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Title: A G4MP2 and G4 Theoretical Study into the Thermochemical Properties of Explosophore Substituted Tetrahedranes and Cubanes

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Full Paper
A G4MP2 and G4 Theoretical Study into the Thermochemical
Properties of Explosophore Substituted Tetrahedranes and
Cubanes
Sierra Rayne,*a Kaya Forestb
a

b

Ecologica Research, Kelowna, British Columbia, V1Y 1R9, Canada
e-mail: rayne.sierra@gmail.com
Department of Chemistry, Okanagan College, Penticton, British Columbia, V2A 8E1, Canada

Received: December 21, 2010; revised version: April 25, 2011
DOI: 10.1002/prep.201000165
Supporting information for this article is available on the WWW under
http://dx.doi.org/10.1002/prep.201000165 or from the author.

Abstract
High level G4MP2/G4 composite theoretical method thermochemical calculations were conducted on the parent tetrahedrane
and cubane compounds and a suite of 20 mono- and polyfunctionalized derivatives with azo, nitro, and peroxo explosophoric
substituents. The novel azo and peroxo derivatives of these Platonic solid hydrocarbons are likely to be local minima on their
respective potential energy surfaces, suggesting these compounds
may be priority synthetic targets. The high, mass normalized gas
phase enthalpies of formation for both the tetrahedranes and cubanes exceed those of well-established primary (mercury fulminate and lead azide) and secondary (RDX and HMX) explosives
by up to an order of magnitude. Other known (TNT, HMX, CL20, octanitrocubane) or proposed (aminonitroalkanes and acetylenes, nitroboranes) high energy materials generally have substantially less favorable mass normalized gas phase enthalpies of
decomposition than the most promising tetrahedrane or cubane
derivatives presented herein.
Keywords: High Energy Materials, Tetrahedranes, Cubanes,
Explosophoric Substituents, Theoretical Study

Results and Discussion
Molecular forms of the regular Platonic solids (tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron; Supplementary Materials Figure S1) have been
the focus of interest regarding their potential uses in high
energy materials (HEMs) [1–8]. Among the analogs with
entirely carbon atom frameworks, only the parent cubane
[9] and dodecahedrane [10, 11] have been synthesized, in
410

addition to some substituted derivatives of tetrahedrane
(the unsubstituted compound remains experimentally unknown) [12–14]. Octahedrane has not yet been reported,
and icosahedrane contains five-coordinate vertices which
complicate the use of carbon atoms. A substantial body
of theoretical work also exists on the parent and variously
functionalized Platonic solids, including heteroatom substitution in the frameworks (see additional references
provided in the Supplementary Materials and references
cited therein).
Following the synthesis of cubane, subsequent experimental efforts obtained a variety of mono- through octanitro-substituted cubanoid derivatives that are promising
HEMs [15–22]. Additional purely theoretical studies have
investigated the addition of nitrato [23, 24], nitroso [25],
and difluoroamino groups [24, 26], as well as continuing
computational work on the series of nitrocubanes [24,
27–34]. Similar theoretical work has been conducted on
the nitro substituted tetrahedranes [35–37]. Although
there has been synthetic success in preparing nitro-substituted cubanes, corresponding explosophoric tetrahedranes
remain hypothetical molecules. To better constrain potential high-value synthetic targets in this area, we have employed high-level theoretical methods towards estimating
the thermochemical properties for a range of tetrahedranes and cubanes substituted with representative explosophoric functionalities (azo, nitro, and peroxo) (Figure 1
and Figure 2).
Gaussian-4 level G4MP2 [38] and G4 [39] ab initio
post-Hartree–Fock composite method calculations were

2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Propellants Explos. Pyrotech. 2011, 36, 410 – 415

Explosophore Substituted Tetrahedranes and Cubanes

Figure 1. Structures of the parent (1) and explosophore substituted (2–6) tetrahedranes under consideration.

conducted using Gaussian 09 [40]. Singlet and triplet calculations were performed on all compounds. Calculations
to obtain global minimum singlet and triplet state geometries for all compounds were each fully optimized on
their respective potential energy surfaces starting from
the same corresponding MMFF94 molecular mechanics
force field optimized geometry. Monoazotetrahedrane
yields a ground electronic state triplet; the singlet calculation converges on a dissociated N2···C4H2 ring-opened
structure (rN C = 0.333 nm) with one imaginary frequency.
All other compounds are ground state singlets without
imaginary frequencies. Atomic and molecular enthalpies

include zero-point and thermal corrections. Geometries,
molecular enthalpies, and full G09 archive entries with
energies at each stage of the optimization processes for
all final structures are provided in the Supplementary
Materials. Gabedit v.2.3.0 was used for geometry visualizations [41]. G4MP2 and G4 calculations on the syntrans-diazocubane (i.e., parallel azo groups spanning opposite faces of cubane, as opposed to the orthogonal antitrans-diazo orientation (compound 11) shown in
Figure 2), as well as the trans-mono- and syn/anti-diperoxo cubanes, either failed to converge at either level of
theory, or gave cage-opened non-cubanoid final geometries. The novel azo and peroxo derivatives of these compounds are – according to high level calculations – local
minima on their respective potential energy surfaces, suggesting that these compounds are potentially amenable to
experimental synthesis.
Gas phase (298.15 K, 1.013 105 Pa) enthalpies of formation (DfH8(g)) for all compounds were estimated via
the atomization method [42–44] at each level of theory
(Tables 1–3). In addition to the extensive benchmarking
efforts undertaken by the inventors of the G4MP2 and
G4 methods, we have also shown that these levels of
theory provide effective DfH8(g) chemical accuracy across
a wide range of organic compounds (including highly
strained and functionalized molecules) when using the
atomization approach [8, 45–48]. Gas phase (298.15 K,
1.013 105 Pa) enthalpies of combustion (DcombH8(g)) were
calculated via balanced stoichiometries assuming reaction
with dioxygen gas (O2(g) ; DfH8(g) = 0 kJ·mol 1) and the corresponding production of gas phase carbon dioxide
(CO2(g) ; DfH8(g) = 393.3 0.4 kJ·mol 1 [49]) and dinitrogen gas (N2(g) ; DfH8(g) = 0 kJ·mol 1) as well as liquid water

Figure 2. Structures of the parent (7) and explosophore substituted (8–22) cubanes under consideration.

Propellants Explos. Pyrotech. 2011, 36, 410 – 415

2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.pep.wiley-vch.de

411

S. Rayne, K. Forest

Full Paper

Table 1. Oxygen balances (OB) and estimated gas phase (298.15 K, 1.013 105 Pa) enthalpies of formation (DfH8(g)) and enthalpies of
combustion (DcombH8(g)) for various explosophore substituted tetrahedranes at the G4MP2 level of theory.
G4MP2
a)

compound

ID

OB

tetrahedrane
monoazotetrahedrane
mononitrotetrahedrane
dinitrotetrahedrane
trinitrotetrahedrane
tetranitrotetrahedrane

1
2
3
4
5
6

307 %
184 %
124 %
56 %
21 %
0%

DfH8(g) b)
(kJ·mol 1)

DfH8(g)
(kJ·kg 1)

533.9
1217.5
556.5
585.8
630.1
678.6

10246.6
15598.0
5761.4
4129.6
3368.1
2924.6

DcombH8(g) c)
(kJ·mol 1)
2679.4
3077.8
2561.9
2446.8
2346.8
2252.7

DcombH8(g)
(kJ·g 1)
51.5
39.3
26.4
17.2
12.6
9.6

DdecompH8(g) d)
(kJ·mol 1)
533.9
1217.5
1043.1
1204.6
1215.0
1120.9

DdecompH8(g)
(kJ·g 1)
10.0
15.5
10.9
8.4
6.7
5.0

a) See ref. [50]. b) Calculated using the atomization enthalpy approach [42–44] with zero point and thermal corrections for the lowest
energy conformation. c) Calculated with DfH8(g)(CO2) = 393.3 kJ·mol 1 [49] and DfH8(l)(H2O) = 285.8 kJ·mol 1 [49]. d) Calculated
with DfH8(g)(CO) = 110.5 kJ·mol 1 [49] and DfH8(l)(H2O) = 285.8 kJ·mol 1 [49].

Table 2. Oxygen balances (OB) and estimated gas phase (298.15 K, 1.013 105 Pa) enthalpies of formation (DfH8(g)) and enthalpies of
combustion (DcombH8(g)) for various explosophore substituted tetrahedranes at the G4 level of theory.
G4
compound

ID

OB a)

DfH8(g)
(kJ·mol 1)

DfH8(g)
(kJ·kg 1)

DcombH8(g)
(kJ·mol 1)

DcombH8(g)
(kJ·g 1)

DdecompH8(g)
(kJ·mol 1)

DdecompH8(g)
(kJ·g 1)

tetrahedrane
monoazotetrahedrane
mononitrotetrahedrane
dinitrotetrahedrane
trinitrotetrahedrane
tetranitrotetrahedrane

1
2
3
4
5
6

307 %
184 %
124 %
56 %
21 %
0%

537.6
1219.6
555.6
576.6
c/e b)
c/e

10326.1
15618.9
5723.7
4058.5
c/e
c/e

2683.6
3079.4
2558.5
2436.3
n/a c)
n/a

51.5
39.3
26.4
17.2
n/a
n/a

537.6
1219.6
1039.7
1194.1
n/a
n/a

10.5
15.5
10.9
8.4
n/a
n/a

a) See ref. [50]. b) Not completed due to computational expense. c) Not available.

Table 3. Oxygen balances (OB) and estimated gas phase (298.15 K, 1.013 105 Pa) enthalpies of formation (DfH8(g)) and enthalpies of
combustion (DcombH8(g)) for various explosophore substituted cubanes at the G4MP2 level of theory.
compound

ID

cubane
azocubane
1,2-diazocubane
1,3-diazocubane
anti-trans-diazocubane
triazocubane
tetraazocubane
mononitrocubane
1,2-dinitrocubane
1,3-dinitrocubane
1,4-dinitrocubane
monoperoxocubane
1,2-diperoxocubane
1,3-diperoxocubane
triperoxocubane
tetraperoxocubane

7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22

OB a)
307 %
234 %
184 %
184 %
184 %
149 %
123 %
188 %
124 %
124 %
124 %
203 %
136 %
136 %
91 %
57 %

DfH8(g) b)
(kJ·mol 1)

DfH8(g)
(kJ·kg 1)

603.3 [8]
1051.0
1546.0
1518.4
2214.6
2051.0
2586.1
565.7
552.7
546.8
544.8
740.6
925.9
907.9
1130.1
1367.7

5790.7
8075.1
9899.3
9723.6
14183.8
11259.1
12422.3
3790.7
2845.1
2815.8
2807.5
5522.9
5644.2
5531.2
5824.1
6104.5

DcombH8(g) c)
(kJ·mol 1)
4894.9
5056.4
5266.0
5237.9
5934.6
5484.8
5734.2
4714.1
4558.5
4552.6
4550.5
4746.3
4645.9
4627.9
4564.3
4515.8

DcombH8(g)
(kJ·g 1)
46.9
38.9
33.9
33.5
38.1
30.1
27.6
31.8
23.4
23.4
23.4
35.6
28.5
28.0
23.4
20.1

DdecompH8(g) d)
(kJ·mol 1)
603.3
1051.0
1546.0
1518.4
2214.6
2051.0
2586.1
1137.2
1520.9
1515.0
1512.5
1312.1
1718.8
1700.8
1968.6
2251.8

DdecompH8(g)
(kJ·g 1)
5.9
7.9
10.0
9.6
14.2
11.3
12.6
7.5
7.9
7.9
7.9
9.6
10.5
10.5
10.0
10.0

a) See ref. [50]. b) Calculated using the atomization enthalpy approach [42–44] with zero point and thermal corrections for the lowest
energy conformation. c) Calculated with DfH8(g)(CO2) = 393.3 kJ·mol 1 [49] and DfH8(l)(H2O) = 285.8 kJ·mol 1 [49]. d) Calculated
with DfH8(g)(CO) = 110.5 kJ·mol 1 [49] and DfH8(l)(H2O) = 285.8 kJ·mol 1 [49].

(H2O(l) ; DfH8(l) = 285.8 kJ·mol 1 [49]). Gas phase
(298.15 K, 1.013 105 Pa) enthalpies of decomposition
(DdecompH8(g)) were calculated via the modified Kistiakowsky–Wilson rules [50], assuming production of gas phase
carbon monoxide (CO(g) ; DfH8(g) = 110.5 0.4 kJ·mol 1
[49]), dinitrogen (N2(g) ; DfH8(g) = 0 kJ·mol 1), dioxygen
412

www.pep.wiley-vch.de

(O2(g) ; DfH8(g) = 0 kJ·mol 1), and dihydrogen (H2(g) ;
DfH8(g) = 0 kJ·mol 1), liquid water (H2O(l) ; DfH8(l) =
285.8 kJ·mol 1 [49]), and solid carbon as the graphite allotrope (C(s) ; DfH8(g) = 0 kJ·mol 1). Combustion reactions
assume external oxidizer is available (if needed beyond
internal sources where the oxygen balance [OB] is < 0 %;

2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Propellants Explos. Pyrotech. 2011, 36, 410 – 415

Explosophore Substituted Tetrahedranes and Cubanes

only tetranitrotetrahedrane (OB = 0 %) has a non-negative OB), such as in propellant applications. Conversely,
decomposition reactions assume no additional oxidizer is
present, as may occur in an explosive application.
Excellent agreement between the G4MP2 and G4
DfH8(g) was obtained for the tetrahedranes, with a mean
signed difference of 2.1 kJ·mol 1, a mean absolute difference of 5.0 kJ·mol 1, and a maximum absolute difference of 10.5 kJ·mol 1 (dinitrotetrahedrane). Addition of
explosophore groups to the tetrahedrane framework generally increases the molar DfH8(g) but has varying impacts
on the estimated molar DcombH8(g). When normalized per
unit mass, all explosophoric tetrahedranes studied have
substantially higher (less favorable) DcombH8(g) (ranging
from 9.6 (tetranitrotetrahedrane) to 39.3 (monoazotetrahedrane) kJ·g 1) than the parent compound
( 51.5 kJ·g 1). Increasing nitro content progressively decreases the mass normalized DcombH8(g), but offers a more
favorable oxygen balance. In contrast to typical patterns
for nitro-substituted HEMs [51], increasing nitro-substitution on tetrahedrane increases the DfH8(g) (from 559.4
(mononitro) to 678.6 (tetranitro) kJ·mol 1), whereas there
is a slight decrease in DfH8(g) with increasing nitro-substitution for the cubanes (from 565.7 (mononitro) to 544.8
(1,4-dinitro) kJ·mol 1). For the limited set of compounds
with prior DfH8(g) estimates in the literature, our data is in
good agreement (Supplementary Materials Table S1). Because of the large number of prior theoretical studies on
the DfH8(g) of cubane, we refer readers to a recent previous work [8] that summarizes these parent cubane estimates in comparison to those obtained at the G4MP2 and
G4 levels.
With the exception of the mono- and dinitrocubanes,
all explosophoric cubanes have higher molar DfH8(g) than
the unsubstituted compound (the mono- and dinitrocubanes (DfH8(g) from 544.8 to 565.7 kJ·mol 1) are predicted
to be approximately isoenthalpic with the parent molecule (DfH8(g) = 603.3 kJ·mol 1)). The molar DcombH8(g) for
the cubanes are relatively unaffected by the addition of
explosophore moieties, and when mass normalized, the
parent compound (DcombH8(g) = 46.9 kJ·g 1) retains a
more exothermic DcombH8(g) when compared to its derivatives (DcombH8(g) ranging from 20.1 (tetraperoxocubane)
to 38.9 (azocubane) kJ·g 1). The high mass normalized
DfH8(g) for both the tetrahedranes (up to 15606 kJ·kg 1
for monoazotetrahedrane) and cubanes (up to
14183 kJ·kg 1 for anti-trans-diazocubane) compare very
favorably to representative primary explosives (e.g., mercury fulminate (HgC2N2O2), 1355 kJ·kg 1; lead azide
(PbN6), 1610 kJ·kg 1) and secondary explosives (e.g.,
RDX (C3H6N6O6), 280 kJ·kg 1; HMX (C4H8N8O8),
251 kJ·kg 1).
The parent or substituted tetrahedranes or cubanes are
competitive with existing HEM leaders with regard to
mass normalized DdecompH8(g). Only the addition of an azo
substituent improves the mass normalized DdecompH8(g) of
tetrahedranes (from 10.5 kJ·g 1 for the parent system to
15.5 kJ·g 1 for the monoazo derivative); nitro groups

Propellants Explos. Pyrotech. 2011, 36, 410 – 415

either have little effect on, or decrease, the mass normalized DdecompH8(g). By comparison, all explosophoric substituents improve the mass normalized DdecompH8(g) of the
cubanoids (from 5.9 kJ·g 1 for the parent system to
14.2 kJ·g 1 for the anti-trans-diazo derivative). We infer
from this different predicted thermochemical response
that the addition of explosophoric substituents on tetrahedrane significantly stabilizes the molecule (e.g., reduces
cage strain) with a magnitude that offsets the expected
improvement in DdecompH8(g). Cubane does not appear to
be significantly stabilized by explosophore substitution;
and thus, DdecompH8(g) values display the expected declining trend with increasing substitution. In comparison to
the explosophoric tetrahedranes and cubanes under study,
other known (trinitrotoluene (TNT), 4.6 kJ·g 1 [50]; tetrahexamine tetranitramine (HMX),
5.4 kJ·g 1 [50];
2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane
6.3 to
(CL-20),
6.3 kJ·g 1 [52]; octanitrocubane,
1
[53]) or proposed (aminonitromethane,
7.1 kJ·g
6.7 kJ·g 1 [54]; tetranitrodiborane, 7.1 kJ·g 1 [51]; aminonitroacetylene,
7.9 kJ·g 1 [55]; diaminodinitrome1
[54]; trinitrodiborane,
10.0 kJ·g 1
thane,
8.4 kJ·g
[51]) HEMs generally have substantially less favorable
mass normalized DdecompH8(g) than the most promising tetrahedrane or cubane derivatives considered herein.
Supporting Information (see footnote on the first page of this article): Geometries of the five regular Platonic solids; Additional
references; Comparison of G4MP2 calculated parent and explosophore substituted tetrahedrane and explosophore substituted
cubane gas phase (298.15 K, 1.013 105 Pa) enthalpies of formation (DfH8(g)) with calculations from the literature; Gaussian 09
G4 archive entries; Gaussian 09 G4MP2 archive entries; Gas
phase (298.15 K, 1.013 105 Pa) molecular enthalpies (DH8(g)) at
the G4MP2 and the G4 levels of theory; Visualizations of the optimized structures at the G4MP2 and the G4 levels of theory.

Acknowledgments
This work was made possible by the facilities of the Western
Canada Research Grid (WestGrid: project 100185), the Shared
Hierarchical Academic Research Computing Network (SHARCNET: project sn4612), and Compute/Calcul Canada.

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