ARL-TN-0680 ● JUNE 2015

US Army Research Laboratory

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

by Edward FC Byrd

Approved for public release; distribution is unlimited.
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ARL-TN-0680 ● JUNE 2015

US Army Research Laboratory

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

by Edward FC Byrd

Weapons and Materials Research Directorate, ARL

Approved for public release; distribution is unlimited.

FOR OFFICIAL USE ONLY (delete if not FOUO)
ii

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Technical Note

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July 2014

4. TITLE AND SUBTITLE

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

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-0680

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

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

crystalline density and heat of formation, the performance properties for the 3,7-dinitro-[1,2,4]triazolo[5,1-c][1,2,4]triazin-4

-amine 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, synthesis, energetic materials,

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

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Edward FC Byrd

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Unclassified

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(410) 306-0729

Standard Form 298 (Rev. 8/98)

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iii

Contents

List of Figures iv

List of Tables iv

Acknowledgments v

1. Introduction 1

1.1 Neutral Heat of Formation 1

1.2 Crystalline Density 3

1.3 Impact Sensitivity 3

2. Method of Solution 4

3. Results and Discussion 4

4. Conclusions 7

5. References 8

List of Symbols, Abbreviations, and Acronyms 10

Distribution List 11
iv

List of Figures

Fig. 1 Optimized structure of the 3,7-dinitro-[1,2,4]triazolo[5,1-

c][1,2,4]triazin-4-amine molecule .........................................................5

Fig. 2 Electrostatic potential map of the 3,7-dinitro-[1,2,4]triazolo[5,1-

c][1,2,4]triazin-4-amine molecule, with molecule overlay....................6

Fig. 3 Electrostatic potential map of the 3,7-dinitro-[1,2,4]triazolo[5,1-

c][1,2,4]triazin-4-amine molecule, without molecule overlay...............6

List of Tables

Table Cheetah-predicted properties of the 3,7-dinitro-[1,2,4]triazolo[5,1-

c][1,2,4]triazin-4-amine molecule .........................................................7
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 James 

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

Research Laboratory Department of Defense Supercomputing Resource Center 

[ARL DSRC]) is acknowledged for his gsubmit script, initially written for the ARL 

DSRC. Dr Rice is acknowledged for running the Cheetah calculations. All 

computations were performed at the ARL DSRC, Aberdeen Proving Ground, MD. 

Dr David Chavez (Los Alamos National Laboratory) is acknowledged as originator 

of the molecule modeled herein.
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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 formation1,2

and densities3,4 of energetic materials. This capability, coupled with a growing ARL 

synthetic experimental faculty, allows synthetic and formulation chemists to safely 

and quickly screen candidate materials to focus efforts only on the most promising 

compounds. This technical note will detail theoretical predictions of a notional 

energetic material.

The tools are based on correlations of quantum mechanically derived properties of 

isolated energetic molecules with heats of formation and crystalline densities, 

critical elements in predicting the detonation and propulsion properties, for both 

neutral and ionic solid energetic materials. As the crystal structure of a novel 

material is usually unknown, as it has yet to be synthesized, each of the correlations 

requires quantum mechanical data solely from single molecules and not from 

knowledge of the bulk material. To date, the neutral heat of formation tool can only 

treat molecules containing carbon, hydrogen, nitrogen, and oxygen. Additionally, 

a tool to qualitatively predict the impact sensitivity for neutral molecules was 

developed, also based solely on quantum mechanically derived data based on a 

single molecule. This report details the theoretically predicted performance and 

vulnerability properties for notional energetic molecules; as such, we will recap the 

methodologies used in the predictions in this technical report.

1.1 Neutral Heat of Formation

Developed in 2006,

1 the neutral heat of formation prediction tool is based on Hess’s 

law (Eq. 1),

5 where an atomic or group equivalency prediction for the gas phase 

heat of formation (Eq. 2) is added to a prediction for the heats of vaporization 

(Eq. 3) or sublimation (Eq. 4). Equations 2–4 use information determined from 

quantum mechanical calculations.

ΔH°f (liquid/sold) = ΔH°f (g) - ΔHvap/sub. (1)

ΔH°f (g) = E – Σ njεj. (2)

ΔHvap = a(SA)1⁄2 + b(σ2totν) 1⁄2 + c. (3)

ΔHsub = a(SA)2 + b(σ2totν) 1⁄2 + c. (4)

In Eq. 2, E is the quantum mechanically determined electronic energy, nj is either 

the number of atom or group types j contained in the neutral molecule, and εj is
2

either the atom or group equivalent energy of atom/group j. These equivalent 

energies were determined through the fitting of experiment gas phase heats of 

formation [ΔH°f (g)] to quantum mechanically computed energies E.

Equations 3 and 4 use statistics derived from the electrostatic surface potential 

(ESP), as demonstrated by Politzer et al.6–8

, to correlate to heats of vaporization and 

sublimation. As defined in the Murray et al.9 and Rice and Hare10 papers, the 

definitions of these electrostatic properties are global properties across the 0.001 

electron/bohr3 isosurface of electronic density, an isosurface calculated to contain 

98%–99% of the electronic density. To compute these statistics, the electrostatic 

potential V is required and is defined as

VV(rr) = � ZZii

|RRii−rr| ii

− � ρρ�rr′�drr′

|rr′−rr| , (5)

where Zi and Ri represent the charge and position of atom i, and ρ(r) is the electronic 

density. The statistical tools developed by Murray et al.9,11 used in Eqs. 3 and 4 are 

the surface area (SA), the variance of electrostatic surface potential (σ2), and the 

balance parameter (ν). These are defined as

Σxx = 1

nn� VVxx(rrii) nn

ii=1 , (6)

σσxx

2 = 1

nn� |VVxx(rrii) − Σxx| nn 2

ii=1 , (7)

σσtttttt

2 = σσ+

2 + σσ−2 , (8)

and

ν = σσ+

2σσ−

2

[σσtttttt

2 ]2 , (9)

where V(ri) is the value of the ESP at ri and Σ is the average electrostatic surface 

potential (x is either the positive [+] or negative [–] portion of the ESP). SA is the 

surface area of the 0.001 electron/bohr3 isosurface of the electron density of the 

molecule, σ2tot is a measure of the variability of electronic potential on the surface, 

and ν is the degree of balance between the positive and negative charges on the 

isosurface. Equations 3 and 4 contain a different set of fitted a, b, and c parameters. 

This methodology enjoys considerable accuracy, with the root mean square errors 

for the solid phase heat of formation under 6 kcal/mol. 
3

1.2 Crystalline Density

Initially developed in 20073 and revised in 2013,

4 this method correlates the 

quantum mechanically derived electronic density volume of the molecular unit to 

the crystalline density. This correlation exhibits significant success in predicting 

the crystal density, with errors under 3% for neutral materials. This correlation only 

requires the quantum mechanically derived molecular volume and the molecular 

mass for a single molecular unit, along with associated electrostatic properties

(Eq. 10).

ρcrystal = a(M / VM) + b(νσ2tot) + c, (10)

where a, b, and c are fitted terms, different from those in Eqs. 3 or 4, M is the total 

molecular mass, VM is the total molecular volume, and σ2tot and ν are the same as 

in Eqs. 8 and 9.

1.3 Impact Sensitivity

Besides performance parameters, ARL researchers have also developed a visual 

qualitative indicator of impact sensitivity (David Chavez, Los Alamos National 

Laboratory, private communication, 2014; unreferenced) as a method to assess any 

potential safety concerns with yet to be synthesized novel materials. Rice and 

Hare12 attempted to correlate Politzer-type statistical properties of the electronic 

density to impact sensitivity for a series of polynitroaromatic and benzofuroxan 

molecules. While no strong correlations were found with the statistical parameters, 

there was a qualitative visual correlation related to the degree of electron deficiency 

over covalent bonds contained within the “backbone” of the molecules. Molecules 

that were very sensitive exhibited large electron deficiencies over the main 

structure, while less-sensitive molecules had a more evenly distributed electron 

density. This method, while quite approximate and limited to neutral molecules 

(due to the inherent charge separation found in ionic materials), can still yield a 

relative means of estimating impact sensitivities and thus potential hazards of 

notional materials. The visualizer used in this study, titled EDAT, was originally 

coded by Dr Jennifer Hare and later revised by Dr Anthony Yau. This tool is also 

used to derive the Politzer statistical properties used in the heat of formation and 

density predictors. In this report we shall apply these methods toward the molecule 

3,7-dinitro-[1,2,4]triazolo[5,1-c][1,2,4]triazin-4-amine (David Chavez, Los 

Alamos National Laboratory, private communication, 2014; unreferenced) to 

predict the heat of formation and crystalline density of this material.
4

2. Method of Solution

The analysis was performed using scripts written at ARL to perform the following 

required computations12:

1. A driver script that calls the other scripts, as well as submits the required 

Gaussian0913 calculations and monitors the queues (master_densheat.s.)

2. A script to construct the Gaussian input files (gbuild.s).

3. A script to gather and compute the data needed to determine the heats of 

formation and/or crystalline densities and subsequently calculate said 

properties (arl_densheat.s).

Given a properly formatted input file, the scripts will analyze the .dat input file, 

design the proper Gaussian input files and submit them, monitor the supercomputer 

queues for job completion, postprocess the necessary files, and, finally, compute 

the desired information.

The scripts also perform a limited series of error checking, such as checking that 

structures are optimized (i.e., the structure is not a transition state structure but 

rather a minimum), that the Gaussian calculations ran successfully to completion,

and that, for neutral calculations, the number of atom types listed correspond to the 

number of atoms in the Cartesian coordinates. 

The initial, user-designed structure has its geometry optimized using the B3LYP 

spin-restricted Kohn-Sham density functional theory (KS-DFT)14 with the 6-31G* 

Pople Gaussian basis set,

15 currently done using the Gaussian09 program 

package.

13 For the computation of the electronic energy required in Eq. 2, the 

B3LYP density functional theory energy15 with the 6-311++G(2df,2p) Pople basis 

set16 is obtained on the optimized geometry. For the crystalline density, the initial 

structure is optimized using the B3LYP KS-DFT with the 6-31G** Pople basis 

set,

16 with the associated electronic density used in obtaining the molecular volume 

and electronic statistical properties required in Eq. 10. The visualization of the 

electrostatic potential surface was performed with the EDAT tool.

3. Results and Discussion

The 3,7-dinitro-[1,2,4]triazolo[5,1-c][1,2,4]triazin-4-amine molecule (David

Chavez, Los Alamos National Laboratory, private communication, 2014; 

unreferenced) (Fig. 1) was constucted and submited with the ARL scripts.

12
5

Fig. 1 Optimized structure of the 3,7-dinitro-[1,2,4]triazolo[5,1-c][1,2,4]triazin-4-amine

molecule

The resultant crystal density was computed to be 1.856 g/cc. The gas and solid 

phase heats of formation from the group additivity methodology were 120.12 and 

95.22 kcal/mol, respectively.

Using the ARL-developed EDAT tool, the electrostatic map on the 0.001 isosurface 

was generated and is illustrated in Figs. 2 and 3 (with and without the molecule 

overlaid). For this visualization, the scalar range of the ESP ranges from –0.05 to 

0.075. For this visualization methodology, regions of large positive charge (red)

over the backbone of the structure tend to indicate increased sensitivity. For this 

molecule, this ESP distribution would indicate moderate impact sensitivity. Using 

this predicted data, we then performed Cheetah 7.0 calculations18 to predict the 

performance parameters (Table). 
6

Fig. 2 Electrostatic potential map of the 3,7-dinitro-[1,2,4]triazolo[5,1-c][1,2,4]triazin-4-

amine molecule, with molecule overlay

Fig. 3 Electrostatic potential map of the 3,7-dinitro-[1,2,4]triazolo[5,1-c][1,2,4]triazin-4-

amine molecule, without molecule overlay
7

Table Cheetah-predicted properties of the 3,7-dinitro-[1,2,4]triazolo[5,1-c][1,2,4]triazin-4-

amine molecule

Property Value

Pressure 31.084 GPa

Shock velocity 8.679 km/s

Temperature 3,395.8 K

Total energy of detonation 1.284 TNT equivalence (per cc)

1.145 TNT equivalence (per gram)

4. Conclusions

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

crystalline density of the 3,7-dinitro-[1,2,4]triazolo[5,1-c][1,2,4]triazin-4-amine

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

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

impact sensitivity of this compound using electrostatic potential maps. This 

information has been transferred back to the requesting synthetic chemist, Dr David 

Chavez of Los Alamos National Laboratory.
8

5. 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 (errata) 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. Atkins PW. Physical chemistry. Oxford (England): Oxford University Press;

1982.

6. Politzer P, Murray JS, Brinck T, Lane P. In: Nelson JO, Karu AE, Wong RB, 

editors. Immunoanalysis of agrochemicals. ACS Symposium Series; 1994.

Washington (DC): American Chemical Society. p. 586.

7. Murray JS, Politzer P. In: Politzer P, Murray JS, editors. Quantitative treatment 

of solute/solvent interactions: theoretical and computational chemistry, 1.

Amsterdam (Netherlands): Elsevier Scientific; 1994. p. 243–289.

8. Politzer P, Murray JS. Relationships between lattice energies and surface 

electrostatic potentials and areas of anions. J Phys Chem A. 1998;102:1018.

9. Murray JS, Lane P, Politzer P. Effects of strongly electron-attracting 

components on molecular surface electrostatic potentials: application to 

predicting impact sensitivities of energetic molecules. Mol Phys. 

1998;93(2):187–194.

10. 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;106:1770.

11. Murray JS, Lane P, Politzer P. Relationships between impact sensitivities and 

molecular-surface electrostatic potentials of nitroaromatic and 

nitroheterocyclic molecules. Mol Phys 1995;85(1):1–8.

12. 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.
9

13. Byrd EFC. Simple computation of the heat of formation and density from 

theoretically predicted values. Aberdeen Proving Ground (MD): Army 

Research Laboratory (US); 2012 Sep. Report No.: ARL-TR-6206. Also 

available at: http://www.arl.army.mil/arlreports/2012/ARL-TR-6206.pdf.

14. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, 

Scalmani G, Barone V, Mennucci B, Petersson GA, et al. Gaussian 09, Rev. 

A.1. Wallingford (CT): Gaussian, Inc.; 2009.

15. Becke AD. Density‐functional thermochemistry. III. The role of exact 

exchange. J Chem Phys. 1993:98:5648–5652; Lee C, Yang W, Parr RG. 

Development of the Colle-Salvetti correlation-energy formula into a functional 

of the electron density. Phys Rev B. 1988;37:785–789; Vosko SH, Wilk L, 

Nusair M. Accurate spin-dependent electron liquid correlation energies for 

local spin density calculations: a critical analysis. Can J Phys. 1980;58:1200–

1211; Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ. Ab Initio 

Calculation of Vibrational Absorption and Circular Dichroism Spectra Using

Density Functional Force Fields. J Phys Chem. 1994;98:11623–11627.

16. Krishnan R, Binkley JS, Seeger R, Pople JA. Self-consistent molecular orbital 

methods. XX. A basis set for correlated wave functions. J Chem Phys. 

1980;72:650; Frisch MJ, Pople JA, Binkley JS. Self-Consistent Molecular 

Orbital Methods 25: Supplementary Functions for Gaussian Basis Sets. 

J Chem Phys. 1984;80:3265; Clark T, Chandrasekhar J, Schleyer PVR. 

Efficient diffuse function-augmented basis sets for anion calculations. III. The 

3-21+G basis set for first-row elements, Li–F. J Comp Chem. 1983;4:294.

17. Bastea S, Fried LE, Glaeseman KR, Howard WM, Kuo I-FW, Souers PC, 

Vitello PA. Cheetah 7.0 thermochemical code. Livermore (CA): Energetic 

Materials Center, Lawrence Livermore National Laboratory; 2012.
10

List of Symbols, Abbreviations, and Acronyms

6-31G* Pople’s Gaussian double-zeta polarized basis set with d

polarization functions on each of the atoms Li through Ca

6-31G** Pople’s Gaussian double-zeta polarized basis set with d

polarization functions on each of the atoms Li through Ca

and p polarization functions on H and He

6-311++G(2df,2p) Pople’s Gaussian triple-zeta polarized basis set with 2d and 

f polarization functions on each of the atoms Li through Ca

and 2p polarization functions on H and He along with s and 

p diffuse functions on each of the atoms Li through F and s

diffuse functions on H and He

ν balance parameter

Σ average electrostatic surface potential

σ2 variance of electrostatic surface potential

p electronic density

pcrystal crystalline density

ΔH°f (g) gas phase heat of formation

ΔH°f (l) liquid phase heat of formation

ΔH°f (s) solid phase heat of formation

V electrostatic potential

ARL US Army Research Laboratory

B3LYP Becke 3 parameter exchange with Lee-Yang-Parr 

correlation DFT functional

DFT density functional theory

ESP electrostatic surface potential

g/cc grams per cubic centimeter

kcal/mol kilocalories per mole (unit of energy)

KS-DFT Kohn-Sham density functional theory
11

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