Energy Storage in Cubane Derivatives and Their Real-Time

May 31, 2016 - Energy Storage in Cubane Derivatives and Their Real-Time Decomposition: Computational Molecular Dynamics and Thermodynamics. Vitaly V. ...
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Energy Storage in Cubane Derivatives and Their Real-Time Decomposition: Computational Molecular Dynamics and Thermodynamics Vitaly V. Chaban*,† and Oleg V. Prezhdo*,‡ †

Federal University of São Paulo, 12231-280 São Paulo, SP, Brazil Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States

‡

ABSTRACT: Cubane features one of the highest densities of covalent bonds among all known compounds. Kinetically stable, it constitutes an excellent candidate for efficient storage of large amounts of energy. We employ ab initio and semiempirical quantum-chemical methods to investigate systematically the amounts of energy that can be stored in cubane and its two derivatives known synthetically, octanitrocubane (8-CUB) and heptanitrocubane (7-CUB). Using nonequilibrium molecular dynamics, we establish the energy liberation pathways and molecular decomposition mechanisms. The reaction starts with spontaneous isomerizations of nitrocubanes into nitroannulenes and nitrosooxycubanes, subsequently producing NO and octaone C8O8. Unstable C8O8 decomposes within a picosecond, producing 8 CO molecules. All reactions are exothermic, giving rise to a sharp temperature increase. Ultimately, CO and NO recombine into CO2 and N2. According to the thermochemical calculations, 8-CUB stores 4145 kJ mol−1 of free energy, while 7-CUB stores 4346 kJ mol−1. The reported results foster consideration of cubanes for energy storage.

C

extremely high density of covalent bonds, CUB can be particularly interesting in the context of energy storage. Nitro groups are attached to many compounds to facilitate decomposition. Octanitrocubane (8-CUB) and heptanitrocubane (7-CUB) were synthesized by Eaton and co-workers19,20 starting from CUB. To date, only small amounts were obtained, which were not sufficient for testing these cubane derivatives as explosives.21 Assuming that molecular volume is roughly a group additive property, one would expect highly nitrated cubanes, such as 7-CUB and 8-CUB, to exhibit an unprecedentedly large density. Note that the velocity of wave propagation through an explosive material is directly proportional to its squared mass density. Two fascinating features of 8CUB are independence of an external oxygen source (complete decomposition of 8-CUB requires exactly 16 oxygen atoms already present in the molecule) and water-vapor-free products (4 N2 + 8 CO2). All other nitrocubanes require atmospheric oxygen to undergo complete decomposition. The field of nitrocubanes remains nascent, with a limited number of experimental and simulation studies. In this work, we investigate decomposition of CUB, 7-CUB, and 8-CUB (Figure 1) employing a robust combination of electronic structure methods and MD simulations. The reported nonequilibrium

ubane C8H8 (CUB) has become an outstanding landmark1−15 in the world of “impossible” compounds. Considering the best known allotropes of carbon, the C−C−C angles are equal to 109.5° (diamond), 120° (graphene), and 180° (carbyne). The corresponding hybridizations of atomic orbitals are sp3, sp2, and sp. Carbon nanotubes and fullerenes are very similar to graphene because they originate from the benzene ring, in which all six angles are 120°. Insignificant deviations of the angles from 120° in tubes and fullerenes, which can be revealed using quantum-chemical calculations, are a result of finite curvature. Carbon atoms in CUB create four single bonds, three of which are with other carbon atoms and one is with a hydrogen atom. However, all C−C−C angles in CUB are 90°, instead of an ideal value of 109.5° for the sp3 hybridization. The substantial perturbation (bending) is thermodynamically unfavorable, leading to a greatly strained structure. Cubane backbone can be seen as an elementary unit of the thinnest nanotube.16 Although CUB is unstable thermodynamically, it exhibits high kinetic stability. For instance, Maslov and co-workers17 computed the activation energy of decomposition of CUB, ca. 1.9 ± 0.1 eV, using density functional theory (DFT) tightbinding molecular dynamics (MD). This cornerstone result indicates a surprisingly high thermal stability of CUB. CUB not only maintains integrity at the elevated temperatures but also forms a molecular crystal with a density of 1290 kg m−3.18 According to Biegasiewicz and co-workers,18 CUB can be in the liquid state between 406.6 and 434.8 K. Because of an © XXXX American Chemical Society

Received: April 19, 2016 Accepted: May 31, 2016

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DOI: 10.1021/acsenergylett.6b00075 ACS Energy Lett. 2016, 1, 189−194

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Scheme 1. Chemical Transformations Leading to a Complete Decomposition of 8-CUB (left) and 7-CUB (right)

Figure 1. Optimized structures of the investigated molecules, obtained with M11 hybrid DFT: (a) cubane, (b) octanitrocubane, and (c) heptanitrocubane. Carbon atoms are gray; hydrogen atoms are white; nitrogen atoms are blue; oxygen atoms are red.

simulations are capable of identifying reaction steps and intermediates that cannot be surmised a priori. Chemical reactions can be observed in real time using MD simulations based on electronic structure methods, provided that duration of such simulations is sufficient for reactants to overcome reaction energy barriers. Elevation of temperature is a straightforward approach to accelerate intrinsically slow reactions. We employed PM7-MD simulations, which were used to address a number of sophisticated problems before,22−24 at temperatures between 2000 and 3000 K to observe decomposition pathways of CUB, 7-CUB, and 8-CUB in vacuum. We also tested T < 2000 K but did not observe any chemistry occurring during several nanoseconds of simulation time. A number of nonequilibrium trajectories were recorded, with different distribution of nuclear momenta at the initial moment. The reported results are averages of at least five independent PM7-MD runs. Unrestricted Hartree−Fock Hamiltonian was used in all calculations. The decomposition of CUB in vacuum starts from its isomerization into [8]annulene. This stage takes ca. 10 ps at 3000 K and slows exponentially as temperature decreases to ca. 2000 K. Because the simulated system comprises a single molecule, temperature fluctuates significantly, despite a stiff thermostat coupling parameter applied. Although [8]annulene is a kinetically stable compound at room conditions, it evolves at high temperature, producing benzene and acetylene. The later molecules remain intact up to the end of all PM7-MD simulations, because we did not provide any oxidants. If such were provided, formation of CO2 and H2O is expected, as in the case of any other hydrocarbon. Our observations are in perfect agreement with those of Maslov and co-workers who employed tight-binding DFT.17 8-CUB and 7-CUB decompose following a much more sophisticated series of transformations (Scheme 1). Isomerizations are the first step, taking 5−100 ps depending on temperature. The nitro group attached to the backbone C-NO2 rearranges into the nitrosooxy group C−O−N−O (Figure 2). A competitive reaction is rearrangement of cubane into octanitro[8]annulene (or heptanitro[8]annulene); that is, multiple C−C−C angles reduce to their thermodynamically optimal value and conjugated double bonds emerge. The above two isomerization reactions occur nearly simultaneously and are coupled. The coupling effect can be explained using thermochemical calculations (Table 1). Both isomerizations are exothermic. Therefore, the first one increases temperature of the reaction vessel, accelerating the second one. Polynitrosooxyannulene (Figure 2) are unstable and emit 7 or 8 NO molecules within a few subsequent picoseconds. The resulting polyketones (cyclooctaheptaone and cyclooctaoctaone, Figure

2) are also highly unstable, at both elevated and room temperatures, promptly providing 7 or 8 carbon monoxide CO molecules. Finally, the oxidation−reduction reaction between the gas molecules, NO and CO, leads to the most stable particles, molecular nitrogen N2 and carbon dioxide CO2. Note that molecules in Figure 2 are given in their idealized conformations, as they were subsequently used in the thermochemistry calculations (Table 1). Interestingly, all stages along the decomposition pathways of 8-CUB and 7-CUB are exothermic and increase the Gibbs free energy (Table 1). The reactions forming gas molecules contain a strong entopic component, whereas the isomerizations are guided strictly by enthalpy. The last stage (NO + CO → N2 + CO2) is very important, because it brings almost 3000 kJ mol−1 (the largest fraction) of enthalpy gain. However, the Gibbs free energy gain is smaller, because 16 gas molecules are transformed into 12 gas molecules. Unlike 8-CUB, decomposition of 7-CUB produces molecules of water and requires an additional source of oxygen. In the absence of water formation, decomposition of 8-CUB may be harder to detect. Although 7CUB exhibits a worse oxygen balance, it provides more energy. Despite being a stronger energetic material per mole, we 190

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Figure 2. Optimized geometries of the intermediate products observed upon real-time simulations of decomposition of 8-CUB and 7-CUB, obtained at the M11 hybrid DFT level: (a) cyclooctaoctaone, (b) cyclooctaheptaone, (c) octanitrosooxy[8]annulene, (d) heptanitrosooxy[8]annulene, (e) heptanitro[8]annulene, (f) octanitro[8]annulene, (i) heptanitroxooxycubane, (j) octanitroxooxycubane. Carbon atoms are gray; hydrogen atoms are white; nitrogen atoms are blue; oxygen atoms are red.

Table 1. Standard Thermodynamic Potentials for Isomerization and Decomposition Reactions of Heptanitrocubane and Octanitrocubanea

a

no.

reactants

1 2 3 4 5 6 7

8-CUB 8-CUB octanitro[8]annulene octanitrosooxy[8]annulene C8O8 8 CO + 8 NO 8-CUB

8 9 10 11 12 13 14

7-CUB 7-CUB heptanitro[8]annulene heptanitrosooxy[8]annulene C8O7H + 3/4 O2 8 CO + 7 NO + 1/2 O2 7-CUB + 5/4 O2

products octanitrocubane C8(NO2)8 octanitrosooxycubane octanitro[8]annulene octanitrosooxy[8]annulene octaone C8O8 + 8 NO 8 CO 4 N2 + 8 CO2 4 N2 + 8 CO2 heptanitrocubane C8H(NO2)7 heptanitroxooxycubane heptanitro[8]annulene heptanitrosooxy[8]annulene heptaone C8O7H + 7 NO 8 CO + 1/2 H2O 7/2 N2 + 8 CO2 7/2 N2 + 8 CO2 + 1/2 H2O

ΔU (kJ mol−1)

ΔH (kJ mol−1)

ΔG (kJ mol−1)

−234 −84 −382 −86 −219 −2893 −3664

−234 −84 −382 −66 −202 −2903 −3636

−232 −84 −401 −458 −522 −2680 −4145

−186 −64 −123 −216 −631 −2879 −3913

−186 −64 −123 −199 −614 −2889 −3889

−188 −67 −120 −562 −926 −2670 −4346

Total decomposition reactions of each cubane derivative are marked in bold. The results were obtained using M11 hybrid DFT.

C covalent bond, 1.58 Å in CUB and 1.59 Å in 7-CUB and 8CUB. The second peak corresponds to the noncovalent C−C distance, 2.23 Å (square diagonal). The third peak is the length of the cube diagonal, 2.73 Å. The heights of the peaks decay in accordance with the number of the corresponding bonds. Interestingly, the peak positions do not depend on temperature, suggesting that thermal expansion in cubanes is marginal. Bond dissociation involves a significant bond stretching, which may occur because of either thermal fluctuations or strong intermolecular interactions among the reactants. Critical bond stretching is a rare event in most reactants. Figure 4c depicts the maximum lengths of the C−C and C−N covalent bonds versus temperature assuming that these stretching events launch the decomposition reactions. The maximum bond lengths defined this way are significantly higher, by 10−23%, compared to the average bond lengths. Overall, the simulations suggest that nitrocubanes, similar to pristine CUB, require significant initiation energies, apparently corresponding to more than 1000 K. Irradiation by a laser constitutes one possible initiation mechanism. Vibration frequencies (Figure 5) characterize chemical bonds near the equilibrium. CUB has only three infrared (IR) active bands because of its highly symmetric structure. The

anticipate 7-CUB to be a weaker explosive, because it needs to retrieve oxygen atoms from air to finish the decomposition. This stage is evidently slowest, while explosive power depends on the speed of reaction. Note that performance of energetic materials greatly depends on their mass densities in the stable form. These data are yet unavailable for 8-CUB and 7-CUB. The energetics of bond dissociation are characterized by potential energy scans (Figure 3). The C−C and C−N covalent bonds have similar strengths. Differences are seen at distances larger than 1.85 Å, indicating that the C−N bond is weaker than the C−C bond, in agreement with the bond energies, E(C−C) = 350 kJ mol−1 and E(C−N) = 305 kJ mol−1. The bond energy profiles contain no barrier, which could be used to define the internuclear distance at which the bonds break. The potential energy scans suggest that the decomposition reaction is more likely to start with the C−NO2 → C−O−N−O isomerization rather than the cubane backbone rearrangement, because dissociation of the C−N bond is easier than dissociation of the C−C bond. This hypothesis is in concordance with thermodynamic potentials (Table 1). The carbon−carbon radial distribution function (Figure 4) exhibits three well-defined peaks, whose positions are common for all cubane derivatives. The first peak corresponds to the C− 191

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Figure 3. (a) Potential energy change upon breaking the carbon− nitrogen polar covalent bond (solid line) and carbon−carbon nonpolar covalent bond (dashed line); (b) first derivative of bond energy with respect to bond length, dE/dr; (c) second derivative of bond energy with respect to bond length, d 2 E/dr2 . The computations were performed using the PM7 semiempirical Hamiltonian.

Figure 5. Infrared spectra of (a) CUB, (b) 8-CUB, and (c) 7-CUB obtained at the M11/6-311++G** level of theory.

active in the IR region because it does not change the dipole moment. Other vibrational modes exist at significantly lower frequencies. The C−H peak is the most straightforward means to differentiate 7-CUB from 8-CUB in a mixture of nitration products. The slowest vibration is that of the nitro group, ca. 100 cm−1. The major bands in the computed spectrum of CUB are in satisfactory agreement with the experimental data,25 although many vibrational frequencies are systematically overestimated. The computed infrared spectra of 7-CUB and 8-CUB agree in many aspects with the experimental spectra for 1,3,5-trinitrocubane and 1,3,5,7-tetranitrocubane, as originally reported by Eaton et al.26 Our results are in good agreement with the computations of Zhang and Xiao,27 who also used hybrid DFT but a significantly smaller basis set, 6-31G(d). In the present work, we focused on the intramolecular reaction pathway due to the high temperatures considered in the simulations. At such thermodynamic conditions, cubanes exist in the gas phase, making intermolecular interactions weak and rare. It is important to note that in the condensed phase, the reaction can involve intermolecular pathways in which nitrogroups of neighboring molecules interact electrostatically to initiate the isomerization and subsequent reaction steps. Decomposition stages of polynitrocubanes are, in some aspects, reminiscent of how nitromethane28−30 and other nitro compounds31 explode. The major role in the initiation of the reaction belongs to isomerization of nitro groups into nitrosooxy groups, which happens quickly at high temperatures. Liberation of significant amounts of energy helps to break carbon−carbon covalent bonds. All explosions finish with formation of molecular nitrogen and carbon dioxide. These products are known to be the global minimum for the corresponding ensemble of atoms. To recapitulate, cubane and its nitro-derivatives exhibit an extremely high density of energetic chemical bonds. They are kinetically stable; therefore, they constitute particularly promising candidates for chemical energy storage. Molecular

Figure 4. (a) Radial distribution functions computed using PM7MD for the carbon−carbon atom pairs in CUB at 500 K; (b) distribution of lengths of the carbon−carbon nonpolar covalent bond in 7-CUB at 500, 750, 1000, and 1500 K; (c) maximum recorded lengths of the carbon−carbon and carbon−nitrogen covalent bonds as a function of temperature. Quantitatively, 7-CUB exhibits the same behavior as 8-CUB. Note that CUB, 7-CUB, and 8-CUB do not disintegrate in the course of quite long PM7-MD simulations up to 1500 K.

asymmetric C−H stretch, ca. 3100 cm−1, gives the highest IR active frequency. Note that the symmetric C−H vibration is not 192

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Potential energy scans were conducted to characterize dissociation of the carbon−carbon and carbon−nitrogen bonds and to obtain potential energy penalties for these processes. Forty single-point calculations at the PM7 level34 were performed with the 0.02 Å step to sample the intramolecular bond lengths from 1.6 to 2.4 Å. The thermodynamic properties and infrared spectra were derived from the thoroughly optimized molecular conformations according to the M11 hybrid density functional theory35−37 employing the atom-centered split-valence triple-ζ polarized Gaussian basis set, supplemented with diffuse functions, 6-311++G**. The frequency analysis was performed. The self-consistent field convergence criterion was set to 10−8 Hartree. The energy difference between the subsequent geometries at the end of geometry optimization was less than 10−6 Hartree in all cases. Hybrid DFT offers a very good accuracy for the geometric parameters and standard heat of formation of cubane. In particular, an outstanding coincidence with the experimentally determined heat of formation has been reported,38 +162 versus +163 kcal mol−1. According to Peveratti and Truhlar,35−37 the M11 functional used here offers accurate thermochemistry and generally improved electronic and geometric properties, compared to earlier functionals.

crystals in ambient conditions, cubanes become liquid at temperatures above 400 K, providing convenient means of processing, handling, and storage. To control release of the chemical energy contained in cubanes, one requires a detailed understanding of the decomposition mechanism and reaction intermediates. Such knowledge can be used to determine the thermodynamic conditions suitable for the decomposition, to design catalysts than can lower the activation energy, and to couple the reaction to other known chemistries. For the first time, we simulated decompositions of cubane and its two most representative nitro-derivatives in real-time. We characterized the decomposition thermodynamics and kinetics and identified all elementary steps and intermediates involved in the energy release. We showed by thermochemical calculations that 7-nitro cubane contains more energy than the 8-nitro derivative. At the same time, the release of energy stored in 8-nitro cubane requires no external reactants, because all necessary oxidant atoms are already present within the molecule. Thus, 8-nitro cubane may be preferable over 7-nitro cubane, despite a lesser energy content. Already obtained and characterized experimentally, cubane and its nitro-derivatives still remain a challenge for synthetic chemistry. Nonequilibrium time-domain simulations of chemical reactions discover new moieties and reaction steps, which often cannot be guessed a priori. The detailed knowledge of the cubane decomposition mechanisms obtained in this manner, may generate new ideas and approaches. For instance, current syntheses of 8-nitro and 7nitro cubanes start from cubane as a reactant,19,20 while it would be valuable to produce these energetic compounds in a more direct way.

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AUTHOR INFORMATION

Corresponding Authors

*V.V.C.: Email: [email protected]. *O.V.P.: Email: [email protected].

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Notes

The authors declare no competing financial interest.

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SIMULATION DETAILS The PM7-MD simulations22−24,32−34 were conducted at the unrestricted Hartree−Fock level to ensure proper description of bond-breaking processes. The nonequilibrium PM7-MD studies focused on a series of temperatures between 2000 and 3000 K until the decomposition pathways of CUB, 8-CUB, and 7-CUB were revealed. The time-step of 0.1 fs was used for these simulations to guarantee a very accurate energy exchange between nuclear degrees of freedom. The equilibrium PM7-MD simulations were conducted in the constant temperature ensemble at 500, 750, 1000, and 1500 K, whereby constant temperature was maintained through velocity rescaling every 100 time-steps. The integration timestep in the velocity Verlet equations-of-motion propagation algorithm was set to 0.25 fs. The duration of every simulation depended on temperature, because sampling speed increases exponentially with temperature increase. The simulation times were 736 ps at 500 K, 446 ps at 750 K, 271 ps at 1000 K, and 99.6 ps at 1500 K. Cubane and its derivatives constitute a challenge for PM7 and other semiempirical methods. These molecules contain significant amounts of strain energy and hence differ significantly from those used for method parametrization. The standard heat of formation of cubane, obtained with PM7, equals 126 kcal mol−1, while the experimental value is +163 kcal mol−1. Despite the 23% discrepancy, PM7 correctly reproduces cubane geometry and predicts it to be a stable species (local energy minimum) at room and high temperatures. PM7-MD offers an important tool to observe decomposition pathways in real-time, which are not affordable to ab initio MD, because of high computational cost and significant length of the required trajectory.

ACKNOWLEDGMENTS V.V.C. is grateful to CAPES of Brazil for partial support of this research. O.V.P. acknowledges financial support of the Computational Materials Sciences Program funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award Number DE-SC00014607.

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REFERENCES

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