Stabilization of cyclo-N6 by insertion into [18]-annulene: a DFT study

doi:10.21203/rs.3.rs-5003969/v1

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Stabilization of cyclo-N6 by insertion into [18]-annulene: a DFT study

https://doi.org/10.21203/rs.3.rs-5003969/v1

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published 18 Oct, 2024

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The elusiveness of hexazine (a.k.a. hexaazabenzene) and its perhydrogenated derivative, hexazinane, prompted the author to investigate the possibility of stabilizing the six-membered nitrogen ring by inserting it into [18]-annulene. The resulting compound is made of a central N₆ ring surrounded by an outer ring of 18 carbon atoms that prevents its decomposition into dinitrogen. The N₆ ring is non-planar and with a chair-like conformation that does not undergo conformational isomerization. The designed molecule can be stabilized either by oxidation to a hexa-oxide derivative or by coordination of ZnCl⁺. Furthermore, a triangle-shaped macrocyclic isomer made of three pyridazine moieties connected to each other by ethylene bridges represents a possible precursor in the synthesis of the N₆-embedded hydrocarbon. By employing an alkali or alkaline-earth metal cation that coordinates the three pyridazine monomers it becomes possible to bring their nitrogen atoms in close proximity so that a subsequent aromatic fusion reaction could be attempted.

Hexazine

Hexazinane

Nitrogen rings

DFT

QTAIM

Molecular rings made of nitrogen atoms [1–3] have attracted much attention from research chemists owing to the possibility of synthesizing novel energetic materials as well as for their analogies with the corresponding all-carbon cycles [4, 5]. The crystal structures of several salts containing the pentazolate anion (cyclo-N₅⁻) have been determined by X-ray diffraction analyses [6–10] while the di- and tetra-anionic hexazine derivatives cyclo-N₆²⁻ and cyclo-N₆⁴⁻, respectively, have been recently synthesized and structurally characterized under high pressure [11, 12]. In contrast, the neutral hexazine molecule or hexaazabenzene (cyclo-N₆) is yet an elusive compound whose initial observation in the gas-phase has not been corroborated within the past forty years [13].

The above-mentioned state of affairs originates from the large energy difference between cyclo-N₆ and 3∙N₂ which, according to quantum chemical calculations, amounts to more than 200 kcal/mol [14–20]. Some computational studies suggested the possibility of stabilizing hexazine using oxygen, such as in N₆O₃ [21], calcium, such as in Ca_xN₆ (x = 1,2) [22], or a metal, such as in M(η₆-N₆) with M = Ti, Zr, Hf, Th [23]. However, these theoretical predictions have not been realized in the laboratory yet. A similar situation holds also for the non-aromatic compound hexazinane or cyclo-N₆H₆ which in the gas-phase was predicted to adopt a chair-like conformation with all the N–H bonds oriented in the axial position (ax,ax,ax,ax,ax,ax) whereas the conformer with an all-equatorial orientation of the N–H bonds (eq,eq,eq,eq,eq,eq) is, somewhat surprisingly, the less favored [24]. Furthermore, according to an extensive computational analysis of N₆H₆ isomers, both linear and branched open chain isomers are more stable than ring isomers and among the latter a five-membered ring isomer is the most favored [25]. Nevertheless, one possible strategy for the stabilization of the N₆ ring would be inserting it into a suitable molecular frame thus preventing its decomposition into molecular nitrogen.

Herein, with the aid of density functional theory (DFT) [26], we investigate the molecular and electronic structure of a compound derived from [18]-annulene [27–30] and containing an N₆ ring whose chemical structure is shown in Fig. 1. In it, the six nitrogen atoms are bonded to one another by N–N single bonds thus forming a six-membered ring that is stabilized by an outer ring made of 18 carbon atoms. To the best of our knowledge, we are not aware of the existence of molecular hydrocarbons containing N₆ rings while an N₃ ring supported by a cyclohexane frame was characterized by X-ray diffraction analysis [31, 32]. Also, worthy of note here are the theoretically predicted beryllium-nitrogen monolayers with embedded planar N₆ rings [33, 34].

For the optimization of the molecular geometry and the calculation of the harmonic vibrational frequencies and the zero-point energy (ZPE) we used the B97D3 functional [35, 36] in combination with the def2-SVP and def2-TZVPP basis sets [37, 38]. Moreover, for the sake of comparison, the popular B3LYP hybrid functional [39] and the Möller-Plesset second order perturbation theory method (MP2) [40] were also employed here in combination with the above basis sets. When the number of imaginary frequencies is zero (NIMAG = 0), the optimized geometry corresponds to a global or local minimum on the potential energy surface (PES).

All the quantum chemical calculations were performed with the Gaussian 16 software package [41] which includes the NBO 3.1 program [42] necessary to perform a natural bond orbital (NBO) analysis of the self-consistent field (SCF) density [43]. Pre- and post-processing operations were carried out with the GaussView graphic interface [44]. The AIMAll software [45] was employed in the topological analysis of the charge density based on the quantum theory of atoms in molecules (QTAIM) [46–48].

Geometries

The DFT-optimized geometry of 1 (NIMAG = 0, ν₁ = 29 cm^− 1) is shown in Fig. 2. The D_3d-symmetric structure has three nitrogen atoms (N1, N3, N5) positioned above the molecular plane and the other three (N2, N4, N6) below it. The N–N bonds have a length of 1.493 Å which is longer than the N–N bond in hydrazine (N₂H₄) of 1.449(2) Å determined by gas electron diffraction (GED) [49]. The length of the six radially-oriented C–N bonds corresponds to 1.448 Å while the peripheral C–C bonds labeled c and d in Fig. 1 have lengths of 1.388 and 1.380 Å, respectively. In comparison, the GED value of the C–C bond lengths in D_6h-symmetric benzene corresponds to 1.3975 Å [50]. The bond lengths of 1 computed with the B97D3 method compare reasonably well with those computed with the B3LYP and MP2 methods, as reported in Table 1. Furthermore, from this table we can see that the diameter (L) of 1 computed with these three methods is ~ 7.2 Å, the α(NNN) bond angles are close to 104° while the γ(NNNN) dihedral angles are about ± 72°. The latter value together with the N–N bond length (see above) are indicative of a non-planar cyclo-N₆ ring, as shown in Fig. 2.

Table 1 Structural parameters of 1 optimized with the B97D3, B3LYP, and MP2 methods in combination with the def2-TZVPP basis set. Bond lengths (a, b, c, d) and molecular diameter (L) in Å, bond and dihedral angles (α, γ) in degrees

The DFT-optimized geometries of the macrocyclic isomers 2–4 (NIMAG = 0) are shown in Fig. 3. These are triangle-shaped macrocycles with the same chemical formula of 1 (C₁₈ H₁₂N₆) but with different functional groups: isomer 2 is made of three pyridazine rings bonded to each other by ethylene bridges (C = C), isomer 3 possesses three different rings, namely p-phenylene, pyridazine, and tetrazine which are bonded by ethylene bridges, while isomer 4 is made of three para-phenylene rings connected to each other by dinitrogen bridges (N = N).

Since each macrocyclic isomer contains six rotatable bonds, different conformers are expected to exist. In this regard, three conformers of isomer 2 were identified: 2a (ν₁ = 31 cm^− 1) and 2b (ν₁ = 44 cm^− 1), with a partial cone (paco) conformation and C_s-symmetry, and 2c (ν₁ = 47 cm^− 1), with a cone-like conformation and C_3v-symmetry. Among them, 2a is the most stable conformer which is closely followed by 2b (ΔE_ZPE=0.7 kcal/mol) whereas 2c (ΔE_ZPE=8.8 kcal/mol) has higher energy. As far as isomer 3 is concerned, two non-symmetric conformers were identified: 3a (ν₁ = 55 cm^− 1), with a paco conformation, and 3b (ν₁ = 44 cm^− 1), with a cone-like conformation and higher energy (ΔE_ZPE=6.2 kcal/mol). Finally, a C_s-symmetric paco conformer was identified for isomer 4 (ν₁ = 33 cm^− 1). Each conformer in Fig. 3 is characterized by six pairs of dihedral angles of type C = C–C–C(N) or N = N–C–C. For each pair, the first (second) value corresponds to the dihedral angle identified by four bonded atoms the last of which is located above (below) the plane containing the three C = C or N = N bridges. Thus, for example, the pair of values 120°/−61° shown on the right side of conformer 2c (C_3v-symmetry) correspond to the dihedral angles C = C–C–C (120°) and C = C–C–N (− 61°).

As one may expect, macrocycles 2–4 have lower energy than 1 owing to the aromatic character associated to the π electrons delocalized in their six-membered rings [51]. The computed ZPE-corrected energy differences with respect to the lowest energy conformer are as follows: ΔE(1,2a) = 84.7 kcal/mol, ΔE(1,3a) = 91.3 kcal/mol, and ΔE(1,4) = 81.4 kcal/mol. Furthermore, we notice that isomer 2 represents a possible precursor of 1 given the possibility of bringing the six nitrogen atoms in close proximity using, for example, a suitable metal ion with the ability to coordinate nitrogen (vide infra).

To the best of our knowledge based on a search of the Cambridge Structural Database (CSD) [52], while the triangle-shaped macrocycles shown in Fig. 3 have not been synthesized yet, the crystal structure of [2.2.2]paracyclophanetriene, an analogous macrocycle containing three p-phenylene rings connected by C = C bridges, has been determined both in pure form [53] and in complex with tetracyanoethylene [54]. In the molecular co-crystal of the latter (CSD id: FADXUD), the [2.2.2]paracyclophanetriene molecule adopts a fairly regular paco conformation similar to that of 4 (or 2a) whereas the paco conformers in the pure crystal (CSD id: DHCYPH10) display a significant distortion which most likely originates from the crystal packing effects [55].

Frontier orbitals

The frontier orbitals of 1 in the energy range from 0 to − 8 eV are displayed in Fig. 4. The highest-occupied molecular orbital (HOMO) is non-degenerate and separated from the lowest-unoccupied molecular orbital (LUMO) by an energy gap of 1.3 eV. HOMO-1 and HOMO-2 are both two-fold degenerate whereas HOMO-3 and HOMO-4 are non-degenerate as is the HOMO. We notice that the non-degenerate, filled orbitals (HOMO, HOMO-3, and HOMO-4) do possess a C₃ rotation axis normal to the molecular plane whereas the two-fold degenerate orbitals (HOMO-1 and HOMO-2) have lower rotational symmetry with a C₂ rotation axis normal to the molecular plane. As far as the virtual orbitals are concerned, LUMO has a C₂ rotation axis normal to the molecular plane whereas LUMO + 1 and LUMO + 2 do possess C₃ and C₆ rotation axes, respectively, normal to the molecular plane.

We performed a Mulliken population analysis of the Kohn-Sham wavefunction of 1 to unravel the atomic contributions to the HOMO level and found the following composition: N(p) = 0.1131, N(s) = − 0.0152, C_in(p) = 0.0275, and C_out(p) = 0.0114. The negative value of N(s) likely arises from the triple zeta basis set used herein for the geometry optimization but disappears when the smaller double zeta 6-31G(d) basis set [56] is employed: N(p) = 0.1180, C_in(p) = 0.0107, and C_out(p) = 0.0135. Thus, taking into account the number and type of heteroatoms of 1, the sum of the first and second set of values produces for the p-type orbitals the percentage compositions of 98.0% and 93.4%, respectively. The remaining amounts come from the sums of the atomic orbitals with contributions that are below the threshold value of 1.0%.

Furthermore, we performed an NBO analysis [43] to reveal the lone-pairs of the nitrogen atoms of the embedded cyclo-N₆ of 1. The analysis indicated that the nine NBOs with the highest energy are one- and two-center orbitals distributed over the 18 carbon atoms perimeter. Below them, at lower energy, there is a group of six degenerate NBOs corresponding to one-center orbitals occupied by the lone-pairs of atoms N1 to N6 which are displayed in Fig. 5. Three NBOs (N1, N3, N5) are protruding above and other three (N2, N4, N6) below the molecular plane. Finally, the NBO analysis produced for the nitrogen atoms the natural electron configuration [core] 2s^1.38 2p^3.71 which is close to an sp³-type hybridization. Thus, the six lone-pairs are available to interact with metals through coordinate bonds (vide infra).

QTAIM analysis

To further deepen our understanding of the chemical bonding in 1, we have performed a QTAIM analysis of its charge density obtained at the B97D3/def2-TZVPP level of theory. Hereafter we analyze the bonds in 1 using the terminology of QTAIM [46–48] according to which the interactions between pairs of atoms are either of the shared type (sometime called open-shell) or closed-shell type which roughly correspond to covalent and non-covalent bonding, respectively. The former interactions are characterized by negative values of the local energy density (H = G + V < 0) while the latter have positive H values (H > 0) – for a thorough discussion see ref. [57]. H along with other topological properties (Table 2) are evaluated at the bond critical points BCP(3,-1) located on the molecular graph depicted in Fig. 6. The molecular graph thus represents the molecular structure of 1 according to QTAIM [46–48].

Table 2 reports the values of the bond path length (BPL) along with the electronic charge density, ρ(r), and its Laplacian, ∇²ρ(r), the ellipticity parameter (ε), and the kinetic (G) and potential (V) energy densities along with their sum (H) which are evaluated at the BCP(3,−1) located on the corresponding molecular graphs of 1, hexazinane, benzene, and cyclohexane (Fig. 6). The H value (− 0.2112 au) for the N–N bond in 1 is comparable to that in N₆H₆ (− 0.2250 au) which indicates that embedding of the N₆ ring does not significantly affect the topological properties of this bond. Interestingly, the magnitude of ρ(r) in the neighboring C–N bonds (0.2750 au) is similar to that in the N–N bonds (0.2724 au) whereas the corresponding values of ∇²ρ(r) and H are significantly different suggesting differences in their strengths. As far as the C–C bonds (see c and d in Fig. 1) on the molecular perimeter are concerned, there are no significant differences between them although a comparison with the H values of benzene (− 0.3348 au) and cyclohexane (− 0.2081 au) indicates some similarity with the C–C bonds in the former hydrocarbon. Therefore, the π electrons in the carbon atoms (C_in and C_out) of 1 are delocalized over the entire molecular perimeter.

Table 2 QTAIM descriptors (in au) for 1, hexazinane (N₆H₆), benzene (C₆H₆), and cyclohexane (C₆H₁₂) using the charge density calculated at the B97D3/def2-TZVPP level of theory. Listed in the table are the bond path length (BPL), the electronic charge density, ρ(r), and its Laplacian, ∇²ρ(r), the ellipticity parameter (ε), the kinetic (G) and potential (V) energy densities along with their sum (H)

The molecular graph of 1 (Fig. 6) also contains seven ring critical points RCP(3,+1) each one connected to six BCPs of the corresponding six-atom ring. The central rcp1 which arises from the charge density of non-planar cyclo-N₆ has ρ(r) = 0.0195 au which is slightly smaller than the value of ρ(r) = 0.0223 au computed for rcp2 in the surrounding rings. In comparison, the ρ(r) at the RCPs of the other molecules shown in Fig. 6 are: 0.0219 au (hexazinane), 0.0237 au (benzene), and 0.0203 au (cyclohexane). As far as the atom charges are concerned, the QTAIM analysis revealed the following values: q(N) = − 0.3491 au, q(C_in) = + 0.2699 au, q(C_out) = + 0.0202 au, and q(H) = + 0.0194 au. These results indicate that the charge density of 1 is mainly accumulated in the central part of the molecule while gradually decreasing as one moves toward the peripheral part.

Derivatives

In this section we analyze the structures of some potential derivatives of 1 and 2. The derivatives of the former might be important for the further stabilization of the six-membered ring made of covalently-linked nitrogen atoms while the derivatives of the latter could be useful precursors in the synthesis of 1. The optimized geometries of the six derivatives are shown in Fig. 7. All of them are characterized by positive normal modes of vibration (NIMAG = 0). In 1-O₆ (D_3d symmetry) each nitrogen atom of the inner cycle is bonded to an oxygen atom via a highly polar N⁺–O⁻ bond (1.225 Å), three above and three below the molecular plane. Whereas the hexa-oxide adduct is a local minimum on the PES (ν₁ = 63 cm^− 1), the C_3v-symmetric 1-O₃ derivative (not shown) with three N⁺–O⁻ bonds protruding from one face of the molecule is characterized by one imaginary frequency (ν₁ = − 81 cm^− 1). Hence, in contrast to hexazine which might be stabilized by partial oxidation thereby forming N₆O₃ [21], the partial oxidation of 1 is not useful in stabilizing the embedded nitrogen ring.

The next two structures in Fig. 7 are those of two adducts obtained from the interaction of one or two ZnCl⁺ moieties with 1. In C_3v-symmetrical 1-ZnCl⁺ (ν₁ = 15 cm^− 1) all three nitrogen atoms protruding from one face of the molecule interact with the zinc atom of ZnCl⁺ at Zn–N distances of 2.282 Å. In D_3d-symmetric 1-Zn₂Cl₂²⁺ (ν₁ = 15 cm^− 1) two ZnCl⁺ moieties are coordinated to the nitrogen atoms of 1, one above and the other below the molecular plane, at Zn–N distances of 2.312 Å. Also the Zn–Cl distances in these adducts are affected by the composition being 2.119 Å in the 1:1 complex and 2.087 Å in the 1:2 complex. The formation of these charged complexes will require the presence of a suitable counterion to maintain electroneutrality.

The structures shown at the bottom row of Fig. 7 are those of three adducts formed from the interaction of 2 with K⁺ (2-K⁺), Ba²⁺ (2-Ba²⁺), and Ag⁺ (2-Ag⁺). In the C_3v-symmetrical adducts with K⁺ (ν₁ = 45 cm^− 1) and Ba²⁺ (ν₁ = 59 cm^− 1) the macrocycle adopts a cone-like conformation with the metal ion on the apex that interacts with three pairs of nitrogen atoms belonging to the pyridazine rings at M–N distances 2.855 Å (M = K⁺) and 2.742 Å (M = Ba²⁺), respectively. On the other hand, in the adduct with Ag⁺ (ν₁ = 40 cm^− 1) the macrocycle adopts a C_s-symmetric paco conformation where the metal ion interacts with the nitrogen atoms of two pyridazine rings at Ag–N distances of 2.245 Å while the third ring is not involved in the binding. Thus, in order for 2 to be a potential precursor in the synthesis of 1, alkali or alkaline earth metal ions have the ability to bring the three pyridazine rings in close proximity so that the fusion of six nitrogen atoms in a subsequent chemical reaction may generate cyclo-N₆ embedded within the carbon framework of [18]-annulene (see Fig. 2).

We computed the counterpoise-corrected binding energy [58, 59] of the metal complexes shown in Fig. 7 and obtained the following results: −125.6 kcal/mol (1-ZnCl⁺), − 230.5 kcal/mol (1-Zn₂Cl₂²⁺), − 69.0 kcal/mol (2-K⁺), − 189.8 kcal/mol (2-Ba²⁺), and − 97.9 kcal/mol (2-Ag⁺). It must be noted, however, that the binding of the three ions (K⁺, Ba²⁺, Ag⁺) to the free form of the macrocycle (paco conformer 2a) produces a change in conformation with energy differences corresponding to ΔE(2a,2-K⁺) = 16.3 kcal/mol, ΔE(2a,2-Ba²⁺) = 17.5 kcal/mol, and ΔE(2a,2-Ag⁺) = 3.6 kcal/mol. The low magnitude of the latter energy difference is due to the fact that the macrocycle in 2-Ag⁺ adopts a low-energy paco conformation (see Fig. 7) as done by the free macrocycle (see Fig. 3).

Hexazinanes

In this final section of the paper we analyze the geometries of hexazinane and four of its derivatives obtained by replacing the six hydrogen atoms in cyclo-N₆H₆ by fluorine, chlorine, methyl, and cyano groups. In spite of the high relative energy [24], the all-equatorial conformer (eq,eq,eq,eq,eq,eq) of hexazinane was selected in the generation of the derivatives since the same type of conformation appears in the cyclo-N₆ ring of 1 (see Fig. 2).

The DFT-optimized geometries (NIMAG = 0) of cyclo-N₆H₆ (ν₁ = 305 cm^− 1), cyclo-N₆F₆ (ν₁ = 72 cm^− 1), cyclo-N₆Cl₆ (ν₁ = 45 cm^− 1), cyclo-N₆Me₆ (ν₁ = 43 cm^− 1), and cyclo-N₆(CN)₆ (ν₁ = 37 cm^− 1) are shown in Fig. 8. All the molecules but cyclo-N₆Me₆ are D_3d-symmetric with N–N bond lengths ranging from 1.481 Å (cyclo-N₆H₆) to 1.528 Å (cyclo-N₆Cl₆). On the other hand, cyclo-N₆Me₆ has lower symmetry (C_S) since one of its methyl groups (Me^#) points upwards with respect to the molecular plane while the N–N bonds in this derivative have different lengths, namely 1.477, 1.486, and 1.504 Å. These structural and conformational differences can be attributed to the steric bulkiness of the methyl groups that are present in this hexazinane derivative.

A comparison among the nitrogen rings of D_3d-symmetric cyclo-N₆X₆ (X = H, F, Cl, CN) and 1 indicates that cyclo-N₆(CN)₆ has the N–N bond lengths (1.496 Å) that are closest to those of 1 (1.493 Å) while the γ(NNNN) dihedral angles ranging from ± 73.3° (X = H) to ± 75.2° (X = CN) are all close to the value of ± 71.7° in 1 (see Table 1). In spite of the structural similarities between the nitrogen rings of 1 and cyclo-N₆(CN)₆, the latter may not be an easy synthetic target in comparison to the former where the nitrogen ring is embedded within a carbon framework that prevents its conformational change and decomposition.

The elusive hexazine (cyclo-N₆) and hexazinane (cyclo-N₆H₆) molecules do appear to remain so in the foreseeable future. Thus, the original strategy of embedding N₆ into the molecular framework of [18]-annulene has been put forward in this study. Using DFT, we investigated the molecular and electronic structure of an N₆-embedded hydrocarbon 1 (C₁₈H₁₂N₆) where a cyclic ring made of six nitrogen atoms is prevented to decompose into dinitrogen by covalent bonding with the surrounding carbon atoms. The embedded cyclo-N₆ fragment is non-planar with three nitrogen atoms protruding above and three below the molecular plane of 1. This novel compound can be further stabilized either by oxidation to a hexa-oxide derivative or by using one or two ZnCl⁺ ions coordinated to the central N₆ ring.

A triangle-shaped macrocyle (2) made of three pyridazine moieties connected to each other by ethylene bridges represents a possible precursor of 1. By employing an alkali or alkaline-earth metal ion coordinated to the pyridazine moieties of 2 the three pair of nitrogen atoms can be brought in close proximity so that a subsequent aromatic ring fusion reaction could be attempted via, for example, on-surface chemistry [60–62]. The author hopes that the present study will stimulate further experimental work on the synthesis and characterization of macrocycles with embedded nitrogen rings.

Ethical approval
Not applicable.

Conflict of interests
The author declares no competing interests.

Funding

No funding was received for this study.

Author Contribution

F. P. is responsible for the overall investigation.

Acknowledgement

The School of Engineering of Tohoku University (Sendai) is thanked for general support. The author appreciates the useful comments and suggestions made by an anonymous reviewer.