Introduction

Over the last few decades, the arena of aromaticity has been growing relentlessly and the variety of molecules and ions joining the family of aromatic compounds has grown exponentially. In 1865, August Kekule first used the term ‘aromaticity’ to explain the exceptional stability and low reactivity of Benzene and its derivatives [1]. In 1931, Hückel formulated his famous ‘4n + 2’ rule, which is still a thumb rule in rationalizing the aromatic character of conjugated monocyclic hydrocarbons [2]. According to Hückel rule, a planar cyclic system having 4n + 2 number of pi electrons (where ‘n’ is any positive integer starting from zero), which are delocalized throughout the system, are aromatic in nature. Benzene, the widely recognized aromatic compound with six pi-electrons satisfies the ‘4n + 2’ rule for n = 1. [10]-annulene (where n = 2) is expected to be the next homolog of benzene. However, the situation for higher analogues, such as, cyclodecapentaene, or [10]-annulene, is not favorable. There are nice articles in the literature where reasonable attempts have been reported on the research of 10-π-electron aromatic systems [3,4,5].

In 1969, Masamune and coworkers [6,7,8] isolated two isomers of [10]-annulene in crystalline form. A detailed theoretical study on [10]-annulene using HF, DFT, MP2, and CCSD(T) method was carried out by Schaefer in 1999 [9]. They have suggested five conformers of [10]-annulene, which includes C2 “twist”, a C2 “naphthalene-like”, a Cs “heart”, a C1(or C2) “azulene-like”, and a Cs “boat” form. Among the five conformers, the heart isomer is the only one for which the HF method predicts an aromatic structure, but the CCSD study reveals that this nearly planar structure favors π-bond delocalization at the expense of severe sigma-bond strain. The two largest ring angles are 149.6 and 146.9 degrees, which are far greater than the other conformers. Further large-scale CCSD(T) computations involving 340 basis functions predict that the twist conformation is lowest in energy and the naphthalene-like and heart-shaped conformations lie higher than the twist by 1.40 and 4.24 kcal·mol−1, respectively. On the other hand, Bickelhaupt et al. reported a delocalized structure of the heart-shaped isomer, however there is an admonishing tone that the same adopts a near-planar saddle-shaped conformation to minimize the steric repulsion between vicinal C-H bonds [10]. This inference may rationalize the fact that planar, aromatic, C10H10 (see Fig. 1a) is not achievable and the repulsion between vicinal hydrogens could be the potential reason behind that. Moreover, we are getting nonplanar C2 (see Fig. 1b) and heart-shaped (see Fig. 1c) structures of C10H10.

Fig. 1
figure 1

Geometry of the hypothetical D10h symmetry 10-annulene (a), C2 symmetry twist conformation (b), and Cs symmetry heart conformation (c)

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So far, C8H82− is the only example of a monocyclic 10-π-electron aromatics found in the literature. A neutral, planar, and aromatic, all-carbon, 10-π-electron system has yet to achieved, but there are 10-π-electron heterocyclic compounds that are synthesized and finely reported in the literature [11]. In 2011, Moock et al. reported 1,5,2,4,6,8-dithiatetrazocine ((CH)2S2N4) ring, which is a 10-π-electron planar heterocycle that comprises an eight-membered backbone bearing D2h symmetry [11]. Later, Charistos and Muñoz-Castro et al. reported the significance of the presence of hetero atoms and their π-orbitals in the formation of heterocyclic aromatic systems [12]. So, keeping in mind the concept of vicinal C-H bond repulsion in not attaining the planar 10-π-annulene and the heterocyclic aromatic systems, here we have reported state-of-the-art 10-π-electron (CH)5(XH)5 {X = Si, Ge, Sn} systems using DFT methodologies, which represent a ten-membered ring depicting an aromatic Hückel electron count. Further, to incur proof of aromaticity on the modeled systems, overall magnetic behavior is studied by assessing three-dimensional representation of the shielding and de-shielding regions, besides bonding analysis via NBO calculation.

Computational details

All the initial guesses of the modeled systems were made by using GaussView software and the computations were done using the Gaussian 16 suite of programs [13, 14]. Although DFT-based methods are reported to be inadequate for accurate description of aromatic systems, a major part of the scientific community has been using it with suitable basis set, particularly for qualitative assessment. In the present work, we used B3LYP/def2-TZVP method in conjunction with dispersion via Grimme’s DFT-D3 approximation, employing ultrafine grid for the reported entire computation [15,16,17,18,19,20,21,22]. 2π aromatic C3H3+, C4H42+, 6π aromatic C5H5−, C6H6, C7H7+, C8H82+, and 10-π-aromatic C9H9−, C10H10 were modeled and optimized (see Section S1 for lowest harmonic vibrational frequency and geometric coordinates). Harmonic vibrational frequency analysis confirms the local minima of the found stationary points, excluding C4H42+ and [10]-annulene. (CH)5(XH)5 {X = Si, Ge, Sn} systems were modeled keeping -CH-, -XH- fragments at adjacent positions, thereafter optimization as well as harmonic vibrational frequency analysis were done. In case of Sn, effective core potential was used for the core electrons [23]. Natural population analysis (NPA) charge on each atom of the different systems and Wiberg Bond Index (WBI) [24] were computed by NBO analysis.

The nucleus-independent shielding tensors were calculated within the GIAO formalism, employing the Becke–Perdew (BP86) functional and all-electron STO-TZ2P basis set, by using the ADF Modeling Suite 2016 from the previously optimized geometries [25,26,27,28,29,30,31]. To evaluate the magnetic response or induced field (Bind), upon an external magnetic field (Bext) at the molecular surroundings, both three-dimensional surfaces and map representation of the nucleus-independent shielding tensor (σij) were obtained, where Biind = -σijBjext [25, 27, 32,33,34]. The separation between each amounts to 0.4 Å. For convenience, the i and j suffixes are related to the x-, y-, and z-axes of the molecule-fixed Cartesian system (i, j = x, y, z). Bind is given in ppm in relation to Bext.

Results and discussion

Structural parameters of the CnHn+/− m {where n = 3 – 10 and m = 0 – 2} and (CH)5(SiH)5, (CH)5(GeH)5, (CH)5(SnH)5 systems are provided in Table 1. C-C bond length of the C3H3+, C4H42+, C5H5−, C6H6, C7H7+, C8H82+, C9H9−, and C10H10 systems are in the range, 1.36–1.44 Å. Though each carbon atom of the CnHn+/− m systems are sp2 hybridized, due to their cyclic geometry, CCC angles are away from the trivial value (of sp2 hybridization), only in the case of benzene the value is 120°. rC-H values and HCC angles are in accord with the sp2 C-H bond length and geometrical shape of the systems, respectively. It is interesting to note that excluding C4H42+, only C10H10 gives imaginary harmonic vibrational frequencies (83i, 83i) for the obtained stationary point among the CnHn+/− m systems. The distance between the vicinal hydrogen (dH-H) of the planar CnHn+/− m framework can furnish an equivalent measure of the distance between vicinal C-H bonds. Assessment of dH-H values reveals that from C3H3+ to C10H10, distance between adjacent hydrogens decreases and in cyclodecapentaene the magnitude becomes least. This minimum separation (dH-H = 2.07 Å) exerts substantial repulsion between the C-H bonds, which makes [10]-annulene a nonplanar system. This fact can be easily perceived by observing the displacement vectors of the computed frequencies (83i, 83i). Here the question arises, what is the reason behind non-planarity of [10]-annulene? If the repulsion between vicinal C-H bonds serves as the main reason, then let us model a system where this repulsive force would be minimized by monitoring the distance between adjacent hydrogen. There could be several ways to monitor the repulsion between adjacent hydrogens, but in the modeled systems (CH)5(XH)5 {X = Si, Ge, Sn}, we have placed the mentioned five X atoms at alternate positions replacing Cs in the C10H10 ring. Increments in the distance between adjacent atoms in the modeled (CH)5(XH)5 rings in comparison to C10H10 are substantial, 0.36, 0.44, 0.63 for (CH)5(SiH)5, (CH)5(GeH)5, (CH)5(SnH)5 systems, respectively. In consequence, the adjacent hydrogens stay at some greater distant disposition in comparison to the case of [10]-annulene. Progress in the magnitude of < XCX and rX-H {X = Si, Ge, Sn} corroborates well with the increment of rC-X values. Lengthening of bonds between adjacent atoms as well as increment in rX-H values (in comparison to such values of C10H10) result in substantial increase in the distance between adjacent hydrogens of the ten-membered ring. dH-H values of (CH)5(SiH)5, (CH)5(GeH)5, (CH)5(SnH)5 are 0.51, 0.61, 0.88 Å higher in comparison to the dH-H values of C10H10, respectively. Due to such change, it is noted that among the obtained stationary points of (CH)5(XH)5 {X = Si, Ge, Sn} systems, (CH)5(SiH)5 has reduced value of imaginary lowest harmonic vibrational frequency (νmin = 11i), whereas (CH)5(GeH)5 and (CH)5(SnH)5 are local minima (in Section S1 νmin and geometric coordinates are provided). Optimized structures of (CH)5(XH)5 {X = Si, Ge, Sn} series are collected in Fig. 2.

Table 1 Structural parameters of the studied  systems at B3LYP/def2-TZVP level. rC-C, rC-X, rC-H, rX-H indicate C-C, C-X, C-H, X-H bond lengths, respectively. < XCX, < CXC, < HXC, < HCX are the magnitude of the angle XCX, CXC, HXC, HCX, respectively. dH-H designates the distance between adjacent hydrogens
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Fig. 2
figure 2

Structure of the D5h symmetry 10-π-aromatic (CH)5(SiH)5 (a), (CH)5(GeH)5 (b), and (CH)5(SnH)5 (c) systems obtained at B3LYP-D3/def2-TZVP level of theory

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WBI values of the C-C bonds, 1.45, 1.42 for C6H6, C10H10, respectively, denote the typical resonating systems having single bond–double bond conjugation. However, in the case of (CH)5(XH)5 {X = Si, Ge, Sn} systems, such values become 1.14 (Si), 1.17 (Ge), 1.11 (Sn), which are away from the trivial one-and-half bond of resonating systems. As the electronegativities of C and H are higher than that of Si, Ge, and Sn, NPA charges on C are negative and on the hydrogens bonded to X are also negative. NPA charges on Si, Ge, and Sn are 1.53, 1.40, and 1.72|e|, respectively. Such a population of electrons in the constituent atoms makes it clear that (CH)5(XH)5 {X = Si, Ge, Sn} systems are partly covalent. From the hybridization of C, Si, Ge, and Sn in the systems given in Table 2, it is interesting to note that the ring atoms of benzene and (CH)5(SnH)5 are closer to the sp2 hybridization. Moreover, the Coulomb interaction between adjacent hydrogens are much less in (CH)5(SnH)5 in comparison to C10H10; thus, we can say that the planarity is played at electronic level. Although the ionic character of (CH)5(SnH)5 is greater among the (CH)5(XH)5 {X = Si, Ge, Sn} systems, the highest values of dH-H and most likely sp2 hybridizations of the skeletal atoms make it the superior 10-π-electron aromatic system in comparison to its lower congeners. Occupied and unoccupied π-molecular orbitals (π-MOs) of (CH)5(SnH)5 are shown in Fig. 3. It came out that the obtained π-MOs depict an aromatic (4n + 2) π system with n = 2, i.e., a 10-π electron system. The lowest and highest energy π-MOs (HOMO-2 and LUMO+6, respectively) are non-degenerate, similar to benzene. HOMO-1, HOMO, LUMO, and LUMO+4 are degenerate orbitals, showing one, two, three, and four nodal planes, respectively. The occupied orbitals remain as bonding combinations, as can be seen from Fig. 3 according to the Frost diagram, ensuring a bonding character of the delocalized π-electrons.

Table 2 Wiberg bond indices of C-C (WBIC–C), C–X (WBIC–X), and C–H/X-H (WBIC-H/C-H[X-H]), NPA charge on Y centers (q (Y),|e|) (Y = C,, H), and the hybridizations of C and X (X = Si, Ge, Sn). HC and HX are the hydrogens connected to C and X, respectively
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Fig. 3
figure 3

Occupied and unoccupied π-molecular orbitals of (CH)5(SnH)5

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A Frost diagram was made and nucleus-independent shielding tensors were obtained for the (CH)5(SnH)5 system in order to rationalize and account for its expected planar aromatic behavior. The π levels from (CH)5(SnH)5 are schematically represented by the mnemotechnic Frost diagram describing (see Fig. 4) the bonding/non-bonding/antibonding character of each π-combination. In addition, the percental contribution by both carbon and tin atoms is given. The π1 level is composed by 58% from carbon atoms π-orbitals, which rise to 62 and 79% at {π2, π3} and {π4, π5} levels, respectively. For unoccupied π-orbitals, the contribution from Sn rises to 79, 62, and 61%, at {π6, π7}, {π8, π9} and π10, respectively. This reveals a different composition of the π-orbitals owing to the heteroatomic nature of the ten-membered ring backbone.

Fig. 4
figure 4

Frost diagram of ten-membered 10-π-electron (CH)5(SnH)5 ring

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An inherent characteristic of aromatic rings is the ability to sustain a long-range shielding cone, provoking changes in the measured nuclear shielding in neighboring atoms or groups. This characteristic appears as a useful probe which can be tracked via NMR experiments to study conformation of organic and biological molecules, intermolecular aggregation, and gas storage applications, owing to the shielding patterns resulting from the shielding cone at aromatic rings [25, 27, 35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51]. In this sense, the magnetic criteria of aromaticity have been employed to a large extent to identify aromatic species based on the characterization of the magnetic behavior through a probe at the center of the structure [27, 52,53,54,55,56,57,58]. For such compounds, the induced diamagnetic field (Bind) at the center of the ring opposes the applied field (Bext), leading a shielding response (negative values). In the contrary case, antiaromatic structures exhibit a deshielding response (positive values). Thus, magnetic response illustrates strong differences between aromatic and antiaromatic systems, where multiple probes are needed to achieve a better understanding of the response in the molecular space, such as aromatic ring current shielding (ARCS), contour planes and three-dimensional surfaces [26, 32, 59,60,61,62].

Here we account for the overall magnetic behavior of (CH)5(SnH)5 by obtaining three-dimensional representation of the shielding and deshielding regions. The orientational-averaged magnetic response (isotropic response) accounts for the orientation-averaged behavior, related to the fast molecular tumbling observed from regular NMR experiments [34, 63,64,65]. The isotropic term, given by Bisoind = − (1/3)(σxx + σyy + σzz) Bjext, has been usually employed to characterize aromatic or antiaromatic species according to the generation of shielding or deshielding surface, respectively, at the center of the ring (Fig. 5). For benzene, Bisoind shows a shielding region only, which is also found in the Bisoind of (CH)5(SnH)5.

Fig. 5
figure 5

Isosurface representation of the isotropic response (Iso) and Bindz for benzene (left) and (CH)5(SnH)5 (right). Isosurface value set at ± 2.0 ppm

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In order to address the complexity of the overall magnetic behavior in such novel planar structures, we have analyzed the response under specific orientation of the applied field for the (CH)5(SnH)5 system. Thus, the response under an external field along the z-axis (Bindz) is more appropriate descriptor to account for aromatic properties [26, 27, 61, 66,67,68]. In contrast to the isotropic (averaged) response for Bindz, a long-range shielding response is found for (CH)5(SnH)5, with a complementary deshielding region contained in the perpendicular plane supporting the aromatic behavior. This behavior is similar to the one found for benzene, where the induced shielding cone is an inherent property of aromatic species. For (CH)5(SnH)5, the long-range character of the shielding cone is with shielding strength of −2 ppm at 8.0 Å from the center of the ring, which is sizably larger than the same value for benzene located at 5.1 Å above the ring. This observation indicates an increase of about 3.0 Å of the shielding cone in the ten-membered 10π ring in comparison to benzene, suggesting a stronger aromatic character.

Conclusions

The reason behind the unattainability of planar C10H10 species may be attributed to the repulsion between vicinal hydrogen, as they are only 2.07 Å away from each other. However, in the present series of (CH)5(XH)5 {X = Si, Ge, Sn}, such distance is 2.58 (Si), 2.68 (Ge), 2.95 (Sn) Å. It is shown that among these three systems, (CH)5(GeH)5 and (CH)5(SnH)5 are local minima, planar, and of course they exhibit 10π aromaticity. Existence of magnetic shielding region in (CH)5(SnH)5 like C6H6 as well as the formation of shielding cone of strength −2 ppm at 8.0 Å from the center of the ring discloses the aromaticity in this ten-membered 10π system. Thus, such species represent plausible Hückel aromatic rings retaining a ten-membered backbone, which may serve as a guide for experimental realization of novel species pursuing the expansion of chemistry of larger aromatic rings.