ARL-TN-0749 ● APR 2016

US Army Research Laboratory

Theoretical Prediction of the Heats of 

Formation, Densities, and Relative Sensitivities 

for 5,7-dinitro-5,7-diaza-1,3-dioxabicyclo

(3:3:0)octan-2-one

by Edward FC Byrd

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ARL-TN-0749 ● APR 2016

US Army Research Laboratory

Theoretical Prediction of the Heats of 

Formation, Densities, and Relative Sensitivities 

for 5,7-dinitro-5,7-diaza-1,3-dioxabicyclo 

(3:3:0)octan-2-one

by Edward FC Byrd

Weapons and Materials Research Directorate, ARL

Approved for public release; distribution is unlimited.
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April 2016

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Technical Note

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1–31 May 2015

4. TITLE AND SUBTITLE

Theoretical Prediction of the Heats of Formation, Densities, and Relative 

Sensitivities for 5,7-dinitro-5,7-diaza-1,3-dioxabicyclo (3:3:0)octan-2-one

5a. CONTRACT NUMBER

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6. AUTHOR(S)

Edward FC Byrd

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US Army Research Laboratory

ATTN: RDRL-WML-B

Aberdeen Proving Ground, MD 21005-5069

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ARL-TN-0749

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14. ABSTRACT

Using the US Army Research Laboratory–developed series of scripts, written to dramatically simplify the computation of 

crystalline density and heat of formation, the performance properties for the 5,7-dinitro-5,7-diaza-1,3-dioxabicyclo(3:3:0)octan2-one notional energetic material were evaluated. Additionally, a qualitative estimation of the impact sensitivity has been 

calculated. This report outlines the procedures used to generate this information, as well as Cheetah calculations using the 

predicted crystalline density and heat of formation.

15. SUBJECT TERMS

computational toolbox, script, crystalline density, heat of formation, impact sensitivity, energetic materials

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Edward FC Byrd

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Contents

List of Figures iv

List of Tables iv

Acknowledgments v

1. Introduction 1

2. Results and Discussion 1

3. Conclusions 4

4. References 5

List of Symbols, Abbreviations, and Acronyms 6

Distribution List 7
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iv

List of Figures

Fig. 1 Optimized structure of the 5,7-dinitro-5,7-diaza-1,3-

dioxabicyclo(3:3:0)octan-2-one molecule .............................................1

Fig. 2 Electrostatic potential map of 5,7-dinitro-5,7-diaza-1,3-

dioxabicyclo(3:3:0)octan-2-one, a) with and b-c) without molecule 

overlay. Image c) shows the opposite side of the molecule than b) ......3

List of Tables

Table 1 Cheetah predicted properties for 5,7-dinitro-5,7-diaza-1,3-

dioxabicyclo(3:3:0)octan-2-one using predicted density 

(1.888 g/cm3

)..........................................................................................4

Table 2 Cheetah predicted properties for 5,7-dinitro-5,7-diaza-1,3-

dioxabicyclo(3:3:0)octan-2-one using experimental density (1.952 

g/cm3).....................................................................................................4
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v

Acknowledgments

Dr Betsy Rice and Jennifer J Hare are acknowledged for their efforts in the original 

coding of the neutral heat of formation and EDAT tools, respectively. Dr Anthony 

Yau is acknowledged for his work in revising the EDAT code. Dr James Ianni

(Applications Engineer with Lockheed-Martin, contractor to the US Army 

Research Laboratory Department of Defense [DOD] Supercomputing Resource 

Center [ARL DSRC]) is acknowledged for his “gsubmit” script, initially written for 

the ARL DSRC. Dr Betsy Rice is acknowledged for running the Cheetah 

calculations. All computations were performed at the ARL DSRC, Aberdeen 

Proving Ground, MD. Calculations were performed at the behest of Dr Patrick 

Caruana (Naval Surface Warfare Center – Indian Head). Drs Michael Chaykovsky 

and William M Koppes1 are acknowledged as originators of the molecule modeled 

herein.

 1 Chaykovsky M, Koppes WM, inventors; The United States of America as represented by the Secretary 

of the Navy, assignee. 5,7-dinitro-5,7-diaza-1,3-dioxabicyclo[3:3:0]octan-2-one. United States patent US 

5,262,544. 1993 Nov 16.
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1

1. Introduction

US Army Research Laboratory (ARL) researchers have achieved robust theoretical 

models capable of predicting performance properties, such as heats of formation,

1,2

densities,

3,4 and impact sensitivity5 of energetic materials and have begun growing 

advanced synthesis capabilities to realize notional materials. This dual capability 

allows synthetic and formulation chemists to safely and quickly screen candidate 

materials to focus efforts only on the most promising compounds. For an in-depth 

explanation of the different theoretical methods employed herein, please refer to 

previous works.6,7 This technical note will detail theoretical predictions of heat of 

formation, density, sensitivity, and performance for the 5,7-dinitro-5,7-diaza-1,3-

dioxabicyclo(3:3:0)octan-2-one molecule.

8

2. Results and Discussion

The properties of the 5,7-dinitro-5,7-diaza-1,3-dioxabicyclo(3:3:0)octan-2-one

molecule (Fig. 1) were predicted using the ARL tools.7 For the estimation of the 

impact sensitivities, the electrostatic maps on the 0.001 isosurfaces were generated 

with the scalar range of the electrostatic surface potential (ESP) ranging from –0.05 

to 0.075. Recall that for this visualization methodology, regions of large positive 

charge (i.e., electron deficient regions, labeled as red) over the backbone of the 

structure tend to indicate increased sensitivity. 

Fig. 1 Optimized structure of the 5,7-dinitro-5,7-diaza-1,3-dioxabicyclo(3:3:0)octan-2-one

molecule
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The computed gas and solid heats of formation using the group additivity method 

were –82.11 and –106.43 kcal/mol, respectively. The predicted crystalline density 

was 1.888 g/cm3. The experimental density for this compound is known 

(1.952 g/cm3

), resulting in a –3.3% error, on par with the published root mean 

square error of approximately 3%.4

Additionally, we plot the ESP maps for this molecule (Fig. 2a–c), with and without 

the molecule overlaid on the ESP. When the images are analyzed, we would 

quantify the molecule as marginally sensitive, with the large red section being 

somewhat misleading as it is due to the presence of hydrogens and not the backbone 

structure. The experimental h50 impact sensitivity for this compound is 59 cm (with 

a reference cyclotrimethylenetrinitramine [RDX] sensitivity of 19 cm). We 

performed Cheetah 8.0 calculations9 to predict the performance parameters using 

the predicted heat of formation and density. At the Chapman-Jouguet point, 

Cheetah yields the values shown in Table 1. When the experimental density and the 

predicted heat of formation are used, Cheetah yields the values shown in Table 2.
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Fig. 2 Electrostatic potential map of 5,7-dinitro-5,7-diaza-1,3-dioxabicyclo(3:3:0)octan-2-

one, a) with and b-c) without molecule overlay. Image c) shows the opposite side of the 

molecule than b).

a)

b)

c)
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Table 1 Cheetah predicted properties for 5,7-dinitro-5,7-diaza-1,3-dioxabicyclo(3:3:0)octan2-one using predicted density (1.888 g/cm3

)

Property Value

Pressure 29.783 GPa

Shock velocity 8.196 km/s

Temperature 2974.1 K

Total energy of detonation 1.109 TNT equivalence (per cm3

)

0.971 TNT equivalence (per gram)

Note: TNT = trinitrotoluene

Table 2 Cheetah predicted properties for 5,7-dinitro-5,7-diaza-1,3-dioxabicyclo(3:3:0)octan2-one using experimental density (1.952 g/cm3

)

Property Value

Pressure 32.491 GPa

Shock velocity 8.454 km/s

Temperature 2876.7 K

Total energy of detonation 1.163 TNT equivalence (per cm3

)

0.986 TNT equivalence (per gram)

3. Conclusions

The ARL-developed software tools were used to predict the heats of formation and 

crystalline densities of the 5,7-dinitro-5,7-diaza-1,3-dioxabicyclo(3:3:0)octan-2-

one molecule. Using this predicted data, we then ran Cheetah calculations to predict 

the performance of this material. Additionally, we predicted the qualitative impact 

sensitivity of this compound using electrostatic potential maps. This information 

has been transitioned back to the requesting synthetic chemist, Dr David Caruana 

of Naval Surface Warfare Center – Indian Head.
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4. References

1. Byrd EFC, Rice BM. Improved prediction of heats of formation of energetic 

materials using quantum mechanical calculations. J Phys Chem A. 

2006;110(3):1005–1013; ibid 2009;113:5813. 

2. Byrd EFC, Rice BM. A comparison of methods to predict solid phase heats of 

formation of molecular energetic salts. J Phys Chem A. 2009;113(1):345–352.

3. Rice BM, Hare JJ, Byrd EFC. Accurate predictions of crystal densities using 

quantum mechanical molecular volumes. J Phys Chem A. 

2007;111(42):10874–10879.

4. Rice BM, Byrd EFC. Evaluation of electrostatic descriptors for predicting 

crystalline density. J Comp Chem. 2013;34(25):2146–2151.

5. Rice BM, Hare JJ. A quantum mechanical investigation of the relation between 

impact sensitivity and the charge distribution in energetic molecules. J Phys 

Chem A. 2002;106(9):1770–1783.

6. Byrd EFC. Theoretical prediction of the heat of formation, density and relative 

sensitivity for 3,7-dinitro-[1,2,4]triazolo[5,1-c][1,2,4]triazin-4-amine. 

Aberdeen Proving Ground (MD): Army Research Laboratory (US); 2015 Apr. 

Report No.: ARL-TN-0680.

7. Byrd EFC. On the failure of correlating partitioned electrostatic surface 

potentials using bader’s atoms-in-molecules theory to impact sensitivities. 

Aberdeen Proving Ground (MD): Army Research Laboratory (US); 2013 Sep. 

Report No.: ARL-TR-6206.

8. Caruana P. Naval Surface Warfare Center, Indian Head, MD. Private 

communication, 2015 May.

9. Bastea S, Fried LE, Glaeseman KR, Howard WM, Kuo IFW, Souers PC,

Vitello PA. Cheetah 8.0 thermochemical code. Livermore (CA): Energetic 

Materials Center: Lawrence Livermore National Laboratory; 2015.
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List of Symbols, Abbreviations, and Acronyms

ARL US Army Research Laboratory

g/cm3 grams per cubic centimeter

DSRC Department of Defense (DOD) Supercomputing Resource Center

ESP electrostatic surface potential

kcal/mol kilocalories per mole (unit of energy)

RDX cyclotrimethylenetrinitramine

TNT trinitrotoluene
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