PredictingHeatsofExplosionofNitroaromatic ...downloads.hindawi.com/archive/2012/304686.pdf · 1.Introduction Aromatic molecules with nitro groups are an important class of highly

Hindawi Publishing CorporationAdvances in Physical ChemistryVolume 2012, Article ID 304686, 11 pagesdoi:10.1155/2012/304686

Research Article

Predicting Heats of Explosion of NitroaromaticCompounds through NBO Charges and 15N NMR ChemicalShifts of Nitro Groups

Ricardo Infante-Castillo1 and Samuel P. Hernández-Rivera2

1 Department of Physics and Chemistry, University of Puerto Rico, Arecibo Campus, P.O. Box 8152, Arecibo, PR 08152-00613, USA2 ALERT-DHS Center of Excellence/Center for Chemical Sensors Development, University of Puerto Rico, Mayagüez Campus,P.O. Box 9000, Mayaguez, PR 00681-9000, USA

Correspondence should be addressed to Ricardo Infante-Castillo, [email protected] Samuel P. Hernández-Rivera, [email protected]

Received 23 March 2012; Revised 12 June 2012; Accepted 12 June 2012

Academic Editor: Michael D. Sevilla

Copyright © 2012 R. Infante-Castillo and S. P. Hernández-Rivera. This is an open access article distributed under the CreativeCommons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided theoriginal work is properly cited.

This work presents a new quantitative model to predict the heat of explosion of nitroaromatic compounds using the natural bondorbital (NBO) charge and 15N NMR chemical shifts of the nitro groups (15NNitro) as structural parameters. The values of the heat ofexplosion predicted for 21 nitroaromatic compounds using the model described here were compared with experimental data. Theprediction ability of the model was assessed by the leave-one-out cross-validation method. The cross-validation results show thatthe model is significant and stable and that the predicted accuracy is within 0.146 MJ kg−1, with an overall root mean squared errorof prediction (RMSEP) below 0.183 MJ kg−1. Strong correlations were observed between the heat of explosion and the charges(R2 = 0.9533) and 15N NMR chemical shifts (R2 = 0.9531) of the studied compounds. In addition, the dependence of the heat ofexplosion on the presence of activating or deactivating groups of nitroaromatic explosives was analyzed. All calculations, includingoptimizations, NBO charges, and 15NNitro NMR chemical shifts analyses, were performed using density functional theory (DFT)and a 6-311+G(2d,p) basis set. Based on these results, this practical quantitative model can be used as a tool in the design anddevelopment of highly energetic materials (HEM) based on nitroaromatic compounds.

1. Introduction

Aromatic molecules with nitro groups are an importantclass of highly energetic materials (HEM). One of the mostimportant thermodynamic properties that determine theperformance of these explosives and propellants is the heatof explosion (HE). The HE is the quantity of heat liberatedwhen an HEM undergoes detonation as a high explosive ordeflagration as a low explosive. The processes of detonationand deflagration occur even in the absence of externaloxygen or air because HEM contain oxygen themselves. TheHE can be theoretically calculated [1] and experimentallydetermined [2]. The calculated value is determined by thedifference between the energies of formation of the explosivecomponents and the energies of formation of the explosion

products. Experimentally, the HE is determined using acalorimetric bomb. The sample quantity is usually chosento obtain a loading density of 0.1 g/cm3. If a powder willnot explode (compounds with heat of explosion lower than800 cal/g), a “hot” powder with a known heat of explosion isadded. Thus, the HE of the sample powder can be calculatedfrom the mixture. The calorimetric values used in this workare based on liquid H2O as a reaction product.

Predicting the performance and thermochemical prop-erties of energetic materials from a given molecular structurewith or without using experimental measurements is criticalin the research and development of explosives. Severalrelationships have been found that relate explosive charac-teristics with measured and predicted molecular properties.The relationship between thermal [3], impact [4, 5], and

2 Advances in Physical Chemistry

electric spark [6] sensitivities and molecular structure ofnitrocompounds and nitrates [7] has been the subjectof many investigations. These studies concluded that therate-determining step in the thermolysis was usually thehomolytic cleavage of the C–NNitro, N–NNitro, and O–NNitrobonds. In this context, the NO2 (nitro) functional groupcorresponds to the reaction center of the HEM and shouldbe correlated with the explosive characteristics of individualenergetic materials. The electron configuration and the stericconditions within the reaction center of the molecule canbe represented by NMR chemical shifts of the key atoms ofthe center. The shifts of these atoms should correlate withcharacteristics of initiation reactivity of individual energeticmaterials [6]. The dominant factor in the initiation by shock,electric spark, and in low-temperature thermolysis shouldbe the electronic structure and close chemical ambient ofthe nitrogen atom of the primary leaving nitro group.In addition, for all nitro explosives in which the R-Nitrobond is the weakest, the charge in this group (QNitro) canbe regarded as another structural parameter to assess andpredict explosive properties [8]. Recently, we establisheda quantitative model for predicting and calculating theheat of detonation and heat of explosion for a series ofnitro paraffins, nitramines [9], and nitrate esters [10] byutilizing natural bond orbital (NBO) charge analysis andthe 15N NMR chemical shifts of the nitro groups. Inaddition, the calculated 15NNitro NMR chemical shifts forthe nitramines were obtained using a protocol establishedin our recent work [11], which uses the continuous setof gauge transformations (CSGT) method [12]. The abinitio calculations of the NMR chemical shifts for differentnuclei have proven to be useful structural parameters ininterpreting experimental data in several applications [13,14]. There are many both empirical and theoretical effortsto predict detonation parameters from a given molecularstructure. Rice and Hare [15] introduced a computationalmethodology that uses only quantum mechanical (QM)information about isolated molecules to predict the heats ofdetonation for pure and explosive formulations. In a seriesof studies, Keshavarz has established simple methods forpredicting heats of detonation and other explosive properties[16–19]. In the application of these methods, there is no needto use any experimental and computed data of explosives.A simple approximation is introduced for calculating heatsof detonation using chemical composition of explosives andtheir gas phase heat of formation that can be calculatedby a group additivity rule [16]. Recently, a simple methodto predict heats of detonation of important classes ofenergetic compounds including nitroaromatics, nitramines,nitroaliphatics, and nitrate esters was introduced [17]. Themethodology is based on the ratios of oxygen to carbonand hydrogen to oxygen atoms as well as the contributionof some specific functional groups or structural parameters.Previously, Keshavarz’s showed that the predicted values ofthe heats of detonation for aromatic compounds [18] aredifferent from those of nonaromatic compounds [1] becausearomaticity can affect the values of heats of detonation.The root mean squared (rms) deviation between predictedand experimentally determined heats of detonation was

0.32 and 0.54 kJ/g for aromatic and nonaromatic energeticcompounds, respectively. Also, the heats of detonationfor aromatic energetic materials were estimated assumingthat the heat of detonation of an explosive compoundof composition CaHbNcOd can be approximated as thedifference between the heat of formation of all H2O-CO2arbitrary (H2O, CO2, N2) detonation products and that ofthe explosive, divided by the formula weight of the explosive[19]. The rms deviation for this method was 0.34 kJ/g. Also,an empirical approach to calculate the heats of formation incondensed phase for different energetic compounds has beendeveloped by Keshavarz [20]. It should be mentioned that theheat of explosion is not a constant of a high explosive anddepends on the expansion ratio of the detonations products.The heat of explosion is reasonably included in the energeticcharacterization of the working capacity of commercial highexplosives, but it has no relation to the power of brisance,which is determined by the propellant capacity. Even thedetonation velocity is not a measure of the power of highexplosives [21].

The purpose of this work was to establish a quantitativemodel to calculate and predict the heats of explosion of 35nitroaromatic compounds from two structural parameters,nitro charges and 15N NMR chemical shifts, obtained bytheoretical methods. The predictive ability of the modelwas assessed by the leave-one-out (LOO) cross-validationmethod [22]. To show the reliability of the calculated heat ofexplosion using the quantitative model, the results for eightnitroaromatic compounds that were not used to build themodel were compared with their experimental values. Themodel was applied to calculate heats of explosion of twentyenergetic compounds and compared against results predictedusing other empirical and quantum mechanical methodsand against experimental values available. In addition, themodel was employed to calculate the heat of explosionof fourteen nitroaromatic compounds whose experimentalvalues were unavailable. Importantly, this work provides asimple and rapid method for estimating heats of explosionof HEM without experimental data for a systematic setof nitroaromatic compounds and should be of help insynthesizing and developing new high explosives.

2. Experimental Section

2.1. Computational Details. Gaussian 09 [23] software wasused for all theoretical calculations. Molecular geometrieswere optimized using the B3LYP [24, 25] functional and 6-311+G(d,p) basis set. The absolute energies and C–NNitrobond lengths for the thirty-five nitroaromatic compoundsare shown in Tables 1, 2, and 3. The nitro group charges(QNitro) were calculated according to an NBO scheme, whichwas implemented using Gaussian 09 software [26]. The15NNitro NMR calculations for all tested compounds wereperformed using the CSGT method and are reported inTables 1–3. NMR shifts were computed using B3LYP/6-311+G(2d,p), and the values for the 15N isotropic chemicalshifts were referenced to the corresponding values fornitromethane. The effect of the solvent on the theoretical

Advances in Physical Chemistry 3

Ta

ble

1:A

bsol

ute

ener

gies

,cod

ede

sign

atio

ns,R

C−N

Nit

robo

nd

dist

ance

s,n

itro

char

ges

(QN

itro

),15

NN

itro

NM

Rca

lcu

late

dch

emic

alsh

ifts

,an

dex

per

imen

tala

nd

calc

ula

ted

hea

tsof

expl

osio

nfo

rn

itro

arom

atic

com

pou

nds

use

dto

build

aqu

anti

tati

vem

odel

.

Nu

mbe

rC

hem

ical

nam

eC

ode

desi

gnat

ion

En

ergy

a

(har

tree

s)D

ista

nce

RC−N

Nit

ro(Å

)N

BO

bch

arge

–QN

itro

Cal

cula

tedc

15N

Nit

ro(p

pm)

Exp

erim

enta

lHE

(H2O

liq.)

(MJ

kg−1

)C

alcu

late

ddH

E(M

Jkg−1

)1

Tetr

ylT

ET

RY

L−1

145

1.48

604

0.19

1−2

6.6

4.77

34.

643

22,

3,4,

6-Te

tran

itro

anili

ne

TeN

A−1

105

1.47

980

0.20

6−2

5.6

4.37

84.

336

32,

4,6,

2′,4′ ,6

′ -h

exan

itro

diph

enyl

amin

eH

ND

P−1

746

1.48

079

0.21

022

.84.

075

4.09

94

Eth

ylte

tryl

EtT

ET

RY

L−1

185

1.48

692

0.21

4−2

3.1

4.05

84.

052

52,

4,6-

Trin

itro

ben

zoic

acid

TN

BA

−103

51.

4877

60.

215

−23.

63.

964

4.06

66

2,4,

6-Tr

init

roph

enox

ethy

lnit

rate

TN

PH

N12

801.

4814

30.

213

−21.

33.

911

3.95

97

Met

hylp

icra

teM

ePi

−960

1.47

516

0.22

2−1

9.4

3.77

73.

695

8E

thyl

picr

ate

EtP

i−9

991.

4772

00.

225

−19.

13.

515

3.62

89

2,4-

Din

itro

tolu

ene

24D

NT

−681

1.48

113

0.24

8−1

5.7

3.19

23.

043

102,

4,6-

Trin

itro

phen

ol(p

icri

cac

id)

PiA

c−9

211.

4742

50.

228

−18.

63.

437

3.52

411

2,4,

6-Tr

init

rocr

esol

TN

C−9

611.

4751

60.

231

−17.

63.

370

3.43

812

Din

itro

-ort

ho-c

reso

lD

NoC

−756

1.47

521

0.24

414

.43.

027

3.02

913

met

a-D

init

robe

nze

ne

mD

NB

−641

1.48

414

0.25

09.

52.

666

2.63

2R

MSE

P0.

0817

aC

alcu

late

dw

ith

B3L

YP

/6-3

11+

G(d

,p);

bn

atu

ralb

ond

orbi

tala

nal

ysis

;cca

lcu

late

dw

ith

CSG

T-B

3LY

P/6

-311

+G

(2d,

p);d

pred

icte

dby

(1).


Ta

ble

2:A

bsol

ute

ener

gies

,cod

ede

sign

atio

ns,R

C−N

Nit

robo

nd

dist

ance

s,n

itro

char

ges

(QN

itro

),15

NN

itro

NM

Rca

lcu

late

dch

emic

alsh

ifts

,an

dex

per

imen

tala

nd

calc

ula

ted

hea

tsof

expl

osio

nfo

rn

itro

arom

atic

com

pou

nds

.

Nu

mbe

rC

hem

ical

nam

eC

ode

desi

gnat

ion

En

ergy

a

(har

tree

s)D

ista

nce

RC−N

Nit

ro(Å

)N

BO

bch

arge

–QN

itro

Cal

cula

tedc

15N

Nit

ro(p

pm)

Exp

erim

enta

lHE

(H2O

liq.)

(MJ

kg−1

)C

alcu

late

ddH

E(M

Jkg−1

)14

1,3,

5-Tr

init

robe

nze

ne

TN

B−8

461.

4802

40.

219

−24.

63.

964

4.06

115

2,6-

Din

itro

tolu

ene

26D

NT

−681

1.48

266

0.24

0−9

.63.

325

2.80

216

2,4,

6-Tr

init

roto

luen

eT

NT

−885

1.48

388

0.22

2−1

8.9

3.76

63.

665

172,

4,6-

Trin

itro

xyle

ne

TN

X−9

251.

4839

60.

214

−12.

43.

533

3.40

018

2,4,

6-Tr

init

roan

ilin

eT

NA

−901

1.47

154

0.25

2−2

1.3

3.58

93.

318

192,

4,6-

Trin

itro

-1,3

-dih

ydro

xybe

nze

ne

TN

R−9

961.

4631

20.

243

−20.

02.

952

3.38

720

1,3,

5-Tr

init

ron

aph

tale

ne

135T

NN

−999

1.48

418

0.23

4−1

5.3

3.52

13.

248

21H

exan

itro

stilb

ene

HN

S−1

768

1.48

668

0.20

5−2

0.9

4.08

84.

065

RM

SEP

0.28

4aC

alcu

late

dw

ith

B3L

YP

/6-3

11+

G(d

,p);

bn

atu

ralb

ond

orbi

tala

nal

ysis

;cca

lcu

late

dw

ith

CSG

T-B

3LY

P/6

-311

+G

(2d,

p);d

pred

icte

dby

(1).


Ta

ble

3:A

bsol

ute

ener

gies

,co

dede

sign

atio

ns,

RC−N

Nit

robo

nd

dist

ance

s,n

itro

char

ges

(QN

itro

),15

NN

itro

NM

Rca

lcu

late

dch

emic

alsh

ifts

,an

dpr

edic

ted

hea

tsof

expl

osio

nfo

rso

me

nit

roar

omat

icco

mpo

un

ds.

Nu

mbe

rC

hem

ical

nam

eC

ode

desi

gnat

ion

En

ergy

a

(har

tree

s)D

ista

nce

RC−N

Nit

ro(Å

)N

BO

bch

arge

–QN

itro

Cal

cula

tedc

15N

Nit

ro(p

pm)

Cal

cula

tedd

HE

(MJk

g−1)

22N

itro

ben

zen

eN

B−4

371.

4829

80.

218

−8.7

3.10

923

o-D

init

robe

nze

ne

o-D

NB

−641

1.48

063

0.20

7−1

3.4

3.57

624

p-D

init

robe

nze

ne

p-D

NB

−641

1.48

635

0.24

4−1

9.4

3.34

425

3,5-

Din

itro

tolu

ene

35D

NT

−681

1.48

500

0.21

4−1

9.3

3.39

326

1,3,

5-Tr

imet

hyl-

2,4,

6-tr

init

robe

nze

ne

TN

Ms

−963

1.48

464

0.26

5−7

7.0

2.27

627

1,3-

Dia

min

o-2,

4,6,

-tri

nit

robe

nze

ne

DA

TB

−957

1.45

388

0.31

1−2

1.1

2.33

728

1,3,

5-Tr

iam

ino-

2,4,

6-tr

init

robe

nze

ne

TAT

B−1

012

1.43

669

0.39

0−2

0.0

1.30

129

1,3,

5-Tr

ihyd

roxy

-2,4

,6-t

rin

itro

ben

zen

eT

NP

g−1

071

1.45

308

0.25

2−2

0.9

3.29

430

2-am

ino-

4,6-

din

itro

phen

ol(p

icra

mic

acid

)P

icA

c−7

721.

4735

40.

268

−16.

32.

751

31D

init

roch

loro

ben

zen

eC

DB

−110

11.

4810

10.

225

−17.

63.

537

321-

Ch

loro

-2,4

,6-t

rin

itro

ben

zen

eC

TB

−130

61.

4845

40.

203

−20.

94.

099

331,

3-D

ich

loro

-2,4

,6-t

rin

itro

ben

zen

eD

CT

B−1

765

1.48

489

0.16

9−2

1.7

4.69

834

1,3,

5-Tr

ich

loro

-2,4

,6-t

rin

itro

ben

zen

eT

CT

B−2

225

1.48

645

0.14

3−2

2.6

5.18

835

Tetr

anit

ron

aph

thal

ene

TeN

N−1

204

1.48

469

0.21

7−1

9.5

3.78

3aC

alcu

late

dw

ith

B3L

YP

/6-3

11+

G(d

,p);

bn

atu

ralb

ond

orbi

tala

nal

ysis

;cca

lcu

late

dw

ith

CSG

T-B

3LY

P/6

-311

+G

(2d,

p);d

pred

icte

dby

(1).


R2 = 0.93410.185

0.235

0.285

0.335

0.385

1.435 1.445 1.455 1.465 1.475 1.485

−QN

itro

(e− )

RC−NNitro (Å)

−QNitro = −3.7751RC−NNitro + 5.8181

Figure 1: Dependence of the RC−NNitro bond lengths and the chargeson the nitro group in nitroaromatic compounds.

NMR parameters was included using a default integralequation formalism polarized continuum model (IEF-PCM)[27] provided by the Gaussian 09 software suite. Dimethyl-sulfoxide (DMSO), which has a dielectric constant (ε) of46.7, was used as the solvent. The experimental values of theheat of explosion used in the present paper were obtainedfrom the literature [2].

3. Results and Discussions

3.1. Relationships between the Nitro Charges (QNitro), theRC−NNitro Bond Lengths and Stability. The optimized C–NNitrobond lengths and nitro charges, with the corresponding totalenergies, for thirty-five nitroaromatic compounds are listedin Tables 1, 2 and 3. The charges on the nitro group (QNitro)were calculated as the sum of the atomic charges on thenitrogen and oxygen atoms in the nitro group. It shouldbe noted that the average values of RC−NNitro and QNitro inpolynitro compounds were used for all calculations, andthese are listed in Tables 1–3. These results revealed thatthe compounds with higher stability (lower total energy)had higher nitro group charge values. Figure 1 shows arobust linear relationship (R2 = 0.9341) between the RC−NNitrobond lengths and the nitro charges calculated with the NBOscheme.

Lower (more negative) nitro group charges were consis-tent with a decrease in the C–NNitro bond length. Therefore,the value of the charge on the nitro group reflects the strengthof the corresponding bond and stability in these compounds.From the data shown in Tables 1–3, we concluded that theQNitro was more sensitive to molecular changes than RC−NNitro .For example, the RC−NNitro of all the isomers of dinitrobenzene(o, m and p) was 1.480 ± 0.006 Å; however, the QNitro ofthese isomers was 0.207, 0.250, and 0.244 e, respectively.In addition, the average charge on the nitro groups wasincreased by substituents with σ- and π-donor ability (e.g.,–NH2, –OH, –CH3) and decreased by substituents with σ-

R2 = 0.95332.5

3

3.5

4

4.5

−0.255 −0.235 −0.215 −0.195

Hea

t of

exp

losi

on (

MJ

kg−1

)

HE = 32.495QNitro + 10.944

QNitro (e−)

Figure 2: Relationship between heats of explosion and nitro charges(QNitro) of nitroaromatic compounds.

and π-electron acceptor ability (e.g., –COOH). The QNitro forTNA, PiAc, TNT, TNB, and TNBA was 0.252, 0.228, 0.222,0.219 and 0.215 e−, respectively.

All of the RC−NNitro values for the studied compoundswere in the range of 1.4370 to 1.4880 Å. These valueswere higher than the calculated RC−NNitro bond lengths innitramines (1.3640–1.4021 Å) and nitrate esters (1.4180–1.4370 Å) and lower than the RC−NNitro bond lengths in nitroparaffins (1.5029–1.5565 Å). Our calculations showed thatthe introduction of amino groups into multinitrobenzenedecreased the NBO nitro group charges and shortened theC–NNitro bond length. This effect was strongest when one,two or three amino groups were introduced into 1,3,5-trinitrobenzene (TNB) to form TNA, DATB, and TATB,respectively. Global analysis of the results presented aboveindicated that the nitro group charges can be used toassess the stability and explosive properties of this class ofcompounds.

3.2. NBO Nitro Charges and Heat of Explosion. The exper-imental heats of explosion and calculated QNitro valuesobtained by the NBO scheme for 35 nitroaromatic com-pounds are listed in Tables 1–3. As shown in Figure 2,the relationship between the calculated QNitro values andthe experimental heat of explosion is linear, and the cor-relation coefficient was 0.9533, indicating that the NBOcharge calculated at the B3LYP/6-311+G(d,p) level efficientlyreflected the molecular environment of these compounds.The nitroaromatic compounds with higher average nitrogroup charges had greater experimental heat of explosion.

3.3. 15NNitro NMR Chemical Shifts and Heat of Explosion. Tofind the relationship between the 15NNitro chemical shifts ofthe nitro group and the heat of explosion for the nitroaro-matic compounds, the isotropic 15N NMR shielding tensorswere investigated theoretically at the B3LYP/6-311+G(2d,p)level within the CSGT model. In our recent work, a strong


HE = −0.1177 15NNitro + 1.373R2 = 0.9531

2.4

2.9

3.4

3.9

4.4

4.9

−27 −24 −21 −18 −15 −12 −9

Hea

t of

exp

losi

on (

MJ

kg−1

)

15NNitro chemical shift (ppm)

Figure 3: Relationship between heats of explosion and 15NNitroNMR chemical shifts for nitroaromatic compounds.

correlation was found between the heat of detonationand heat of explosion for nitramines, nitro paraffins, andnitrate esters and the corresponding 15NNitro chemical shifts.Zeman’s work is noteworthy for its correlation betweenexplosive properties (impact and electric sparks sensitivities,detonation, and thermal decomposition) and the 13C and15N NMR chemical shifts of polynitro compounds [28]. The15NNitro NMR chemical shift results for the 35 nitroaromaticstudied are listed in Tables 1–3. The correlation betweenheat of explosion and the calculated 15NNitro chemical shiftsis shown in Figure 3. As seen in this figure, the heat ofexplosion increased with a decreasing 15NNitro chemical shift.The regression coefficient (R2) obtained for the correlationbetween the heat of explosion and 15NNitro chemical shiftswas 0.9531. Although NMR studies in solution neglectimportant crystal-lattice interactions affecting some explo-sive properties, this particular correlation provided a con-sistent method for the assessment of the heat of detonationwithout the use of experimental data for a systematic set ofnitroaromatic compounds.

3.4. Quantitative Relationships between the Heat of Explosion(HE), QNitro and 15NNitro NMR Chemical Shifts. To verifythe relationship between the two parameters described inthe previous section (QNitro and 15NNitro) and the heat ofexplosion, 13 nitroaromatic compounds, each with a heatof explosion that had been measured experimentally, werecorrelated with our calculated values. These were obtainedfrom the theoretical structural parameters (listed in Table 1).The following equation was determined from the linearregression fit:

HE = 16.423× (QNitro)− 0.06×(15NNitro

)− 6.15. (1)

The significance of the results can be evaluated by theresults of the statistical parameters R2 = 0.9782, SE = 0.093,

R2 = 0.9782

2.5

3

3.5

4

4.5

2.5 3 3.5 4 4.5

Cal

cula

ted

hea

t of

exp

losi

on (

MJ

kg−1

)

Experimental heat of explosion (MJ kg−1)

Figure 4: Correlation between calculated and experimental heats ofexplosion for nitroaromatic compounds. Molecules used to build aquantitative model (◦) and other nitroaromatic compounds (•).

and RMSEP = 0.0817 MJ kg−1, where R2, SE, and RMSEPare the correlation coefficient, the standard error, and theroot mean squared error prediction, respectively. As seenfrom (1), a nitroaromatic explosive with a large averageQNitro value and a low 15NNitro chemical shift has a highheat of explosion. The stability and prediction capabilityof the quantitative model established by (1) was assessedusing the leave-one-out (LOO) cross-validation method. Inthe LOO method procedure, one explosive is removed fromthe training set (the explosives are listed in Table 1), and amodel is developed with remaining N-1 explosives. At eachstep, the heat of explosion value of the removed explosiveis predicted. This process was repeated until each moleculeof the training set is predicted. The prediction capability ofthe model was quantified in terms of rcv and Scv, which aredefined as follows:

r2cv = 1.0−∑n

i−1(yi − ŷi

)2

∑ni=1(yi − y

)2 ,

Scv =√√√∑n

i−1(yi − ŷi

)2

N −D − 1 ,

(2)

where yi and ŷi are the experimental and predictive values,respectively, y is the mean value of yi, N is the numberof explosives to be used for building the model, and D isthe number of descriptors in the model. The rcv and Scvvalues were 0.9727 and 0.146, respectively, which indicatedthat (1) was reasonably stable. The predicted accuracy of (1)for the heat of explosion of the nitroaromatic compoundswas within 0.146 MJ kg−1. Figure 4 shows a comparisonbetween the experimental heat of explosion, as predictedby (1), and the corresponding regression coefficient for thenitroaromatic compounds. The calculated heats of explosion


Ta

ble

4:C

ompa

riso

nof

calc

ula

ted

hea

tsof

expl

osio

n,f

orn

itro

arom

atic

com

pou

nds

,acc

ordi

ng

to(1

),H

ER−H

[15]

,HE

MH

K1

[18]

,an

dH

EM

HK

2[1

7]m

eth

odw

ith

expe

rim

enta

lval

ues

[2].

Cod

ede

sign

atio

nE

xper

imen

talH

E(H

2O

liq.)

(MJk

g−1)

HE

R−H

(H2O

liq.)

(MJ

kg−1

)H

EM

HK

2

(MJk

g−1)

HE

MH

K1

(MJk

g−1)

Cal

cula

ted

HE

(MJk

g−1)

(K-J

,t)a

(K-J

,e)b

(K-J

mod

.,e)

c

Tetr

yl4.

773

5.31

86.

234

4.74

04.

118

4.20

54.

643

TeN

A4.

378

5.48

56.

138

4.91

24.

245

4.59

44.

336

TN

B3.

964

5.06

75.

845

4.71

13.

617

4.10

94.

061

24D

NT

3.19

23.

795

5.32

23.

740

3.22

52.

959

3.04

326

DN

T3.

325

3.90

85.

435

3.84

53.

225

2.95

92.

802

TN

T3.

766

4.69

45.

795

4.25

93.

546

3.72

53.

665

TN

A3.

589

4.65

65.

565

4.36

83.

822

4.00

43.

318

PiA

c3.

437

4.85

35.

602

4.30

53.

751

3.32

13.

524

mD

NB

2.66

64.

289

5.44

33.

870

3.22

83.

388

2.63

2H

NS

4.08

85.

017

5.74

94.

284

4.02

73.

934

4.06

5R

MSE

P1.

046

2.02

30.

671

0.33

20.

362

0.20

4aH

eat

ofde

ton

atio

nca

lcu

late

du

sin

gK

amle

t-Ja

cobs

met

hod

.T

he

tde

not

esth

atth

eva

lues

use

dfo

rth

eh

eats

offo

rmat

ion

for

the

prod

uct

sar

epr

edic

ted

.bT

he

ede

not

esth

atth

eva

lues

use

dfo

rth

eh

eats

offo

rmat

ion

for

the

prod

uct

sar

eth

eex

peri

men

talv

alu

es.c

Mod

ified

Kam

let

and

Jaco

bsm

eth

od.


Table 5: Comparison of calculated heats of explosion for nitrate esters according to HEI−H [10] and HE MHK2 method [17] with experimentalvalues [2].

Chemical name Experimental HE (H2O liq.) (MJ kg−1) HEMHK2 (MJ kg−1) HEI−H (MJ kg−1)

Erythritol tetranitrate 6.356 6.555 6.362

Glycerol trinitrate 6.671 6.520 6.847

n-propyl nitrate 3.272 2.963 3.377

Isopropyl nitrate 3.126 2.963 3.106

Diethylene glycol dinitrate 4.566 4.624 4.389

Dioxiethylnitramine dinitrate 5.458 5.019 5.307

Dipentaerythritol hexanitrate 5.143 4.995 5.523

Butanetriol trinitrate 6.022 5.464 5.824

Metriol trinitrate 4.945 4.774 5.202

Pentaerythritol tetranitrate 6.322 5.717 6.316

RMSEP 0.333 0.186

values were very similar to the values obtained in theexperiments. These results validate our new method forcalculating heat of explosion using the NBO charges onand 15N NMR chemical shifts of nitro groups as structuralparameters.

3.5. Predicting the Heat of Explosion for NitroaromaticExplosives. The predicted detonation heat by (1) for 14nitroaromatic explosives with unmeasured HEs is givenin Table 3. Based on the HE predictions for the halogenderivatives of nitrobenzene, the HE had the following trend:CDB < CTB < DCTB < TCTB. Nitroaromatic compoundswith a higher number of halogen atoms exhibit a higherheat of explosion. However, this theoretical study was carriedout in solution neglect important crystal-lattice effects thatare important in the determination of explosive proper-ties. Zeman’s work [29] established an inverse relationshipbetween the volatility and Chapman-Jouguet (C-J) pressure.The increased volatility due to multiple substitution is linkedwith the deformation of the molecules that accompanythe substitution. Therefore, it is of utmost importancethe intermolecular nonbonding interaction. Global analysisof the results presented in Tables 1–3 indicated that theHE values of 2,4,6-trinitrobenzene derivatives decreasedsystematically with the number of activating groups in themolecular structure of the nitroaromatic explosive. The HEtrend for the halogenated nitrobenzenes agreed with the σ-and π-donor ability of the compounds. In addition, theheat of explosion for 2,4,6-trinitrobenzene monosubstitutedderivatives increased with substituents that had a larger σ-and π-electron acceptor ability, which was consistent withsmaller nitro group charges and 15NNitro chemical shifts.

3.6. Comparison of the Calculated Heats of Explosion withOther Empirical and Quantum Mechanical Methods. Theheats of explosion for various nitro-aromatic and nitrateesters are given in Tables 4 and 5 and compared withexperimental values, two empirical methods (KHM1 [18]and KHM2 [17]) and Rice-Hare methods [15]. Predictedheats of explosion for H2O(l) using quantum mechanicalapproach including predicted and experimental values for

the heat of formation have RMSEP from experiment of1.046 and 2.023 MJ kg−1, respectively, whereas the modifiedversion of Kamlet-Jacobs’s method results has a substantiallylower deviation from experiment (0.671 MJ kg−1). As shownin Table 4, the RMSEP of empirical methods (0.332 and0.362 MJ kg−1) are lower than the quantum mechanicalmethods. As indicated in Tables 4 and 5, the predicted heatsof explosion calculated by the new model deviated fromexperiment by less than 0.204 MJ kg−1. As is evident, theproposed model based on the calculation of two structuralparameters shows the best agreement with experimentaldata.

This method for predicting the heat of explosion ofnitroaromatic explosives, that is, using NBO charges and15N NMR chemical shifts as references, can be generalizedfor other homologous systems if these parameters arecalculated with the same computational approach. Hence,the computation of the heat of explosion equation will beuseful in the design and development of strong nitroaro-matic explosives when experimental data are not available.However, the heat of explosion depends on many factorsbesides nitro group charges or 15NNitro NMR chemical shifts;a completely monotonic correlation between these factorswas not found, which indicates that this quantitative modelis only applicable to the nitroaromatic explosives whosestabilities are determined by the chemical bonds linked tothe nitro group. Based on the previous discussion, it can beconcluded that a consistent correlation between the heat ofexplosion and the QNitro and 15NNitro chemical shifts exists insuch explosives.

4. Conclusion

NBO charge and 15N NMR chemical shift analyses are twokey parameters that can be used to determine the heat ofexplosion of aromatic explosives. Using these two structuralparameters, a good quantitative model was established forpredicting the heat of explosion of 35 nitroaromatic explo-sives. The model was significant and stable and displayedprediction accuracy within 0.146 MJ kg−1, with an overallroot mean squared error of prediction (RMSEP) below


0.183 MJ kg−1. The heat of explosion of nitroaromatic com-pounds decreased systematically with the type and numberof activating substituents (σ- and π-donors) and increasedwith the number of σ- and π-electron acceptors added to thecorresponding molecular structure. Based on these results,the proposed model could be used to predict the heat ofexplosion without experimental data for a systematic setof nitroaromatic compounds and could aid in the designof these highly energetic materials. The calculated heatsof explosion by this model give better results than otherempirical and quantum mechanical methods available in theliterature.

Acknowledgments

This work was supported by the Center for Chemical SensorsDevelopment (CCSD) of the Chemistry Department of theUniversity of Puerto Rico, Mayagüez and the Research andCreation Center (RCC) of the University of Puerto Rico,Arecibo. The authors also acknowledge the U.S. Departmentof Homeland Security for its support (Award number2008-ST-061-ED0001). However, the views and conclusionscontained in this document are those of the authors andshould not be interpreted as necessarily representing theofficial policies, either expressed or implied, of the U.S.Department of Homeland Security.

References

[1] M. H. Keshavarz, “Determining heats of detonation of non-aromatic energetic compounds without considering theirheats of formation,” Journal of Hazardous Materials, vol. 142,no. 1-2, pp. 54–57, 2007.

[2] R.. Meyer, J. Köhler, and A. Homburg, Explosives, Wiley-VHC,Weinheim, Germany, 2007.

[3] A. Delpuech and J. Cherville, “Relation entre La structureelectronique et la sensibilité au choc des explosifs seconairesnitrés,” Propellants Explosives, Pyrotechnics, vol. 4, no. 6, pp.121–128, 1979.

[4] C. Cao and S. Gao, “Two dominant factors influencingthe impact sensitivities of nitrobenzenes and saturated nitrocompounds,” Journal of Physical Chemistry B, vol. 111, no. 43,pp. 12399–12402, 2007.

[5] B. M. Rice and J. J. Hare, “A quantum mechanical investigationof the relation between impact sensitivity and the charge dis-tribution in energetic molecules,” Journal of Physical ChemistryA, vol. 106, no. 9, pp. 1770–1783, 2002.

[6] S. Zeman, “New aspects of initiation reactivities of energeticmaterials demonstrated on nitramines,” Journal of HazardousMaterials, vol. 132, no. 2-3, pp. 155–164, 2006.

[7] M. A. Hiskey, K. R. Brower, and J. C. Oxley, “Thermaldecomposition of nitrate esters,” Journal of Physical Chemistry,vol. 95, no. 10, pp. 3955–3960, 1991.

[8] C. Zhang, “Review of the establishment of nitro group chargemethod and its applications,” Journal of Hazardous Materials,vol. 161, no. 1, pp. 21–28, 2009.

[9] S. P. Hernández-Rivera and R. Infante-Castillo, “A systematictheoretical investigation of the relationship between heats ofdetonation and NBO charges and 15N NMR chemical shiftsof nitro groups in nitramines and nitro paraffins,” Journal ofMolecular Structure, vol. 960, no. 1–3, pp. 57–62, 2010.

[10] S. P. Hernández-Rivera and R. Infante-Castillo, “Predictingheats of explosion of nitrate esters through their NBOcharges and 15N NMR chemical shifts on the nitro groups,”Computational and Theoretical Chemistry, vol. 963, no. 2-3,pp. 279–283, 2011.

[11] R. Infante-Castillo and S. P. Hernández-Rivera, “On the choiceof optimal protocol for calculation of 13C and 15N NMRisotropic chemical shifts in nitramine systems,” Journal ofMolecular Structure, vol. 940, no. 1–3, pp. 124–128, 2010.

[12] T. A. Keith and R. F. W. Bader, “Calculation of magneticresponse properties using a continuous set of gauge transfor-mations,” Chemical Physics Letters, vol. 210, no. 1–3, pp. 223–231, 1993.

[13] R. Infante-Castillo and S. P. Hernández-Rivera, “Experimentaland theoretical studies of the molecular structure of 1-(2-pyridinylmethyl)-2-methylbenzimidazole,” Journal of Molecu-lar Structure, vol. 968, no. 1–3, pp. 6–12, 2010.

[14] R. Infante-Castillo and S. P. Hernández-Rivera, “DFT studiesof the structure and vibrational and NMR spectra of 1-(2-methylpropenyl)-2-methylbenzimidazole,” Journal of Molecu-lar Structure, vol. 917, no. 2-3, pp. 158–163, 2009.

[15] B. M. Rice and J. Hare, “Predicting heats of detonation usingquantum mechanical calculations,” Thermochimica Acta, vol.384, no. 1-2, pp. 377–391, 2002.

[16] M. H. Keshavarz, “Simple procedure for determining heats ofdetonation,” Thermochimica Acta, vol. 428, no. 1-2, pp. 95–99,2005.

[17] M. H. Keshavarz, “A simple way to predict heats of detonationof energetic compounds only from their molecular structures,”Propellants, Explosives, Pyrotechnics, vol. 37, no. 1, pp. 93–99,2012.

[18] M. H. Keshavarz, “Quick estimation of heats of detonation ofaromatic energetic compounds from structural parameters,”Journal of Hazardous Materials, vol. 143, no. 1-2, pp. 549–554,2007.

[19] M. H. Keshavarz, “Estimating heats of detonation and detona-tion velocities of aromatic energetic compounds,” Propellants,Explosives, Pyrotechnics, vol. 33, no. 6, pp. 448–453, 2008.

[20] M. H. Keshavarz, “Theoretical prediction of condensed phaseheat of formation of nitramines, nitrate esters, nitroaliphaticsand related energetic compounds,” Journal of HazardousMaterials, vol. 136, no. 2, pp. 145–150, 2006.

[21] V. I. Pepekin and S. A. Gubin, “Heat of explosion of commer-cial and brisant high explosives,” Combustion, Explosion andShock Waves, vol. 43, no. 2, pp. 212–218, 2007.

[22] L. M. Hall, L. H. Hall, and L. B. Kier, “QSAR modelingof β-lactam binding to human serum proteins,” Journal ofComputer-Aided Molecular Design, vol. 17, no. 2–4, pp. 103–118, 2003.

[23] M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., Gaussian 09Rev. A.1., CT. Gaussian, Wallingford, UK, 2009.

[24] A. D. Becke, “Density-functional thermochemistry. III. Therole of exact exchange,” Journal of Chemical Physics, vol. 98,no. 7, pp. 5648–5652, 1993.

[25] C. Lee, W. Yang, and R. G. Parr, “Development of the Colle-Salvetti correlation-energy formula into a functional of theelectron density,” Physical Review B, vol. 37, no. 2, pp. 785–789, 1988.

[26] E. D. Glendening, A. E. Reed, J. E. Carpenter, and F. Weinhold,NBO Version 3.1, 2009.

[27] B. Mennucci and J. Tomasi, “Continuum solvation models: anew approach to the problem of solute’s charge distributionand cavity boundaries,” Journal of Chemical Physics, vol. 106,no. 12, pp. 5151–5158, 1997.


[28] S. Zeman, “Modified Evans-Polanyi-Semenov relationship inthe study of chemical micromechanism governing detonationinitiation of individual energetic materials,” ThermochimicaActa, vol. 384, no. 1-2, pp. 137–154, 2002.

[29] S. Zeman, “The relationship between differential thermalanalysis data and the detonation characteristics of polyni-troaromatic compounds,” Thermochimica Acta, vol. 41, no. 1,pp. 199–212, 1980.

Submit your manuscripts athttp://www.hindawi.com

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttp://www.hindawi.com

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014


CatalystsJournal of

Documents

PredictingHeatsofExplosionofNitroaromatic ...downloads.hindawi.com/archive/2012/304686.pdf · 1.Introduction Aromatic molecules with nitro groups are an important class of highly