 150 34 1.18002 1.59302Methyl-2,2,2-trinitroethylnitramine 3 5 5 8 239 9 1.696466 1.739667Trinitroethylnitroguanidine 3 5 7 8 267 15 1.593772 1.632443Cyclotrimethylenetrinitramine 3 6 6 6 222 26 1.399077 1.678131N-Methyl-N,N�-dinitro-1,2-

ethanediamine 3 8 4 4 164 114 0.736685 1.492173Trinitroethylcyanomethyl-nitramine 4 4 6 8 264 11 1.546454 1.702893Bis-(2,2,2-trinitroethyl)-nitramine 4 4 8 14 388 5 2.042223 1.829336N-Methyl-N-nitro-(trinitroethyl)-

carbamate 4 5 5 10 283 17 1.496769 1.533253N,N�-dimethyl-N,N�-dinitrooxamide 4 6 4 6 206 79 0.791192 1.292405N-Nitro-N-(trinitroethyl)-glydinamide 4 6 6 9 282 17 1.401971 1.548425Cyclotetramethylene-tetranitramine 4 8 8 8 296 29 1.341618 1.620672N,N�-Dinitro-N-[2-(nitramino)-ethyl]-

1,2-ethanediamine 4 10 6 6 238 39 0.910115 1.5174681,3,3,5,5-Pentanitropiperidine 5 6 6 10 310 14 1.468571 1.6684092,2,2-Trinitroethyl-3�,3�,3�-

trinitropropylnitramine 5 6 8 14 402 6 1.821154 1.769786N,N�-Bis-(2,2,2-trinitroethyl)-N,N�-

dinitromethanediamine 5 6 10 16 462 5 1.925174 1.791083Trinitroethyl-N-ethyl-N-nitro-carbamate 5 7 5 10 297 19 1.230234 1.473585Trinitroethyl-2-methoxyethylnitramine 5 9 5 9 283 42 1.160222 1.561547N-nitro-N-(3,3,3-trinitropropyl)-2,2,2-

trinitroethyl carbamate 6 6 8 16 446 9 1.687023 1.6407232,2,2-Trinitroethyl-N-(2,2,2-

trinitroethyl)-nitramino acetate 6 6 8 16 446 9 1.680369 1.634069Trinitropropyl-(2,2-dinitropropyl)-

nitramine 6 9 7 12 371 17 1.370036 1.6205072,2,2-Trinitroethyl-3,3-dinitrobutyl

nitramine 6 9 7 12 371 20 1.45185 1.702322N,N�-Dinitro-N,N�-bis-[2-(nitroamino)-

ethyl]-1,2-ethanediamine 6 14 8 8 326 53 0.791993 1.488772



The correlation between the sensitivity and theheat of detonation along paths (1) and (2) areshown in the following plots at the PM3 and B3LYPlevel of theory, respectively. The slight correlationbetween the number of oxygen atoms and NO2

groups and the experimental sensitivity are re-ported in Figures 11 and 12. The R2 values for eachplot are also reported. Figures 7–10 previouslyshown display the correlation between sensitivityand the HOMO and LUMO energy gaps using dif-ferent quantum mechanical methods.

TABLE II ______________________________________________________________________________________________Formula weights, experimental h50 values, calculated heats of detonation (DFT B3LYP/6-31G* level) with nocarbon and no carbon monoxide products of 24 nitroamines. Six of the previous compounds are not reported.

Name C H N OMwt(amu)

h50

(cm)Hdet(C)

(kcal/g)Hdet(CO)

(kcal/g)

N,N�-Dinitromethanediamine 1 4 4 4 136 13 �2580.53 �2580.53N-Nitro-N-methylformamide 2 4 2 3 104 320 �2491.96 �2492.51N,N�-Dinitro-1,2-ethanidiamine 2 6 4 4 150 34 �2503.87 �2504.25Methyl-2,2,2-trinitroethylnitramine 3 5 5 8 239 9 �2601.48 �2601.52Trinitroethylnitroguanidine 3 5 7 8 267 15 �2585.6 �2585.63Cyclotrimethylenetrinitramine 3 6 6 6 222 26 �2532.54 �2532.8N-Methyl-N,N�-dinitro-1,2-

ethanediamine 3 8 4 4 164 114 �2440.33 �2441.03Trinitroethyl-cyanomethylnitramine 4 4 6 8 264 1.82 �2573.99 �2574.14Bis-(2,2,2-trinitroethyl)-nitramine 4 4 8 14 388 5 �2656.46 �2656.26N-Methyl-N-nitro-(trinitroethyl)-

carbamate 4 5 5 10 283 17 �2614.42 �2614.46N,N�-dimethyl-N,N�-dinitrooxamide 4 6 4 6 206 79 �2512.57 �2513.03N-Nitro-N-(trinitroethyl)-glydinamide 4 6 6 9 282 17 �2579.54 �2579.68Cyclotetramethylene-tetranitramine 4 8 8 8 296 29 �2532.57 �2532.83N,N�-Dinitro-N-[2-(nitramino)-ethyl]-

1,2-ethanediamine 4 10 6 6 238 39 �2469.05 �2469.611,3,3,5,5-Pentanitropiperidine 5 6 6 10 310 14 �2575.43 �2575.622,2,2-Trinitroethyl-3�,3�,3�-

trinitropropylnitramine 5 6 8 14 402 6 �2625.23 �2625.18Trinitroethyl-N-ethyl-N-nitro-

carbamate 5 7 5 10 297 19 �2574.14 �2574.36Trinitroethyl-2-methoxyethylnitramine 5 9 5 9 283 42 �2537.57 �2537.94N-methyl-N�-trinitroethyl-N,N�-dinitro-

1,2-ethanidiamine 5 8 7 10 327 11 �2549.85 �2550.08N,N�-3,3-Tetranitro-1,5-

pentanediamine 5 10 6 8 282 35 �2502.5 �2502.97N-nitro-N-(3,3,3-trinitropropyl)-2,2,2-

trinitroethyl carbamate 6 6 8 16 446 9 �2078.27 �2078.232,2,2-Trinitroethyl-N-(2,2,2-

trinitroethyl)-nitramino acetate 6 6 8 16 446 9 �2631.11 �2631.06Trinitropropyl-(2,2-dinitropropyl)-

nitramine 6 9 7 12 371 17 �2286.38 �2286.612,2,2-Trinitroethyl-3,3-dinitrobutyl

nitramine 6 9 7 12 371 20 �2845.04 �2845.27

TABLE III _____________________________________Optimized heats of formation energies of thedetonation products at the PM3 and B3LYP/6-31G*levels of theory.

Detonationproduct

�Hf (detonation products)

B3LYP/6-31G* (kcal/mol) PM3 (hartree)

N2 0.00 �109.5H2O �57.8 �76.4CO2 �94.1 �188.6CO �26.4 �113.3


718 VOL. 100, NO. 5

Conclusions

This work shows the use of an approximatemethod for the calculation of heat of detonation ofseveral nitroamine compounds using two differentlevels of quantum mechanical theory. These calcu-lated values showed various levels of correlationbetween the experimentally determined sensitivityand the calculated heats of detonation at both levelsof theory, PM3, and DFT.

There was correlation in exponential decay of theHOMO and LUMO energies versus sensitivity atthe DFT level of theory. However, this correlationdid not exist at the semiempirical level of theory.This persisted with very little correlation betweensensitivity and HOMO-LUMO energy gaps at bothlevels (not shown).

Finally, there existed some correlation betweensensitivity and the substituent atoms and nitrogroups of the explosive compounds. There was avery slight correlation exhibited between numberof NO2 groups and sensitivity. There also appearsto be slight correlation exponentially between sen-sitivity and the number of nitrogen atoms; how-ever, this correlation fails at a threshold between 6and 8 nitrogen atoms.

There also appears to be a small exponentialcorrelation between sensitivity and the number ofoxygen atoms; however, this slight correlation failsat a threshold between 10 and 12 oxygen atoms. Thesmall correlation that exists between the number ofatoms of oxygen and nitrogen and NO2 groups andsensitivity may only be within families of com-pounds like the family of nitroamines that we ex-amined in this work. Further studies are needed toconclude with any certainty that sensitivity is cor-related in general with heats of detonation.

ACKNOWLEDGMENTS

We extend our sincere thanks to Dr. Betsy Rice ofthe ARL. We would also like to thank Dr. GenzoTanaka of Network Computing Services, Inc./AH-PCRC for his many contributions. This researchwas supported in part by the Army High Perfor-mance Computing Research Center, under the aus-pices of the Department of the Army, Army Re-search Laboratory cooperative Agreement numberDAAD19-01-2-0014, the content of which does notnecessarily reflect the position or the policy of thegovernment, and no official endorsement should beinferred.

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