1

Cubane Decomposition Pathways – A Comprehensive Study

Bimal B. S. a, Arindrajit Chowdhury a, Irishi N. N. Namboothiri b, Neeraj Kumbhakarna a,* a Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai 400076.

India b Department of Chemistry, Indian Institute of Technology Bombay, Mumbai. 400076. India

* Corresponding author E-mail address: neeraj_k @iitb.ac.in

1. Introduction

Strained hydrocarbons are an emerging area of research from thermodynamic and chemistry

perspective on account of the enormous amount of energy which molecules of this class can

contain within them [1]. This makes them suitable for potential use as propallants (directly, or

in a mixture) in launch vehicles or as explosives. Among strained hydrocarbons, cage

compounds are highly energetic. Cubane is one such cage compound which has been realised

and multiple efforts have been made to analyse other cage structures as well. Presently, active

research is in progress on synthesizing and testing high energy derivatives of cubane. Cubane

was first synthesised in 1964 by Philip Eaton and his co-workers [2]. The synthesis/existence

of such a strained compound was considered impossible till then. High energy of the cage

structure in cubane can be attributed to the highly strained carbon-carbon bonds. Apart from

the angle strain, the torsional strain that prevents free rotation about a single bond also

contributes to the high energy. The simplest of these cages have been derived directly from

the platonic solids, which are highly symmetric. Cubane’s structure is such that it

accommodates three 19o strains at each of the 8 vertices. This is a huge deviation from the

normal 109.5o bond angle of a sp3 bond [3]. It is because of this strain that cubane has a heat

of formation as high as 148 kcal/mol [4]. Although this large bending is energetically very

demanding, the hydrogen atoms on the main diagonals stabilize the cubic configuration

corresponding to a local instead of the global minimum of potential energy as a function of

the atomic coordinates.

Addition of a single methyl group decreases the heat of formation as was indicated in the

study of methyl cubane by Li and Anderson [1]. Since these compounds are highly strained, a

study of their decomposition pathway helps in analysing their behaviour under pyrolysis.

There is a high built in strain energy which may lead to an unusual combustion process. An

analysis of the decomposition hence would suggest where during the pathway the energy is

released. The physical and chemical properties as well as the decomposition pathway of these

cage structures can be altered with functionalization. A study of the decomposition pathways

of cubane and methylcubane have been done earlier by Li and Anderson [1]. Cubane is a

solid, so it can either be used as an energetic binder or as an additive in liquid propulsion

systems depending on its solubility. Cage compounds such as cubane have a realistic potential

to be the future fuels; however, the limited synthetic capabilities have been a hindrance and

have led to restriction of their quantitative and qualitative analysis to droplet combustion

experiments, thermogravimetric analysis and fast pyrolysis studies among others. Hence,

analysing these compounds through ab-initio computation methods to get a first-hand idea of

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their overall behaviour during decomposition would benefit the research community. In the

present work, a theoretical study by means of ab initio calculations as implemented in

Gaussian 09 [5] has been carried to explore the various reaction pathways existing in the

decomposition of cubane. Optimised molecular structures of reactants, products and transition

in the pathways were obtained. The formulated chemical pathways were validated by

comparing the computed data with that available literature (both computational and

experimental). The heats of formation of the chemical species were calculated by using the

procedure proposed by Curtiss et al. [6]. The calculation methodology explained in the

Gaussian 09 thermochemistry literature [7] was also used. Reaction rate constants were

determined for all the elementary reactions [7] and the key reactions were identified.

Thermodynamic data for all the species under consideration in the reaction mechanism was

generated and simulations were carried out to analyse the growth and decay of the various

species in the cubane decomposition process using the combustion models available Chemkin

[8].

2. Molecular modelling

The modelling of short-lived, unstable intermediates and even transition states can be carried

out using quantum mechanics based molecular modelling. Density Functional Theory (DFT)

[9] as implemented in Gaussian 09 [5] was used to perform all calculations and optimizations

in this study. The geometries of the intermediates (from reactants to products) and transition

states were optimized using B3LYP functional with 6-31++G(d,p) basis set. CBS-QB3

compound method was also used, which strikes a good balance between accuracy and

computational effort [10] for the molecular sizes encountered in the present study.

Relaxed potential energy scan was carried out by means of B3LYP functional along with 6-

31+G(d) basis set, on optimized molecular structures of reactants and products for obtaining

the initial guesses for transition state structures which were then subjected to transition state

optimisation calculations. Presence of a single negative frequency in the molecular vibration

modes confirmed the obtained transition state to be correct for the elementary reaction under

consideration as it corresponds to a saddle point on the potential energy surface. These

optimised structures were then used as starting structures or CBS-QB3 calculations for faster

convergence. Intrinsic reaction coordinate (IRC) calculations are done in both the forward and

reverse directions for all the transition states to make sure that the transition states precisely

corresponded to the envisioned reaction paths. Reactions in the condensed phase were studied

by applying the polarizable continuum model (PCM) along with the integral equation

formalism variant (IEFPCM) [10] to reflect the assumption that the liquid-phase reactions can

be treated as occurring in a solution phase. Cyclohexane is used as the solvent in all the

optimization, frequency and IRC calculations except for benzene (where benzene itself was

used as the solvent), since cubane or any of its isomers are not directly available as a solution

medium in Gaussian 09. Cyclohexane being a ring compound containing only carbon and

hydrogen atoms, similar to most of the species involved in the decomposition of cubane is

expected to closely match the exact solution phase medium. The effect of change in solution

medium is found to be negligible on the calculated reaction parameters [10].

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3. Results and Discussion

3.1 Cubane decomposition and its isomers

The decomposition behaviour of cubane in both gas phase and condensed phase was studied

to explaining the formation of the major products: COT, benzene, acetylene, phenyl

acetylene, hydrogen, styrene and dihydropentalenes (DHPs). Experimental and computational

results available in the literature were used as a guidline [11]. Various reaction pathways

identified in cubane decomposition are shown in Table 1. The rate constants for gas phase

reactions were calculated at at 573 K (sufficiently above the boiling point of cubane which

434 K), and those for condensed phase reaction were calculated at 420 K (melting point of

cubane being 406 K) [12]. The pyrolysis of cubane studied by Martin et al. showed

Acetylene, Benzene, COT, Styrene and three dihydropentalenes (DHPs) as the products [11].

This investigation also showed that the time and temperature dependence on the reaction was

minor but has striking pressure dependence [11]. Benzocyclobutene (BCB), Phenyl acetylene

(PA) and hydrogen were also discussed as the decomposition products in the plug flow

reactor study by Li and Anderson [1] and hence was considered in the present analysis. The

energy values given in the Table 1 correspond to the CBS-QB3 calculations in the gas phase.

The transition states pertaining to these reactions are shown in .

4

CH

CH2

Cubane STCO BCT Intermediate COT /

COT Stereomer

BCT

Styrene

BCD Biradical SBV

1,8-DHP 1,2-DHP 1,5-DHP 1,4-DHP

BCB Styrene Intermediate

STCO

Intermediate

Figure 1: C8H8 compounds

CH CH C CH H2

Benzene Acetylene PA Hydrogen

Figure 2: C8H8 decomposition products

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Figure 3: 3D spatial orientation of C8H8 isomers

Table 1: Key reactions in the decomposition of cubane (gas phase) along with rate parameters

calculated using the CBS-QB3 method.

No. Reaction ∆‡Gf ∆‡Gb ∆Hf ∆Hb ∆HR

R1a

R1b

R1c

Cubane STCO

TS1a

Cubane BCT

TS1b

Cubane

TS1c

STCO Intermediate

65.79

56.09

-

94.55

126.09

-

69.55

59.15

41.00*

94.23

124.32

-1.15*

-24.67

-65.17

42.15*

6

R1d

R2

R3

R4

R5

R6a

R6b

STCOSTCO Intermediate

TS1d

STCO BCT Intermediate

TS2

BCT Intermediate BCT

TS3

COTBCT

TS4

CH CH

BCT Benzene Acetylene

+TS5

COT SBV

TS6a

COT StereomerBCT Intermediate

TS6b

15.21

28.77

44.71

18.66

73.38

41.24

13.01

81.58

14.12

100.60

27.82

101.29

37.36

57.16

15.28

28.37

45.74

18.28

74.65

39.00

12.49

82.10

13.10

101.50

25.88

80.02

39.14

55.06

-66.82

15.26

-55.76

-7.60

-5.38

-0.14

-42.57

7

R6c

R7

R8

R9a

R9b

R9c

R9d

R10

COT Stereomer BCD Biradical

TS6c

BCT Intermediate

TS7

COT

C

CH

H2

PA HydrogenBCT

TS8

+

BCD Biradical 1,8-DHP

TS9a

1,8-DHP 1,4-DHP

TS9b

1,8-DHP 1,2-DHP

TS9c

1,5-DHP1,4-DHP

TS9d

45.09

15.40

78.10

12.76

22.18

52.17

27.52

93.52

25.22

80.45

102.76

59.29

30.80

61.88

27.65

141.60

43.56

15.31

82.37

11.37

21.34

53.31

26.24

95.07

24.69

78.67

86.43

59.01

29.44

62.35

26.70

140.20

18.87

-63.36

-4.07

-47.63

-8.10

-9.03

-0.46

-45.13

8

R11

R12

R13a

R13b

R14

BCT

CH

CH2

Styrene

TS10

BCBBCT

TS11

BCB

CH

CH2

Styrene

TS12

BCB Styrene Intermediate

TS13a

Styrene Intermediate

CH

CH2

Styrene

TS13b

CH

CH2

Styrene

CH CH

Benzene Acetylene

+TS14

71.63

123.85

97.26

14.45

112.39

104.70

138.86

63.97

62.75

92.23

71.43

125.96

97.70

13.67

111.48

105.19

137.33

63.89

58.85

71.72

-33.76

-11.37

33.81

-45.18

39.76

3.1.1 Formation of STCO, BCT and COT

The initial step in cubane decomposition is the scission of one C-C bond, causing the cube

structure to open up, leading to the formation of STCO and BCT through the transition state

TS1a and TS1b respectively. The reaction R1a matches with the literature findings [3], but the

energy barrier is around 69 kcal/mol, which is higher than that given by Martin et al. [11], and

Li and Anderson [1]. The reverse reaction energy barrier is around 25 kcal/mol higher than

that of the forward reaction, and hence the forward reaction is highly favoured. The negative

value of the enthalpy of reaction (-25 kcal/mol) signifies the enormous amount of energy

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released during this step. However, details regarding the estimation of energy barrier to be

around 43 kcal/mol for the elementary reaction obtained from experiments [1, 11] are not

available. The reaction R1b is a direct transformation of cubane to BCT through a forward

reaction barrier of around 59 kcal/mol. This is also a highly exothermic reaction causing an

energy release of 65 kcal/mol. The reverse reaction has a very high barrier of 124 kcal/mol

and appears to be less favourable. The enormous amount of energy release shall create an

increase in temperature and is expected to assist the further reactions to occur. A

computational study carried out by Ji Zhang and Heming Xiao [13] also shows an energy

barrier of around 41 kcal/mol for the formation of a biradical ‘STCO Intermediate’ as a

preliminary step (Reaction R1c), for which a transition state could not be identified in the

present study. This STCO Intermediate leads to the formation of STCO through a transition

state as in reaction R1d, which has been identified as mentioned in literature [13]. The

reaction from STCO to BCT is not found to be a direct one as mentioned in the previous

studies; instead it passes through an intermediate complex (BCT Intermediate), causing two

transition energy barriers. STCO transforms to the compound ‘BCT Intermediate’ through the

transition state TS2, via an endothermic reaction. The energy required for this reaction is

available from the first reaction steps (R1a, R1b, R1c and R1d) itself. The reverse reaction

energy barrier is lesser than that of the forward reaction by 15 kcal/mol, but the intermediate

product formed not being a stable one, it gets favourably decomposed swiftly to BCT, COT or

a COT steroemer. The decomposition of this intermediate product to BCT in gas phase

happens through TS3 and this forward reaction energy barrier is lesser than the reverse

reaction by 55 kcal/mol and hence is highly likely to happen once the intermediate product is

formed. The enthalpy of this reaction is around -55 kcal/mol and hence signifies the enormous

amount of energy release during the formation of the stable product from the unstable

intermediate. It is significant to note that this reaction causing formation of BCT is not

observed in the condensed phase. Another reaction possible from the same intermediate is

through the transition state TS7 to give rise to the formation of COT, the forward reaction

energy barrier of which is lesser than the reverse reaction by 64 kcal/mol. The enthalpy of this

reaction is -63 kcal/mol, which is also another energy release pathway. A stereomer of COT

can also be formed from BCT Intermediate through transition state TS6b with a favourable

enthalpy of reaction of -42 kcal/mol. The forward reaction barrier is lesser than that of the

reverse reaction by 44 kcal/mol. The transformation reaction R4 of BCT to COT through the

transition state TS4 is also favoured on account of the lesser forward reaction energy barrier

of 18 kcal/mol compared to the reverse reaction barrier of 27 kcal/mol. This reaction also

causes energy release of around 7 kcal/mol. Martin, H.-D., et al. have reported that once

STCO is formed from cubane, reaction proceeds fast to COT [11]. This has been established

through this present study, based on the enthalpy of reaction of the elementary reactions and

the transition state barriers. The original strain energy in cubane is converted to vibrational

energy in COT. It is reported that COT is partially stabilized by high enough barriers. Further

reactions are to proceed if the pressure is low enough [11]. However, in the present study, it

could be understood that the energy release from the previous elementary reaction steps is so

high that COT decomposition is also possible, depending on the reactor conditions (adiabatic

conditions, homogenous or flow reactor) and its geometry. The details are covered in a later

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section.

3.1.2 Decomposition of BCT

The transformation of BCT to COT has been discussed in the previous section itself. BCT can

undergo decomposition to benzene, acetylene, phenyl acetylene, hydrogen, benzocyclobutene

(BCB) and styrene. It has been reported through pyrolysis and photochemistry analysis that

BCT is thermally unstable, and it can decompose to COT, benzene and acetylene under

various environments [14]. The decomposition reaction R5 of BCT to benzene and acetylene

through the transition state TS5 has a comparatively higher forward reaction barrier of

73 kcal/mol, but is sufficiently lesser than the reverse reaction energy barrier of 101 kcal/mol.

This reaction also causes energy release of around 5 kcal/mol. The reaction R8 signifying the

formation of phenyl acetylene and hydrogen from BCT also is energetically favourable under

suitable environment, as the forward and reverse reaction energy barriers are 78 kcal/mol and

102 kcal/mol respectively causing an energy release of 4 kcal/mol.

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BCT decomposition to styrene which releases 45 kcal/mol of energy is possible through three

different pathways in the present study. The first possibility signifies a direct transformation

of BCT to styrene by the reaction R10 through a single transition state TS10 which has very

high forward and reverse reaction energy barriers of 93 kcal/mol and 141 kcal/mol

respectively. But this reaction is not observed in the condensed phase. The second and third

possibilities involve a preliminary reaction step R11 involving the formation of BCB from

BCT through TS11, which is observed in the condensed phase as well. The forward reaction

barrier is 71 kcal/mol, and is lesser than the direct transformation of BCT to styrene. The

reverse reaction barrier is 104 kcal/mol. The second possibility leading to the formation of

styrene is by reaction R12 through a single transition state TS12 from BCB. This reaction also

has very high forward and reverse barriers of 123 kcal/mol and 138 kcal/mol respectively.

This reaction is also not observed in condensed phase. The third possibility signifies the

conversion of BCB into a compound ‘Styrene Intermediate’ by reaction R13a with a forward

reaction barrier of 97 kcal/mol and then, the transformation of this compound to styrene

through reaction R13b with a forward reaction barrier of 14 kcal/mol. This third possibility of

styrene formation is possible in condensed phase as well. A reaction signifying the carbon

atoms shifting their attachment position to the benzene ring of BCT has been observed, but is

not considered in the reaction pathway mechanism as it has the equal forward and reverse

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reaction barriers (since product is the same).

3.1.3 Decomposition of COT

COT and its stereomer can either undergo a transformation to BCT or decompose to SBV and

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BCD biradical, which can further lead to the formation of DHPs. However, it appears that

these reactions have sufficiently high reaction barriers and are endothermic as well, and hence

may be favoured in such environments only. This could possibly be the reason for COT to be

reported as a major product in many previous studies [3, 11]. As more energy becomes

available, it becomes probable for most of the COT to be decomposed further. However, the

reverse reaction barriers being still higher, the formation of COT again from these compounds

is not expected normally. COT can get decomposed to SBV through the transition state TS6a

as per reaction R6a; the forward and reverse reaction barriers being 41 kcal/mol and

37 kcal/mol respectively. It was reported previously that the heat of formation of SBV is

71 kcal/mol, implying almost similar stability to that of COT [15]. It was also reported that

SBV decomposition leads to COT as the product, while at the same time, SBV is reversible

with 1,5-DHP [15].

Figure 4: Transition states of cubane decomposition

The reaction R6c indicates the transformation of COT stereomer to BCD biradical through the

transition state TS6c with a higher forward reaction barrier of 45 kcal/mol against the reverse

reaction barrier of 25 kcal/mol. This reaction is endothermic as well, requiring around

18 kcal/mol as input. BCD biradical is a non-planar compound which decomposes to the

planar DHPs through multiple elementary reactions, which have favourable energy barriers.

1,8-DHP is primarily formed through the transition state TS9a with a low forward reaction

barrier of 12 kcal/mol and a reverse reaction barrier of 59 kcal/mol. The enthalpy of this

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reaction is -47 kcal/mol. 1,8-DHP decomposes to either 1,4-DHP or 1,2-DHP with forward

reaction barriers of 22 kcal/mol and 52 kcal/mol respectively. The enthalpy release during

these reactions is around 8 kcal/mol each. 1,4-DHP can further undergo transformation to

1,5-DHP as shown in reaction R9d through transition state TS9d having almost equal forward

and reverse reaction barriers of 27 kcal/mol.

3.1.4 Condensed phase decomposition of cubane

Computations have been carried out in Gaussian 09 in condensed phase as well. Cyclohexane

has been used as the condensed phase medium for all the species except benzene (for which

benzene itself is available in Gaussian 09 as the condensate medium). The transition state

structures remain almost similar to that in the corresponding gas phase reactions. However,

certain reactions were missing in the condensed phase pathway. The most significant

observation is the omission of reactions involving the formation of BCT (Reactions R3 and

R1a). This probability has been reported earlier also [16]. The reaction R10 and R12 leading

to the formation of styrene from BCT and BCB respectively, are also missing in the condensed

phase. This leads to the conclusion that styrene can be formed through a single longer route

only in condensed phase in contrast to three possibilities existing in gas phase. The

condensed phase formation of styrene requires initial conversion of BCT to BCB, then leading

to the formation of ‘Styrene Intermediate’ and finally to styrene. Overall, it could be inferred

that most of the gas phase elementary reaction mechanisms remain similar in condensed

phase as well, except for those involving formation of BCT.

The decomposition pathways explored through Gaussian 09 are in tandem with the pathways

available in literature. The enthalpy of reaction values for the intermediate steps in the

decomposition pathway are closely matching with that in the literature. With the above data,

the enthalpy of formation of the various important species and the rate constants of the

individual reactions are calculated in the following sections.

3.2 Calculation of heat of formation

The heat of formation of solid cubane was determined by combustion with oxygen in a bomb

calorimeter by Kybett, B., et al. [4]. ΔH0f,298 was found as 129.5 ± 0.8 kcal/mol. The vapour

pressure was determined over the temperature range of 239 K to 262 K and ΔH0sub at 298 K

was estimated as 19.2 ± 0.4 kcal/mol. This leads to ΔH0f (Cubane, gas) value of 148.7 ± 1.0

kcal/mol. ΔH0f,298 of cyclooctatetraene (COT), which is an isomeric gas of cubane molecule is

71.1 ± 0.1 kcal/mol. These values are in close agreement with Weltner prediction that cubane

should be 80 kcal/mol less stable than COT. Roux et al. have estimated the enthalpy of

formation of cubane through computational methods at various Gaussian-n levels and the

value is reported as 602.7 ± 7.3 kJ/mol, which is closely matching with the above value [17].

The positive value of the heat of formation shows the amount of energy contained in the

molecule, and that could be extracted by its combustion or decomposition. Statistical

thermodynamics is used for correlation between the molecular energy levels and macroscopic

properties such as enthalpies and heat capacities [18]. The principle behind the calculation of

ΔH0f (298 K) for compounds is explained by Lewars EG [19]. The compound, the enthalpy of

which is to be calculated is conceptually atomized at 0 K to its constituent atoms; the

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elements in their standard states are used to make these atoms. The ab initio atomization

energy of a compound is the energy difference between the atoms and the compound. This

atomization energy is used to compute the enthalpy of formation at 0 K. ΔH0f (0 K) thus

calculated is then corrected to 298 K. Curtiss et al. have described the methodolgy of

calculating the heat of formation of compounds optimized through density functional methods

[6]. The procedure has been established in Gaussian thermochemistry reference as well [7].

This has been employed for calculation of heat of formation of all the involved species for

CBS-QB3 results from Gaussian 09. For any molecule, such as Ax By Hz, the enthalpy of

formation at 0 K is given by:

ΔH0f (Ax By Hz , 0 K) = xΔH0

f (A, 0 K) + yΔH0f (B, 0 K) + zΔH0

f (H, 0 K) – ΣD0 (3.1)

where ΣD0 is the sum of calculated nonrelativistic atomization energies

ΔH0f experimental data for the atoms are taken from the gas phase ion and neutral

thermochemistry in the journal of physical and chemical reference data [20].

ΣD0(M) = Σatomsxε0(X) - ε0(M) - εZPE(M) (3.2)

where x is the number of constituent atoms

ε0(X) is the zero point of energy of the constituent atoms

ε0(M) is the total energy of the molecule

εZPE(M) is the zero point correction for the molecule.

Theoretical enthalpies of formation at 298 K are calculated by correction to ΔH0f (0 K) as

follows:

ΔH0f (Ax By Hz , 298 K) = ΔH0

f(Ax By Hz , 0 K) +

[H0(Ax By Hz , 298 K) - H0(Ax By Hz , 0 K)] –

x[H0(A, 298 K) - H0(A, 0 K)]st –

y[H0(B, 298 K) - H0(B, 0 K)]st –

z[H0(H, 298 K) - H0(H, 0 K)]st (3.3)

The heat capacity corrections in square brackets are treated differently for compounds and

elements. The formula shall be directly used for CBS-QB3 method as all the values are

known from the Gaussian 09 output directly. The heat capacity corrections for the elements

(H298-H0) are directly available in literature [7, 20].

A Osmont et al. have explained the procedure for computing the enthalpies of formation from

the data generated through Gaussian 09 [21]. This procedure is adopted for computing the

heat of formation of the species using B3LYP/6-31++G(d,p) results from Gaussian 09 as it

gives better match with the experimental data, whatever is available. The gas-phase standard

enthalpy of formation of molecule j at 298.15 K can be determined from the equation:

ΔH0f, 298.15 K (g) (kcal/mol) = 627.51 × (Ej + ZPEj + thermal corrections + ∑ 𝛼𝑖𝑐𝑖

∗𝑖 ) (3.4)

where αi : Number of atoms i in molecule j

𝑐𝑖∗ : Atomic correction for atom i (Hartree/atom)

Ej : Absolute electronic energy calculated using Gaussian 09

(Hartree/molecule)

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ZPEj : Zero-point energy, calculated using the Gaussian 09 (Hartree/molecule)

The atomic corrections for the atoms 𝑐𝑖∗ are determined by curve fitting of experimental

enthalpies of formation of certain compounds and were modified based on group-based and

atom-based corrections [21]. These corrections even though computed at B3LYP/6-31G(d,p)

technique, have been applied here based on the excellent match observed with experimental

values. The carbon atom corrections were selected for each compound based on the presence

of double bond as single and double bond presence demands application of different atomic

corrections. In the species which have been considered, cubane alone is treated as having

single carbon-carbon bonds. The heat of formation computed for all the species are given in

Table 2.

Table 2: Heat of formation of species: Computed and experimental (Gas phase)

Compound B3LYP/6-

31++G(d,p)

(kcal/mol)

CBS-QB3

(kcal/mol)

Experimental/

Reference data

[1, 22] (kcal/mol)

Cubane 144.221 148.326 142.710

Benzene 13.303 21.207 19.814

Acetylene 55.263 55.873 54.350

COT 67.586 74.908 71.128

BCT 78.258 82.724 79.111

STCO 121.782 123.163 117.830

SBV 75.068 75.116 -

DHP Biradical 113.976 114.289 -

BCT Intermediate 137.650 138.295 -

Phenyl acetylene 71.354 78.407 73.279

Hydrogen -1.111 -1.119 0.000

Styrene 28.502 37.437 35.110

BCB 41.541 49.152 47.658

Sty Inter 76.605 82.776 -

1,2-DHP 52.316 58.219 -

1,4-DHP 54.143 59.012 -

1,5-DHP 53.292 58.600 60.946

1,8-DHP 63.979 67.215 -

COT Inter 87.892 95.654 -

STCO Inter 180.440 189.685 -

The computed values using both CBS-QB3 and B3LYP methods show excellent match with

the experimental or already available computed data for almost all the species. Reliable data

sources were not available for certain species considered in the mechanism. A recent study

through Wn-F12 explicitly correlated thermochemical protocols states that the heat of

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formation of cubane is 144.8 kcal/mol, and suggests that the NIST thermochemical database

(142.7 ± 1.2 kcal/mol) is to be revised upwards by around 2 kcal/mol [23]. The computed data

matches closely with this recent prediction as seen in Table 4.5. The excellent prediction of

heat of formation for many species shows that this computational route can be used for

estimation of heat of formation of any unknown species. Data was generated in Gaussian 09

in the condensed phase also for all the species. However there is no standard procedure

available for computationally finding the heat of formation of condensed phase species, as all

the correlations in Gaussian thermochemistry for calculation of heat of formation are meant

for gas phase species alone.

3.3 Calculation of reaction rate constant

The critical role of transition state in controlling the rate of reactions was quantitatively

formulated from the potential energy surface concept [24]. The procedure for calculation of

rate constant or reaction rates from Gaussian 09 output is explained in 'Gaussian

Thermochemistry’ [7]. The variation of the rate of a reaction with temperature is described

using the Eyring–Polanyi equation. This equation could be applied to compute the rate

constants of the forward and reverse reactions for elementary reaction steps involving

transition states.

k (T) = 𝑘𝐵𝑇

ℎ𝑐𝑜 𝑒−∆‡𝐺𝑜

𝑅𝑇 (3.5)

where k(T) : Reaction rate constant

kB : Boltzmann constant (1.38064852 × 10-23 m2 kg s-2 K-1)

T : Temperature (K)

∆‡Go : Standard Gibbs energy of activation

R : Universal gas constant

co : standard state concentration (often taken as 1 mol/dm3)

This equation in chemical kinetics of transition state theory is derived from the statistical

thermodynamics in kinetic theory of gases [25, 26]. ∆‡Go can be calculated at each reaction

step for both reactants and products with respect to the corresponding transition state. The

forward and backward reaction rate constants can be calculated for each of the elementary

reactions and thus, suitable inferences can be made for these reactions in tandem with the

energy values obtained for the elementary reactions in the overall reaction pathway

mechanism. The value of co need to be considered based on the units of k(T). Considering the

units of k(T) in terms of (cm, s, mol, K), co needs to be taken as 1 for unimolecular reactions

and 1000 for bimolecular reactions) [25].

The rate constants can be matched better by multiplying the factor Ftunnel (Wigner correction)

with the calculated rate constant to account for the effects of quantum mechanical tunneling

[18]. However, the tunnelling factor is not applied while supplying the Arrhenius rate

coefficients to the CHEMKIN input format.

Ftunnel = 1 +1

24(

ℎ𝛾

𝑘𝐵𝑇)

2

(3.6)

19

where h : Planck’s constant (6.62607004 × 10-34 m2 kg / s)

𝛾 : Imaginary vibrational frequency (Hz)

kB : Boltzmann constant (1.38064852 × 10-23 m2 kg s-2 K-1)

T : Temperature (K)

The rate constants were computed for both gaseous and condensed phase for the reactions

considered in the present mechanism. The gaseous phase reaction rate constants were

calculated at a temperature of 573 K (sufficiently above the cubane boiling point temperature

of 434 K). The condensed phase calculations were carried out at 420 K (temperature lying in

between the melting and boiling point temperatures of 406 and 434 K respectively) [12]. The

results are shown in the table below. Wigner tunnelling is also computed corresponding to the

imaginary frequency and this factor is multiplied with the computed rate constant for better

match. The reaction number R1a has a very low forward reaction rate constant, implying that

the direct decomposition of cubane through a single transition state to STCO is a slow one on

account of its very high energy barrier. The reaction R1b signifying decomposition of cubane

to BCT also has a low reaction rate constant, though slightly better than R1a. The reverse

reaction becomes insignificant as is evident from the reaction rate which is orders of

magnitude lesser. The reaction R1c denotes the transformation of cubane to STCO

Intermediate through a transition state having the lowest activation energy of 41 kcal/mol

[13], which is followed by reaction R1d causing transformation of this compound to STCO

with an energy barrier of 15 kcal/mol. This mode of cubane decomposition has the highest

probability of occurrence at low temperatures based on the low energy barriers required for

the reactions as suggested previously [13]. However, the transition state for reaction R1c

could not be located and hence reaction rate constant has not been computed. Once the

temperature increases, the other pathways may also become active. The next reaction step R2

is having a rate constant which is around 14 orders of magnitude higher than the initial step,

signifying that once STCO is formed, its decomposition to the intermediate compound is a

quick reaction. The backward reaction rate constant shows a much higher amplitude but is not

much favourable as seen earlier from the energy point of view, where the decomposition of

this unstable compound to BCT, COT and stereomer of COT have an exothermic character.

Also, it might be possible that other transition states exist which facilitate the direct

conversion from STCO to BCT, COT or COT stereomer; which has not been covered in this

study. In reaction number R3, R6b and R7 where the intermediate compound decomposes to

BCT, COT stereomer and COT respectively, the forward reaction rate magnitudes are many

orders of magnitude higher than that of the reverse reaction and are highly favoured, also

from energy point of view. The reaction R4, signifying the conversion of BCT to COT is a

very rapid one, leading to the conclusion that COT shall be a major product in the reaction

since this reaction is favourable from the energy values also. The conversion of BCT to

benzene and acetylene in reaction number R5 is a comparatively slow one compared to

conversion to COT and hence, it could be inferred that the composition of the decomposition

reaction products shall depend on temperature of the mixture. This is because, as temperature

is varied, the reaction rate constant of reactions R4 and R5 change, and hence the production

of COT or benzene and acetylene will be a compromise between the energy values and the

rate constants.

20

Table 3: Rate constants – Gas phase

Reaction

No.

B3LYP/6-31++G(d,p) CBS-QB3

Forward rate

constant*

Backward rate

constant*

Forward rate

constant*

Backward rate

constant*

R1a 1.8x10-13 1.6 x10-24 1.0 x10-12 1.1 x10-23

R1b 1.3x10-13 2.1 x10-41 5.5 x10-9 1.1 x10-35

R1c - - - -

R1d 3.9x107 2.5 x10-17 2.0 x107 9.8 x10-19

R2 9.3x101 8.8 x107 1.4 x102 5.3 x107

R3 1.6 x10-2 2.9 x10-25 1.3 x10-4 6.3 x10-26

R4 3.6 x106 1.7 x102 9.8 x105 3.1 x102

R5 4.5 x10-13 3.5 x10-18 1.3 x10-15 3.0 x10-23

R6a 2.3 x10-4 8.4 x10-1 2.4 x10-3 7.2 x10-2

R6b 3.8 x108 2.0 x10-11 1.4 x108 2.0 x10-9

R6c 2.9 x10-5 4.7 x105 8.4 x10-5 3.2 x103

R7 3.1 x108 2.7 x10-19 1.7 x107 2.6 x10-18

R8 3.1 x10-19 5.5 x10-23 3.0 x10-17 1.2 x10-23

R9a 8.8 x1010 8.8 x10-9 2.1 x108 3.8 x10-10

R9b 2.8 x105 4.3 x101 5.7 x104 2.9 x101

R9c 3.9 x10-7 1.0 x10-11 1.7 x10-7 3.3 x10-11

R9d 1.1 x103 6.0 x102 5.4 x102 4.8 x102

R10 1.2 x10-14 4.3 x10-34 2.5 x10-23 1.1 x10-41

R11 9.4 x10-14 1.2 x10-27 8.0 x10-15 1.9 x10-27

R12 1.2 x10-34 3.7 x10-40 7.4 x10-35 1.4 x10-40

R13a 1.1 x10-24 2.2 x10-11 1.3 x10-24 6.6 x10-12

R13b 2.2 x108 3.2 x10-11 4.1 x107 1.5 x10-11

R14 1.1 x10-28 2.2 x10-14 1.8 x10-30 8.9 x10-20

* Rate constant has unit s-1 for unimolecular and cm3mol-1s-1 for bimolecular reactions respectively

The transformation of COT to SBV through reaction R6a doesn’t have a very high reaction

rate constant, but the equilibrium between the two compounds shall depend on the

temperature of the mixture and energy available after the previous elementary reaction steps.

In previous studies, it was reported that COT samples when heated at greater than 270 ᵒC

yields SBV and this yield increases with temperature [15]. The reaction R6c which

demonstrates the formation of BCD biradical from the COT stereomer also has similar low

reaction rate constant, but shall be enhanced in the environment enriched by sufficient energy

from previous elementary reactions. The previous study on thermal stability of SBV points to

an intermediate biradical in the transformation to COT [15], which appears to be the

compound BCD biradical and this is an important intermediate in the formation of DHPs.

21

Table 4: Rate constants – Condensed phase

Reaction

No.

B3LYP/6-31++G(d,p) CBS-QB3

Forward rate

constant*

Backward rate

constant*

Forward rate

constant*

Backward

rate constant*

R1a 6.3 x10-21 3.7 x10-36 1.3 x10-21 8.5 x10-36

R1b NA NA NA NA

R1c - - - -

R1d 3.5 x105 3.0 x10-28 1.3 x105 2.7 x10-30

R2 8.2 x10-3 7.3 x10+5 1.4 x10-2 6.2 x105

R3 NA NA NA NA

R4 1.1 x104 1.3 x10-2 2.1 x103 7.8 x10-2

R5 2.1 x10-20 5.8 x10-29 6.1 x10-25 2.6 x10-31

R6a 1.3 x10-10 9.7 x10-6 1.0 x10-8 1.2 x10-7

R6b 5.4 x106 3.3 x10-20 1.8 x106 5.0 x10-17

R6c 1.2 x10-11 7.7 x102 9.1 x10-11 9.9 x10-1

R7 7.3 x106 9.6 x10-31 1.2 x105 4.3 x10-29

R8 2.6 x10-30 1.0 x10-36 3.5 x10-30 2.9 x10-35

R9a 1.4 x1010 2.0 x10-16 6.0 x106 2.3 x10-18

R9b 4.7 x102 2.8 x10-3 7.9 x101 3.3 x10-3

R9c 9.4 x10-14 4.4 x10-20 4.1 x10-15 4.7 x10-20

R9d 2.5 x10-1 1.1 x10-1 1.7 x10-1 1.3 x10-1

R10 NA NA NA NA

R11 4.5 x10-23 5.0 x10-42 8.0 x10-25 3.7 x10-42

R12 NA NA NA NA

R13a 4.7 x10-38 6.9 x10-20 3.9 x10-38 1.1 x10-20

R13b 3.2 x106 3.2 x10-20 4.9 x105 1.5 x10-19

R14 3.2 x10-43 5.3 x10-25 3.2 x10-45 3.3 x10-27

NA – Data not available; Transition state not available in condensed phase

* Rate constant has unit s-1 for unimolecular and cm3mol-1s-1 for bimolecular reactions respectively

The reaction R8 showing decomposition of BCT to PA and hydrogen has very low reaction

rate constants, but shall be feasible in thermally favouring environments. The reverse reaction

leading to formation of BCT however remains improbable on account of further lower

reaction rate constant value. The forward reaction rate constant of reaction 9a shows the swift

transformation of BCD biradical to 1,8-DHP. The reverse reaction is unlikely on account of

the rate constant which is orders of magnitude lesser than the forward one. The transformation

of 1,8-DHP to 1,4-DHP is the favoured pathway in comparison with the transformation of

1,8-DHP to 1,2-DHP on grounds of the reaction rate constant values. The transformation of

1,4-DHP to 1,5-DHP is also feasible based on the higher rate constant values. However, these

two compounds might be in equilibrium with each other, as the reverse reaction rate constants

are also considerable. The reaction R10 showing direct transformation of BCT to styrene is

not a preferred pathway on account of the very low reaction rate constant in addition to the

high energy barrier which was discussed earlier. The reaction R11 involves transformation of

BCT to BCB, and has a low reaction rate constant, even though it is many orders better than

R10. BCB decomposition to styrene through a single transition state as in R12 also has a very

22

low rate constant, however it might be feasible in the environment where adequate energy has

been released in the previous reaction steps. The conversion of BCB to Styrene Intermediate

also requires favourable reactor conditions as the rate constant of the forward reaction is low

by itself, and is lesser than the backward reaction as well. However, in case where this

intermediate compound is formed, its conversion to styrene is a highly favoured reaction on

account of its high reaction rate constant. The equilibrium of styrene with benzene and

acetylene is shown through reaction R14, where the formation of styrene is favoured under

the computed temperature conditions. However, this equilibrium may shift depending on the

temperature and the reactor conditions.

3.4 CHEMKIN simulation results

The detailed reaction mechanism has been studied from an energy perspective and by

analysing the reaction rate constants separately. But a complete picture of the reaction

mechanism involving the decay and growth of each species over time or with reactor

geometry in case of a flow reactor shall depend on all these parameters collectively. This

comprehensive study of the chemical kinetics of cubane decomposition shall be analysed by

means of CHEMKIN software package [27]. This requires thermodynamic data and gas phase

kinetics data of all the species to be provided as an input file [28]. Thermodynamic data

includes the species name, elemental composition, low and high temperature range details,

and the NASA polynomial coefficients (seven each for high and low temperature range).

Thermodynamic data of certain species are available in literature and can be used directly

[29]. For the other species considered in the mechanism, the polynomials have to be generated

by carrying out curve fitting with molar entropy, heat capacity, and enthalpy content using the

following correlations:

𝐶𝑝𝑖

𝑅= 𝑎1𝑖 + 𝑎2𝑖𝑇 + 𝑎3𝑖𝑇2 + 𝑎4𝑖𝑇

3 + 𝑎5𝑖𝑇4

ℎ𝑖

𝑅𝑇= 𝑎1𝑖 +

𝑎2𝑖

2𝑇 +

𝑎3𝑖

3𝑇2 +

𝑎4𝑖

4𝑇3 +

𝑎5𝑖

5𝑇4 +

𝑎6𝑖

𝑇

𝑠𝑖

𝑅= 𝑎1𝑖 log𝑒 𝑇 + 𝑎2𝑖𝑇 +

𝑎3𝑖

2𝑇2 +

𝑎4𝑖

3𝑇3 +

𝑎5𝑖

4𝑇4 + 𝑎7𝑖

These ideal-gas thermodynamic functions (molar entropy, heat capacity, and enthalpy

content) are not directly available in the Gaussian 09 output. They can be computed at several

temperatures using the essential data from the Gaussian 09 output by means of a Perl script

from NIST [30]. This data generated at both high (1000 K – 6000 K) and low (200 K - 1000

K) temperature ranges is used for generating the NASA polynomial coefficients by means of

curve fitting, using the data at certain known points and the heat of formation at 298 K of the

concerned species. Thus the thermodynamic data section is prepared. The gas phase kinetics

data is already available for all the elementary reactions, but needs to be manipulated to suit

the CHEMKIN input which interprets the data in the form of modified Arrhenius equation.

23

𝑘 = 𝐴𝑇𝑏𝑒−𝐸𝑎

𝑅𝑇⁄

Arrhenius coefficient (A), temp factor (b) and activation energy (Ea) for all the reactions were

extracted from the already available data as used in the Eyring-Polanyi equation for rate

constant computation, and used for the gas phase kinetics input section as mentioned in the

guidelines available in literature [25].

Two types of reactor models were used in CHEMKIN for simulating the decomposition

mechanism. The homogenous closed reactor was considered for knowing the mole fraction of

the components after complete combustion. The initial temperature is specified in the model

and the growth and decay of various species with time is analysed. This analysis is carried out

for different initial temperatures for understanding the effect of product composition on

complete combustion. Plug flow reactor was also selected for generating the comparison with

the experimental data [1]. The activation energy required for direct transformation of cubane

to STCO is around 69 kcal/mol, which doesn’t favour the cubane decomposition at

temperatures of 573 K. The transition state for the first step in the two step decomposition

process involving cubane transformation to the compound STCO Intermediate could not be

located, and hence the pre-exponential factor for the Arrhenius form has to be borrowed from

other similar reactions, even after considering the activation energy as 41 kcal/mol from

literature [13]. However, this requires the inhibition of the reverse reaction to cubane in the

simulation input in order to induce the reaction leading to formation of STCO. This is

expected, as the heat of formation of the compound ‘STCO Intermediate’ is around 189

kcal/mol, which is higher than that of cubane and its reverse reaction to cubane is barrierless.

The possibility that another lower energy transition state might exist in the direct path from

cubane to STCO is very strong. The pre-exponential factor computed earlier is used along

with an activation energy barrier of 41 kcal/mol.

Closed homogenous batch reactor

The simulations have been carried out for a constant pressure condition inside a closed

homogenous reactor and the energy equation was solved till steady state was attained for

various initial temperature conditions. The steady state temperature value increases along with

the initial temperature. It could be conclusively established that the final products is a mixture

of benzene, acetylene, PA and hydrogen. The relative mole fraction of each component varied

in correspondence with the initial temperature. The typical temperature profile variation with

time and the variation of mole fractions of the final products with different initial

temperatures are shown below in Figure 4.3 and 4.4 respectively.

24

As mentioned in previous studies, COT also develops as a major product at one stage of the

reaction as shown in Figure 4.5. However, in this reaction mechanism where all the reactions

are considered simultaneously in a closed reactor, the energy released during the previous

reactions is sufficient enough for its further decomposition as is evident from the enormous

temperature increase at that point as shown in Figure 4.3. DHPs are also getting slowly

decomposed to the final products as shown in Figure 4.5. Styrene is also formed in minor

quantities, which decomposes slowly over time.

Figure 5: Closed Reactor-Temperature increase profile for inlet temperature of 773 K

Figure 6: Closed reactor-Product distribution at steady state for different initial

temperatures

25

(a) Larger time step – final products evolving from reaction

(b) Minor time step showing intermediate products formation

Plug flow reactor

Simulations were carried out in a plug flow environment also in order to compare the

computed reaction mechanism with the available experimental data. Cubane in its gas phase is

considered to be mixed with Argon as done for the experiment [1]. Mole fraction of Argon

and cubane are taken as 0.93 and 0.07 respectively. The reactor dimensions (Length of 10 cm,

diameter of 1.9 mm), pressure (1.7 Torr) and flow velocity were fixed to simulate the

experimental conditions [1] and simulations were carried out at different temperatures to

Figure 7: Closed reactor-Evolution of species during cubane decomposition

26

analyse the product composition at the flow reactor exit. The flow velocity was roughly

computed as 32.25 m/s assuming a residence time of 3.1 ms for the species inside the reactor.

The major difference observed in comparison with the closed reactor was that the mixture of

species was not reaching steady state, and hence many more species could be detected at the

reactor exit depending on the inlet temperature. The relative mole fraction of the different

species at the reactor exit showed variations for different inlet temperature conditions. The

model has the provision to either solve the gas energy equation or keep the gas temperature

constant. The simulations were carried out by solving the gas energy equation, which causes

increase in the surface as well as gas temperature along the axial length of the reactor. The

temperature profile of the gas (as well as the reactor surface) along the axial direction of the

plug flow reactor is shown in Figure 4.6. The exothermic nature of the major elementary

reactions accelerates the cubane decomposition process, and this causes sudden rise in

temperature along the axial direction. This higher temperature can cause further

transformation of the intermediate products. However, such a steep temperature rise may not

be physically happening in a flow reactor, but a faster cubane disappearance is expected in the

simulation due to the aforesaid reasons.

Figure 8: Plug flow reactor: Temperature variation in axial direction

27

The experimental data shows the intensity data, and hence a direct one-to-one comparison is

not possible with the simulation data wherein mole fraction has been used. In the simulation

model, cubane shows the onset of decomposition at around 623 K, which is very close to

experimental results where initiation of decomposition is mentioned to be above 573 K. The

detailed behaviour of the C8H8 compounds and the decomposition products are shown in

Figure 4.8 and 4.9. The model considers the exothermic nature of many elementary reactions

causing acceleration of cubane decomposition and steep temperature rise, which might not be

happening in the experimental case.

Figure 9: Plug flow reactor: Comparison of experiment and simulation results

Figure 10: Plug flow reactor: Comparison of C8H8 compounds in experiment and simulation

28

COT behaviour in simulation and experiment shows close match in behaviour, except for a

minor difference in the temperature at which peaking is observed. The experiment data has

not considered/detected presence of DHPs, while in simulation data, they are evident. The

presence of DHPs in cubane decomposition has been reported previously [11, 14]. The

experiment data has shown presence of styrene at higher temperatures which could possibly

be DHPs, since the molecular mass of both these compounds are equal and the presence of

DHPs were not analysed in the experiment. The simulation shows styrene presence in trace

quantities only.

Benzene and acetylene are identified in both experiment as well as simulations. The complete

decomposition of cubane in closed reactor showed benzene and acetylene as a major product,

whereas in the flow reactor, it is developing at higher temperatures only probably due to the

low pressures and the presence of inert gas at high velocity flow conditions. The trend of

increasing benzene and acetylene composition is visible in the experiment data as well. PA

and hydrogen evolvement during the reaction in simulation is almost matching with that of

the experimental results.

4. Conclusion

The thermal decomposition pathway of cubane through computational route has been

validated by comparison with the already available theoretical and experimental data. COT,

benzene, acetylene, DHPs, PA and hydrogen were identified as the major species which get

revealed during cubane decomposition. Heats of formation values for all the species have

been computed and both B3LYP and CBS-QB3 methods give good predictions as compared

with the literature data. NASA polynomials have been generated for all the species in the

reaction pathway wherever reference data is not available. The rate constants were calculated

Figure 11: Plug flow reactor: Comparison of decomposition products in

experiment and simulation

29

for the elementary reactions and it was found that once cubane is decomposed to STCO or

BCT, subsequent reactions occur very fast. Simulations carried out with rate constant

parameters have given insight into the variations of mole fractions of various species in

accordance with temperature under plug flow conditions. STCO and BCT are the major

intermediate products formed during cubane decomposition.

The computational methodology has been validated to devise the decomposition pathway

mechanism of cubane, thereby enabling us to propose the similar methodology to be applied

on other high energy compounds as well. Also, these results may give inroads into the

exploration of similar compounds of cubane with more functional groups and their shorter

routes of synthesis.

30

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