About the Aromaticity of symm-Triaminotrinitrobenzene - The Journal

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

About the Aromaticity of Symm-triaminotrinitrobenzene Iryna V. Omelchenko, Oleg V Shishkin, Przemyslaw Dopieralskie, and Zdzislaw Latajka J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b00433 • Publication Date (Web): 27 Feb 2019 Downloaded from http://pubs.acs.org on March 1, 2019

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The Journal of Physical Chemistry

About the Aromaticity of Symmtriaminotrinitrobenzene Iryna V. Omelchenkoa,b,*, Oleg V. Shishkina,b,†, Przemyslaw Dopieralskic, Zdzislaw Latajkac a Department

of X-ray Diffraction Study and Quantum Chemistry, SSI “Institute for Single

Crystals” NAS of Ukraine, 60 Nauky ave., Kharkiv 61072, Ukraine b

Faculty of Chemistry, V.N.Karazin Kharkiv National University, 4 Svobody sq., Kharkiv

61077, Ukraine c

Faculty of Chemistry, University of Wroclaw, F. Joliot-Curie 14, 50-383 Wroclaw, Poland

*

Corresponding author. E-mail: [email protected]. Phone/Fax: +380573410258

†

Deceased.

ACS Paragon Plus Environment

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Abstract Aromaticity and structural features of the isolated symm-triaminotrinitrobenzene (TATB) were examined using the non-empirical ab initio quantum chemical method and molecular dynamics at the Car-Parrinello level. Different criteria of the aromaticity were combined with the study of conformational flexibility of molecule and analysis of the electron density distribution. It was found that cooperative effect of the resonance-assisted hydrogen bonds results in the ultimate decreasing aromaticity of the benzene ring in TATB. Values of HOMA index indicate that it could be classified as low-aromatic in equilibrium state at zero temperature but completely nonaromatic at the room temperature. An extremely high flexibility of the molecule is also not typical for aromatic rings. The electron delocalization in H-bonded O=N–C=C–N–H quasiaromatic rings was found to be greater than in the benzene ring of TATB.


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Introduction Symm-triaminotrinitrobenzene (TATB) is a well-studied compound known for its non-linear optical and explosive properties combined with the extraordinary thermal, impact, and shock stability in the solid state1,2. Its’ individual molecular structure overcrowded with both π-donor and π-acceptor substituents is the subject of the particular theoretical interest because of the strong intramolecular push-pull interactions3–5. One of the main questions about the structure concerns the aromatic interactions in the TATB molecule. They are associated with the tendency to the tautomerization and the proton transfer, the properties are believed to be the main factors that affect impact sensibility and explosion dynamics6,7. Also the aromaticity interferes with the charge-transfer effect that is responsible for the non-linear optical (NLO) properties8,9. Although the degree of aromaticity of some well-known conjugated molecules, as well as its quantitative criteria, is still under discussion10,11, all benzene derivatives have always been an islet of consistency in the turbulent sea of the aromatic definitions, undoubtedly treated as highly aromatic substances10,12–14. However, the case of TATB seems to need deeper investigation of the matter. One of the most remarkable features of its structure is the number of strong intramolecular resonance-assisted hydrogen bonds15–17 between amino and nitro substituents18. It is known that influence of such intramolecular H-bonding on the aromaticity and π-electron delocalization could be rather strong19–24, especially for the ortho-substituted rings with strong H-bonding between substituents. In some particular non-aromatic conjugated systems, such as malonaldehyde or malondialdehyde derivatives, the electron delocalization in the hydrogenbonded quasi-aromatic rings25 could be comparable to the delocalization in the aromatic πsystems26–28. In the previous studies of the structure and aromaticity of the series of


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aminonitrobenzenes29 it was found that the degree of benzene ring aromaticity decreases essentially with the increasing of the number of such hydrogen bonds between amino and nitro groups, mutually enhancing each other in the non-additive manner. The substituent effect on aromatic ring could also be strongly affected by involving the substituent into intermolecular hydrogen bonding21. Structural consequences of the intramolecular push-pull effect in aminonitrobenzenes have also been associated with the H-bonding, too29. Also it is known that conformations of overcrowded benzene derivatives with 5 to 6 substituents could be strongly affected direct interactions between substituents, either attractive or repulsive, and it could result in strong deformation of benzene ring from planar geometry30,31. The planarity of the benzene ring is known as a property – and the necessary condition – of the aromaticity of cyclic conjugated system, however it was already shown that small deviation from planarity does not disrupt aromatic conjugation and could be used as a measure of the degree of aromaticity32,33, and the Car-Parrinello molecular dynamics (CMPD) studies revealed that the slightly non-planar conformations are even typical for aromatic molecules including benzene at the room temperature in gas phase34,35. Presence of several substituents could force the major out-of-plane deformation unfavorable for aromatic delocalization31. Thus, the TATB molecule contains six substituents that could affect properties of benzene ring by push-pull effect, by resonance-assisted hydrogen bonding and by sterical hindrance, so that is the question in what extent the direct intramolecular interactions between substituents could disturb the persistent electronic structure of the benzene ring. The particular issue concerns limitations of methods that are reasonable for investigation of aromaticity-related properties of TATB. The experimental structural studies of individual TATB molecule are still complicated due to the explosibility of the compound and its extraordinary


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stability in the crystalline phase2. Thus the most precise experiments were carried out for the substance in the solid state5,36. However, the molecular structure is obligatory affected with the intermolecular interactions that are observed in the crystals and solutions. Effects of the crystal packing could introduce essential corrections to the structure of individual molecule5,37,38 . That seems to be important for TATB molecule for two main reasons: (a) the intermolecular hydrogen bonds in the crystal compete with intramolecular5 and may affect their influence, and (b) the overcrowded nitroaromatic molecules are known to be rather flexible31,39 but the TATB planarity may be enforced by the crystal surrounding. Also, it is usually not possible to measure the physico-chemical properties of individual molecule in the crystal directly due to the collective effects. The quantum chemical studies is the perspective way to investigate the TATB properties, both individual and collective, however it is known to be very sensible against the computational methods40. Therefore some of the results obtained in the previous studies of TATB (HOMA and NICS aromaticity values with MP2/cc-pVDZ method, as well as flexibility investigation29) need the careful revision. In the present study, we examined the structure, conformational properties, NICS indices, and intramolecular interactions in the TATB molecule in order to ascertain its actual aromaticity degree and the degree of changes of structural and electronic features associated with the aromaticity. Computational Details Ab initio calculations: the structure of isolated TATB molecule has been optimized using the Møller-Plesset second order perturbation theory (MP2)41 with series of Dunning correlationconsistent basis sets42 and also using the DFT M06-2X method43. The character of stationary point on potential energy surface was checked by calculations of the Hessian matrix at the M062X level of theory only, no negative eigenvalues of the Hessian were found. The deformation


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energy at zero temperature was defined as increasing of the total energy of the molecule upon the relaxed potential energy surface (PES) scan along the endocyclic torsion angles by the given angle value, from 0° to 30°, as described in previous studies14,33. PES scans were performed at the MP2/cc-pVTZ level. Since the molecule is not strictly symmetrical in calculations, different angles revealed slightly different values of deformation energies, but only the smallest values were taken as “deformation energy”. Amino group pyramidality was calculated as the sum of bond angles centered on the corresponding nitrogen atom. Aromaticity was estimated by HOMA aromaticity index44 and values of the z-component of nuclear independent chemical shifts at the point located 1 Å above the ring critical point, NICS(1)zz45, the last calculated at the M062X/cc-pVTZ level. Considering that the molecule is not perfectly planar in that calculation, the mean plane of the non-hydrogen atoms were taken as (xy) plane, and the results for the points 1 Å above and below the plane were averaged out. AIM analysis46 was performed with AIMALL program47 using the wavefunction from MP2/aug-cc-pVTZ calculation, and the NBO analysis48 was performed at the MP2/cc-pvtz (orbital decomposition, Wiberg bond orders) and M06-2X/ccpVTZ (atomic charges and E(2) interaction energies) levels. CPMD calculations: all calculations are based on ab initio molecular dynamics49 using the efficient Car–Parrinello50 propagation scheme as implemented in the CPMD program package51. These pseudopotential calculations have been carried out using the PBE52 exchange–correlation functional within the spin–restricted Kohn–Sham formalism together with a plane-wave basis set at a kinetic energy cutoff of 100 Ry, gamma–point sampling of the Brillouin zone, and Troullier– Martins53 normconserving pseudopotentials. The supercell for all these calculations was a cubic box 16 Å in length. All dynamic simulations were performed in the canonical ensemble at 298 K using Nosé–Hoover chain thermostats54 in order to control the kinetic energy of the nuclei as


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well as the fictitious kinetic energy of the orbitals. A molecular dynamics time step of Δt = 3 a.u. (≈ 0.073 fs) was used for the integration of the Car–Parrinello equations of motion using a fictitious mass parameter for the orbitals of 400 a.u. together with the proper atomic masses. After initial equilibration period (ca. 30 000 steps) the Car-Parrinello molecular dynamics simulations were performed and the data were collected over trajectories spanning 300 000 steps (ca. 22 ps). Additional processing of the experimental X-ray diffraction data of the TATB molecule taken from the CSD database55 was accomplished in order to normalize all N–H distances (N–H bonds were fixed at 1.015 Å) except the data sets containing already normalized N–H distances. All experimental N–H…O bond lengths were given for the normalized N–H distances. Benchmark of reproducibility of computations results. It should be noted that the geometrical parameters at the equilibrium point crucially depend on the basis set but much less depend on the method (Table 1). Unfortunately the effect of the basis set extending and improving the method cannot be verified due to the lack of experimental data in the gas phase. One can see the drastic shortening of the endocyclic C–C bonds as well as C-NH2 and C-NO2 bonds with extending the basis set from double-zeta to triple-zeta. Values of the torsion angles are strongly affected by the presence of the diffuse functions in the basis set but that effect is much less pronounced in the triple-zeta basis. It is possibly due to the intramolecular basis set superposition error56, so in this case at least the triple-zeta basis is obligatory for the correct estimation of the geometrical parameters: the smaller sets presumably would give the erroneous results. Also, it is worth mention that in all calculations, the TATB molecule adopted the C1 symmetry. Here and further in Results&Discussion section, we give the range of the values of


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geometrical parameters if they differ for different positions in molecule but merge them in one value if the difference is negligible. Table 1. Selected structural parameters of the TATB molecule (bonds lengths and H-bonds distances, Å, torsion angles, deg, amino groups pyramidalities Ʃ(NH2), deg) estimated using different basis sets and methods at the equilibrium point in vacuum. method/basis C–C

C–NH2

C–NO2

H…O

C-C-C-C

C-C-N-O

Ʃ(NH2)

MP2/ccpvdz

1.443

1.336

1.445

1.702 - 1.705

5.7

7.8 - 14.6

360.0

MP2/aug-cc1.445 pvdz

1.338

1.436

1.704

0.0

10.4

360.0

MP2/cc-pvtz

1.430

1.329

1.431

1.719

2.3 - 2.4

15.4 - 18.1 360.0

MP2/aug-cc1.432 pvtz

1.329

1.428

1.714 - 1.716

0.1 - 0.3

15.2 - 15.8 360.0

M062X/aug-ccpvtz

1.325

1.435

1.760

0.1 - 0.3

19.5

1.431

360.0

Results and discussion Selected geometrical parameters and HOMA aromaticity index of single molecule, obtained at the equilibrium point (MP2/aug-cc-pVTZ results), in the dynamical motion at room temperature (CPMD results), and taken from the single crystal X-ray diffraction study36 are given in the Table 2. For CPMD results, mean HOMA value was calculated as the mean value of HOMA index at every point of trajectory. 1. Molecular geometry, intramolecular hydrogen bonding, and aromaticity. Specific features of molecular geometry are among the most important evidences of the aromatic character of the ring10. The structural properties of TATB molecule indicate its drastic difference


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from benzene as well as mono- and disubstituted benzene derivatives having the same substituents (aniline, nitrobenzene, ortho-nitroaniline). Endocyclic C–C bond lengths (Table 2) are quite far from the C–C bond lengths for benzene (ca. 1.396 Å), Cipso–Cα bonds in aniline, nitrobenzene and ortho-nitroaniline (ca. 1.395 – 1.410 Å). These bonds are longer in CPMD simulation, likely due to the dynamical vibration motion of the molecule that is not considered in equilibrium point calculations, but both CMPD and ab initio C–C bond lengths fit the range of the bond lengths observed in the crystal. Presence of the neighboring substituents in benzene ring causes elongation of C–C bonds, however, the magnitude of the elongation is much smaller (Cipso–Cα bond length in ortho-nitroaniline with the same pair of substituents is 1.410 Å). Table 2. Geometrical details and aromaticity of TATB (covalent and non-covalent bonds lengths, Å, torsion angles, deg, amino groups pyramidality Ʃ(NH2), deg, and HOMA aromaticity index44 derived from C–C bond lengths) estimated with different methods method

C-C

C-NH2

C-NO2

H…O

C-C-C-C

C-C-N-O

equilibrium

1.432

1.329

1.428

1.715

0.1 - 0.3

15.2 - 15.8 360.0

0.50

1.437

1.7751.786

8.5 14.3

13.5 - 18.9 357.8

0.06

experiment 1.435- 1.309(crystal)[a]36 1.450 1.319

1.4171.422

1.6931.791

1.575.00

3590.70 - 3.22 360

0.24

experiment (crystal)5

1.4141.420

1.6951.720

2.505.78

1.37 - 3.23 360

0.08

CPMD

1.441

1.335

1.445- 1.3181.449 1.321

Ʃ(NH2)

HOMA

-

[a] Experimental geometry with renormalized N–H distances. At the same time, the values of the exocyclic C–N bonds in TATB (1.309 – 1.335 Å for NH2 group and 1.417 – 1.437 Å for NO2, depending on the method) is dramatically smaller than values of similar bonds in all isolated isomeric nitroanilines (1.370 – 1.390 Å and 1.456 – 1.470 Å, respectively). Amino group is planar or almost planar in isolated molecule as well as


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molecule in the crystal, and the whole molecule is slightly bent in both calculations (C-C-N-O torsion angles are 13.5 – 18.9°) but it is planar in the crystal, perhaps due to the extremely low energy of nitro group rotation39,40 that makes the molecular shape very sensitive to the features of intermolecular interaction, like hydrogen bonds and stacking interactions1,57 . The structural aromaticity index HOMA of the benzene ring of TATB is extremely low. Even the highest value of 0.50 obtained by QC modeling at equilibrium geometry and zero temperature is more typical for semi-aromatic and non-aromatic heterocycles44 rather than for benzene derivatives58. Moreover, the dynamical aromaticity of TATB varies from -1.87 to 0.82 (Fig. 1) with the most probable value of 0.06. Thus one can state that at the room temperature in gas phase, more than 95% of TATB molecules are completely non-aromatic.

Figure 1. The HOMA distribution in TATB from the CPMD simulation To verify these conclusions, also the magnetic NICS(1)zz indices were calculated for the molecule in equilibrium geometry. The values in the projections of ring critical points of the benzene ring and all six H-bonded rings were investigated in the MP2/aug-cc-pVTZ geometry


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with M06-2X method. The value for the benzene ring is -7.85 ppm that corresponds to the semiaromatic or even non-aromatic ring (it equals to ca. -35 for benzene and -23 ÷ -35 for the most aromatic structures45). 2. Intramolecular hydrogen bonding. The presence of the resonance-assisted hydrogen bonds is known to have substantial effect on the structure of the conjugated molecules26,27,59. Particularly it could reinforce the electron localization due to the positive non-additive interaction with the charge-transfer effect60 that is known to have notable influence on the equilibrium electronic structure of TATB8. The lengths of the H…O contacts in the intramolecular N–H…O bonds (Table 2) indicate strong H-boding. Interestingly, the range of the H…O distances in the crystal embraces the range derived from ab initio and CPMD calculations. They are notably shorter than the H-bond in ortho-nitroaniline (~1.95 Å29,61). At the time, C– NH2 and C–NO2 bonds are notably shortened too but C–C endocyclic bonds are significantly elongated (Table 2) as compare to mono- or disubstituted benzene derivatives with amino and nitro substituents14,29,61. All these are well known structural features of the resonance-assisted Hbonding62 indicating strong π-conjugation of electron density localized in the hydrogen-bonded ring H–N–C–C–N–O, so that ring could be defined as a quasi-aromatic. The QTAIM study of the properties of hydrogen bond critical points reveals their high density values (~0.048 e/a03) close to experimentally observed (0.044 … 0.047 e/a03)5 and low but negative Laplacian (~ 0.039 e/a05) that slightly differs from experimental results (+0.184 … +0.200 e/a05)5. That indicates the considerable contribution of covalent bonding. Energy of each of these intramolecular H-bond estimated following the Espinosa equation63 is 16.4 – 16.5 kcal/mol that almost perfectly matches results from experimental electron density analysis (15.1 – 15.8


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kcal/mol)5. Therefore the cumulative energy of intramolecular H-bonds is about 98 kcal/mol. That is three times above the known resonance energy in the benzene ring (ca. 36 kcal/mol58). NICS(1)zz values calculated for quasi-aromatic H-bonded rings are about -11.4 that indicates higher π-electron delocalization than in carbocyclic ring, whereas the ring size is approximately the same (the 1…4 N–N distance in the H-bonded ring is 2.81 Å while the 1…4 C–C distance in the carbocyclic ring is 2.86 Å). One can state that π-delocalization in H-bonded rings of TATB is higher than in the carbocyclic ring. Thus the key energetic factor that defines the properties of the TATB molecule is not the benzene aromaticity but the intramolecular H-bonding. 2. Conformational flexibility. It was previously found that the isolated benzene and its derivatives are moderately flexible: the energy of deformation of any torsion angle by 30° is about 7 kcal/mol

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for benzene, slightly dropping down with the aromaticity decrease14,29,33.

Also it was found that the vibrations at room temperature drastically increase the degree of nonplanarity for all aromatic rings34,35,64. The TATB molecule is extremely flexible as compared to benzene. Its deformation energy is 1.8 kcal/mol at zero temperature. Another particular feature of this potential energy surface (PES) is it's anharmonicity (Fig. 2). The dependence between total energy gain and the value of the endocyclic torsion angle for highly aromatic cycles is commonly strictly harmonic (follows the E = kφ2 equation; the corresponding ideal parabolic curve is denoted with a red color on the fig. 2)14,33. One can see that PES of TATB doesn't meet this rule: is has a plateau in the range of ±15° with almost constant value of energy that is not typical for benzene derivatives14 but is rather common for non-aromatic partially saturated rings65,66.


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2.0 1.8 1.6 1.4

Energy (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -30

-20

-10

0

10

20

30

Torsion angle (deg)

Figure 2. Changes of the energy with the change of the endocyclic torsion angle at equilibrium point. The red curve plots the harmonic energy dependence inherent to highly aromatic rings. CMPD study reveals that at the room temperature TATB is far more flexible than benzene34 (see Fig. 3). The module of each single torsion angle could reach 35°, and the puckering amplitude67 changes from 0 to 0.6. The mean puckering amplitude S is 0.27 here, while it does not exceed 0.16 in benzene and other aromatic rings34,35. That value indicates rather strong puckering: the approximate limit of the near-planar configuration is S~0.1 that corresponds to torsion values ~5°. The typical conformation is far from planar, only 5.6% of the molecules are planar at every moment, puckering parameters67 indicate that 48.9% adopt slightly flattened twist-boat and 27.9% - flattened boat conformation. That agrees well with the extremely low aromaticity in the gas phase and explains a great difference between the values of torsion angles estimated with different methods: the energy of deformation is so small that even the minimal influence or negligible computational error can change the torsion angles up to 20°.


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12

Relative Frequency, %

10

8

6

4

2

0 0

5

10

15

20

25

30

35

Torsion, deg

7 6

Relative Frequency, %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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5 4 3 2 1 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

S (puckering parameter)

Figure 3. Distribution of the torsion angle C(1)–C(2)–C(3)–C(4) (module value) and ring puckering amplitude S at the room temperature according to the CPMD data. 3. Orbital decomposition and intramolecular conjugation: NBO and AIM results. The constructing of the natural bonding orbitals for the TATB molecule leads to unexpected results. The NBO algorithms of the natural localized molecular orbitals (NLMO) threat its molecular structure in a completely different way than the common aromatic benzene derivatives. While the most derivatives retain the orbital structure of the parent benzene ring with both σ and π orbitals at C–C bonds, only the σ orbitals at the C–C bonds were located in the TATB molecule


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indicating dramatic weakness of these bonds compared to benzene C–C bonds. However, the substituents effect is not strong enough to form the radialene-like picture of the π orbitals, and all C–N bonds are treated as σ bonds too. This is supported by the values of the Wiberg bond orders (1.14 for C–C bonds, 0.96 for C–NO2 and 1.29 for C–NH2 bonds). In the frame of these limitations, all π electrons of the ring were localized by NBO algorithms as lone pairs on carbon atoms. It rather does not mean the actual presence of the lone pair. In order to find the arguments, we have calculated critical points (CPs) of the L(r) function68, which is defined as minus the Laplacian of the electron density, ∇2ρ46, in the vicinity of all non-hydrogen atoms (see Fig. 4).

Figure 4. Bond critical points (BCPs) of the electron density (small green spheres) and maximums (3;+3 critical points) of L(r) function (large yellow spheres) in the vicinity of the C– NH2, C–NO2 and C–C bonds of TATB. Black lines show bond paths.


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The L(r) function is a powerful tool for exploring the electron density map in order to locate the electron pairs68. It provides a quantitative physical basis for the valence-shell electron pair repulsion model69,70. Maximums of the L(r) mapped with (3;+3) CPs represent the local charge concentration areas that could be associated with the spatially localized electron pairs70. The distribution of the (3;+3) CPs of L(r) presented on Fig. 4 is common for a π-conjugated system with sp2-hybridized C, N and O atoms. Each C–C, C–N and N–O bond reveals two L(r) maxima located on the bond path, representing the valence shell charge concentration areas for double bond. It is worth mention that these maxima are located symmetrically or almost symmetrically with respect to the geometrical center of each bond, but the bond critical points are not. BCP position on each of C–N bonds meets the position of (3;+3) CP of L(r) that is closer to the C atom. Thereby the local charge concentration on C–N bonds is strongly shifted to the basin of the N atom that determines highly negative charge of N atom (see below). Two non-bonding (3;+3) CPs of L(r) near O atoms represent positions of the lone pairs, directed at H atoms of neighboring NH2 groups. One can see that there are no non-bonding (3;+3) CPs of L(r) that could be attributed to the lone pair of carbon atoms. Therefore one can suppose that lone pairs on carbon atoms in the NBO interpretation of TATB are no more than erroneous construction due to the extremely delocalized structure with the strong interaction between the ring and substituents. The forced orbital localization is somewhat tricky in the case but it still could provide valuable quantitative estimation of the relative energies of intramolecular conjugation. Analysis of the E(2) energies (Table 3) reveals that the three strongest interactions (264 – 336 kcal/mol) along with six weaker interactions (126 – 139 kcal/mol) correspond to the conjugation of this virtual ‘lone pair’ with the π-system of the substituents. The fourth to sixth ones (158 –


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179 kcal/mol) are due to resonance inside nitro group. The remarkable finding is that conjugation interactions between C atoms and N–O bonds are stronger than interactions between neighboring C and N atoms. That is a clear evidence of strong charge transfer from the carbon ring to the oxygen atom and π-system of nitro group that reinforces the intramolecular hydrogen bonds. Such type of conjugation is much more typical for non-aromatic conjugated systems71. At the time no conjugative coupling between the carbon atoms were found among the interactions with highest E(2) energies. That accounts for the low aromaticity of carbon ring. We have compared the present data for TATB with E(2) energies of the ortho-nitroaniline having the same substituents but only one intramolecular H-bond. The strongest interaction of the 186 kcal/mol corresponds to the resonance inside nitro group and two interactions of 120 – 146 kcal/mol correspond to the resonance inside the benzene ring. The similar energy disposition could be found in para-nitroaniline: the strongest interaction here (360 kcal/mol) is due to the conjugation inside the benzene ring, the second one (211 kcal/mol) is due to the resonance inside the nitro group. All other E(2) energies in both these molecules are much weaker (40 kcal/mol and smaller). There are no strong interactions that correspond to the conjugation between the ring and the substituent in nitroanilines, in contrast to TATB. Thus, the overall picture of conjugation energies in TATB is drastically different from the benzene derivatives, and the TATB could not be treated as the benzene derivative from the energetic point of view. Table 3. E(2) orbital interaction energies from the NBO/NLMO study donor

acceptor

energy, kcal/mol

lone pair carbon

antibonding N = O

336

lone pair carbon

antibonding N = O

332

lone pair carbon

antibonding N = O

264


17


lone pair oxygen

antibonding N = O

179

lone pair oxygen

antibonding N = O

165

lone pair oxygen

antibonding N = O

158

lone pair carbon

antibonding C – N

139

lone pair carbon

antibonding C – N

133

lone pair carbon

antibonding C – N

131

lone pair carbon

antibonding C – N

130

lone pair carbon

antibonding C – N

127

lone pair carbon

antibonding C – N

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Natural charges are equal to -0.37e for each nitro group and +0.18e for each amino group. Carbon atoms connected to the nitro group bear negatively charges (-0.12e), and those connected to amino groups — positively charges (+0.30e). Generally, the structure is strongly charge alternating. The magnitude of the charge separation is also much higher than in isomeric nitroanilines (which carry -0.23 … -0.27e on nitro group and about zero on amino group), and the carbon atoms connected to substituents in nitroanilines are all positively charged (+0.04 +0.16e) in more or less uniform way. The atomic charges estimated from the AIM study are rather different from the NBO charges because of the reciprocal polarization46 but emphasize the redistribution of the electron density from the benzene ring to the substituents. Both nitro and amino groups in the case carry negative charges, and these charges are different, -0.31…-0.71e for nitro groups and -0.07…-0.24e for amino groups (previously reported values are 0.70e/+0.62e 4 and -0.72…-0.75e / -0.16…-0.18e 5). The negative charge on each amino group is mainly due to the amino nitrogen atoms that bear charges of -1.3 - -1.5e (previously reported values are -1.21e

4

and -1.305…-1.326e 5). Carbon atoms bear all extra positive charge but the

charge alternating is observed here as well (+0.28…+0.36e on C atoms connected to nitro groups


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and +0.63…0.69e on C atoms connected with amino groups, previously reported values are +0.28e/+0.62e 4 and +0.27…+0.28e / +0.63…+0.64e 5). Conclusions Structural features, aromaticity indices, deformation energies and features of intramolecular interactions of the TATB molecule were examined with different quantum chemical methods and compared with known experimental data. Geometrical parameters of the molecule strongly differ from the parameters of benzene and benzene derivatives with smaller number of substituents. Values of aromaticity indices clearly reveal that carbon ring in TATB is non-aromatic, and its extremely high flexibility at zero and room temperatures is also not typical for aromatic rings. The consolidated strength of six intramolecular resonance-assisted N–H…O hydrogen bonds is about 98 kcal/mol that is three times higher than resonance energy of the benzene aromatic πsystem (~37 kcal/mol), and these interactions are the governing factor that determine the molecular structure. According to NICS(1)zz aromaticity indices, the electron delocalization in H-bonded O=N–C=C–N–H quasi-aromatic rings is greater than in the carbon ring. The strongest π-π interactions in TATB molecule correspond to the conjugation between the carbon ring and the substituents, and the values of natural charges reveal highly charge alternating structure that supports the strong hydrogen bonding. ACKNOWLEDGMENT The authors (P.D. and Z.L.) would like to gratefully acknowledge the Wroclaw Centre for Networking and Supercomputing (WCSS) for use of BEM cluster. P.D. gratefully acknowledges financial support from the National Science Centre of Poland (2016/23/B/ST4/01099). I.O. gratefully acknowledges financial support from the National Academy of Sciences of Ukraine (2017-2018, 0117U001685).


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