Nitro-, cyano-, and methylfuroxans, and their bis-derivatives: From green primary to melt-cast explosives

Article abstract of DOI:10.3390/molecules25245836

In the present work, we studied in detail the thermochemistry, thermal stability, mechanical sensitivity, and detonation performance for 20 nitro-, cyano-, and methyl derivatives of 1,2,5-oxadiazole-2-oxide (furoxan), along with their bis-derivatives. For all species studied, we also determined the reliable values of the gas-phase formation enthalpies using highly accurate multilevel procedures W2-F12 and/or W1-F12 in conjunction with the atomization energy approach and isodesmic reactions with the domain-based local pair natural orbital (DLPNO) modifications of the coupled-cluster techniques. Apart from this, we proposed reliable benchmark values of the formation enthalpies of furoxan and a number of its (azo)bis-derivatives. Additionally, we reported the previously unknown crystal structure of 3-cyano-4-nitrofuroxan. Among the monocyclic compounds, 3-nitro-4-cyclopropyl and dicyano derivatives of furoxan outperformed trinitrotoluene, a benchmark melt-cast explosive, exhibited decent thermal stability (decomposition temperature >200 ^?C) and insensitivity to mechanical stimuli while having notable volatility and low melting points. In turn, 4,4⁰-azobis-dicarbamoyl furoxan is proposed as a substitute of pentaerythritol tetranitrate, a benchmark brisant high explosive. Finally, the application prospects of 3,3⁰-azobis-dinitro furoxan, one of the most powerful energetic materials synthesized up to date, are limited due to the tremendously high mechanical sensitivity of this compound. Overall, the investigated derivatives of furoxan comprise multipurpose green energetic materials, including primary, secondary, melt-cast, low-sensitive explosives, and an energetic liquid.

Full text of DOI:10.3390/molecules25245836

molecules
Article
Nitro-, Cyano-, and Methylfuroxans, and Their
Bis-Derivatives: From Green Primary to
Melt-Cast Explosives
Alexander A. Larin 1, Dmitry M. Bystrov 1, Leonid L. Fershtat 1, Alexey A. Konnov 1,
Nina N. Makhova 1, Konstantin A. Monogarov 2, Dmitry B. Meerov 2, Igor N. Melnikov 2,
Alla N. Pivkina 2 , Vitaly G. Kiselev 2,3,4 and Nikita V. Muravyev 2,
*
1
Zelinsky Institute of Organic Chemistry, Russian Academy of Sciences, 47 Leninsky Ave.,
119991 Moscow, Russia; roby3@mail.ru (A.A.L.); teslatron@yandex.ru (D.M.B.); fershtat@bk.ru (L.L.F.);
alkonnoff@yandex.ru (A.A.K.); mnn@server.ioc.ac.ru (N.N.M.)
Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences, 4 Kosygina Str.,
119991 Moscow, Russia; k.monogarov@gmail.com (K.A.M.); mmeerov@mail.ru (D.B.M.);
igor.n.melnikov@yandex.ru (I.N.M.); alla_pivkina@mail.ru (A.N.P.); kiselev@phys.nsu.ru (V.G.K.)
Novosibirsk State University, 1 Pirogova Str., 630090 Novosibirsk, Russia
2
3
4
Institute of Chemical Kinetics and Combustion SB RAS, 3 Institutskaya Str., 630090 Novosibirsk, Russia
Correspondence: n.v.muravyev@ya.ru; Tel.: +7-499-137-8203
*
ꢀꢁꢂꢀꢃꢄꢅꢆꢇ
ꢀꢁꢂꢃꢄꢅꢆ
Academic Editor: Vladislav Tomisic
Received: 5 November 2020; Accepted: 8 December 2020; Published: 10 December 2020
Abstract: In the present work, we studied in detail the thermochemistry, thermal stability,
mechanical sensitivity, and detonation performance for 20 nitro-, cyano-, and methyl derivatives of
1,2,5-oxadiazole-2-oxide (furoxan), along with their bis-derivatives. For all species studied, we also
determined the reliable values of the gas-phase formation enthalpies using highly accurate multilevel
procedures W2-F12 and/or W1-F12 in conjunction with the atomization energy approach and
isodesmic reactions with the domain-based local pair natural orbital (DLPNO) modifications of the
coupled-cluster techniques. Apart from this, we proposed reliable benchmark values of the formation
enthalpies of furoxan and a number of its (azo)bis-derivatives. Additionally, we reported the
previously unknown crystal structure of 3-cyano-4-nitrofuroxan. Among the monocyclic compounds,
3-nitro-4-cyclopropyl and dicyano derivatives of furoxan outperformed trinitrotoluene, a benchmark
melt-cast explosive, exhibited decent thermal stability (decomposition temperature >200 ◦C) and
insensitivity to mechanical stimuli while having notable volatility and low melting points. In turn,
4,40-azobis-dicarbamoyl furoxan is proposed as a substitute of pentaerythritol tetranitrate, a benchmark
brisant high explosive. Finally, the application prospects of 3,30-azobis-dinitro furoxan, one of the
most powerful energetic materials synthesized up to date, are limited due to the tremendously high
mechanical sensitivity of this compound. Overall, the investigated derivatives of furoxan comprise
multipurpose green energetic materials, including primary, secondary, melt-cast, low-sensitive
explosives, and an energetic liquid.
Keywords: energetic materials; 1,2,5-oxadiazole-2-oxide; furoxan; regioisomerism; melt-cast
explosives; thermochemistry; mechanical sensitivity; detonation performance; quantum chemistry
1. Introduction
The design and synthesis of new organic functional materials are among the most important parts
of modern materials science. Among various desired properties, high energy density materials
are a long-sought goal for numerous ongoing research programs [
1–4]. Moreover, traditional
energetic materials, such as trinitrotoluene (TNT), hexogen (RDX), pentaerythritol tetranitrate (PETN),
Molecules 2020, 25, 5836; doi:10.3390/molecules25245836
www.mdpi.com/journal/molecules

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and nitroglycerine (NG), suffer from inefficient and unsafe methods for their synthesis and limited
environmental compatibility [ ]. Therefore, the search for novel high-energy materials with balanced
5,6
properties for a wide range of applications, while adhering to strict demands regarding safety and
ecology concerns, remains highly urgent.
In general, the current design of energetic materials is driven by two contradictory trends:
an increase of energy content and a decrease of hazards associated with the preparation, handling,
and storage of energetic compounds [7]. Indeed, combining high density with thermal stability and
moderate sensitivity to external stimuli in the same molecular moiety is a tricky issue. To this end,
modern synthetic approaches have shifted, e.g., from hydrocarbon backbones to strained N,O-rich
heterocycles [
the 1,2,5-oxadiazole-2-oxide (often referred to as furoxan) ring is indeed prominent due to its attractive
oxygen balance, high density of energetic derivatives, and high positive enthalpy of formation [10 18].
8,9]. Among a variety of energetic patterns considered for further functionalization,
–
Although only two positions in the furoxan ring are available for the introduction of energetic
substituents, the N-oxide regioisomerism is a promising strategy for tuning the detonation performance
of furoxan-based energetic materials [19–22].
To the best of our knowledge, among a huge variety of energetic furoxan derivatives,
the experimentally measured velocities of detonation (Vd) have been reported so far only for two
representative species. More specifically, 3-methyl-4-nitrofuroxan (
nitro groups typical of melt-cast explosives, e.g., a well-known 2,4,6-trinitrotoluene (TNT) or its
potential replacement, 2,4-dinitroanisole (DNAN) [23]. Indeed, combines an easily attainable
1) bears adjacent methyl and
1
melting point of 67–68 ◦C and a decent detonation performance evidenced by an experimental Vd of
7.45 km s−1
(Figure 1). Although the melting point of
[
24]. The latter value exceeds that of the benchmark TNT explosive (6.93 km s−1) [2◦5
]
1 is lower than the temperature range of 80–120 C
typical of melt-cast explosives [23],
high energy content is desirable. Even though the decomposition kinetics of
some extent [26 27], its phase-change data and mechanical sensitivity have not been reported so far.
Apart from this, given the possible tunability of the energetic properties and sensitivity of furoxans
1
indeed can be used in low-temperature applications where the
1
has been studied to
,
provided by N-oxide regioisomerism [19,20], the study of the isomeric 3-nitro-4-methylfuroxan (2) is
also of remarkable interest.
Figure 1. Two promising furoxan-based energetic compounds considered in the present work (1 and 3)
in comparison with the reference high explosives trinitrotoluene (TNT) and CL-20 along with their
experimental velocities of detonation (Vd) [24,25,28,29].
Another energetic furoxan derivative, dinitrodiazenofuroxan (DDF,
“landmark” explosive with a sound crystal density of 2.002 g cm−3
28]. The reported synthesis of
DDF is a laborious multistep procedure with only a 6% overall yield [28]. The experimental Vd of
3, Figure 1), is a novel
[
3
extrapolated to a crystal density at room temperature is extremely high, viz., 9.87 km s−1 (Figure 1) [28].
The latter value remains among the highest experimentally measured Vd throughout all organic
compounds, e.g., outperforming hexanitrohexaazaisowurtzitane (CL-20), so far the most powerful
explosive produced on the industrial scale (Figure 1).
However, as could be expected, the mechanical sensitivity of
3 is high. In particular, the critical
initiation pressure value is 2.2 kbar [30], which is very close to 1.8 kbar of lead azide, a typical primary

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explosive [31]. The literature data on the thermal stability of
3
are contradictory. Remarkably different
DSC decomposition peak temperatures at a ca. 2 K min−1 heating rate were reported, i.e., 145 ◦C [32
]
and 127 ◦C [33]. Note that the latter value agrees well with the decomposition without melting at
127–128 ◦C mentioned earlier in the original work [28]. Therefore, in the present study, we performed
a detailed characterization of the thermal stability of DDF.
A similar idea of a combination of two highly energetic nitrofuroxan moieties has recently been
implemented yielding an extremely powerful bisnitrofuroxan [21,34]. In the present study, we consider
in detail the important methylfuroxan and nitrofuroxan structural motifs as functional explosophoric
building blocks in the design of multipurpose energetic materials (Figure 2). The cyanofuroxan
fragment is also scrutinized due to its great importance as a functional moiety in the synthesis
of various energetic materials [15,19]. It should be noted that information on the thermal, safety,
and energetic properties for nitro-, cyano-, and methylfuroxans remains very limited. At the same
time, comprehensive data on a versatile set of these compounds and the in-depth structure–properties
relationships are important for the target- and diversity-oriented syntheses of novel advanced energetic
materials. Moreover, these data can be useful as a training set for calibration of the neural networks
and other machine learning approaches [35,36]. Apart from this, we modified synthetic approaches
and reported the missing crystalline structures for some of the species under study.
Figure 2. Schematic illustration of the methyl-, nitro-, and cyano-derivatives of furoxan studied in the
present work.
2. Results and Discussion
2.1. Synthesis of Furoxan Derivatives
3-Methyl-4-nitrofuroxan
1 was synthesized through a domino reaction of methacrylic acid with
N2O3 generated in situ from sodium nitrite in acidic media [37]. This approach enables the preparation
of the compound
1
in a single synthetic step from cheap and commercially available reagents (Scheme 1).
Scheme 1. Synthesis of 3-methyl-4-nitrofuroxan 1.
For the synthesis of 3-nitrofuroxans, we used our recently developed approach based on the
cascade one-pot reactions of aldoximes. This approach includes the chlorination of initial aldoximes,

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the acylation of intermediate chloroximes with a dinitromethane sodium salt with a subsequent
nitrosation of dinitromethyl derivatives, and in situ intramolecular cyclization [38 40]. 3-Nitrofuroxans
were obtained in high yields in one synthetic step and did not require additional purification
(Scheme 2).
–
2, 4–7
Scheme 2. Syntheses of nitrofuroxans 2, 4–7.
The isomerization of the corresponding 3-nitrofuroxans afforded 4-nitro isomers
quantitative yields [39 41]. The compound was additionally nitrated to afford a dinitrophenyl
derivative 10 in a yield of 91% (Figure 3).
8 and 9 in
,
8
Figure 3. Aryl-substituted nitrofuroxans 8–10.
The functionally substituted 4-nitrofuroxans 11 and 12 incorporating amide or nitrile moieties
were synthesized by an oxidation of the corresponding amines [42 43] (Scheme 3). The oxidation
of (carbamoyl)furoxan had been known [43]; however, we improved a synthetic procedure by the
,
addition of Na2WO4 to an oxidation mixture, which resulted in an increase of the yield of 11
The synthesis of 3-cyano-4-nitrofuroxan 12 was accomplished previously by the dehydration of
4-nitrofuroxan-3-carboxylic acid amide [44], whereas the oxidation approach provided direct access to
the compound 12 through a smaller number of steps starting from the corresponding amine 13.
.
Scheme 3. Syntheses of carbamoyl- and cyano-nitrofuroxans 11 and 12.
Dicyanofuroxan 14 was synthesized according to a previously published procedure [45].
3-Methylfuroxan 15 was prepared via nucleophilic substitution of the nitro group in compound
1
by hydride-anion under the action of NaBH4 [46]. The oxidative N-N coupling of aminofuroxans
afforded a series of symmetrically substituted azo compounds 16 18 43 46]. The tandem Mannich
reaction of 4-amino-3-methylfuroxan with subsequent nitration yielded dinitramine 19 47] (Scheme 4).
–
[ ,
[

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Dimethylazoxyfuroxan 20 (Figure 2, X: -N(O)=N-) was synthesized through the reductive condensation
of 1 [46].
Scheme 4. Syntheses of azofuroxans 16–18 and a dinitramine-bridged bis-methylfuroxan 19.
The purity of all synthesized compounds was determined as 99+% using a set of physicochemical
methods including multinuclear (1H, 13C, 14N) NMR spectroscopy, mass spectrometry, and elemental
analysis. The structure of 3-cyano-4-nitrofuroxan 12 was additionally confirmed by the X-ray diffraction
study (Figure 4). The analysis of structural data revealed the formation of a quite strong intermolecular
contact between the O(2) atom of the nitroxyl fragment and the nitro group oxygen atom in 12
(i.e., the O . . . O distance is 2.984 Å), which is responsible for its high density (1.865 g cm−3 at 100 K).
Figure 4. The crystal structure of 3-cyano-4-nitrofuroxan 12. All atoms are shown as probability
ellipsoids of atomic displacements (p = 50%).
2.2. Thermal Behavior of the Furoxan Derivatives: Melting and Decomposition
Upon linear heating, most of the analyzed compounds exhibit the three features registered
by differential scanning calorimetry (DSC)—viz., melting, thermal isomerization, and thermal
decomposition. These three processes will be discussed separately for all compounds studied.
Melting was observed for all monocyclic and aryl-substituted furoxans, except 15, which is liquid
at room temperature. The respective melting points are given in Section 2.5, and the raw DSC data for all
compounds are shown in Supplementary Materials (Section S2). In general, the melting of monocyclic
species
of the amino-group increases the melting temperature to 114 and 117 ◦C for 11 and 13, respectively.
It is worth noting that 3-methyl-4-nitrofuroxan ( ) exhibits two resolved endothermic peaks (Figure 5),
1, 2, 4, 5,
12, and 14 occurs in the temperature range of 39–65 ◦C (Figure 5). The introduction
1
although the compound has no impurities detectable by the conventional physicochemical methods
employed here. To explain this behavior, the sample was heated up to melting, cooled, and reheated
(Figure S1, Supplementary Materials). During the second heating cycle, only a single endothermic
peak was observed at 65 ◦C. This value is believed to be a true melting temperature for 1.

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Figure 5. Thermal stability of monocyclic furoxans 1, 2, 4, 11–15. The differential scanning calorimetry
(DSC) curves were recorded at a heating rate of 5 K min−1. The stars indicate a weak heat release due
to the thermal isomerization of 2 and 4.
The aryl-substituted furoxans
83–111 C, compared to monocyclic nitrofuroxans
nitrophenyl-bridged 4-nitro furoxan
bridged bicyclic furoxans, only 3-methyl-3’-nitro-4,40-bifuroxan
visible melting endotherms. The melting point of the latter compound is 173 ◦C, which is the highest
value within the set of the furoxans considered.
5
,
8
, and 10 melt at higher temperatures, i.e., in the range of
2, 4 12, and 14 (Figure 6). Note that the
undergoes melting, whereas the isomeric does not. Among the
and dimethylazoxyfuroxan 20 exhibit
◦
1,
, 5,
9
7
6
Figure 6. Thermal stability of aryl-furoxans 5 and 7–10. The differential scanning calorimetry (DSC)
curves were recorded at a heating rate of 5 K min−1. The star indicates a weak heat release due to the
thermal isomerization of 5 and 7.
It is interesting to note that all monocyclic 3-nitrofuroxans
features on the DSC curves starting at 110–120 C (indicated by stars in Figures 5–7). A detailed
analysis of this process is complicated either due to the vaporization of the respective compounds
2
,
4
, and
5
–
7
exhibit weak exothermic
◦
(in the case of 2 and 4) or the overlap with the thermal decomposition peaks (5–7). We hypothesized
these peaks to represent the thermal isomerization of 3-nitrofuroxans to the thermodynamically more
preferable 4-nitro isomers. This reaction is known to occur at elevated temperatures (t > 100 ◦C) for a
wide set of nitrofuroxans [10,19–21].

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Figure 7. Thermal stability of the bicyclic furoxans 3, 6, and 16–20. The differential scanning calorimetry
(DSC) curves were recorded at a heating rate of 5 K min−1. The star indicates a weak heat release due
to a thermal isomerization of 6.
The third thermal process tracked by DSC is the exothermal thermal decomposition. For several
compounds under study, the vaporization rate is high and the broad endotherm of evaporation is
observed instead of the exothermic peak of thermal decomposition. This behavior is common for
energetic materials and previously some of us proposed the pressure DSC method as a convenient tool
to suppress the evaporation and observe the sole thermal decomposition process [48
,49]. The elevated
pressure DSC curves for the isomeric methylnitrofuroxans and are shown inFigure S2 (Supplementary
1
2
Materials). Figures 2–4 show a comparison of the decomposition exotherms for the investigated
compounds, i.e., in some cases the pressure is atmospheric, otherwise the elevated pressure was used
to suppress the vaporization (details are given in Section S2 of the Supplementary Materials).
The methyl-substituted furoxans
estimated using the extrapolated decomposition onset temperature of 180 C. The cyanofuroxans
1
,
2
, and 15 exhibit a similar therm◦al stability that can be
12–14 demonstrate much more scattered results—from a thermally stable dicyanofuroxan 14 with the
decomposition onset of 204 ◦C to 4-amino-3-cyanofuroxan 13 with that as low as 96 ◦C (Figure 5).
3-Cyano-4-nitrofuroxan 13 and 3-carbamoyl-4-furoxan 11 exhibit slightly better thermal stability than
that for 13. The introduction of a cyclopropyl substituent improves the thermal stability of
above 200 ◦C, which is acceptable for applications (Figure 5).
4 to a level
Three nitrophenyl furoxans
temperatures within the range of 150–175 ◦C. The two nitrofuroxans linked by a nitrophenyl bridge
and
5, 8, and 10 show a complex thermal decomposition profile with onset
7
9
decompose at temperatures higher than 170 ◦C with a complex shape of the corresponding heat
flow traces (Figure 6).
Among the bicyclic structures, 3-methyl-3’-nitro-4,40-bifuroxan
6
has the lowest thermal stability,
which is evidenced by an exothermic peak after the melting at 103 ◦C (Figure 7). The comparison of 16
and 20 shows that the azoxy bridge significantly improves the thermal stability of 20 compared to its
counterpart with the azo bridge 16. The symmetric bicyclic species with carbamoyl (17) and cyano (18
)
functionalities exhibit sharp DSC peaks along with those acceptable for application decomposition
onsets above 150 ◦C (Figure 7). Finally, DDF (
3) releases a large amount of heat upon thermolysis.
However, the use of samples as low as 0.16 mg allowed us to obtain a smooth DSC curve with a clear
two-stage decomposition behavior (Figure 7). The overall decomposition process starts above 117 ◦C,
and the maximal rate of the heat release is registered at 145 ◦C. Thus, the literature discrepancy of the
decomposition peak temperatures of 3 is resolved: the dominant second stage was observed in [32],
whereas the authors of [33] track only the first stage that developed into thermal explosion due to the
high sample mass used.

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2.3. Thermal Behavior of the Furoxan Derivatives: Vaporization
As mentioned in the Introduction (Section 1), some furoxan derivatives (namely
1
,
4, and 14) are
considered to be possible replacements to trinitrotoluene in the melt-cast compositions. Therefore,
we compared their thermal behavior at atmospheric pressure with the reference melt-cast compounds
TNT and DNAN (Figure 8). The prospects of
1 and 14 [23] as melt-cast explosives were considered
before, and 3-nitro-4-cyclopropylfuroxan also has a beneficially broad separation of melting and
4
decomposition processes (61 ◦C and 211 ◦C, respectively, Figure 8). Note that the temperature of the
DSC endothermic evaporation peak can be used for semiquantitative estimations. This temperature is
generally close to the boiling point of a species [49] (for a more rigorous determination of the boiling
point with DSC, a specific restriction has to be applied to the pan lid orifice along with modified
experimental conditions) [50]. As seen from Figure 8, the compounds studied are arranged in the
following row of this characteristic temperature: 14 (161 ◦C) ≈ 1 (171 ◦C) <
4
(206 ◦C) < TNT (281 ◦C
vs. the estimated boiling point of 300 ± 10 ◦C [51]) ≈ DNAN (289 ◦C).
Figure 8. DSC profiles illustrating the melting and subsequent evaporation of selected furoxans
14 and the reference energetic materials TNT and 2,4-dinitroanisole (DNAN). The heating rate is
5 K min−1
1,
4,
.
Therefore, at the time being, we infer that the high volatility is the main problem hindering the
application of , and 14 as standalone melt-cast explosives. This feature is attributed to the absence
of strong intra- and intermolecular interactions (e.g., hydrogen bonds or -stacking) in the structural
1, 4
π
motif of the species studied. The previous structural investigations demonstrated that most of the
furoxan derivatives have only short O· · · O contacts that do not provide sufficient stabilization via a
supramolecular organization [20,52]. The possible ways to resolve this issue could be: (i) the design of
novel materials with high-molar mass substituents capable of formation of strong intermolecular bonds
to decrease the volatility (cf. and ); (ii) the use of lower amounts of , and 14 in the formulations
with a proper selection of other components; (iii) the strict temperature control of the manufacturing
1
4
1, 4
process. Apart from this, the melting points of 1, 4, and 14 (Figure 8) are notably lower than the
temperature range of 80–120 ◦C typical of melt-cast explosives [23]. However, these compounds still
can find their room in low-temperature applications and proper compositions.
2.4. Gas-Phase Formation Enthalpies of Furoxan, Its Monocyclic, and Bis-Derivatives
The solid-state formation enthalpy and density of a particular energetic material are the key
input parameters for computational models of detonation performance. Due to natural hindrances
with the combustion calorimetry of high-energy compounds, solid-state formation enthalpies are
often calculated using quantum chemical values for the gas-phase thermochemistry and empirical
estimations for sublimation enthalpy. The latter values generally lie in the narrow range on the

Molecules 2020, 25, 5836
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enthalpic scale, while the former values are prone to error accumulation and require highly accurate
levels of theory [53].
To this end, earlier, some of us proposed a “bottom-up” approach, that is, the multilevel procedures
W2-F12 and/or W1-F12 in conjunction with the atomization energy approach for smaller species
complemented with the domain-based local pair natural orbital coupled cluster (DLPNO-CCSD(T))
enthalpies of isodesmic reactions for medium-sized compounds [54,55]. The overall accuracy of these
methods on a test set composed of nitrogen-rich heterocyclic compounds turned out to be close to
“chemical” (~4 kJ mol−1). Thus, we commenced the study of the gas-phase thermochemistry of the
furoxan derivatives 1–20 from the multilevel calculations of atomization energies for furoxan (21),
its hypothetical mononitro derivatives 22 and 23, and several related heterocyclic frameworks (3,30-
and 4,40-bisfuroxans 24 and 25, as well as 3,30- and 4,40-azobisfuroxans 26 and 27, Figure 9).
Figure 9. The parent furoxan species (21), its nitro derivatives (22, 23), and bis- (24, 25) and azobis
bicyclic derivatives (26, 27) considered in the thermochemical calculations.
The most reliable W2-F12 formation enthalpies for 21
molecular point group symmetries, we drastically reduce the computational time and resources
needed to perform heavy multilevel calculations. For several species (e.g., 17 18 20), we combined
–27 are listed in Table 1. By exploiting
3
,
,
,
the W1-F12 atomization energies for a symmetrical less favorable energetically conformer with the
DLPNO-CCSD(T) enthalpy difference between conformers. Note that the (carbamoyl)nitro (11) and
dicyano derivatives of monocyclic furoxan (14) are the largest species, for which the W2-F12 calculations
are feasible, and the azobis derivatives of furoxan
respectively. Thus, in order to consider the nitrobenzene derivatives
compound , and dinitramine-bridged bis-methylfuroxan 19, we used a “bottom-up” ab initio
computational approach. Namely, we proposed a series of isodesmic reactions of the target compounds
, and 19 with simpler species (Scheme 5). Moreover, to reduce another source of computational
3
and 17 are at the limit of the W1-F12 feasibility,
5
and 10, the methylnitro
8–
6
6, 8
uncertainties, the reactions (1)–(4) (Scheme 5) were designed to be homodesmotic (i.e., those conserving
the number of carbon and nitrogen atoms in corresponding states of hybridization) [56]. This minimizes
the error due to differences in the ring strain and cyclic delocalization. The enthalpies of these reactions
are calculated with the DLPNO-CCSD(T) technique, and the formation enthalpies of all simpler species
are calculated using the atomization energy approach at the W1-F12 level of theory. The most reliable
calculated gas-phase formation enthalpies for the species
summarized in Table 1.
1–20 along with computational details are

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Scheme 5. The isodesmic reactions employed in the present work to calculate the formation enthalpies
∆fH0(g) of the species 5–10 and 19.
Table 1. Summary of the most reliable gas-phase formation enthalpies at 298 K (∆
fH0(g)) of furoxan
and its derivatives (1–27, Figures 2, 3 and 9, Schemes 1–4), calculated using W2-F12 and W1-F12
multilevel procedures along with the atomization energy approach and domain-based local pair natural
orbital (DLPNO)-CCSD(T)/aVQZ values of the enthalpies of isodesmic reactions. All values are given
in kJ mol−1
.
∆fH0(g), kJ mol−1
Compound
Source
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
186.4
194.7
800.4
306.1
335.3
437.5
615.8
324.9
594.6
328.9
66.4
421.3
360.8
554.0
158.6
588.4
341.1
[a]
[a]
[b]
[b]
[c]
[d]
[c]
[c]
[c]
[c]
[a]
[a]
[a]
[a]
[a]
[b]
[b]

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Table 1. Cont.
∆fH0(g), kJ mol−1
Compound
Source
18
19
20
21
22
23
24
25
26
27
1053.2
479.9
552.6
205.2
246.6
237.1
418.2
425.6
697.3
699.5
[b]
[e]
[b]
[a]
[a]
[a]
[a]
[a]
[a]
[a]
[a] W2-F12 along with the atomization energy approach. [b] W1-F12 along with the atomization energy approach.
[c] W1-F12 atomization energies of the reactants and DLPNO-CCSD(T) enthalpy of the isodesmic reactions (1), (3),
and (4). The W1-F12 formation enthalpies ∆
fH0(g) = 343.9 and 333.0 kJ mol−1 were used for 28 and 29, respectively.
[d] W2-F12 atomization energies of the reactants and DLPNO-CCSD(T) enthalpy of the isodesmic reaction (2). [e]
W1-F12 atomization energies of the reactants and DLPNO-CCSD(T) enthalpy of the isodesmic reaction (5).
Note that the W2-F12 gas-phase formation enthalpies for the monocyclic furoxan and bicyclic
furoxan derivatives (21–23, 1, 2, 11–15, Table 1) can be used for reliable thermochemical estimations
using the “bottom-up” approach [55] for a huge variety of novel furoxan derivatives.
2.5. Detonation Performance
Having obtained the gas-phase formation enthalpies for the species
1
–
20, we complemented them
with the sublimation enthalpies
∆
subH0 estimated with the use of the Westwell formula (often referred
to as Trouton’s rule) [57]. The resulting solid-state formation enthalpies ∆f H0(s) are shown in Table 2.
To estimate the accuracy of our computational approach, it is instructive to compare the calculated
∆f H0(s) values with the available experimental data. However, the reliable experimental value is
reported only for
1
:
∆f H0(s) = 100.8
±
0.8 kJ mol−1
[24]. For three other species from the present
study, viz., 3, 12, and 14, the ICT database [58] suggests the following values of ∆f H0(s): 667.8, 380.7,
and 465.3 kJ mol−1, respectively. However, it is not clear whether these data are true experimental
values or they were estimated using the group increment method. The comparison of these data with
those calculated in the present work (123, 725, 361, and 495 kJ mol−1 for
shows that the discrepancy is less than 25 kJ mol−1 for all species except
uncertainties in the ∆f H0(s) values is obviously the use of empirical estimations of the sublimation
enthalpies
subH0. We also compared the empirical values of subH0 with the experimental values
for , and 13 obtained from thermogravimetry experiments [59]. In line with the above-discussed
uncertainties, the average discrepancy was around 20 kJ mol−1
It should be emphasized that we aimed foremost at the reliable estimations of the detonation
performance of the species studied. The use of the two enthalpies of formation values for 1, 3,
1,
3
,
12, and 14, respectively)
. The main source of
3
∆
∆
1, 2
.
12, and 14, calculated in the present study and those from literature, leads to the errors less than
0.15 km s−1 for detonation velocities and less than 0.2 kJ g−1 for heats of explosion. Furthermore,
the available experimental values of the detonation velocities (VD) for
More specifically, the experimental VD of
is 7.45 km s−1 (the sample density 1.60 g cm−3) [24],
which agrees well with the calculated value of 7.56 km s−1. In the case of DDF (
), the calculated
detonation velocity of 10.0 km s−1 is also close to the reported experimental values 9.78 km s−1
33] and
9.87 km s−1 28]. Therefore, the errors due to the uncertainties in the ∆f H0(s) and the computational
methodology employed are quite low and allow for reliable evaluation of the energetic performance of
the furoxan derivatives studied. Thus, the computed detonation velocities of 20 are shown in Table 2.
1 and 3 also justify this assumption.
1
3
[
[
1–

Molecules 2020, 25, 5836
12 of 19
Table 2. The summary of the physical, safety, and energetic properties of the compounds 1–20 along
with the reference energetic materials: trinitrotoluene (TNT), pentaerythritol tetranitrate (PETN),
and hexogen (RDX). All data, except otherwise noted, are from the present work.
∆fH0(s),
kJ mol−1
tdec
,
ρ, g
Qex,
VD, km s−1
#
Stoichiometry
OB a
tm,
◦C
IS, J
FS, N
◦C
cm−3
kJ g−1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
NG
C3H3N3O4
C3H3N3O4
C4N8O8
0.53
0.53
1.00
0.32
0.33
0.52
0.47
0.33
0.47
0.46
0.71
0.67
0.29
0.25
0.25
0.27
0.43
0.33
0.44
0.33
1.06
0.36
0.86
0.67
1.66
1.68
1.98 b
1.62
1.60
1.76
1.70
1.58
1.77
1.75
1.85
1.87
1.90
1.59
1.24
1.52
1.88
1.72
1.68
1.58
1.59
1.64
1.78
1.8
101 c
136
65
40
–
61
90
103
–
83
133
111
114
46
117
39
<RT
–
–
188
176
117
211
162
129
199
175
173
153
114
133
96
5
7
0.7
23
2
3
5
8
3
4
18
5
45
>100
>100
13
4
270
180
6
170
>360
70
150
>360
150
190
180
130
90
280
–
160
120
90
110
210
–
>360
70
7.8
7.9
10.0
7.3
6.9
8.2
7.6
6.8
7.8
7.6
8.4
9.1
8.5
7.4
6.1
7.2
8.3
8.3
7.9
7.5
7.8
6.8
8.4
8.9
5.4
5.6
7.4
5.4
4.6
5.8
5.3
4.5
5.3
5.1
5.1
6.4
4.9
4.3
4.1
5.0
4.5
5.2
5.4
5.2
5.9
4.2
5.7
5.5
668 d
243
C5H5N3O4
C8H4N4O6
C5H3N5O6
C10H3N7O10
C8H4N4O6
C10H3N7O10
C8H3N5O8
C3H2N4O5
C3N4O4
267
365
527
258
518
257
−6
381 d
288
C3H2N4O2
C4N4O2
465 d
70 e
510
204
180
145
188
168
125
172
C3H4N2O2
C6H6N6O4
C6H4N8O6
C6N8O4
C7H8N8O8
C6H6N6O5
C3H5N3O9
254
970
405
469
−370
−75
−539
62
–
–
3
3
4
<0.3
30
3
172
13 f
81
141
204
143 g
306
181
TNT C7H5N3O6
PETN C5H8N4O12
RDX C3H6N6O6
204
8
140
a
b
c
d
The oxygen balance with respect to CO2 and H2O: OB = [O]/(2*[C]+[H]/2). Ref. [33]. Ref. [24]. Ref. [58].
e
15 is liquid at room temperature, therefore, we used the value of
∆
vapH0 = 70 kJ mol−1 obtained by a group
f
g
increment method [60]. Ref. [61]. Ref. [62].
The isomeric methylnitrofuroxans
a slightly higher density and formation enthalpy. These two compounds as well as other monocyclic
nitro ( 11 12) and cyano-derivatives of furoxan (13 14) outperform the benchmark trinitrotoluene
1 and 2 exhibit close detonation parameters, even though 2 has
4,
,
,
both in terms of the detonation velocity and heat of explosion (Table 2). 3-Methylfuroxan 15 is a
surprisingly stable liquid with a moderate detonation velocity of 6.1 km s−1. Its energetic properties are
inferior to those for nitroglycerin, but thermal stability and sensitivity are much better (Table 1). In the
case of bicyclic furoxan derivatives 16–20, it is reasonable to compare their detonation performance with
that of the commonly used secondary explosive pentaerythritol tetranitrate (PETN, Table 2). The two
azo-bridged furoxans 17 and 18 exhibit the close values of VD with slightly better sensitivity without
melting, which is typical of PETN. The extremely high explosive performance of
3 is remarkable;
however, this comes at the cost of high sensitivity (vide infra). The impact and friction sensitivity
values of 3 are close to those of common primary explosives (e.g., lead azide).
2.6. Sensitivity to Mechanical Stimuli
The impact (IS) and friction sensitivity (FS) values for the investigated compounds are summarized
in Table 2 and Figure 10. Most of the species studied exhibit high impact sensitivity, viz., below the
level of nitramines (8 J). The clear outlier is dicyanofuroxan 14, which remains intact at the maximal
drop energy of 100 J. Note, however, that 14 has a very low melting point of 39 ◦C. The errors associated
with the low-melting-point samples have been mentioned in a recent review of the sensitivity test
methodology [63]. The aminocyanofuroxan 13 also exhibits a low impact sensitivity, but its FS value
is very low (Table 2, Figure 10). Another group of the compounds clustered in the region IS ~15 J
includes
case of tetryl). The friction sensitivity exhibits a higher span (Figure 10) from an extremely sensitive
(FS = 6 N) to insensitive and (less than 50% of explosions at the maximal accessible load of 360 N).
4, 11, and 16. This level corresponds to explosives with moderate sensitivity (e.g., 14 J in the
3
5
8

Molecules 2020, 25, 5836
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100
10
1
14
13
4
11
16
2
1
RDX level
18
8
5
20
12
17
7
10
6
19
9
3
PETN level
100
200
300
Friction sensitivity, N
Figure 10. The impact and friction sensitivities of the species under study (1–20). The whole dataset
of the mechanical sensitivity values, including the uncertainties, is given in Table S6 (Supplementary
Materials). The filled black circles correspond to the monocyclic species, the empty circles—to the
benzene derivatives of furoxan, and the gray-filled circles—to the bicyclic derivatives.
3. Experimental and Computational Methods
All reactions were carried out in well-cleaned oven-dried glassware with a magnetic stirring.
1H and 13C NMR spectra were recorded on a Bruker AM-300 (300.13 and 75.47 MHz, respectively)
spectrometer and referenced to a residual solvent peak. 14N NMR spectra were measured on a
Bruker AM-300 (21.69 MHz) spectrometer using MeNO2 (δ14N = 0.0 ppm) as an external standard.
The chemical shifts are reported in ppm (δ); the multiplicities are indicated by s (singlet), d (doublet),
t (triplet), q (quartet), m (multiplet), and br (broad). The coupling constants J are reported in Hertz.
Elemental analyses were performed by the CHN Analyzer Perkin-Elmer 2400. The high-resolution
mass spectra were recorded on a Bruker microTOF spectrometer with electrospray ionization (ESI).
All measurements were performed in a positive (+MS) ion mode (interface capillary voltage: 4500 V)
with scan range m/z: 50–3000. External calibration of the mass spectrometer was performed with
Electrospray Calibrant Solution (Fluka). A direct syringe injection was used for all analyzed solutions
in MeCN (a flow rate: 3 µ
L min−1). Nitrogen was used as a nebulizer gas (0.4 bar) and as a dry gas
(4.0 L min−1); the interface temperature was set at 180 ◦C. All spectra were processed with the Bruker
DataAnalysis 4.0 software package. Analytical thin-layer chromatography (TLC) was carried out on
Merck 25 TLC silica gel 60 F254 aluminum sheets. The visualization of the TLC plates was accomplished
with UV light. The densities were measured with a Micromeritics AccuPyc II 1340 gas pycnometer.
The thermal stability of the species studied was monitored using DSC 204 HP apparatus (Netzsch).
◦
The samples of 0.5–1.5 mg weight were linearly heated up to a 350 C at 5 K min−1 rate under a
nitrogen flow. Most of the experiments were run under atmospheric pressure, but for several highly
volatile compounds, the elevated pressure of 2.0 MPa was applied. This methodology (referred to as
the pressure DSC) is discussed in detail elsewhere [48,49].
Electronic structure calculations were performed using the Gaussian 09 [64], Molpro 2015 [65],
and ORCA 4.0 [66] program packages. The gas-phase enthalpies of formation (at p0 = 1 bar and
0
T = 298.15 K,
∆
Hf (g)) were calculated using the explicitly correlated W1-F12 and W2-F12 multilevel
procedures [67] and the atomization energy and isodesmic reaction approaches described in detail
elsewhere [55 68]. Note that the W1-F12 procedure employed in the present work had been slightly
modified in comparison with the originally proposed technique: namely the B3LYP-D3BJ/def2-TZVPP
optimized geometries (the ZPE correction factor of 0.99) were used [69 70] and the diagonal
,
,
Born–Oppenheimer corrections were omitted. The multireference character of the wave functions
of the reagents, intermediates, and transition states considered in the present work was estimated

Molecules 2020, 25, 5836
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using the T1 diagnostic for the CCSD calculation [71]. The modest T1 values obtained in all cases
(<0.025) justify the reliability of the single reference-based electron correlation procedure employed
in the present study. Apart from this, to estimate the possible contributions from post-CCSD(T)
excitations to the valence component of the atomization energies, the %TAE[(T)] diagnostics (viz,
the percentage of the perturbative triples (T) in the CCSD(T) atomization energy) was employed [72].
For all species studied, the latter value did not exceed 5%. This fact also justifies the reliability of the
CCSD(T) atomization energies calculated in the framework of the W1-F12 procedure. The heats of
formation at 0 K for the elements in the gas phase
51.63 kcal mol−1 fHgas0K(N) = 112.53 kcal mol−1, and
from the NIST-JANAF tables [73].
∆
fHgas0K(C) = 169.98 kcal mol−1
, ∆
fHgas0K(H) =
,
∆
∆
fHgas0K(O) = 58.99 kcal mol−1 were taken
For several isodesmic reactions, single-point electronic energies were calculated using the
DLPNO-CCSD(T) methodology (the “NormalPNO” truncation thresholds were set) [74] along with the
aug-cc-pVQZ basis set [75]. For the sake of brevity, it is denoted henceforth as aVQZ. The RIJK density
fitting (DF) approximation [76] was used to accelerate the convergence of the SCF components of
DLPNO-CCSD(T) energy. The corresponding auxiliary basis sets (aug-cc-pVQZ/JK and aug-cc-pVQZ/C
in the ORCA nomenclature) [66] were used in the DF calculations of the SCF and correlation energies.
All computational approaches for the calculation of ∆f H0(g) employed in the present work were
benchmarked on a series of energetic N-rich heterocycles and exhibited an average “chemical” accuracy
(~4 kJ mol−1) [49,54,55].
Mechanical sensitivities were determined in accordance with the STANAG standards for the
impact [77] and friction [78] sensitivity evaluation. Computational estimations of the detonation
parameters were performed using the Pepekin–Lebedev empirical method [79]. This method is
similar to the Kamlet approach, however, exhibits a better accuracy when compared with the available
experimental data for the CHNO and CNO explosives (see more details in the Supporting Information
of [21]).
The X-ray diffraction data were collected at 100 K on a Bruker Quest D8 diffractometer equipped
with a Photon-III area-detector (graphite monochromator,
ω-scan technique), using Mo K-radiation
(0.71073 Å). The intensity data were integrated by the SAINT program [80] and were corrected for
absorption and decay using SADABS [81]. The structure was solved by direct methods using SHELXS
and was refined on F2 using SHELXL-2018 [82
–84]. All atoms were refined with the particular
anisotropic displacement parameters. The SHELXTL program suite was used for molecular graphics.
4. Conclusions
In the present work, we thoroughly characterized the thermal stability, mechanical sensitivity,
and detonation properties for a wide set of 20 functionalized energetic furoxan derivatives. Differential
scanning calorimetry revealed that the melting points of the species studied vary drastically in a broad
range from ca. 40 ◦C (e.g.,
2
and 14) to 172 ◦C (20). This fact gives evidence that the phase-change
properties of the furoxan derivatives can efficiently be tuned by introducing different substituents in
the furoxan ring and/or the linkers between the two rings in the bicyclic species. Several monocyclic
furoxans, viz., 1, 4
, and 14, showed no evidence of thermal decomposition below 180 ◦C and therefore
are promising for applications. Although the estimated energetic performance (viz., detonation
velocity and the heat of explosion) for these species is much higher than that of benchmark melt-cast
explosives (TNT, DNAN), they are more volatile in comparison with the latter compounds. The study
of the thermal behavior also showed that all 3-nitro furoxan derivatives (2, 4–7, Scheme 2) exhibit an
exothermic transformation near 120 ◦C. This fact was attributed to the thermal isomerization of the
3-nitrofuroxan moiety to the more thermodynamically preferable 4-nitrofuroxans.
The mechanical sensitivity of the furoxan derivatives varied from a low-to-insensitive level (14
to the highly sensitive bicyclic furoxans and 18 20 (Table 2, Figure 6). From the safety viewpoint
of complementary thermal stability and mechanical insensitivity, the most promising compounds
are and 14. They can find applications in the melt-cast explosive formulations. At the same
)
3
–
4

Molecules 2020, 25, 5836
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time, the compound 17 exhibits the same thermal and energetic parameters as a benchmark PETN
explosive, whereas its sensitivity to impact and friction is slightly lower (Table 2, Figure 6). In turn,
3-methylfuroxan 15 is a remarkable mechanically insensitive energetic liquid that has a detonation
velocity above 6 km s−1, at the cost of moderate thermal stability, though. Finally, the application
prospects of DDF (3), one of the most powerful energetic materials synthesized up to date, are most
probably limited due to the very high mechanical sensitivity of this compound.
Supplementary Materials: The following are available online. Table S1: Crystal data and structure refinement for
12, Table S2: Atomic coordinates and equivalent isotropic displacement parameters for 12, Table S3: Bond lengths
[Å] and angles [◦] for 12, Table S4: Anisotropic displacement parameters for 12, Table S5: Torsion angles [◦] for 12
.
Figure S1: Thermal cycling of
1
: first heating up to melting, cooling with crystallization and reheating with a
single endothermic event, Figure S2: The DSC curves of
1
and at atmospheric pressure (solid curves) and under
2
elevated nitrogen pressure of 2.0 MPa (dashed curves) at the heating rate at 5 K min−1. Figure S3: DSC traces
for investigated furoxans 1–20 acquired at 5 K min-1 heating rate. The red curves correspond to the elevated
pressure (2.0 MPa), the blue curves—to the atmospheric pressure. Table S6: A full set of the safety properties of
the compounds studied.
Author Contributions: Conceptualization, N.V.M. and L.L.F.; methodology, L.L.F. and V.G.K.; validation, V.G.K.,
L.L.F. and N.V.M.; formal analysis, N.N.M. and A.N.P.; investigation, A.A.L. and D.M.B.; resources, A.A.L., D.M.B.,
L.L.F., and N.N.M.; data curation, A.A.K., K.A.M., D.B.M., and I.N.M.; writing—original draft preparation, L.L.F.
and N.V.M.; writing—review and editing, V.G.K., L.L.F., and N.V.M.; supervision, N.N.M. and A.N.P.; project
administration, N.V.M. and A.N.P.; funding acquisition, N.N.M. and A.N.P. All authors have read and agreed to
the published version of the manuscript.
Funding: This work was funded by the Russian Science Foundation (project 19-73-20217).
Acknowledgments: The characterization of the compounds and the crystal structure determination were
performed at the Department of Structural Studies of Zelinsky Institute of Organic Chemistry. The support by the
Supercomputer Centers of Novosibirsk State University and SB RAS is also acknowledged.
Conflicts of Interest: The authors declare no conflict of interest.
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