Accurate Prediction of Bond Dissociation Energies and Barrier Heights

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Accurate Prediction of Bond Dissociation Energies and Barrier Heights for High-Energy Caged Nitro and Nitroamino Compounds Using a Coupled Cluster Theory Vitaly G. Kiselev, and C. Franklin Goldsmith J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b01506 • Publication Date (Web): 28 Mar 2019 Downloaded from http://pubs.acs.org on March 29, 2019

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The Journal of Physical Chemistry

Accurate Prediction of Bond Dissociation Energies and Barrier Heights for High-Energy Caged Nitro and Nitroamino Compounds Using a Coupled Cluster Theory Vitaly G. Kiseleva,b,c* and C. Franklin Goldsmitha*

a Brown

University, School of Engineering, 184 Hope Str., Providence, RI 02912, USA

b Novosibirsk

c

State University, 2 Pirogova Str., 630090 Novosibirsk, Russia

Institute of Chemical Kinetics and Combustion SB RAS, 3 Institutskaya Str., 630090

Novosibirsk, Russia

ACS Paragon Plus Environment

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ABSTRACT

Highly accurate theoretical values of bond energies and activation barriers of primary decomposition reactions are crucial for reliable predictions of thermal decomposition and detonation-related phenomena of energetic materials (EM). However, due to the prohibitive computational cost, high-level ab initio calculations had been impractical for a large number of important EMs, including, e.g., hexanitrohexaazaisowurtzitane (CL20). In the present work, we obtained accurate bond dissociation energies and the activation barriers for primary decomposition reactions for a series of novel promising caged polynitroamino and polynitro EMs, viz., CL-20, octanitrocubane (ONC), and hexanitro derivatives of adamantane, using the recently proposed domain-localized pair natural orbitals (DLPNO) modifications of coupled cluster techniques. DLPNO-CCSD(T) allows for routine quadruple-zeta basis set quality coupled cluster calculations for the species comprised of ~30 non-H atoms. The benchmarks on a number of simpler congeners of CL-20 and ONC revealed that the DLPNO approach does not deteriorate the quality of the quadruple-zeta coupled cluster procedure. With the aid of this technique, the full set of gas-phase primary decomposition reactions for all 9 conformers of CL-20 was considered. For all species studied, C-NO2 or N-NO2 radical decomposition channels dominate over molecular counterparts. The best theoretical results reported in the literature so far, viz., DFT energies of nitro group radical elimination in CL-20 and ONC, underestimate the value by ~10 kcal/mol. We also


2

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present reliable and accurate gas-phase formation enthalpies for CL-20, ONC and related species. In a more general sense, these results offer a new level of predictive computational kinetics for polynitro caged energetic materials.


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1. INTRODUCTION Caged nitrocompounds, as well as their nitroamine congeners, are a promising class of energetic materials. A favorable combination of high density and energetics due to strained hydrocarbon cages along with the presence of typical explosophoric oxidizing groups render them to be powerful explosives.1-3 Hexanitrohexaazaisowurtzitane (HNIW, CL-20, 1, Chart 1), first reported in 1987,4 is one of the most widespread high-performance caged nitroamine energetic materials produced on the industrial scale. A detailed survey of the literature on CL-20 performance is beyond the scope of this paper; interested readers are directed to the comprehensive reviews and references therein.1,5-7 Another high-energy congener of CL-20, which is extensively studied now, is 4,10-dinitro-2,6,8,12-tetraoxa-4,10diazatetracyclo[5.5.0.05,9.03,11]-dodecane (TEX, 2, Chart 1). While the detonation parameters of TEX are slightly inferior to those of CL-20, it is profoundly less sensitive toward mechanical stimuli.8 Moreover, nitro hydrocarbon compounds are typically less sensitive and more thermally stable in comparison with nitroamines.2,9 Among the former, octanitrocubane (ONC, 3, Chart 1) is a long-sought representative of fully nitrated caged hydrocarbon compounds reported at the beginning of the 21st century.10,11 A main hindrance to the widespread use and even lab-scale study of ONC properties remains its tremendously complicated synthesis procedure.2,11


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Chart 1. Caged energetic nitrocompounds considered in the present work. A detailed understanding of the decomposition kinetics of both slow-heating and detonation processes is crucial for applications of a particular material. Reactive molecular dynamics (MD) has become an increasingly popular theoretical tool to obtain insights into the mechanism of detonation and thermal decomposition of CL-20 and TEX containing energetic formulations and co-crystals,12-23 as well as those of ONC.24,25 Both empirical reactive force fields and simple density functional theory (DFT) calculations are used in these simulations as a source of forces necessary to compute the time evolution of the system studied. However, in order to provide valuable insights, the force fields should be properly calibrated and benchmarked against accurate and reliable data, foremost, on the bond energies and activation barriers of primary decomposition reactions.


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Because of the natural experimental challenges in quantifying the kinetic properties of energetic materials, electronic structure calculations are essential sources of such data. However, due to the large size of CL-20 and ONC (and, more generally, polynitro caged compounds, since they typically have ~30 non-hydrogen atoms), the existing literature data are scarce: only DFT and semi-empirical calculations have been reported so far. Leszczynski et al.26 studied the gas-phase monomolecular decomposition channels of CL-20 at the B3LYP/cc-pVTZ level of theory. The authors considered the sole conformer of CL-20 and found the homolytic N-NO2 bond cleavage with a “bare” electronic energy ∆𝐸𝑒𝑙 of 37.6 kcal mol-1 to be the predominant decomposition channel. Apart from this study, only the gas-phase thermodynamics of several conformers of CL20 was considered at B3LYP27,28 and MP229 levels of theory. In the latter work, the six low-lying energetically accessible conformers of CL-20 were identified. ONC (3, Chart 1) has been rarely studied as well. Only semi-empirical and simple B3LYP computations for ONC and related nitrosubstituted cubanes have been reported so far.30-33 Note that the C-C simple bond rupture yielding a biradicoloid intermediate was proposed to be the primary decomposition reaction on the basis of B3LYP computations.32 At the same time, MD simulations with the use of the semi-empirical PM7 force field suggest a nitro-nitrite isomerization to dominate the thermolysis of ONC.25


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The direct experimental measurements of the gas-phase decomposition kinetics are also hindered. The standard states of CL-20, TEX, and ONC are crystalline, and their thermolysis occurs in the solid state.34,35 It is therefore difficult to match directly the gasphase theoretical kinetics with experiment. In this connection, it is worth to mention the isothermal decomposition kinetics measurements of CL-20 in acetone solution under high pressure performed by Oxley et al.36 The authors obtained the Arrhenius parameters of the first-order kinetics of CL-20 decomposition to be Ea = 42.4 kcal mol-1 and log (A/s-1) = 17.6 in the temperature interval 420-500 K. The subsequent experiments on the thermolysis of CL-20 in a 1,3-dinitrobenzene solution in the temperature interval 413-468 K yielded the similar values of Ea scattered between 41.0 and 45.3 kcal mol-1 and log (A/s-1) = 16.3 and 18.6, respectively.37 Another important experimental study with the use of electron paramagnetic resonance spectroscopy gives evidence of radical intermediacy in the decomposition mechanism of CL-20.38 These findings are generally in line with a high pre-exponential factor typical of radical bond rupture reactions.36 Apart from these studies, the first-order isothermal decomposition kinetics of TEX in a dibutyl phthalate solution was reported39,40 to have the Arrhenius parameters Ea = 40.0 kcal mol-1 and log (A/s-1) = 13.5 in the temperature interval 483-523 K. It is therefore seen that only the simple DFT calculations have been attempted on decomposition pathways of CL-2026 and ONC32 so far. However, to provide the convincing evidence, ultimately more sophisticated wave-function based methods, such


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as coupled cluster theory with at least a quadruple-zeta basis set, are desirable. Until recently, these calculations had been prohibitively expensive. Fortunately, recent progress in coupled cluster methodology now renders high-accuracy calculation of large energetic materials possible. In the present contribution, for the first time we applied the DLPNO-CCSD(T) methodology proposed by Neese et al.41-43 for computational kinetics of

promising

energetic

materials.

We

studied

several

representative

caged

polynitroamino energetic compounds, including CL-20, TEX, and ONC. Additionally, for the sake of completeness, we also considered representative polynitro species containing gem-dinitro groups, viz., 2,2,4,4,6,6-hexanitroadamantane (HNA, 4, Chart 1),44,45 and two very recently reported nitramino derivatives: 2,4,4,8,8-pentanitro-2azaadamantane (PNAA, 5) and 2,4,4,6,8,8-hexanitro-2,6-diazaadamantane (HNDAA, 6) containing mixed dintro- and nitroamino functionalities.46,47 Ultimately, we considered the radical and molecular primary decomposition reactions of all species studied at the DLPNO-CCSD(T)/jun-cc-pVQZ level of theory and obtained the most accurate values of bond energies and activation barriers of molecular channels among those reported up to date. 2. COMPUTATIONAL DETAILS Electronic structure calculations were carried out using the Gaussian 09,48 Molpro 2015,49 and ORCA 4.041 program packages. The geometries of all structures corresponding to the stationary points on the potential energy surface (PES) of the


8

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species studied were fully optimized using density functional theory at the M06-2X/6311++G(d,p) level.50 All the equilibrium and transition state structures were ascertained to be the minima and first-order saddle points, accordingly, on the potential energy surfaces. The nature of all localized transition states was verified using the intrinsic reaction coordinate (IRC) procedure. Zero-point energies and thermal corrections to enthalpy and Gibbs free energy were computed at the same DFT level of theory. Singlepoint electronic energies were afterward refined using the DLPNO-CCSD(T) methodology (the “NormalPNO” truncation thresholds were set)42 along with the jun-ccpVQZ “seasonally” augmented basis set.51 The corresponding auxiliary basis set (augcc-pVQZ/C in the ORCA nomenclature) was used for density fitting calculations. In the benchmark calculations, an explicitly correlated coupled-cluster formalism CCSD(T)F12b in conjunction with VDZ-F12 and VTZ-F12 basis sets was employed.52 The gas 0 ) were calculated phase enthalpies of formation (at p0 = 1 bar and T = 298.15 K,  f H gas

using the explicitly correlated W1-F1253 multi-level procedure and atomization energy and isodesmic reaction approaches described in detail elsewhere.54,55 Note that the W1F12 procedure employed in the present work had been slightly modified in comparison with the originally proposed technique: namely, the B3LYP-D3BJ/def2-TZVPP optimized geometries (the ZPE correction factor of 0.99) were used56 and the diagonal BornOppenheimer corrections were omitted. The heats of formation at 0 K for the elements 0K 0K 0K in the gas phase  f H gas (C) = 169.98 kcal mol-1,  f H gas (H) = 51.63 kcal mol-1,  f H gas (N)


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0K = 112.53 kcal mol-1, and  f H gas (O) = 58.99 kcal mol-1 were taken from the NIST-JANAF

tables.57

3. RESULTS AND DISCUSSION

3.1. Benchmarking of the computational methodology Accurate calculations of bond dissociation energies are crucial for computational kinetics. Therefore, we started with a thorough benchmark of the DLPNO-CCSD(T) methodology. To this end, we considered C-NO2 and N-NO2 bond dissociation energies at CCSD(T)-F12 level of theory with double- and triple-zeta basis sets for a number of nitro derivatives of cubane and hexaazaisowurtzitane cages (Scheme 1). The results are given in Table 1. Apart from this, the highly accurate CCSD(T)-F12/VTZ-F12 calculations are affordable for TEX (Table 1). Table 1. N-NO2 and C-NO2 Bond Dissociation Electronic Energies (∆𝐸𝑒𝑙) and Enthalpies at 298 K (∆𝐻0) Corresponding to the Gas-Phase Nitro Group Radical Elimination Reactions of the Derivatives of Aza-Isowurzitane Cage (8 – 12), TEX (2), and Cubane (14 – 17). The Reactions are Named in Accordance with Scheme 1. All Energy Values are Given in kcal mol-1. ∆𝐸𝑒𝑙,b kcal/mol Speciesa

CCSD(T)-F12/ VTZ-F12

∆𝐻0,d

CCSD(T)-F12/

DLPNO-

VDZ-F12

CCSD(T)/

M06-2Xc

kcal/mol


10

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jun-VQZ

a

2

53.0

52.8

53.0

55.7

49.3

7

50.1

49.7

50.2

53.4

46.7

8

55.7

55.2

55.8

59.1

52.0

9

48.7

49.2

52.3

45.4

10

46.8

47.0

50.2

43.6

11

54.1

54.2

57.7

50.7

12

72.9

72.5

72.8

74.7

68.8

13

69.7

69.3

69.7

70.6

66.1

14

70.6

70.2

70.4

71.8

66.6

15

72.1

71.7

72.6

73.4

69.7

The nitro groups in imidazolidine (5-membered) rings in the species 7, 9, and 10 are in the axial

conformation and those in a piperazine (6-membered) ring in the species 2, 8, and 11 are in the equatorial conformation. See full geometries and raw data in the Supporting Information (Section 2). b The electronic energies were calculated by means of various CCSD(T) modifications using the M06-2X/6311++G(d,p) optimized geometries. Zero-point energies and thermal corrections were computed at the same level of theory. c M06-2X/6-311++G(d,p) level of theory was used. d The DLPNO-CCSD(T)/jun-VQZ electronic energies and M06-2X/6-311++G(d,p) zero-point vibrational energies and thermal corrections were used.


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Scheme 1. Decomposition reactions of simple nitro derivatives of aza-isowurzitane cage (8 – 12), TEX (2), and cubane (14 – 17) used for benchmarking of DLPNO-CCSD(T) methodology. Table 1 demonstrates excellent agreement (within 0.5 kcal mol-1) between the CCSD(T)-F12/VTZ-F12 and DLPNO-CCSD(T)/jun-cc-pVQZ used in the present work. Note that the accuracy of the explicitly correlated results with triple-zeta basis sets is typically comparable with the conventional coupled cluster with quadruple-zeta (and even 5Z) basis set.52,58 It is therefore seen that the DLPNO approach does not deteriorate the quality of the coupled cluster procedure and the results of the present work are generally not worse than of the CCSD(T)/QZ quality. It is also worth mentioning that the M06-2X values differ from those of CCSD(T) impressively by a mere ~3-4 kcal mol-1 (Table 1). This fact is in line with general performance of the Minnesota functionals in thermochemistry and kinetics.50 Properly benchmarked DFT functionals indeed can be used for meaningful estimations but cannot provide the “chemical accuracy” (around 1 kcal mol-1) and, ultimately, the convincing mechanistic evidence on the decomposition pathways.

3.2. DLPNO-CCSD(T) activation barriers of decomposition reactions and bond energies of the compounds 1 – 6 Having benchmarked the DLPNO-CCSD(T)/jun-cc-pVQZ methodology, we applied this procedure for comprehensive study of the potential energy surface (PES) regions relevant for primary decomposition reactions of the energetic species 1 – 6 (Scheme 2). The results are presented in the Table 2. Note that only the properties of the lowest


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energy conformers are discussed, the full datasets are given in the Section 1 of the Supporting Information. The DLPNO-CCSD(T)/jun-cc-pVQZ calculations turned out to be quite affordable: e.g., in the case of CL-20 (30 non-H atoms, 2310 basis functions, 222 electrons) a typical timing on the Intel Xeon E5-2670 (2.5 GHz, 16 Gb RAM per core) using 4 CPU cores was ~80 hours. Consequently, 9 conformers of CL-20 and 36 conformers of the products of radical elimination of •NO2 were considered (SI, Section 1, Tables S1 and S2). As seen from Table 2, the primary gas-phase decomposition reaction of CL-20 (1) is a radical N-NO2 bond rupture. It is also worth mentioning that for all conformers of CL20 studied, the •NO2 radical elimination from the imidazolidine (5-membered) cycles is slightly more favorable than that from the piperazine (6-membered) ring (Table 2, Table S2). The direct accurate calculations therefore does not confirm assertions made before on the basis of comparison of the corresponding harmonic frequencies.29 Table 2. Bond Dissociation Enthalpies at 298 K (∆𝐻0) Along with the Enthalpies of 0

Activation for the Molecular Elimination Channels (∆ ≠ 𝐻 ) for the Primary Gas-Phase Decomposition Reactions of the Caged Nitramines (1 – 6). The Energies Were Calculated at the DLPNO-CCSD(T)/jun-cc-pVQZ//M06-2X/6-311++G(d,p) Level of Theory.a All Energy Values are Given in kcal mol-1. Reactionb

∆ ≠ 𝐻0, kcal/mol

∆𝐻0, kcal/mol

CL-20 (1) → •R1a + •NO2

44.6

CL-20 → •R1b + •NO2

47.4


14

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CL-20 → P1 + HONO

a

53.3

22.0

TEX (2) → •R2 + •NO2

49.3

ONC (3) → •R3 + •NO2

63.0

ONC → I1

62.3

-10.6

ONC → I2

64.6

58.9

ONC → I3

74.0

-16.7

HNA (4) → •R4a + •NO2

40.4

HNA → •R4b + •NO2

34.7

PNNAA (5) → •R5a + •NO2

47.6

PNNAA → •R5b + •NO2

45.5

HNDAA (6) → •R6a + •NO2

51.8

HNDAA → •R6b + •NO2

44.4

The details of calculations and raw data are given in the Supporting Information (Section 2, Tables S2

and S3). b The reaction pathways and numeration are in accordance with Scheme 2.

Note that the DLPNO-CCSD(T) value of ∆𝐸𝑒𝑙 of N-NO2 bond in CL-20 from the present work is ~10 kcal mol-1 higher than that calculated at the B3LYP level.26 Given the fact that the N-NO2 bond dissociation reactions are typically barrierless,59 the theoretical value ∆𝐻0 = 44.6 kcal mol-1 (Table 2) is remarkably close to the measured activation energy Ea = 42.4 kcal mol-1 of CL-20 decomposition in an inert solution.36 Finally, it is worth mentioning that the lowest molecular elimination channel of CL-20 decomposition, viz., the HONO elimination, cannot compete with the N-NO2 bond fission in the gas phase (Table 2, more details are given in Table S3).


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Scheme 2. Primary decomposition reactions of the compounds 1 – 6 studied in the present work (Table 2). In the case of TEX (2), both CCSD(T)-F12 and DLPNO-CCSD(T) yield consistent values of N-NO2 bond energy (Table 2). This value is slightly higher (~2 kcal mol-1) than


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that of the highly strained 1 structure. Note that the theoretical value of the bond enthalpy ∆𝐻0 = 49.3 kcal mol-1 is remarkably higher than the activation energy of Ea = 40.0 kcal mol-1 reported for the TEX thermolysis in an inert solution.39,40 Taking into account the fact that the reported pre-exponential factor is (log (A/s-1) = 13.5) is 2-3 orders of magnitude lower than that of the barrierless radical bond scission60,61 and the rate constants were measured in a very narrow temperature interval, the experimental activation energy39,40 is quite possibly underestimated. In contrast to the case of 1 and 2, several molecular decomposition channels closely compete with the C-NO2 radical dissociation in the case of octanitrocubane 3 (Table 2). The nitro-nitrite rearrangement 3 → I1 is even energetically slightly more preferable for ONC (Table 2). It is worth discussing that apart from conventional nitronitrite rearrangement channel yielding an intermediate I1 (Scheme 2, Table 2), a similar rearrangement accompanied by a concerted breaking of the adjacent C-C bond 3 → I2, which is specific for the particular cage structure of ONC, may occur with a similar activation barrier (Table 2). Nevertheless, the barrierless radical decomposition should dominate at any practical temperatures of thermal decomposition due to the higher value of the pre-exponential factor.60 Note that the C-NO2 bond energy in ONС, where the hydrocarbon cage is highly strained,2 is even slightly higher (Table 2) than those in the prototypical nitro derivatives of aliphatic species (methane and ethane).54,62 It is also instructive to compare the accurate C-NO2 bond energies of 3 from the present work (Table 1) with those calculated at the B3LYP level.32 Similarly to the case


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of 1, the latter value is underestimated by ~ 12 kcal mol-1. Unfortunately, such a poor performance of B3LYP and several other widespread DFT functionals (e.g., PBE0) for computational kinetics of nitrocompounds is well documented.54,62 The use of a reliable computational methodology is indeed crucial for proper kinetic modeling, as an error of 10 kcal mol-1 leads to an uncertainty in the rate constants of more than 4 orders of magnitude at a typical thermolysis temperature of 500 K. This difference becomes even more pronounced at lower temperatures. Given the reliable values of the bond energies and activation barriers of primary thermolysis reactions (Table 1), the kinetic predominance of the nitro-nitrite rearrangement recently proposed for octanitrocubane on the basis of MD simulations employing the PM7 PES,25 seems questionable. At the PM7 level, the values of the enthalpy of C-NO2 bond scission is 46.6 kcal mol-1 (cf. 63.0 kcal mol-1, Table 1) and the activation enthalpy of 3 → I2 isomerization is 48.6 kcal mol-1 (cf. 64.6 kcal mol-1, respectively, Table 1). Finally, it is interesting to compare the properties of the C-NO2 bonds in the species 1 – 3 with their counterparts in adamantane derivatives 4 – 6 (Chart 1, Scheme 2). In agreement with general trends,54,60 the gem-dinitro C-NO2 bonds in 4 are notably weaker than those in 3 (Table 2). Especially weak (~35 kcal mol-1) is the C-NO2 bond in the moiety of 4, which is directly bound to the two other carbons bearing dinitro functionality (Table 1, Scheme 1). At the same time, the presence of nitroamino groups


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instead of gem-dintro in the structures of 5 and 6 (Scheme 2) renders the latter species notably more thermally stable (cf. the bond energies in 4 and 5 or 6, Table 2).

3.3. Accurate gas-phase formation enthalpies of CL-20, TEX, ONC, and their simpler congeners Having accurate DLPNO-CCSD(T) reaction enthalpies at hand, we were able to 0 ) for CL-20 (1), TEX (2), and refine the gas-phase formation enthalpies at 298 K ( f H gas

ONC (3) using the isodesmic reaction approach. To this end, we calculated first the formation enthalpies of simpler aza-isowurzitane and cubane nitro derivatives (Chart 2) using the atomization energy approach along with the highly accurate W1-F12 procedure. The results of these calculations are given in Table 3.

Chart 2. Aza-isowurzitane cage (16) and its simple mono- (8) and dinitro derivatives (10 and 11) used in the isodesmic reactions (ID1 – ID3) with CL-20 (1) along with cubane (17) and its simple mono- (12) and dinitro derivatives (13) used in the isodesmic reactions (ID4 – ID5) with octonitrocubane (3). Along with W1-F12 values, we also included in Table 3 the results of widely used G4 multi-level procedure. As was already reported, the G4 remarkably underestimates 0  f H gas for nitro species,55,63,64 and the uncertainty increases with the number of nitro


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groups. The use of highly accurate W1-F12 procedure is therefore crucial in the present case.

Table 3. The Gas Phase Formation Enthalpies at 298 K (  f H gas ) of Aza-Isowurzitane 0

(16), Cubane (17) and Their Nitroamino (8, 10, and 11, Chart 2) and Nitro Derivatives (12 and 13, Chart 2) Calculated Using the Atomization Energy Approach and W1-F12 and G4 (in Parentheses) Multi-Level Procedures. All Values are Given in kcal mol-1. Compoun d 0  f H gas

a

8

10

11

73.8a

79.1

81.3

136.4

(68.9)b

(71.6)

(73.9)

(133.6)

The most reliable W1-F12 values are marked in bold.

12

b

13

16

17

133.7

68.9

144.1

(128.3)

(66.5)

(144.8)

Calclulated using the G4 multi-level procedure

and atomization energy approach.

Then we employed a series of isodesmic reactions (ID1) – (ID3): CL-20 (1) + 5 (16) → 6 (8)

(ID1)

CL-20 (1) + 2 (16) → 3 (10)

(ID2)

CL-20 (1) + 2 (16) → 3 (11)

(ID3)

The DLPNO-CCSD(T)/jun-cc-pVQZ reaction enthalpies

0  r H gas

(the M06-2X

geometries and vibrational frequencies were used, see the footnotes to Table 1) of (ID1) – (ID3) are –33.6, –30.9, and –24.7 kcal mol-1, respectively. Using all these values, we


20

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0 calculated the corresponding values of  f H gas of CL-20 to be 132.1, 130.3, and 130.9 0  131.1 ± kcal mol-1. Finally, the average value for CL-20 was determined to be  f H gas

1.5 kcal mol-1. The uncertainty of 1.5 kcal mol-1 is estimated on the basis of the scatter 0 of DLPNO-CCSD(T) calculated  r H gas values and the ~0.2 kcal mol-1 root mean square

0 deviation of W1-F12 on a wide benchmarking set.53 Note that the  f H gas of CL-20

turned out to be ~12 kcal mol-1 higher than the recent theoretical value obtained at the highest feasible level of theory (G4MP2) level using a series of isodesmic reactions (Table 4).65 The similar strategy was employed in the case of octonitrocubane (3). The formation enthalpies of simpler nitro derivatives of cubane (Chart 2) were calculated using the atomization energy approach along with the highly accurate W1-F12 procedure (Table 3). Then we employed the following isodesmic reactions (ID4) – (ID5): ONC (3) + 7 (17) → 8 (12)

(ID4)

ONC (3) + 3 (17) → 4 (13)

(ID5)

0 The DLPNO-CCSD(T)/jun-cc-pVQZ reaction enthalpies  r H gas of (ID4) and (ID5) are 0 –85.4 and –67.1 kcal mol-1, respectively. The corresponding values of  f H gas of ONC 0  168.2 ± are 167.2 and 169.2 kcal mol-1. Finally, the average value for ONC is  f H gas

1.5 kcal mol-1. It is more than 5 kcal mol-1 lower than the DFT estimations reported before (Table 4).32


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0 Additionally, in the case of TEX (2), we were able to calculate the  f H gas directly at

the W1-F12 level without resorting to isodesmic reactions. Note that the resulting value 0  f H gas  –95.6 ± 1.5 kcal mol-1, which is again ~12 kcal mol-1 higher than the best DFT

estimations reported so far.66 In Table 4, we summarized all of the most important quantitative thermochemical data of CL-20, TEX, and ONC obtained in this work. Recall that only the DLPNO-CCSD(T) enthalpies of the corresponding isodesmic reactions made these estimations feasible. Table 4. The Gas Phase Formation Enthalpies of CL-20 (1), TEX (2), and ONC (3) at 298 K (  f H gas ) Calculated at Various Levels of Theory Using the Atomization Energy 0

Approach and Isodesmic Reactions. All Values are Given in kcal mol-1. Compound

0  f H gas

131.1 ± CL-20 (1)

1.5a 119.6b –95.6 ±

TEX (2)

1.5c –107.2d 168.2 ±

ONC (3)

1.5e 173.6f

The average value from this work calculated using the DLPNO-CCSD(T) enthalpies of isodesmic reactions (ID1-ID3). b The average value from isodesmic reactions at the highest level of theory (G4MP2) among those reported in the literature so far, Ref 65. c Calculated in this work using the W1-F12 multi-level procedure and the atomization energy approach. d The best theoretical value (B3LYP along with isodesmic reactions) reported so far, Ref. 67. e The average value from this work calculated using the DLPNO-CCSD(T) enthalpies of the a


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isodesmic reactions (ID4-ID5). f The best theoretical value (B3LYP along with isodesmic reactions) reported so far, Ref. 32.

4. CONCLUSIONS In conclusion, we emphasize that DLPNO-CCSD(T) allows for routine QZ-quality coupled cluster calculations for the energetic species comprised of ~30-40 non-H atoms (such as CL-20, ONC, and nitro derivatives of adamantane considered in this work). At the same time, the benchmarking of the present work revealed that the DLPNO approach does not deteriorate the quality of the coupled cluster procedure. The accurate bond energies for CL-20 and ONC obtained in the present work are ~10 kcal mol-1 more accurate than the best available theoretical values so far. In addition, due to very favorable scaling with the size of the molecule, this level of theory is still affordable, e.g., for the dimers of the latter species. The obtained highly accurate activation barriers and bond energies are particularly useful for benchmarking and calibration of the existing force fields, which are indeed highly desirable for reliable predictions of thermal decomposition and detonation-related phenomena of energetic materials. In a more general sense, this offers a new level of predictive computational kinetics for polynitro caged energetic materials. The reliable coupled cluster quality computational techniques provide convincing evidence on the key thermochemical values and are a viable step beyond the commonly used DFT procedures. ASSOCIATED CONTENT


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Supporting Information. Supporting Information (SI) available: the full set of the conformer energies of CL-20; relative enthalpies and enthalpies of the radical reactions and activation barriers of the molecular channels; raw computational data (optimized geometries, electronic energies, and thermal corrections to thermodynamic potentials of all compounds under study). The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.xxx

AUTHOR INFORMATION

Corresponding Author *To whom correspondence should be addressed:

V.G.K.: E-mail: [email protected] C.F.G.: E-mail: [email protected] ORCID Vitaly G. Kiselev: 0000-0002-2721-539X C. Franklin Goldsmith: 0000-0002-2212-0172

Notes


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The authors declare no competing financial interest.

ACKNOWLEDGMENT

The authors thank Professor Amir Karton for providing the scripts for W1-F12 calculations. C.F.G. gratefully acknowledges financial support from Brown University and ONR (grant Number N00014-1-61-2054, with Dr. Chad Stoltz as the program manager). V.G.K. acknowledges the Supercomputer Center of Novosibirsk State University and Russian Science Foundation for a financial support of the computational part of this work (project 16-13-10155). This work was also supported by Brown University through the use of the facilities of its Center for Computation and Visualization.

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