Computationally Based Measures of Amine Azide Basicity 

and Their Correlation With Hypergolic Ignition Delays

by Michael J. McQuaid

ARL-TR-3122 December 2003

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Army Research Laboratory

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ARL-TR-3122 December 2003

Computationally Based Measures of Amine Azide Basicity 

and Their Correlation With Hypergolic Ignition Delays

Michael J. McQuaid

Weapons and Materials Research Directorate, ARL

Approved for public release; distribution is unlimited.
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Computationally Based Measures of Amine Azide Basicity and Their Correlation 

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Michael J. McQuaid

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14. ABSTRACT

To explore a hypothesis that hypergolic ignition delays for fuel-nitric acid combinations are a function of the fuel’s basicity, 

measures of base strength are computed for various azides, amines, amine azides, and hydrazines and compared to ignition 

delay data. Measures of base strength considered include gas-phase proton affinities, heats of neutralization for reactions 

leading to ion pairs, and heats of reaction for fuel-nitric acid complexation. The measures quantify substituent-mediated 

basicity differences between sites with lone pair electrons, but they do not appear to be good predictors of ignition delay. The 

failure of the hypothesis is discussed.

15. SUBJECT TERMS

computational chemistry, hypergolic ignition delay, base strength

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Michael J. McQuaid

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iii

Contents

List of Figures iv

List of Tables iv

Acknowledgments v

1. Introduction 1

2. Theoretical Methods 3

3. Results 4

3.1 Solvated Reactions via a Polarizable Continuum Model................................................4

3.2 Gas-Phase Cluster Reactions...........................................................................................5

3.3 Gas-Phase PAs.................................................................................................................7

3.4 Fuel Cluster-Nitric Acid Complexation........................................................................13

3.5 Binary Fuel-Nitric Acid Complexation.........................................................................16

4. Discussion 17

5. Summary 19

6. References 20

Distribution List 22
iv

List of Figures 

Figure 1. Ignition delay ordering derived from experimental testing.............................................3

Figure 2. Electrostatic potentials on electronic isodensity surfaces for DMAZ and hydrazine. 

Dark gray regions correspond to sites with lone pair electrons. ................................................4

Figure 3. DHr(0) for B + HNO3 ® BH

+

+ NO3

−

 as a function of dielectric constant, B being 

ammonia, hydrazine, or MMH...................................................................................................5

Figure 4. DHr(0) for Bx + HNO3 → (BH

+

)Bx-1 + NO3

−

, where B is ammonia or hydrazine............7

Figure 5. B3LYP/6-311++G(d,p) calculated PAs for alkylamines.................................................8

Figure 6. DMAZ conformers B, D, and E. Black circles denote nitrogen, gray circles denote 

carbon, and white circles denote hydrogen. .............................................................................11

Figure 7. ADMCPA isomers. Black circles denote nitrogen, gray circles denote carbon, and 

white circles denote hydrogen..................................................................................................11

Figure 8. B3LYP/6-311++G(d,p) calculated PAs for the lone pair sites of amine azide fuels. 

The PAs for the lone pair sites of ethylazide, dimethylamine, and trimethylamine are 

shown for comparison. .............................................................................................................12

Figure 9. B3LYP/6-311++G(d,p) calculated PAs for the lone pair sites of hydrazines. ..............14

Figure 10. O-Ha and N-Ha bond distances for (NH3)x-HNO3 complexes.....................................15

Figure 11. O-Ha and N-Ha bond distances for (N2H4)x-HNO3 complexes....................................15

Figure 12. The energies of (NH3)3-HNO3 and (N2H4)3-HNO3 complexes as a function of 

O-Ha bond distance. .................................................................................................................16

Figure 13. Heats of complexation for fuel-nitric acid complexes. ...............................................18

List of Tables

Table 1. PAs as calculated via B3LYP/6-311++G(d,p) and their comparison with 

recommended values..................................................................................................................6

Table 2. DHr for B+(BH

+

)(B)x ® (BH

+

)(B)x+1 reactions as calculated via 

B3LYP/6−311++G(d,p) and their comparison with experiment. ..............................................6

Table 3. B3LYP/6-311++G(d,p) calculated PAs for azides............................................................8

Table 4. B3LYP/6-311++G(d,p) calculated PAs for amine azides.................................................9

Table 5. B3LYP/6-311++G(d,p) calculated PAs for hydrazines. .................................................10

Table 6. Exothermicity of fuel-nitric acid complexation. .............................................................17
v

Acknowledgments

The author is grateful to Dr. C. Chabalowski (U.S. Army Research Laboratory) for his guidance 

in the use and application of computational quantum chemistry codes, and to Mr. D. Thompson

(U.S. Army Aviation and Missile Research, Development, and Engineering Center) and Dr. W. 

Stevenson for sharing their knowledge of amine azide hypergolicity. The vast majority of 

calculations were performed at the Department of Defense Major Shared Resource Center at 

Aberdeen Proving Ground, MD.
vi

INTENTIONALLY LEFT BLANK.
1

1. Introduction

Storable hypergolic liquid (or gel) fuel-oxidizer combinations (i.e., those that react 

spontaneously upon mixing) provide an extremely reliable basis on which to design intermittent 

and/or variable thrust rocket propulsion systems. As such, they are expected to propel beyond 

line-of-sight weapons carried by the U.S. Army’s Future Combat System, an example being the 

loitering attack missile being developed under the NetFires technology demonstration program. 

Unfortunately, the best performing propellant combinations developed to date have fuels derived 

from hydrazine, monomethylhydrazine (MMH), and/or unsymmetrical dimethylhydrazine 

(UDMH)—all of which are acutely toxic and suspected carcinogens. Thus, their utilization 

requires the implementation of burdensome and costly handling procedures.

Searching for alternatives to hydrazine-based fuels, the U.S. Army, led by the U.S. Army 

Aviation and Missile Research, Development, and Engineering Center (AMRDEC), has found 

that 2-azido-N,N-dimethylethanamine (DMAZ) performs competitively with Aerozine-50 (a 

50/50 mixture of hydrazine and UDMH) in inhibited red fuming nitric acid (IRFNA) oxidized 

experimental systems (1, 2). DMAZ has also been found to be less toxic than hydrazine-based 

fuels. DMAZ-IRFNA systems do not, however, meet “ignition delay” standards set by MMHIRFNA systems, which, negatively impacting engine design, may preclude DMAZ’s fielding. 

To address the ignition delay issue, 2-azidoethanamines with substituents other than the two 

methyl groups in DMAZ have been synthesized and tested. Trial and error testing of a class of

compounds related to a promising candidate is a traditional approach to fuel development, and it 

was employed in developing the fuel-oxidizer combinations that are fielded in hypergolic 

propulsion systems today. Clark provides an excellent history of the era that led to those 

combinations (3). Involving the testing of hundreds of different amines, hydrazine s, and 

alcohols during the 1950s, accessible data on these systems are, however, sparse because at that 

time the best combinations were classified or held proprietary. 

With the establishment of hydrazines as fuels of choice in the mid-1950s, some of the work on 

discarded candidates began to appear in the open literature, with the issue of ignition delay the 

subject of several papers. Relevant to (the amine) DMAZ were experimental studies by Rapp 

and Strier (4) and (separately) Schalla and Fletcher (5, 6). Both groups discuss the differences in 

ignition delay found for a wide variety of amines when they were oxidized by (nominally) white 

fuming nitric acid (WFNA). Rapp and Strier (4) suggest that the ignition delays for amines 

correlate with whether the amine is primary (R-NH2), secondary (R2-NH), or tertiary (R3-N), 

ignition delays decreasing in that order, and (by inference) with base strength. Schalla and 

Fletcher (5, 6) also recognize the importance of (acid-base) neutralization, but, finding ignition 

delays sensitive to oxidizer/fuel (O/F) ratios, propose that the best combinations will be those for

which the ratios, (1) optimal for combustion and (2) optimal for neutralization, are nearly the 
2

same. In the absence of an amine or other strong reducing group, compounds with azide groups 

are very weak bases and are not hypergolic. 

Given that alkyl amines have long ignition delays and that alkyl azides are not hypergolic, the 

relatively short ignition delays of DMAZ and some other amine azides are surprising. Moreover, 

there are performance differences between fuels in this class of compounds that are at odds with 

the expectation that shorter ignition delays will be found for compounds that are stronger bases. 

For example, a typical measure of a compound’s base strength, namely aqueous pKa, 

[ H ]

[ ][H O ] 3

+

+

= −

B

B

pKalog , (1)

which describes the equilibrium of the system

BH

+

+ H2O « B + H3O

+

, (2)

expresses the base strength of B in terms of the acid strength of the ion BH

+

, a higher pKa

indicating a higher base strength. As such, this measure would predict that 2-azido-Nmethylethanamine (MMAZ, pKa = 9.3) (1), which has one methyl group in lieu of the two in 

DMAZ, would ignite faster than DMAZ (pKa = 8.5) (1). But MMAZ has not been observed to 

be hypergolic. 

In considering this contradiction with expectations, it was noted that the ignition delays of 

dimethylamine (pKa = 10.9) (7) and trimethylamine (pKa = 9.8) (7) also fail to correlate with 

their pKas. And a comparison of pKas would suggest that the simple alkyl amines would have 

shorter ignition delays than their corresponding amine azides. Given the trend from ammonia 

(pKa = 9.25), to methylamine (pKa = 9.8), to dimethylamine (pKa = 10.9) (7), the pKas of 

trimethylamine (relative to dimethylamine) and DMAZ (relative to MMAZ) are surprising. (In 

the case of trimethylamine, the observation has been attributed to steric effects that oppose 

protonation [7].) But the gas–phase proton affinities (PAs) of these compounds, i.e., the 

exothermicity of proton attachment to the fuel,

B + H

+ ® BH+

, (3)

which are a site-specific measure of base strength, do, for this limited series, correlate with 

ignition delays. Coupled with the fact that the reaction of interest is

B + HA ® BH

+

+ A-(4)

in a bath of B and the acid HA, the dielectric constant of which is likely to be lower than that of 

water, the deficiency of aqueous pKa as a predictor of ignition delay can be rationalized. 

However, since (neat) hypergolic fuels (by definition) react violently with acids, experimental 

determinations of reaction (4) equilibria are problematic. Moreover, any experimental measure 

requires a development step that one hopes to avoid, i.e., the synthesis and testing of a compound 

that is not going to perform well. 
3

Bespeaking the need for computationally based estimates of reaction (4) exothermicites (re: heats 

of neutralization), a density functional theory-based model was employed to estimate them for a 

variety of fuels whose ignition delays have been experimentally measured. For modeling the 

influence of the solvating medium, a polarizable continuum model (PCM) was employed. As 

will be discussed, the results obtained suggest deficiencies in the approach/model. Therefore, 

other measures of fuel base strength were sought, and various gas-phase measures were 

calculated. They include (1) heat of neutralization for ion pair formation resulting from nitric 

acid reacting with a fuel cluster, (2) proton affinity (PA), and (3) the exothermicity of fuel-nitric 

acid complexation. Selected results are presented, and their correlation with ignition delay is 

evaluated based on the (qualitative) rankings of fuel ignition delays given in figure 1. These 

rankings, which were established from the highly test-dependent absolute values reported by 

Rapp and Strier (4), Schalla and Fletcher (5, 6), Stevenson (1), and Thompson et al. (2), assume 

that orderings are test independent.

Figure 1. Ignition delay ordering derived from experimental testing.

2. Theoretical Methods

The Gaussian 98 (G98) suite of quantum chemistry (QM) codes was employed to identify 

equilibrium molecular structures and obtain their zero point corrected energies (ZPE) (8). 

Hydrogen bonding and proton transfer to fuel sites with lone pair electrons were the only 

interactions considered. (Figure 2 shows such sites for representative molecules.) The choice of 

model—DFT using the B3LYP exchange-correlation functionals and a 6-311++G(d,p) atomic

Different Families

Hydrazines < Amine Azides < Alkyl Amines < Azides

Same Family

— Hydrazines

MMH < N2H4

MMH ≤ UDMH

— Alkyl Amines 

Tertiary < Secondary < Primary < Ammonia

— Amine Azides

CPAZ ≤ DMAZ < MORPHAZ < MMAZ
4

Figure 2. Electrostatic potentials on electronic isodensity surfaces for DMAZ and hydrazine. Dark gray regions 

correspond to sites with lone pair electrons.

orbital basis set on a G98-defined “ultrafine” grid—was based on the success achieved with it in 

characterizing DMAZ (9). Following the work of Tao and coworkers (10), who studied

ammonia-nitric acid proton transfer reactions mediated by water, use of the self-consistent 

isodensity PCM (SCI-PCM) for simulating solvent effects was attempted. However, after 

encountering difficulties in applying the method, it was learned that Gaussian Incorporated’s 

attempt to upgrade the model from the G92 version used by Tao had rendered it unusable. 

Therefore, based on a recommendation (11), the polarizable conductor PCM (CPCM) (12) was 

employed to obtain optimized structures, and it was employed to obtain energies as well. 

Unfortunately, the method appears to produce anomalous results (tha t are to be discussed), and 

attempts to address concerns by employing (1) finer grids and (2) more tesserae to define the 

solute cavity did not resolve them. Thus, the focus of the study was shifted to characterizing the 

energetics of gas-phase reactions, a second study by Tao (13), this time on HNO3-NH3-(H2O)x

systems, guiding the effort.

3. Results

3.1 Solvated Reactions via a Polarizable Continuum Model

Figure 3 shows the DHr(0) dependence on dielectric constant (e) for reactions,

B + HNO3 ® BH

+

+ NO3

−

, (5)

where B is ammonia, hydrazine, or MMH. At −16.5 kcal/mol, the computed exothermicity of

Amine lone pair

Azide lone pairs Lone pair sites

Hydrazine DMAZ
5

Figure 3. DHr(0) for B + HNO3 ® BH

+

+ NO3

−

 as a function of dielectric 

constant, B being ammonia, hydrazine, or MMH.

ammonia’s neutralization by nitric acid in water (e = 78) is in line with the value for its 

neutralization by HF in water (−15.2 kcal/mol) (13). For the neutralizations of hydrazine and 

MMH (in which case it is assumed that the proton transfers to the methylated nitrogen), the 

exothermicities are observed to be nearly identical to each other and less than ammonia. Also 

comparable to the values for these compounds when they are neutralized by HF (13), the values

are again considered reasonable. However, for dielectric constants in the range that HNO3 (ε =

50 ± 10) (14), hydrazine (e = 52) (15), MMH (e = 19) (15), and ammonia (e = 17) (16) fall, the 

results are contrary to expectations. First, as the dielectric constant decreases, electrostatic 

effects become more important and it is expected that the DHr(0) will steadily increase, not 

zigzag up, to its gas-phase value. In addition it is expected that these reactions will still be 

exothermic in a medium whose dielectric constant (e = 21, the value for acetone [16]) is slightly 

higher than that of MMH. Given the suspected unreliability of the method and the fact that the 

dielectric constant appropriate to use for the comparison would be uncertain, no attempt was 

made to apply it to amine azides. 

3.2 Gas-Phase Cluster Reactions

Unable to rely on the PCM results for estimating a compound’s heat of neutralization per 

reaction (5), the possibility of estimating this property via gas-phase reactions involving fuel 

molecule clusters (Bx),

Bx + HNO3 ® (BH

+

)Bx-1 + NO3

−

, (6)

was investigated. As a check of the reliability of the theoretical model for calculating the 

energetics of such reactions, PAs and exothermicities for ion cluster reactions, 

-20.0

-16.0

-12.0

-8.0

-4.0

0.0

4.0

0 20 40 60 80 100

dielectric constant

DHr(0) (kcal/mol)

ammonia

hydrazine

methylhydrazine

-20.0

-16.0

-12.0

-8.0

-4.0

0.0

4.0

0 20 40 60 80 100

dielectric constant

DHr(0) (kcal/mol)

ammonia

hydrazine

methylhydrazine
6

B + (BH

+

)Bx-1 ® (BH

+

)Bx, (7)

were obtained for systems for whom these values have been experimentally determined. Table 1 

shows the PAs determined for ammonia, methylamine, dimethylamine, and trimethylamine, their 

values being ~2 kcal/mol less than values recommended by Hunter and Lias (17). The calculated 

PA of NO3

−

 is also less than the most recently reported experimental value (identified via the 

National Institute of Standards and Technology [NIST] Chemistry WebBook [18]). Thus, a 

slight systematic error in the model results is indicated. However, it is considered that the results 

are still useful as a relative measure of base strength, and gas-phase heats of neutralization 

calculated from the values, i.e.,

DHr(0) = PA(HNO3) - PA(Bx), (8)

should be reasonably accurate because the errors cancel. Table 2 compares calculated DHr(0) 

values for ammonia cluster reactions, the agreement with experimentally obtained values* again 

being reasonable. 

Table 1. PAs as calculated via B3LYP/6-311++G(d, p) and their comparison with recommended 

values.

ZPE

(Hartrees)

PA

(kcal/mol)

Compound B BH

+ Calc. Exp. Diff

NH3 −56.548462 −56.870875 202.3 204.0 −1.7

CH3NH2 −95.830097 −96.169918 213.2 214.9 −1.8

(CH3)2NH −135.117679 −135.468575 220.2 222.2 −2.0

(CH3)3N −174.408125 −174.765789 224.4 226.8 −2.4

NO3

-

−280.443771 −280.952367 319.1 324.5 −5.4

Table 2. DHr for B+(BH

+

)(B) x ® (BH

+

)(B) x+1 reactions as calculated via B3LYP/6−311++G(d, p) and 

their comparison with experiment.

ZPE

(Hartrees)

DHr

(kcal/mol)

(RH

+

)(R)x B (BH

+

)(B)x (BH+)(B)x+1 Calc. Exp.

NH4

+

−56.548462 −56.870875 −113.462147 26.9 21±10

(NH4

+

)(NH3) −56.548462 −113.462147 −170.038614 17.6 13±10

(NH4

+

)(NH3)2 −56.548462 −170.038614 −226.609823 14.3 14±6

(NH4

+

)(NH3)3 −56.548462 −226.609823 −283.176876 11.7 12±6

(CH3)3NH+−174.408125 −174.765789 −349.204815 19.4 22±6

The theoretical model so validated, reaction (6) DHr(0) values for various ammonia and 

hydrazine clusters were computed with it. Shown in figure 4, the results indicate that even for an 

(NH3)5 + HNO3 reaction, the process is endothermic. (As will be discussed in section 3.4,

 

*The experimental values reported are from a search of the NIST Chemistry WebBook that was checked in March 2003. The 

values are the average of data from up to nine different studies.
7

Figure 4. DHr(0) for Bx + HNO3 → (BH

+

)Bx-1 + NO3

−

, where B is 

ammonia or hydrazine.

on the basis of bond lengths, a proton will transfer from nitric acid to ammonia when their 

interaction is mediated by just two other ammonia molecules.) Demonstrating tha t larger 

Bx/(BH

+

)Bx-1 clusters and/or (By)HNO3/ByNO3

−

 clusters would have to be characterized in order 

to approximate the energetics of condensed-phase proton transfer reactions, the results indicated 

that such studies would not be feasible (within program resources) for amine azides. Therefore, 

the effort was terminated.

3.3 Gas-Phase PAs

Beyond a validation exercise, the table 1 results, which are shown graphically in figure 5, are 

interesting because the trend in base strength expected for the series ammonia, methyl amine, 

dimethylamine and trimethylamine is in fact observed in this gas-phase measure and, as opposed 

to pKa, correlate with ignition delay rankings reported for the set. Therefore, it was decided to 

simply compute the gas-phase PAs of various fuels in the hope that they might provide some 

insight or predictive capability. Tables 3, 4, and 5 present the results for selected azides, amine 

azides, and hydrazines, respectively. 

As shown in table 3, the two lone pair sites associated with the azide group have significantly 

different PAs, the PA of the site associated with Na (for a generically labeled azide R-Na-Nb-Nc) 

ranging from 11–20 kcal/mol higher than the PA of Nc. The PAs of both azide sites are also 

observed to be considerably lower than those of the amines or hydrazines, which, given the

nonhypergolic nature of alkyl azides, is consistent with the hypothesized correlation between 

basicity and ignition delay.

40

50

60

70

80

90

100

110

120

1 2 3 4 5 6

x

r DHr(0) (kcal/mol)

ammonia

hydrazine

40

50

60

70

80

90

100

110

120

1 2 3 4 5 6

x

r DHr(0) (kcal/mol)

ammonia

hydrazine
8

Figure 5. B3LYP/6-311++G(d,p) calculated PAs

for alkylamines.

Table 3. B3LYP/6-311++G(d,p) calculated PAs for azides.

ZPE

(Hartrees)

B BH

+

PA

(kcal/mol)

Azide Na

hydrazoic acid −164.814684 −165.096042 176.6

methylazide −204.103331 −204.402324 187.6

gauche-ethylazide −243.402659 −243.707492 191.3

anti-ethylazide −243.403173 −243.707329 190.9

cyclopropylazide −281.472790 −281.779361 192.4

Azide Nc

hydrazoic acid −164.814684 −165.064259 156.6

methylazide −204.103331 −204.378959 173.0

gauche-ethylazide −243.402659 −243.684641 176.9

anti-ethylazide −243.403173 −243.684643 176.6

cyclopropylazide −281.472790 −281.761122 180.9

0.0

50.0

100.0

150.0

200.0

250.0

NH3

(CH3)NH2(CH3)2NH

(CH3)3N

Proton Affinity (kcal/mol) 
9

Table 4. B3LYP/6-311++G(d, p) calculated PAs for amine azides.

ZPE

(Hartrees)

B BH

+

PA

(kcal/mol)

Amine N

MMAZ_B −338.036614 −338.391753 222.9

MMAZ_D −338.038432 −338.391758 221.7

CPAZ_B −415.408210 −415.763606 223.0

CPAZ_D −415.409896 −415.763057 221.6

MORPHAZ_B −529.956689 −530.316497 225.8

MORPHAZ_D −529.955307 −530.316508 226.7

DMAZ_B −377.325354 −377.686803 226.8

DMAZ_D −377.323743 −377.686788 227.8

DMAZ_E −377.324671 −377.675547 220.2

cis-ADMCPA_A −415.399113 −415.759059 225.9

cis-ADMCPA_B −415.397585 −415.759061 226.8

trans-ADMCPA_A −415.401984 −415.751610 219.4

trans-ADMCPA_B −415.401658 −415.750070 218.6

Azide Na

MMAZ_B −338.036614 −338.355892 200.3

MMAZ_D −338.038432 −338.354366 198.3

CPAZ_B −415.408210 −415.724676 198.6

CPAZ_D −415.409896 −415.724265 197.3

MORPHAZ_B −529.956689 −530.272798 198.4

MORPHAZ_D −529.955307 −530.273465 199.6

DMAZ_B −377.325354 −377.649957 203.7

DMAZ_D −377.323743 −377.649952 204.7

cis-ADMCPA_A −415.399113 −415.722159 202.7

cis-ADMCPA_B −415.397585 −415.721171 203.1

trans-ADMCPA_A −415.401984 −415.712909 195.1

trans-ADMCPA_B −415.401658 −415.711713 194.6

Azide Nc

MMAZ_B −338.036614 −338.337588 188.9

MMAZ_D −338.038432 −338.334267 185.6

CPAZ_B −415.408210 −415.704070 185.7

CPAZ_D −415.409896 −415.707896 187.0

MORPHAZ_B −529.956689 −530.255856 187.7

MORPHAZ_D −529.955307 −530.253360 187.0

DMAZ_B −377.325354 −377.631078 191.8

DMAZ_D −377.323743 −377.628630 191.3

cis-ADMCPA_A −415.399113 −415.770410 233.0

cis-ADMCPA_B -415.397585 −415.770397 233.9

trans-ADMCPA_A −415.401984 −415.769915 230.9

trans-ADMCPA_B −415.401658 −415.769935 231.1
10

Table 5. B3LYP/6-311++G(d,p) calculated PAs for hydrazines.

ZPE

(Hartrees)

B BH

+

PA

(kcal/mol)

Unmethylated N

N2H4 −111.857403 −112.182796 204.2

MMH −151.148318 −151.480130 208.2

UDMH −190.439913 −190.777564 211.9

Methylated N

MMH −151.148318 −151.486580 212.3

SDMH −190.464929 −190.810947 217.1

UDMH −190.439913 −190.787748 218.3

Selected from a larger set of 2-azidoethanamines whose PAs were calculated, the choice of 

compounds included in table 4 deserves comment. As two ends of the ignition delay spectrum 

observed in the 2-azidoethanamines synthesized and tested by AMRDEC, the PAs of MMAZ 

and DMAZ are obviously of interest. The results for 2-azido-N-cyclopropanamine (CPAZ), 

which based on AMRDEC testing has an ignition delay similar to DMAZ, are considered 

instructive because CPAZ’s stoichiometry (C5H10N4) is similar to that of DMAZ (C4H10N4), but

as a secondary amine, it is similar to MMAZ (C3H8N4). To include a comparison with a second 

tertiary amine azide, results for 4-(2-azidoethyl)morpholine (MORPHAZ) are presented. 

Reported to be “weakly hypergolic” (1), its ignition delay is assumed to be longer than DMAZ 

and shorter than MMAZ’s. The cis and trans forms of 2-azido-N,N-dimethylcyclopropanamine 

(ADMCPA) are notional molecules designed to promote and prevent, respectively, the shielding 

of the amine lone pair electrons by the azide group (19). 

The conformers listed in the table were selected from a larger set generated in the course of 

searching for geometry-dependent differences in each compound. Those chosen are considered 

representative of the larger group. Conformer details can be found elsewhere (9, 19, 20). For 

MMAZ, CPAZ, MORPHAZ, and DMAZ, the designations B and D define a nominal

configuration of the -CH2-CH2-N3 chain. Those definitions are the same for each molecule, and 

are consistent with a previous publication (9). Figure 6 depicts them for the case of DMAZ. 

Conformer B is DMAZ’s lowest energy structure (9). Conformer D analogs are the lowest 

energy conformers found for MMAZ and CPAZ (20). Conformer E is the 2-azidoethanamine 

structure most analogous to the cis and trans isomers of ADMCPA. ADMCPA conformers A 

and B are the two lowest energy structures of the se molecules. (The A conformers are shown in 

figure 7.) In the case of cis-ADMCPA, conformer A is ~1 kcal/mol lower in energy than 

conformer B (21). In the case of trans-ADMCPA, the energies of A and B are nearly identical.

Selected results from table 4 are presented graphically in figure 8. The PAs calculated for the 

secondary amines in MMAZ and CPAZ (222–223 kcal/mol) and the tertiary amines in 
11

Figure 6. DMAZ conformers B, D, and E. Black circles denote nitrogen, gray circles denote carbon, and 

white circles denote hydrogen.

Figure 7. ADMCPA isomers. Black circles denote nitrogen, gray 

circles denote carbon, and white circles denote hydrogen.

MORPHAZ and DMAZ (226–227 kcal mol) are nearly identical to those for dimethylamine 

(222 kcal/mol) and trimethylamine (227 kcal/mol), respectively. And as in the case of the alkyl 

amines, the ignition delays of MMAZ and DMAZ correlate with this measure. However, the 

nearly identical PAs for the amine sites in (1) hypergolic CPAZ and nonhypergolic MMAZ, and 

(2) weakly hypergolic MORPHAZ and hypergolic DMAZ, deny a strong correlation between the 

PA of the amine site and ignition delay in 2-azidoethanamines.

The results for the ADMCPA isomers are somewhat surprising. It was expected that, as tertiary 

amines with one substituent being a cyclopropyl group, their PAs would meet or exceed those of 

DMAZ. But the PAs of the cis-ADMCPA conformers are slightly lower than DMAZ_B and 

DMAZ_D PAs, and the PAs of the trans-ADMCPA isomers are even lower than MMAZ_B and 

MMAZ_D PAs. The results for the PA of DMAZ_E, however, appear able to reconcile the 

disagreement with expectations. The PA of DMAZ_E is less than the PAs for MMAZ_B and 

MMAZ_D, but this is a spurious result. Based on simply using the energy of the BH

+

 structure 

resulting from a geometry optimization started with a configuration in which a proton has been 

attached to the neutral conformer, the protonated structure is a strained configuration that is not 

representative of the end state of the reaction. Thus the result can be discounted. Given that the 

ADMCPA isomers are most closely analogous to DMAZ conformer E, it is possible that the

B D E

cis trans
12

0

50

100

150

200

250

Ethylazide

MMAZ

CPAZ

MorphAZ

DMAZ

Ethylazide

MMAZ

CPAZ

MorphAZ

DMAZ

(CH3)2NH

MMAZ

CPAZ

(CH3)3N

MorphAZ

DMAZ

Proton Affinity (kcal/mol) 

Azide Nc

Azide Na

Amine N

Figure 8. B3LYP/6-311++G(d, p) calculated PAs for the lone pair sites of amine azide fuels. The PAs for the lone 

pair sites of ethylazide, dimethylamine, and trimethylamine are shown for comparison. 

protonated ADMCPA structures upon which the PA calculations are based are also relatively 

high in energy. This would result in an underestimation of the ir value. A search for lower 

energy protonated structures for the ADMCPA isomers might address this issue, but given the 

lack of correlation between amine PA and ignition delay for compounds that have been 

synthesized and tested, the matter was not pursued for these notional ones.

The PAs of the lone pair sites associated with the bonding (Na) nitrogen of the azide group in the 

amine azides all fall within a fairly narrow range that is ~10 kcal/mol higher than that of their

“analogous” alkyl azide, (analogous meaning ethyl azide for molecules with ethyl azide chains 

and cyclopropyl azide for the ADMCPA isomers). However, the similarity of the increases 

observed in MMAZ, CPAZ, and DMAZ indicates that there is not a strong correlation between 

the PA of this site and ignition delay. Originally observed in DMAZ_B, where the amine and 

azide groups are in close proximity, it was thought that the increased PA was related to the direct 

interaction between the two groups. However, the effect is also observed in the D conformers of 

DMAZ, MMAZ, and CPAZ. Thus, it is assumed that the effect is passed through/from the ethyl 

chain connecting the groups. 

The PAs of the terminal (Nc) nitrogen of the azido groups in MMAZ and DMAZ are also 

observed to be 10–15 kcal/mol higher than those of the analogous site in alkyl azides, and again, 
13

the increase in DMAZ_B and DMAZ_D PAs are marginally higher than the PA increases found 

for their MMAZ analogs. The increases also appear to be independent of amine and azide group 

proximity. However, the increases in CPAZ and MORPHAZ are similar to those of MMAZ, 

denying a strong correlation between the PA of this site and ignition delay. The extremely high 

values observed for the ADMCPA isomers are related to the fact that the attachment of a proton 

at this site induces the cyclopropyl ring to break. Coupled with the indication that the increase in 

the PA of azide sites in 2-azidoethanamines is passed through/from the ethyl chain connecting 

the amine and azide groups, the possibility that the short ignition delay observed for DMAZ is 

related to a mechanism involving the ethyl chain is suggested and will be discussed in section 4.

Table 5 shows the PAs calculated for the lowest energy hydrazine, MMH, UDMH, and 

symmetric dimethylhydrazine (SDMH) structures. (Having a relatively high freezing point, 

SDMH is not a standard hypergolic fuel component.) The results are presented graphically in 

figure 9. The PAs for the hydrazine lone pair sites are, like amine sites, substituent dependent, 

increasing with the number of attached methyl groups. It is also observed that the PAs of the 

unmethylated nitrogens in the methylated hydrazines increase with the total number of methyl 

groups on the hydrazine. Finally, similarities in the PAs of the hydrazines and the amines (in 

table 1) are notable: (1) ammonia (204.0 kcal/mol) vs. hydrazine (204.2 kcal/mol), (2) 

methylamine (214.9 kcal/mol) vs. methylated nitrogen of MMH (213.3 kcal/mol), and (3) 

trimethylamine (226.8 kcal/mol) vs. the methylated nitrogen of UDMH (221.4 kcal/mol). These 

similarities are in contrast to the ignition delay differences observed for these compounds. Even 

within the hydrazine family, the PA-ignition delay correlation breaks down, MMH having an 

ignition delay equal to or shorter than UDMH, yet having a PA less than UDMH. Thus, a 

correlation between site-specific PAs and ignition delays does not appear to exist. 

3.4 Fuel Cluster-Nitric Acid Complexation 

Given that gas-phase reactions leading to separated ions are endothermic, questions about their 

relevance as a measure of an exothermic neutralization process can be raised. Therefore, the 

possibility that DHr(0) values for ion pair formation reasonably estimate the heat of 

neutralization (and correlate with ignition delay) was considered. As an approach to this 

problem, the work of Tao (13) was initially followed. Characterizing the effect of water 

molecules on the interaction between ammonia and nitric acid in NH3-HNO3-(H2O)x complexes, 

he showed that for complexes with as few as two water molecules, based on O-Ha and N-Ha

bond distances, where Ha is the hydrogen atom originally associated with nitric acid, ammonia 

and nitric acid will exist as an ion pair—(NH4

+

)(NO3

−

). In addition, Tao profiles the potential 

energy of the complex along a proton transfer reaction pathway (specified by fixing the O-Ha

bond distance at values down to those approaching those in the unsolvated NH3-HNO3 complex) 

and interprets the results as a measure of the (energetic) stabilization provided by the stepwise 

addition of more water molecules. An intriguing approach because its results expose the 
14

Figure 9. B3LYP/6-311++G(d, p) calculated PAs for 

the lone pair sites of hydrazines.

competition between electrostatic attraction and the formation of more hydrogen bonds that drive 

proton transfer; analogous studies of (NH3)x-HNO3 and (N2H4)x-HNO3 complexes were 

undertaken.

As shown in figures 10 and 11, on the basis of O-Ha and N-Ha bond distances, Ha is effectively 

transferred to the fuel molecule when the fuel-oxidizer interaction is mediated by two other fuel 

molecules. Figure 12 shows the increase in energy associated with reducing the O-Ha bond

distance for the (NH3)3-HNO3 and (N2H4)3-HNO3 systems. The results for the (NH3)3-HNO3

system are very similar to those obtained by Tao for the NH3-HNO3-(H2O)2 system. The 

minimum energy is associated with an O-Ha bond distance of ~1.6 Å, and the energy increases

~4 kcal/mol when this bond distance is reduced to 1.0 Å. The results for the (N2H4)3-HNO3

system are similar to those of the (NH3)3-HNO3 system, but the energy increase is slightly 

greater, a result one would expect for a fue l with a shorter ignition delay. Further consideration 

of the matter, however, raised questions about the validity of the comparison. For one, though 

each system has the same number of molecules, the system sizes are not the same.

0

50

100

150

200

250

N2H4MMH

UDMH

MMH

SDMH

UDMH

Proton Affinity (kcal/mol) 

Unmethylated

N

Methylated

N
15

number of ammonia molecules

0 1 2 3 4 5

N...H bond distance (Angstroms)

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

O...H bond distance (Angstroms)

Figure 10. O-Ha and N-Ha bond distances for (NH3)x-HNO3 complexes.

number of hydrazine molecules

0 1 2 3 4

N...H bond distance (Angstroms)

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

O...H bond distance (Angstroms)

Figure 11. O-Ha and N-Ha bond distances for (N2H4)x-HNO3 complexes.

O-H bond distance (Å)

O-H bond distance (Å)

N-H bond distance (Å)

N-H bond distance (Å)
16

O-H Bond Distance (A)

0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

ΔE(kcal/mol)

0

1

2

3

4

5

6

7

(NH3)

3

...H...ONO2

(N2H4)

3

...H...ONO2

Figure 12. The energies of (NH3)3-HNO3 and (N2H4)3-HNO3

complexes as a function of O-Ha bond distance.

The hydrazine system has three hydrazine-hydrazine hydrogen bonds while the ammonia system 

has only two ammonia-ammonia hydrogen bonds. This inequality could account for the 

observed differences. 

Another potential problem with the approach has to do with the fact that the energy difference 

considered relevant is between the minimum energy structure and the energy of a structure with 

an O-Ha bond distance near 1.0 Å. But it is not clear that the latter distance (or any other) is 

optimum for the comparison. As shown in figure 12, the energy of the (NH3)x-HNO3 complexes 

begins to increase rapidly as the O-Ha distance is reduced below 1.0 Å. This behavior is 

assumed to occur because forces associated with the repulsive inner wall of the oxygen atom’s 

potential begin to dominate the interaction. Coupled with the system size issue, the author 

decided to abandon this computationally intensive method.

3.5 Binary Fuel-Nitric Acid Complexation

As a final method for measuring the base strength of a fuel, the exothermicity of fuel-nitric acid 

complexation,

B + HNO3 ® B...HNO3, (9)

was calculated for many of the fuels considered previously. Provided in table 6 and shown 

graphically in figure 13, it is observed that there are some differences between the trends of this 

measure and the trends indicated by simple PAs. For example, in the case of the hydrazines

though (consistent with base strengths based on gas-phase PAs) the bond strength at the 

methylated nitrogen is higher than the strength at the unmethylated nitrogen of the same 

molecule, the strength of the bonding at unmethylated nitrogen is inversely proportional to the 

total number of methyl groups on the molecule. The trends in bond strengths at amine sites do 

ΔE (kcal/mol)

O-H Bond Distance (Å)
17

Table 6. Exothermicity of fuel-nitric acid complexation.

Compound DE

(kcal/mol)

DHv

a

(kcal/mol)

DE+DHv

(kcal/mol)

Ignition Delaysb

(s)

Hydrazines

Unmethylated N

N2H4 −13.2 10.7 −2.5 —

MMH −12.8 — — —

UDMH −12.4 — — —

Methylated N

MMH −14.0 9.6 −4.4 —

UDMH −14.5 8.4 –6.1 —

Amines

NH3 −12.4 4.8 −7.6 —

CH3NH2 −13.8 5.8 −8.0 ∞

CH3CH2NH2 −14.2 6.4 −7.8 2.03

(CH3)2NH −14.6 6.0 −8.6 —

CH3CH2CH2NH2 −14.2 7.5 −6.7 1.73

(CH3)2CHNH2 −13.9 6.8 −7.1 0.94

(CH3)3N −14.5 5.2 −9.3 —

DMAZ −11.1 — — —

Azides

Terminal N

Ethylazide −4.8 — — —

DMAZ −5.5 — — —

Bonded N

Ethylazide −8.0 — — —

DMAZ −8.8 — — —

a DHv

 values for hydrazines are from reference (21), while those for amines are as reported in 

Lange’s Handbook of Chemistry, 15th Edition, J.A. Dean, ed.; McGraw-Hill Inc.: New York, 

1999.

b Reported in reference (4).

not track PA results either, indeed seeming to correlate better with pKa results. Table 6 includes 

amine ignition delay results reported byRapp and Streier (4). No correlation with DHr(0) values 

is observed. Even with differences in DHv taken into consideration, the expected correlation 

does not emerge. The DHr(0) values for the two azide lone pair sites do follow PA results, but 

the differences are not as compelling. Therefore, investigations along this line were terminated.

4. Discussion

Despite the expectation that (“all else being equal”) a stronger base will have a shorter ignition 

delay, such a correlation was not observed. In retrospect, the information already available for 

hydrazine and its derivatives presaged the lack of correlation. As measured through their
18

Figure 13. Heats of complexation for fuel-nitric acid complexes.

titration with hydrochloric acid in an aqueous solution, the pKa and heat of neutralization of 

MMH are lower than those of hydrazine. Moreover, MMH has a lower dielectric constant than 

hydrazine, so the differences in reaction (5) heats of neutralization should be even larger than 

indicated by the aqueous-phase results. But in all RFNA-oxidized studies of which the author is 

aware, MMH yields shorter ignition delays. 

In the case of amines, the work by Rapp and Strier (4) seems to support a correlation between 

fuel basicity and ignition delay, but Schalla and Fletcher’s (6) results clearly point to the 

correlation’s shortcomings as a predictive tool. Looking at variations in ignition delay as a 

function of a number of variables, including (1) O/F ratio, (2) bomb volume, (3) volume of 

propellant charge, (4) gas-phase oxygen concentration, and (5) water content, these researchers 

did find that the shortest ignition delays for a triethylamine-WFNA system were for a fuel mole 

fraction near 0.41 (O/F = 1.4), a value that is closer to stoichiometric for neutralization (i.e., O/F 

= 1.0) than stoichiometric for combustion (O/F ~ 8). (However, it is only on either side of these 

limits that the delays get really long.) Indicating the importance of neutralization, these 

researchers nonetheless sought to rationalize why neutralization stoichiometry did not yield the 

shortest delays (though they should produce the largest liquid-phase temperature rises). They 

postulate that the mixture needs to be somewhat lean in order to produce/have available gasphase oxidizers. (If all the oxidizer goes towards neutralizing the amine, none are left for gas 

phase oxidation.) The shortest ignition delays observed in their study were for systems that were 

0

2

4

6

8

10

12

14

16

N2H4MMH

UDMH

MMH

UDMH

NH3

(CH3)NH2(CH3)2NH

(CH3)3N

DMAZ

Ethylazide

DMAZ

Ethylazide

DMAZ

-DE (kcal/mol)

Unmeth. N

Meth. N

Azide Nc

Azide Na 

Amine N
19

stoichiometric with respect to neutralization and had gas phase oxidizers (O2 and NO2) already 

available in the initial atmosphere. 

As a final note, Schalla and Fletcher (5, 6) speculate that the best amine-acid propellant 

combinations would be those whose stoichiometries for both neutralization-nitration and fastefficient combustion are about the same, the case for (at that time standard) propellant 

combinations like hydrazine-WFNA and aniline-WFNA. In view of this speculation, it is 

interesting to consider the O/F ratios that optimize DMAZ, MMAZ, and CPAZ performance. 

Based on National Aeronautics and Space Administration (NASA)-Lewis thermochemical code 

calculations presented elsewhere (19), O(IRFNA)/F ratios that optimize the impulse of DMAZ, 

MMAZ, and CPAZ are 2.4, 2.4, and 2.6, respectively. In the case of MMH with IRFNA, the 

value is also 2.6. Thus, even with this added consideration, the nonhypergolicity of MMAZ is 

not explainable.

Despite the failure of the computed measures of base strength to correlate with ignition delays, 

the study suggests an alternate explanation for the relatively short ignition delays observed for

2-azidoethamines compared to alkyl amines or alkyl azides. The relatively high PAs of the lone 

pair sites of azide groups in 2-azidoethamines and the fact that the effect is passed from/through 

the chain linking the amine and azide groups indicate that bond cleavage or H-atom abstraction 

from the chain might be facilitated. Such mechanisms might also explain the difference in 

performance of MMAZ and CPAZ. To investigate this possibility, a study to characterize (gasphase) reactions of MMAZ, CPAZ, and DMAZ is planned.

5. Summary

Various approaches to the computation of basicity have been applied in an attempt to 

characterize this property for hypergolic fuels with measured ignition delays. The CPCM as 

implemented in the G98 suite of QM codes produces condensed-phase heats of neutralization for 

amine and hydrazine compounds reacting with nitric acid that are questionable. The energetics 

of proton transfer from nitric acid to small (gas-phase) fuel clusters appear to be reasonably 

calculated via density functional theory methods, but even for the largest clusters considered 

tractable, the neutralizations are endothermic, raising concerns about their relevance as a 

measure of the exothermic condensed-phase process of interest. Gas-phase PAs, which are 

relatively simple to calculate, identify substituent-dependent differences in the basicity of lone 

pair sites, but correlations with ignition delay were not observed for the 2-azidoethanamines 

considered. Differences between the PAs of azide lone pair sites in alkyl azides and analogous 

amine azides are striking, but a correlation with ignition delay was not observed. The study does 

suggest the possibility that reactions involving the ethyl chain connecting the amine and azide 

groups are responsible for the unexpectedly short ignition delays observed in 2-azidoethanaminefueled systems.
20

6. References

1. Stevenson, W. H. Synthesis and Characterization of Hypergolic Amino Azides. 

Proceedings of the 30th JANNAF Propellant Development and Characterization 

Subcommittee Meeting, CPIA Publication 708, 2002, Vol. II, pp 95–102.

2. Thompson, D. M.; Wilson, B. F.; Stevenson, W. H. Hypergolic Azide Liquid Fuels. 

Proceedings of the 1998 JANNAF Propulsion Meeting, CPIA Publication 675, 1998, 

Vol. III, pp 515–523.

3. Clark, J. D. Ignition! An Informal History of Liquid of Liquid Propellant Rockets; Rutgers 

University Press: New Brunswick, NJ, 1972.

4. Rapp, L. R.; Strier, M. P. The Effect of Chemical Structure on the Hypergolic Ignition of 

Amine Fuels. Jet Propulsion 1957, 27, 401–404.

5. Schalla, R. L.; Fletcher, E. A. The Behavior of the System Triethylamine-White Fuming 

Nitric Acid Under Conditions of Rapid Mixing. 6th Symposium (International) on 

Combustion, The Combustion Institute: Pittsburgh, PA, 1956, 911–917.

6. Schalla, R. L.; Fletcher, E. A. The Ignition Behavior of Various Amines With White 

Fuming Nitric Acid. ARS Journal 1959, 33–39.

7. Sedgwick, N. V. The Organic Chemistry of Nitrogen; Clarendon Press: Oxford, 1966.

8. Frisch, M. J., et al. Gaussian 98, Revision A.4.; Gaussian, Inc.: Pittsburgh, PA, 1998.

9. McQuaid, M. J.; McNesby, K. L.; Rice, B. M.; Chabalowski, C. F. Density Functional 

Theory Characterization of the Structure and Gas-Phase, Mid-Infrared Absorption Spectrum 

of 2-azido–N,N-dimethylethanamine (DMAZ). J. Mol. Struct. (THEOCHEM) 2002, 587, 

199–218.

10. Nguyen, M. T.; Jamka, A. J.; Cazar, R. A.; Tao, F. M. Structure and Stability of the Nitric 

Acid-Ammonia Complex in the Gas Phase and in Water. J. Chem. Phys. 1997, 106, 8710–

8717.

11. Fox, D. J. Gaussian, Inc. Private communication, 2000.

12. Barone, V.; Cossi, M. Analytical Second Derivatives of the Free Energy in Solution by 

Polarizable Continuum Models. J. Phys. Chem. A. 1998, 109, 6246–6254.

13. Tao, F. M. Gas-Phase Proton Transfer Reaction of Nitric Acid–Ammonia and the Role of 

Water. J. Chem. Phys. 1998, 108, 193–202. 
21

14. Glavic, P. Synthesis and Properties of N2H5F (in Slovenian); NISJ-P-227, N69-32986;

Yugoslav. Nukl. Inst. (As reported in Schmidt, E. W. Hydrazine and Its Derivatives: 

Preparation, Properties, Applications; John Wiley & Sons: New York, 2001.)

15. Gillespie, R. J.; White, R. F. M. The Force Method of Determining the Static Dielectric 

Constant of Conducting Liquids With Particular Reference to Sulphuric, Nitric and 

Chlorosulphonic Acids. Trans. Farad. Soc. 1958, 54, 1846.

16. Maryott, A. A.; Smith, E. R. Table of Dielectric Constants of Pure Liquids. National 

Bureau of Standards Circular 514, U.S. Government Printing Office, Washington, DC, 1951.

17. Hunter, E. P.; Lias, S. G. Evaluated Gas Phase Basicities and Proton Affinities of 

Molecules: An Update. J. Phys. Chem. Ref. Data 1998, 27, 413–656.

18. Davidson, J. A.; Fehsenfeld, F. C.; Howard, C. J. The Heats of Formation of NO3

-

 and NO3

-

Association Complexes With HNO3 and HBr. Int. J. Chem. Kinet. 1977, 9, 17.

19. McQuaid, M. J. Computational Characterization of 2-Azidocycloalkanamines: Notional 

Variations on the Hypergol 2-Azido-N,N-Dimethylethanamine (DMAZ); ARL-TR-2806; 

U.S. Army Research Laboratory: Aberdeen Proving Ground, MD, 2002.

20. McQuaid, M. J. The Structure of Secondary 2-Azidoethanamines: A Hypergolic Fuel

Versus A Nonhypergolic Fuel; technical report; U.S. Army Research Laboratory: Aberdeen 

Proving Ground, MD, to be submitted for publication.

21. Schmidt, E. W. Hydrazine and Its Derivatives: Preparation, Properties, Applications; John 

Wiley & Sons: New York, 2001.
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