Bicyclic CN₂O₂ as a high-energy density material: promising or not?

Abstract

Besides their fundamental importance, compounds containing C, N and O have great potential as so-called “high-energy density materials” (HEDMs). Due to their explosive nature, HEDMs usually have great difficulty in laboratory synthesis and characterization. Thus, reliably finding a HEDM candidate with good kinetic stability (i.e., rate-determining barrier is above 20 kcal mol⁻¹) in computation has proven to be a key base for the subsequent experimental study, as well as being documented by two recent examples, i.e., diazirinone ([C,N₂,O]-A, Angew. Chem., Int. Ed., 2011, 50, 1720) and nitryl cyanide ([C,N₂,O₂]-B, Angew. Chem., Int. Ed., 2014, 53, 6893). What is the next synthetic target for molecular HEDMs? Having been predicted to possess both large exothermicity (190 kcal mol⁻¹) and a large decomposition barrier to N₂ + CO₂ (29 kcal mol⁻¹) at the CCSD(T)/TZ2P//MP2/6-31G(d) level (J. Phys. Chem., 1996, 100, 19840), C with a bicyclic [C,N₂,O₂] structure appears to well deserve a synthetic trial for HEDMs. In this work, by re-evaluating the stability of C, we located a new rate-determining transition state for decomposition (TS2). With TS2, a significantly reduced decomposition barrier was arrived at, i.e., 11.6–13.0 kcal mol⁻¹ at the G3B3, CBS-QB3, G4, W1BD and CCSD(T)_CBS//B3LYP/aug-cc-pVTZ composite energy calculated levels using a restricted wave function. Strikingly, TS2 possesses a significant open-shell feature and the barrier was further reduced to be 6.9 kcal mol⁻¹ at the UCCSD(T)_CBS//UB3LYP/aug-cc-pVTZ level. Thus, the bicyclic isomer C is unlikely to be a molecular HEDM, though its spectroscopic detection could still be feasible. Finally, the ring-opening stability of the c-CO₂ moiety in the present [C,N₂,O₂]-C largely contrasts with that in the well-known methyldioxirane, demonstrating a different influence on the complexation to c-CO₂.

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1. Introduction

Due to the great energy necessities at present, scientists have been devoted to seeking novel energetic species to replace traditional fossil fuels. Carbon (C), nitrogen (N) and oxygen (O) are very important elements both on Earth and in space. Besides, they can form very stable multiply bonded diatomic or tri-atomic molecules, e.g., CO, N₂ and CO₂ with bond energies of 256.5, 225.4 and 382.3 kcal mol⁻¹, respectively.¹ This has raised great hope for developing the so-called high-energy density materials (HEDMs). In general, energetic compounds containing light and nonmetallic elements (i.e., C, N, O, etc.) are superior in explosiveness and environmentally benign compared to heavy-metal-based explosives. Thus, study of such HEDMs has never ceased, though the number of successful examples grows slowly because of the synthetic difficulties.^2–6

What makes a molecular HEDM? First, the most feasible pathway of the molecule should release a large amount of energy upon unimolecular decomposition to CO, N₂ or CO₂. Second, the barrier of the most feasible pathway (also named as “rate-determining barrier”) is larger than 20 kcal mol⁻¹ in order to be persistent for further application and handling.⁷ That is, the molecule should be “thermodynamically quite unstable and yet kinetically very stable”. The two factors are so critical that most molecules cannot satisfy both.

The HEDMs study faces two rigorous challenges. One is to computationally find a candidate with both high energy and high barrier towards decomposition. The other is to find suitable synthetic routes and conditions for the candidate and then experimentally realize it. A computational proof for a kinetically stabilized energetic molecule would greatly encourage synthetic chemists to work on that molecule. On the contrary, a negative proof of a molecule to act as a HEDM would to a large extent reduce or block meaningless synthetic attempts. To help lower the synthetic cost, a reliable computational prediction on the intrinsic stability of a HEDM would be highly desired. Growing examples have firmly demonstrated that the identification of an excellent candidate predicted computationally should be just a matter of time! (e.g., see the ref. 2, 4–6 and 8–12).

The simplest HEDM containing C, N and O is [C,N₂,O]. In 1994, Korkin et al. proposed that a three-membered ring structure A (diazirinone) (see Scheme 1) could be feasible as a HEDM since A has large exothermicity (around 100 kcal mol⁻¹) yet is highly resistant to decomposition to N₂ + CO (the barrier is 27 kcal mol⁻¹).¹⁰ In 2011, Zeng et al. confirmed the existence of A via IR spectrum in the photolysis process of gaseous OC(N₃)₂.⁴ The second C, N, O-containing HEDM family is [C,N₂,O₂]. In 1996, Bartlett and coworkers theoretically explored the potential energy surface of [C,N₂,O₂].¹¹ Among the various structures they obtained, they found that a branched isomer B (nitryl cyanide) and a bicyclic isomer C (see Scheme 1) both contain large exothermicity (150 and 190 kcal mol⁻¹, respectively) and high decomposition barrier (54 and 29 kcal mol⁻¹, respectively) to N₂ + CO₂ at the CCSD(T)/TZ2P//MP2/6-31G(d) level. Since their barriers surpassed the general energy threshold 20 kcal mol⁻¹,⁷ both B and C were proposed as potential molecular HEDMs at that time. Inspiringly, B was very recently (in 2014) synthesized via the reaction between tBuMe₂SiCN and NO₂BF₄ in nitromethane at −30 °C.² Note that existence of the chainlike OCNNO with much lower energy than B and C has been experimentally verified by several groups.^13,14 Since there exists very easy cis-trans interconversion of OCNNO and the decomposition barrier to N₂ + CO₂ is less than 20 kcal mol⁻¹,^11,15 we would not consider OCNNO as a typical HEDM.

Scheme 1 Structures of compounds containing C, N and O reported in previous literature references.

A and B are two nice HEDMs examples that were earlier computationally predicted and later experimentally verified. What could be the next synthetic target for the molecular HEDMs after A and B? Scrutinizing the available computational references, it seems that we already have a good HEDM candidate at hand, i.e., the bicyclic [C,N₂,O₂] isomer C, which possesses predicted high exothermicity (by 40 kcal mol⁻¹ larger than the synthesized B) and a high decomposition barrier (29 kcal mol⁻¹).¹¹ As is the case for B, if the stability of C can be well confirmed, it should have sufficient interest for synthetic chemists. Unfortunately, during the re-evaluation of the stability of C in this work, we found that C seems unlikely to act as a molecular HEDM! A previously unreported decomposition transition state TS2 was located, which could significantly reduce the decomposition barrier of C to be less than half of the previously reported value via TS1 at the G3B3, CBS-QB3, G4, W1BD and CCSD(T)_CBS//B3LYP/aug-cc-pVTZ levels.

2. Computational methods

All calculations were carried out with GAUSSIAN03 and GAUSSIAN09 program packages.¹⁶ The geometrical and frequency calculations of the stationary points (both minima and transition states) were performed at the B3LYP/aug-cc-pVTZ level. To ensure accurate description of the energies of key structures, we applied various theoretical methods including (1) single-point energy calculations at the CCSD(T)/aug-cc-pVTZ and CCSD(T)/aug-cc-pVQZ levels based on the B3LYP/aug-cc-pVTZ geometries, (2) the standard composite methods such as G3B3,¹⁷ CBS-QB3,¹⁸ G4 ¹⁹ and W1BD,²⁰ which have been designed to satisfy the thermochemical accuracy within several kcal mol⁻¹, and (3) the complete basis set (CBS) limit extrapolation based on the CCSD(T)/aug-cc-pVTZ and CCSD(T)/aug-cc-pVQZ energies (denoted as UCCSD(T)_CBS//UB3LYP/aug-cc-pVTZ).²¹ The zero-point vibrational energy (ZPVE) corrections were automatically included in the G3B3, CBS-QB3, G4 and W1BD calculations, whereas in the UCCSD(T)_CBS//UB3LYP/aug-cc-pVTZ study, the ZPVE correction was manually added. The connection of each transition state was checked by the intrinsic reaction coordinate (IRC) method at the B3LYP/6-31G(d) level.

3. Results and discussion

According to the general criteria of a HEDM, a species should be (1) thermodynamically quite unstable with respect to the most feasible fragments, and (2) kinetically very stable with the least decomposition barrier of more than 20 kcal mol⁻¹.⁷ The first point can be evaluated easily. Yet, the second point is usually challenging since one has to consider various possible pathways. In the following discussions, we will discuss the properties of isomer C in terms of its structure, heat and barrier.

3.1. Structure

The optimized structure of C at the B3LYP/aug-cc-pVTZ level was shown in Fig. 1. The two three-membered ring planes of C, i.e., c-CN₂ and c-CO₂, are perpendicular to each other, resulting in a C_2v-symmetry. The two identical C–N bonds (1.390 Å) are significantly shorter than the typical single bond (1.465 Å in H₃CNH₂ computed at the B3LYP/aug-cc-pVTZ level in this work). The N–N bond distance 1.275 Å is just slightly longer than the typical double bond (1.235 Å in trans-HNNH), and far shorter than the single bond (1.480 Å in H₂NNH₂). The somewhat elongation of the N=N bond must be caused by the strain within the c-CN₂ ring. Accordingly, the π-bonding of NN (HOMO−6 in Fig. 2) is delocalized to the peripheral C–N bonds, leading to the severe shortening of C–N. Such a bond-averaging situation also occurs in the c-CO₂ moiety. The O–O bond (1.549 Å) is longer than the typical single bond (1.451 Å in HOOH) (also caused by the ring strain). The reduced O–O electronic density (HOMO−5 in Fig. 2) is delocalized to the peripheral C–O bonds that have a much shorter C–O bond (1.351 Å) than a typical single bond (1.424 Å in CH₃OH).

Fig. 1 Geometrical parameters (Å) and point group of C, D, TS1, TS2, (U)TS2, TS3 at the B3LYP/aug-cc-pVTZ level.

Fig. 2 Representative valence molecular orbitals of C at the B3LYP/aug-cc-pVTZ level.

3.2. Heat

The released heat of isomer C to the eventual product N₂ + CO₂ is listed in Table 1. It can be seen that various methods predict a huge exothermicity for C towards fragmentation, i.e., ca. 190 kcal mol⁻¹. The value is much larger than those of the experimentally known A (96 kcal mol⁻¹)^8,10 and B (150 kcal mol⁻¹).¹¹ This can be expected since C has only one double bond (N=N) and five single bonds (i.e., two C–N, two C–O and one O–O), and these six bonds are all converted into the very stable molecules N₂ and CO₂ with the strong N≡N and cumulenic O=C=O bonding, respectively. Simply based on the bond energy from references,¹ the reaction heat can be obtained as 132.5 kcal mol⁻¹ for C → N₂ + CO₂. The large difference between our computed and the estimated value could mostly be ascribed to the inherent strain energy within the two rings.²² As a result, C seems to be very suitable as a HEDM in thermodynamics.

Table 1 Relative energies (kcal mol⁻¹) of C, D, TS1, TS2, (U)TS2, TS3 and the corresponding decomposition products

	C (C2v)	D (C1)	TS1 (Cs)	TS2 (C2v)	(U)TS2^a (C2v)	TS3 (C1)	N2 + CO2	N2 + c-CO2
a The calculation is performed with electronic unrestricted method.
B3LYP/aug-cc-pVTZ	0.0	36.3	29.3	14.4	8.8	43.1	−189.7	−46.5
G3B3	0.0		29.9	12.4			−189.2	−48.5
CBS-QB3	0.0		29.5	11.9			−187.5	−47.7
G4	0.0		29.9	11.6			−188.0	−48.6
W1BD	0.0		30.5	13.0			−189.0	−48.6
CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ	0.0	43.1	29.3	12.4	6.2	48.4	−186.0	−49.3
CCSD(T)/aug-cc-pVQZ//B3LYP/aug-cc-pVTZ	0.0		29.8	12.8	6.6		−187.4	−52.5
CCSD(T)_CBS//B3LYP/aug-cc-pVTZ	0.0		30.0	13.0	6.9		−188.3	−54.9

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3.3. Barrier

To determine the intrinsic kinetic stability of C, the consideration of various possible isomerization and fragmentation pathways is indispensible. After numerous attempts, three processes were identified to be associated with the transition states TS1, TS2 and TS3 respectively. Note that TS1 was also reported by Bartlett et al. in 1996,¹¹ while TS2 and TS3 were studied for the first time in this work. The bond lengths in the c-CO₂ ring of TS1 are almost the same as those (1.340 and 1.549 Å, respectively) of the isomer C. However, in the c-CN₂ ring, the two C–N bonds are unequivalently elongated to 1.531 and 1.792 Å (both longer than the typical C–N single bond), whereas the N–N distance 1.187 Å is close to that (1.091 Å) of the N≡N triple bond. Overall, TS1 describes the leaving process of N₂ while keeping c-CO₂ intact. In fact, the IRC calculations showed that TS1 is connected to C and P₂ N₂ + c-CO₂ rather than to C and P₁ N₂ + CO₂. This was not revealed in the 1996 study.¹¹ Surely, the large released heat (more than 46 kcal mol⁻¹ for C → P₂) could easily drive the ring-opening of c-CO₂ to the linear CO₂.²³ The evolutation of C to P₂ N₂ + c-CO₂ is shown in Fig. 3a. Strikingly, the three single-step energy calculation methods, i.e., B3LYP/aug-cc-pVTZ, CCSD(T)/aug-cc-pVTZ and CCSD(T)/aug-cc-pVQZ at the B3LYP/aug-cc-pVTZ-optimized structures, give very similar predictions to the composite methods G3B3, CBS-QB3, G4, W1BD and CCSD(T)_CBS. In all, the decomposition barrier is calculated to be around 30 kcal mol⁻¹, and is very close to the value 29 kcal mol⁻¹ predicted by Bartlett et al. at the CCSD(T)/TZ2P//MP2/6-31G(d) level. Thus, the N₂-leaving process of C can be well described by various quantum chemical methods.

Fig. 3 The intrinsic reaction coordinate (IRC) connection of transition states (a) TS1 and (b) TS2 at the B3LYP/6-31G(d) level.

Unlike TS1, the newly located TS2 with C_2v symmetry is related to the concerted and one-step decomposition of C to N₂ + CO₂, as shown by the IRC curve in Fig. 3b. In the c-CN₂ moiety of TS2, the two C–N (1.452 Å) bonds are elongated, whereas the N–N bond (1.239 Å) is shortened, in comparison with the respective C–N (1.390 Å) and N–N (1.275 Å) bond lengths in isomer C. In addition, in the c-CO₂ moiety, the two C–O (1.307 Å) bonds are shortened and one O–O (1.866 Å) bond becomes lengthened compared to the bonds in C. Energetically, the barrier of such a cooperative N₂ and CO₂-leaving process amounts to 11.6–14.4 kcal mol⁻¹ at the eight computational levels. The B3LYP/aug-cc-pVTZ level predicts the highest value of 14.4 kcal mol⁻¹. Clearly, the decomposition barrier via TS2 is less than half of the value (29.3–30.5 kcal mol⁻¹) via the non-concerted TS1.

The wave function stability diagnostics showed that TS2 has “wave function instability”, whereas C and TS1 are stable. Thus, we used the “guess = (mix, always)” keyword to break the orbital symmetry of TS2 at the unrestricted level. With the new TS2 (we denote (U)TS2), the barrier becomes significantly lowered to 8.8 kcal mol⁻¹ at the UB3LYP/aug-cc-pVTZ level. As the standard composite methods G3B3, CBS-QB3, G4 and W1BD have not been developed for the open-shell singlet cases, we only considered the unrestricted calculations at the UCCSD(T)/aug-cc-pVTZ and UCCSD(T)/aug-cc-pVQZ level using the UB3LYP/aug-cc-pVTZ geometries. The two high-level single-point energy barriers are 6.2 and 6.6 kcal mol⁻¹, respectively. If we extrapolate to the complete basis set (CBS) limit, then we obtain a barrier of 6.9 kcal mol⁻¹. Thus for TS2, the barrier based on the open-shell wave function is more reliable than that based on the closed-shell wave function. It's interesting to discover that in the couple-cluster procedure, the convergence from the triple zeta to the quadruple zeta basis set excitation and to the CBS limit is quite good for both the restricted and unrestricted wave functions. Finally, the T1 diagnostic values of C, TS1, TS2 and (U)TS2 are 0.016, 0.021, 0.029 and 0.019, respectively. Being smaller than or around 0.02,²⁴ the present calculations for C, TS1 and (U)TS2 based on the single-determinant should be reliable.

The newly found TS3 is associated with another kind of ring-opening process for both c-CN₂ and c-CO₂ rings. As for TS3, we can see that the N=N bond and one of the C–O bonds are cleaved to give a branched isomer D, lying 43.1 kcal mol⁻¹ above C. Understandably, such a ring-opening barrier is as high as 48.4 kcal mol⁻¹ at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level. The reverse ring-closure barrier is as small as 5.3 kcal mol⁻¹. Since TS3 cannot compete with TS1 and TS2, other high-level or composite calculations were not conducted further for TS3 and isomer D.

The significant energy ordering of the three barriers, i.e., 14.4 (TS2), 29.3 (TS1), and 48.4 (TS3) kcal mol⁻¹ at the RCCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level, correlates well with the simple bond energy considerations. In the bicyclic isomer C, the bond energies of O–O, C–O, C–N and N=N are 142, 358, 305 and 418 kJ mol⁻¹, respectively.¹ Clearly, the rupture of the O–O bond (followed by the concerted C–N cleavage) via TS2 should be the easiest in kinetics, in accordance with our calculation.

The most important finding of the present study is that we located a previously unknown transition state TS2 for the decomposition of the bicyclic isomer C, which results in the concerted formation of N₂ and CO₂. With this new transition state, the rate-determining barrier of C is refined to be 11.6–13.0 kcal mol⁻¹ at the G3B3, CBS-QB3, G4, W1BD, CCSD(T)_CBS//B3LYP/aug-cc-pVTZ levels with inclusion of ZPVE. Consideration of the open-shell feature of TS2 further lowers the value to be 6.9 kcal mol⁻¹ at the ZPVE-corrected UCCSD(T)_CBS//UB3LYP/aug-cc-pVTZ level. Clearly, as to the usage of a molecular HEDM, that value should be considered as being far from sufficient, compared to the threshold (20 kcal mol⁻¹) that has been widely accepted.⁷ We thus conclude that the bicyclic C has little hope to be a candidate for HEDMs!

It is worth mentioning that the failure of C to act as a HEDM does not exclude its spectroscopic detection. In fact, irrespective of intermolecular reactivity, the lifetime of a species is influenced by temperature, pressure and concentrations. Under very extreme conditions, e.g., 4 K in a He matrix, or in high vacuum, the rate-determining barrier of only 1 kcal mol⁻¹ or even less is enough to make a species detectable.²⁵ Therefore, for C, the rate-determining barrier height of 6.9 kcal mol⁻¹ at the UCCSD(T)_CBS level would render its laboratory characterization via spectroscopic techniques at low temperatures. By means of the conventional transition state theory by considering TS2 as the rate-determining activated complex, we computed the rate coefficient of C at the UCCSD(T)_CBS//UB3LYP/aug-cc-pVTZ level²⁶ at three temperatures (100, 200 and 298.15 K). Based on the rate coefficients, we can obtain the corresponding half-life of C (see Table 2). The key spectroscopic parameters of C (harmonic vibrational frequencies, rotational constants, and dipole moment) computed at the analytic CCSD/aug-cc-pVTZ level were also provided in Table 2.

Table 2 The key spectroscopic parameters including harmonic vibrational frequencies M_freq (cm⁻¹) with infrared intensity (km mol⁻¹) in parentheses, rotational constants R (GHz) and dipole moment D (Debye) of C at the CCSD/aug-cc-pVTZ level, and the half-life of C at different temperatures

	Mfreq (cm^−1)	R (GHz)	D (Debye)	t1/2^298.15 K (s)	t1/2^200 K (s)	t1/2^100 K (s)
C	435.8 (0), 479.9 (14), 484.0 (12), 649.4 (6), 919.6 (0), 1078.1 (33), 1124.2 (5), 1444.4 (19), 1778.4 (245)	3.78572, 0.79679, 0.65831	8.3193	1.2 × 10^−8	5.4 × 10^−6	376.4

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With the large exothermicity of the ring-opening process (up to 137.6 kcal mol⁻¹),²³ c-CO₂ has a great potential as a building block for HEDMs. Since the ring-opening barrier of the free c-CO₂ is not so large (14.0 kcal mol⁻¹), further complexation could stabilize the c-CO₂. The methyldioxirane has been generated in laboratories and used as an effective oxidizing agent.^27,28 Its ring-opening barrier is significantly increased to 21.5 kcal mol⁻¹,²⁹ indicative of the effective complexation-induced kinetic stabilization to c-CO₂. Inspired by this, chemists have computationally designed many substituted dioxiranes, e.g., CO₂FOF, CO₂NF, CO₂(NH)₂, CO_n (n = 4–6), and CN₂O₂.^30,31 Amongst them, the present target CN₂O₂ C can be viewed as the N₂-complexed c-CO₂. However, our study showed that the ring-opening barrier of c-CO₂ is as small as 6.9 kcal mol⁻¹ at the UCCSD(T)_CBS level, in sharp contrast to the previous view on the stability of complexed c-CO₂. Thus, the kinetic stability of c-CO₂ in complexed molecules should highly depend on the complexation moieties. To better guide experimental synthesis and characterization, the quantitative complexation influence of diverse ligands to the c-CO₂ deserves to be explored in detail in the future.

4. Conclusions

The successful experimental characterization of two molecular HEDMs, i.e., diazirinone ([C,N₂,O]-A) and nitryl cyanide ([C,N₂,O₂]-B) that were computationally predicted much earlier, has greatly inspired chemists to design novel molecular HEDMs. Here, we reinvestigated the stability of a bicyclic [C,N₂,O₂] isomer C, which was predicted as a potential candidate for a HEDM in an early computational work. By re-evaluation of the kinetic stability of C, we found two new transition states TS2 and TS3 for the first time. In particular, the decomposition barrier of C via TS2 was shown to be as small as 11.6–13.0 kcal mol⁻¹ at the G3B3, CBS-QB3, G4, W1BD, and CCSD(T)_CBS//B3LYP/aug-cc-pVTZ levels, and 6.9 kcal mol⁻¹ at the UCCSD(T)_CBS//UB3LYP/aug-cc-pVTZ level with inclusion of zero-point energy correction. Thus, it's unlikely that the bicyclic C can be used as a HEDM. Surprisingly, the ring-opening stability of the c-CO₂ moiety in the present [C,N₂,O₂]-C is much lower than that in the well-known methyldioxirane molecule, demonstrating the different influence of it on the complexation to c-CO₂.

Acknowledgements

This work was funded by the National Natural Science Foundation of China (no. 21273093, 21473069, 21073074). The authors are very grateful for the reviewers' invaluable comments and suggestions.

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