Aromatic nature of neutral and dianionic 1,4-diaza-2,3,5,6-tetraborinine derivatives

Abstract

The aromatically relevant parameters of boron-rich inorganic benzenes—neutral and dianionic 1,4-diaza-2,3,5,6-tetraborinine derivatives (B₄N₂R₆)—have been computationally estimated and evaluated from geometric, electronic, magnetic, and energetic points of view. The majority of the criteria (ASE, NICS_zz, ELF, and PDI) indicate that the aromaticity of the neutral B₄N₂ benzene analogue stabilized by Lewis bases lies in between those of benzene and borazine. On the other hand, the aromaticity of the dianionic B₄N₂ benzene analogue 4′ is controversial. The pronounced aromatic nature of 4′ is supported by ELF_π, PDI, and NICS_πzz, but ASE, the FiPC-NICS plot, and ACID oppose this. These data confirm that even with the same B₄N₂-skeletal framework of a 6π-system, the aromatic feature varies depending on the overall charge of the B₄N₂ systems.

The parameters relevant to aromaticity of boron-rich inorganic benzene analogues (B4N2R6) have been computationally investigated by using HOMA, ELF, PDI, NICSzz, ACID and ASE.

Introduction

Since the discovery of the cyclic feature of benzene (CH)₆1 in 1865, “aromaticity” has represented one of the most significant fundamental concepts in modern chemistry.^1–3 Nowadays, its implication is not limited to the molecules obeying the [4n + 2] Hückel rule, but extended to those satisfying various criteria—structural, electronic, magnetic and energetic indices can be employed to assess the aromatic nature of a molecule comprehensively. It is well known that benzene 1, an archetypal aromatic molecule, displays a planar geometry, cyclic delocalization of 6π electrons, peculiar magnetic properties and extra thermodynamic stability.^4,5

Synthetically, incorporation of isolobal heteroatom units into the benzene scaffold is one of the useful strategies to modify the intrinsic electronic property of aromaticity without significant change of the geometric feature. Indeed, a variety of inorganic benzenes have been developed thus far,⁶ most of which are mainly based on the (XY)₃ system, such as borazine (HBNH)₃2, boroxines (RBO)₃ and phosphazenes (R₂PN)₃.^7–10 The six-membered ring aromatics based on heavier elements have little been described.^11–15

Theoretically, the aromaticity of inorganic benzenes has been evaluated using computational methods such as nucleus-independent chemical shift (NICS), aromatic stabilization energies (ASE) and electron localization function (ELF) analyses.^16–26 In 1991, Fink and Richards reported the calculated ASE values of the (XY)₃ ring systems (X = BR, AlR; Y = NR, PR),¹⁶ and revealed that the ASE values increase in order AlN < BN < BP < CC. In 1997, the group of Schleyer estimated the NICS values of the (XY)₃ rings (X = BH, AlH, CH; Y = NH, PH, O, S), as well as, the E₆ rings (E = SiH, GeH, N, P).¹⁷ The NICS values of the (XY)₃ systems are found to be less negative than that of benzene whereas the E₆ systems are comparable to benzene. In 1998, Jemmis et al. systematically evaluated the aromaticity of the (XY)₃ molecules (X = BH, AlH, GaH, PH₂; Y = NH, PH, AsH, N, O, S, Se) using ASE, magnetic susceptibility exaltation (MSE), and NICS analyses. As a result, they concluded that judicious use of all criteria is needed in gauging aromaticity of those systems.¹⁸ In 2005, Jenneskens and coworkers reported the electronic structure of the (XY)₃ (X = BH, AlH; Y = NH, PH, O, S) and E₆ (E = SiH, GeH, N, P) systems by using valence bond (VB) theory and ring-current maps. The authors unveiled that in general, the heteronuclear systems (XY)₃ show localization of the lone pair of electrons on the electronegative atoms, and Kekulé-like structures do not contribute.¹⁹ In 2010, Phukan and Silvi et al. calculated the NICS, ASE, and ELF values for the substituted (XY)₃ systems (X = BR, AlR; Y = NH, PH, AsH, O, S, Se). The results clarified the substituent effect—the bulky electronegative substituents (R) on B or Al atoms dramatically increases the stability and aromaticity.²⁰ Recently, Alvarez-Thon and Tiznado examined the (XYH)₃ systems (X = C–Pb, Y = N–Bi) by magnetically induced current density (MICD) and the zz component of NICS, and revealed that most of them are aromatic except for (XNH)₃ (X = Si–Pb).²¹

The extant theoretical study on the aromaticity of inorganic benzenes mainly focuses on the above-mentioned (XY)₃ and E₆ systems, because those types of analogues have been isolated to date. Recently, we have reported the synthesis of a neutral B₄N₂-based benzene analogue, namely 1,4-diaza-2,3,5,6-tetraborinine derivative 3,²⁷ being the first examples of the Lewis base-stabilized X₄Y₂ system.⁶ Preliminary theoretical investigations including NICS, natural bond orbital (NBO), and anisotropy of the current-induced density (ACID) analysis suggested the pronounced aromatic nature of 3. By contrast, the dianionic B₄N₂ ring system 4: [(Ph-N)₂(Me₂N-B)₄]^2– is found to furnish a non-aromatic twisted structure despite its 6π-electron configuration isoelectronic with 3.²⁸ With the isolable neutral and dianionic B₄N₂ derivatives in hand, we wondered (i) how the aromatic nature of the B₄N₂ ring systems differs from the reported (XY)₃ systems, and (ii) whether the charge of molecules affects the aromaticity or not. Here, we have investigated the aromaticity of 1,4-diaza-2,3,5,6-tetraborinine derivatives, B₄N₂ analogues of benzene, by using modern computational aromaticity descriptors involving structure, molecular orbital, electron density, magnetic shielding, and energetics.²⁹ For purpose of comparison, reference molecules—benzene (CH)₆1, and borazine (HBNH)₃2 have also been examined (Scheme 1). The substituent effect on the aromaticity in benzene as well as in borazine has been reported.^30–36 According to those prior studies, while the aromaticity of benzene resists substituent influences, that of borazine is significantly affected by the nature of substituents. In borazine, generally the electron-donating group (EDG) on B decreases the aromaticity, although electron-withdrawing group (EWG) on B and both EDG and EWG on N lead to the pronounced aromaticity. Therefore, we employed model compound 3′, and a dianionic B₄N₂H₆ derivative 4′ (Scheme 1).

Scheme 1. The list of the molecules discussed in this article (Mes = 2,4,6-Me₃C₆H₂).

To evaluate the aromatic nature, five criteria including the harmonic oscillator model of aromaticity (HOMA), ELF, para-delocalization index (PDI), NICS, and ASE have been assessed.^16–20 Moreover, we have carried out ACID analysis to visualize the ring current.

Computational methods

All density functional theory calculations have been performed using the Gaussian 16 program package at the B3LYP/6-311+G(d,p) level,³⁷ which is widely employed for the estimation of aromaticity of monocyclic heterobenzenes and inorganic benzenes.^17,38–40 Note that when the basis sets as 6-311+G(2df,2pd) and 6-311+G(3df,3pd) in the optimization and NICS calculations for dianionic 4′ were employed, almost no significant improvement was observed (Table S2†). We used the NBO method in the current NBO 7.0 version of the general NBO analysis program.⁴¹ PDI, ELF, and atoms in molecules (AIM) studies were generated with the Multiwfn 3.6 program.⁴²

Results and discussion

Fig. 1 displays the optimized structures and selected bond lengths of benzene (1), borazine (2), and three B₄N₂ systems (3, 3′, and 4′). All molecular geometries were fully optimized as closed-shell species and characterized as energy minima by the absence of imaginary vibrational frequencies. The central six-membered ring in compounds 1, 2, 3 and 3′ exhibits a planar geometry. Notably, dianionic 4′ also bears a planar B₄N₂ ring, which is in stark contrast to the twisted ring framework experimentally observed for 4, implying the impact of substituents at the B and N atoms on the skeletal geometry.^30,32–36 The selected π-type molecular orbitals (π-MOs) of 3′ and 4′ are summarized in Fig. 2. Three explicit π-MOs are seen in 3′ and 4′, which are similar to those of benzene 1 and borazine 2. While 1 and 2 have two degenerated highest occupied molecular orbitals (HOMOs), the B₄N₂ systems (3, 3′, 4′) possess non-degenerate π-MOs.²⁷ In the π-MOs of 3, some contributions from 3p-orbitals of the substituents (Cl and PMe₃) are found. To assess the essential nature of the six-membered skeleton without consideration of the significant electronic perturbation from the substituent, 3 is omitted from NICSπ and ELFπ calculation (vide infra).

Fig. 1. Optimized structures and selected bond lengths (in Å) of 1, 2, 3, 3′ and 4′.

Fig. 2. Plots of the π molecular orbitals of 3′ and 4′ (in eV).

Firstly, a structural criterion is evaluated using the HOMA index, which is based on the equalization of the bond lengths and symmetry.^43–45 The calculated HOMA values, resonance energy (EN), and bond length alternation (GEO) are summarized in Table 1 (for the details of bond number, see Table S2†).^46,47 It should be noted that the HOMA index reflects only the geometrical features and does not consider the polarization effect on electronic distribution. Besides, HOMA values may depend on the choice of reference bond lengths and normalization constant. The reported constants of B–B and B–N bond are calculated in different way.^48,49

Calculated HOMA, bifurcation values of ELF functions and PDI (electrons) values.

	HOMA	EN	GEO	ELFave	ELFπ	ELFσ	PDI
1: (CH)6	0.990	0.010	0.000	0.81	0.91	0.70	0.105
2: (HBNH)3	1.000	0.000	0.000	0.56	0.72	0.40	0.041
3: [(MesN)(BCl)(BPMe3)]2	0.698	0.189	0.113	—	—	—	0.068
3′: [(HN)(BH)(BPH3)]2	0.654	0.163	0.183	0.64	0.81	0.47	0.078
4′: [(HN)2(BH)4]2–	0.288	0.428	0.284	0.66	0.81	0.50	0.118

The HOMA values increase in the order 4′ < 3′ < 3 < 1 ≈ 2, from 0.288 for 4′ up to 1.000 for 2. There is little bond alternation in 1 and 2, in line with their essential D_6h and D_3h symmetries. For the B₄N₂ systems (3, 3′, 4′), both EN and GEO values are larger than those for benzene 1 and borazine 2. Particular diagnostic is that the HOMA value of 4′ is mainly dominated by EN term (0.428) rather than GEO term (0.284), indicating elongation of the skeletal bonds. The bond numbers of 3 [1.143 (B–B), 1.444–1.513 (B–N)], and 3′ [1.101 (B–B), 1.504–1.561 (B–N)] indicate partial bond alternation in 3 and 3′, which results in the large GEO values. The average bond numbers of 3 [1.367] and 3′ [1.388] are smaller than that of benzene 1 [1.533] and borazine 2 [1.582], which leads to the increased EN values of 3 and 3′. The bond numbers of 4′ show B–B single bond [0.950] and B–N multiple bond [1.437] characters, suggesting that the π electrons are relatively localized on each B–N–B unit. The average of the bond number of 4′ [1.275] is smaller than other systems, in agreement with the relatively large EN value.

Secondly, as an electronic criterion, the ELF and PDI values have been computed.^50–55 The calculated average ELF values together with its σ- and π-contributions and PDI values are listed in Table 1,^56–58 and the ELF isosurfaces at the bifurcation points of the σ and π systems are depicted in Fig. 3.⁵⁹ The ELF_ave values increase in the order 2 < 3′ < 4′ < 1, from 0.56 for 2 to 0.81 for 1, and the ELF_π values are found to be larger than the ELF_σ values for all molecules. The ELF_π values greater than 0.70 indicate that all molecules may have some aromatic character.⁶⁰ Benzene 1 shows the high ELF_π value of 0.91, in line with the pronounced aromatic nature. Borazine 2 presents an ELF_π value of 0.72 lower than that of benzene 1, implying the less aromatic character. In contrast to highly symmetric benzene 1 (D_6h) and borazine 2 (D_3h), the B₄N₂ systems with the lower symmetry exhibit several distinguishable ELF_π values. For the neutral B₄N₂ system 3′, the separations at the (H₃P)B–N bonds, HB–N bonds, and B–B bonds occur at the ELF_π values of 0.68, 0.82, and 0.94, respectively. The dianionic B₄N₂ system 4′ shows the first separation at the B–N bonds with a relatively high ELF_πvalue of 0.75 and the B–B bonds are split at a significantly higher ELF_π value of 0.92. The average ELF_π values of 0.81 for 3′ and 0.81 for 4′ are between those of benzene 1 (0.91) and borazine 2 (0.72), indicating moderate delocalization of π-electrons in those B₄N₂ systems.

Fig. 3. The ELF isosurfaces at the bifurcation points of the σ and π systems of 1, 2, 3′, and 4′.

The ELF_σ values of inorganic benzenes [2 (0.40), 3′ (0.47), 4′ (0.50)] are much smaller than that of benzene 1 (0.70), reflecting the difference of electronegativity between B and N atoms. The PDI values increase in the order 2 (0.041) < 3 (0.068) < 3′ (0.078) < 1 (0.105) < 4 (0.118), suggesting the moderate aromaticity of 3 and 3′, which is in agreement with the ELF_π values. However, the PDI value of 4 greater than that of benzene 1, as inconsistent with those ELF_π values, points out that the PDI measures might not be suitable for the evaluation of the relative aromaticity among the differently charged molecules, as well as, compounds consisting of different skeletal atoms.^61,62 The calculated ring critical point properties of compounds 1, 2, 3, 3′, 4′ are summarized in Table S4.†

Thirdly, as a magnetic criterion, a series of NICS values have been estimated (Table 2).^63–68 Isotropic NICS can be represented by the anisotropic components: NICS = (NICS_xx + NICS_yy + NICS_zz)/3 = NICS_in-plane + NICS_out-of-plane, in which (NICS_xx + NICS_yy)/3 = (NICS_in-plane) and (NICS_zz)/3 = NICS_out-of-plane. Free of in-plane component NICS (FiPC-NICS) indicates the NICS value at a point above the molecular ring with zero of NICS_in-plane. Fig. 4(a) presents the NICS-profiles of the full-NICS_zz and σ- and π-electron contribution to the NICS_zz for 3′ and 4′, from the center of the six-membered ring and above up to 5.00 Å, and Fig. 4(b) shows FiPC-NICS plot, respectively.

Calculated NICS values (ppm).

	NICSzz		NICSπzz		FiPC
Distance (Å)	0	1	0	1	—
1: (CH)6	−14.48	−29.25	−35.78	−29.07	−9.07
2: (HBNH)3	11.98	−5.17	−7.89	−5.88	−2.34
3: [(MesN)(BCl)(BPMe3)]2	−3.36	−12.32	—	—	−4.03
3′: [(HN)(BH)(BPH3)]2	−3.75	−15.18	−19.73	−16.54	−3.85
4′: [(HN)2(BH)4]2–	−5.49	−15.42	−20.73	−17.02	—

Fig. 4. (a) Dissected NICS_zz (ppm) vs. distance (Å) of 3′ and 4′. (b) Plots of the NICS_in-planevs. NICS_out-of-plane of 1, 2, 3, 3′ and 4′, to identify the FiPC-NICS.

While the NICS_zz(0) values of 1 (−14.48), 3 (−3.36), 3′ (−3.75), and 4′ (−5.49) are negative, borazine 2 shows the highly positive NICS_zz(0) values of 11.98, which is due to the significantly positive NICS_σzz(0) contribution.⁶⁶ It has been demonstrated that NICS_πzz in addition to NICS_zz(1) could be the most reliable aromaticity indexes, with statistically good correlation with aromatic stabilization energies.^64,69 The NICS_zz values of 3 [NICS_zz(1) = −12.32], 3′ [NICS_zz(1) = −15.18, NICS_πzz(0) = −19.73, NICS_πzz(1) = −16.54] and 4′ [NICS_zz(1) = −15.42, NICS_πzz(0) = −20.73, NICS_πzz(1) = −17.02] lie in between those of benzene 1 [NICS_zz(1) = −29.25, NICS_πzz(0) = −35.78, NICS_πzz(1) = −29.07] and borazine 2 [NICS_zz(1) = −5.17, NICS_πzz(0) = −7.89, NICS_πzz(1) = −5.88].

The NICS_zz profiles of 3′ and 4′ (Fig. 4(a)) confirm that the NICS_σzz values are significantly positive near the ring center [NICS_σzz(0) = 15.98 (3′), 15.25 (4′)], and they decrease as being apart from the ring and become negative around at 1 Å. On the other hand, the NICS_πzz values are significantly negative at the molecular center, and gradually become less negative as being away from the ring. The greatly negative NICS_πzz contribution over the NICS_σzz component leads to the overall negative NICS_zz values. A similar trend of the NICS_zz profile is found for benzene.⁶⁶ The FiPC-NICS value corresponds to the interception on the vertical axis (NICS_out-of-plane) in Fig. 4(b). The FiPC-NICS values of −4.03 for 3 and −3.85 for 3′, appear to be between those of benzene 1 (−9.07) and borazine 2 (−2.34), supporting the moderate aromatic character of 3 and 3′. The shape of FiPC-NICS plots of 3 and 3′ is similar to that of 1 but different from that of 2. The positive NICS_out-of-plane values are observed near the ring center of 2, which is due to the pronounced σ-contribution but marginal π-contribution in the region.⁶⁶ The significant deviation of the FiPC-NICS plot of 4′ from others can be rationalized by the largely positive NICS_xx values, and therefore, the FiPC-NICS value of 4′ could not be gained.

ACID plot of 4′ is shown in Fig. 5 (For the plots of 1, 2, 3′, see Fig. S1†). While the clear clockwise current–density vectors are confirmed on the ACID isosurface of benzene 1, borazine 2 shows the imperceptible ring current consisting of the three localized circulations on the nitrogen atoms, which is consistent with previous studies.²⁴ The clockwise current–density vectors on the ACID isosurface also observed in 3.²⁷ Despite somehow weak vectors, an explicit diatropic ring current is seen over the B₄N₂ ring of 4′ with the pronounced stopover at the B–H moieties.

Fig. 5. ACID plot of the selected π orbitals of 4′, at an isosurface value of 0.03.

Finally, an energetic criterion is evaluated using the ASE method (Table 3). The ASE values computed by the reactions (a)–(d) (Scheme 2, Table S5–S8†)^65,70 decrease in the order 1 (33.4 kcal mol⁻¹) > 3′ (23.8 kcal mol⁻¹) > 4′ (11.0 kcal mol⁻¹) > 2 (10.1 kcal mol⁻¹). Based on the ASE values, it can be estimated that inorganic benzene analogues 2, 3′, 4′ present 30%, 71% and 33% of aromaticity in comparison to benzene, respectively. Note that the significantly smaller ASE value of 4′ compared with that of 3′ is not in line with those NICS_πzz(0) values [3′ = −19.73; 4′ = −20.73], indicating that magnetic and energetic criteria are not in good correlation with each other when comparing the differently charged molecules.⁶⁴

Calculated ASE values (kcal mol⁻¹).

	ASE
1: (CH)6	33.4 (100)
2: (HBNH)3	10.1 (30)
3: [(MesN)(BCl)(BPMe3)]2	—
3′: [(HN)(BH)(BPH3)]2	23.8 (71)
4′: [(HN)2(BH)4]2–	11.0 (33)

Scheme 2. Homodesmotic reaction schemes used to estimate the aromatic stabilization energy (ASE).

Conclusions

In conclusion, we have assessed the aromatics-relevant indices of B₄N₂-based inorganic benzene analogues together with benzene and borazine, with the aid of HOMA, ELF, PDI, NICS, ACID and ASE methods. It has been demonstrated that the aromaticity of the neutral B₄N₂ systems 3 and 3′ clearly differs from that of borazine 2 of the (XY)₃ system. The major parameters (ELF, PDI, NICS_zz, and ASE) other than HOMA suggest that the neutral B₄N₂ systems 3 and 3′ are less aromatic than benzene and more aromatic than borazine 2. While ELF_π, PDI and NICS_πzz values propose the pronounced aromatic nature of the dianionic B₄N₂ system 4′, the ASE result estimates the aromaticity of 4′ to be smaller than that of 3′ and similar to borazine 2. Moreover, the FiPC-NICS plot of 4′ is different from those observed for the aromatic molecules.⁶⁵ Besides, ACID plot of 4′ shows that in addition to the ring current over the six-membered ring, localized currents in the RB-BH fragment significantly contributes to magnetic anisotropy. These data indicate that even with the same B₄N₂-skeletal framework of 6π-system, the index value of each criterion varies depending on the overall charge of the B₄N₂ systems,^32,33,36 giving rise to the different aromatic nature.^71,72 This study paves a way for the further design and development of aromatic inorganic benzenes.

Conflicts of interest

There are no conflicts to declare.