The novel link between planar möbius aromatic and third order nonlinear optical properties of metal–bridged polycyclic complexes

Metal–bridged polcyclic aromatic complexes, exhibiting unusual optical effects such as near-infrared photoluminescence with particularly large Stokes shifts, long lifetimes and aggregation enhancement, have been established as unique “carbonloong chemistry”. Herein, the electronic structures, aromaticities, absorption spectra and third order nonlinear optical (NLO) responses of metal–bridged polcyclic aromatic complexes (M = Fe, Re, Os and Ir) are investigated using the density functional theory computations. It is found that the bridge–head metal can stabilize and influence rings, thus creating π–, σ– and metalla–aromaticity in an extended, π–conjugated framework. Interestingly, metal radius greatly influence the bond, aromaticity, liner and third order NLO properties, which reveals useful information to develop new applications of metal regulatory mechanism in NLO materials field. Significantly, the novel relationship between the aromaticity and third order NLO response has firstly been proposed, that the metal-bridged polycyclic complex with larger aromaticity will exhibit larger third order nonlinear optical response. It is our expectation that the novel link between aromaticity and NLO response could provide valuable information for scientists to develop the potential NLO materials on the basis of metal–bridged polycyclic complexes.

In this work, the oxygen and nitrogen atom in the literature was replaced with carbon atoms to obtain the complex 4*[Os]. Then, 6*[Os] was surrounded with the completion of a metal-bridged polycyclic aromatic system, in which all of the five coordinated carbons lie in the equatorial plane. It is the largest planar Möbius aromatic system synthesized to date [30][31][32][33] . Hereto, a whole new aromatic system as well as the unique "carbonloong chemistry" have been established. Although the aromaticities of these metal-bridged polcyclic aromatic complexes have been studied, other properties such as the bonding properties, optical properties, etc, have not attracted much attention.
The third order nonlinear optical (NLO) properties of organic π-conjugated compounds have been extensively investigated because of their flexible molecular design and potentially low processing cost 34 . The link with NLO properties has been deduced for several parameters including the length of the π-conjugated linkers 35 , the charge 36 , the shape and the dimensionality of the π-electron network 37 and the donor/acceptor substituents 38 . However, the relationship between the aromaticity and NLO response was rarely studied 39 . In this work, continuing our research on NLO response, we would carry out the density functional theory (DFT) computations on complexes 1-6*[M] (M = Fe, Re, Os and Ir). Systematic studies of bond properties between M and C, aromaticity, spectroscopic and NLO properties would be performed. The particular aim of the present paper is to propose the novel relationship between the aromaticity and NLO response.

Method
The structural optimization calculations for the complexes are carried out using B3LYP functional with def2-TZVPP basis set 40 . UV/Vis absorption spectra were calculated with two kinds of polarizable continuum model (PCM) solvents (dichloromethane and methanol) at TD-B3LYP/def2-TZVPP 41 . All of the calculations were carried out by using the Gaussian 09 W program package 42 . Localized-orbital locator (LOL), a bond descriptor based on the kinetic-energy density, is used to characterize the nature of the chemical bond in transition-metal hydride and dihydrogen complexes.
where η i is occupation number of orbital i, ϕ is orbital wavefunction. D 0 (r) can be considered as Thomas-Fermi kinetic energy density. Localized orbital locator (LOL) were obtained by employing the Multiwfn software version 3.3.6 43 . The linear optic property was reflected by the isotropic average polarizability (α tot ) calculated as: 44 The third-order NLO properties of the complexes were measured by the second hyperpolarizability (γ tot ), which has been calculated using the following expression: 45 Three methods CAM-B3LYP, BHandHLYP and M06-2X have been employed to ensure the reliability of the DFT approach for the evaluation of electric response properties, and in particular for the estimation of hyperpolarizabilities. The γ tot trends of three methods are consistent with each other. Among them, the CAM-B3LYP has been employed with success in prediction of (hyper)polarizabilities 46,47 . Specifically, the α and γ values of CAM-B3LYP reproduce the corresponding CCSD(T) figures with 1% and 2%, respectively 46 . Therefore, the results of CAM-B3LYP will be discussed in detail.

Results and Discussion
The bonding property and orbital energy level. To elucidate the bonding and electronic structures of these unique pentadentate carbon chain chelates, the structure optimization was performed on B3LYP/def2-TZVPP level of theory (Fig. 2). It estimates the geometric parameters like bond angle and length (Table 1, S1, S2, S3 and S4). Complexes 1-6*[M] (M = Fe, Re, Os and Ir) are essentially planar metal bridged aromatic molecules because the dihedral angles between different rings are ranging from 179.5° to 180.0° (Figs 2, S1, S2 and S3). The C-C bond lengths (1.37-1.42 Å) are similar to those of benzene (1.40 Å), suggesting the aromatic π-conjugation. Results in Table 1 show that the calculated values of bond length in 1-6*[Os] were well coincident with literature values (Table S1). The LOL of the complexes were drawn to interpret the chemical bond in a clear and intuitive manner. The light red and yellow regains between Os and C indicate that covalent bonds are formed, however, these bonds are relatively weaker when compared to the strong covalent C-C bond as depicted in red regains (Fig. 2). In order to qualitatively and quantitatively study the bond strength, bond order (Tables S2-S4) were also taken into account. The calculated wiberg bond indices (WBI) for the Os-C bonds in 1*Os are 1.78, 0.73 and 0.91 for Os1≡C2, Os1-C3, and Os1-C4, respectively, indicating little covalent Os-C bonding characters between the osmium center and these carbons. On the other hand, the bonding characters of the Os-C bonds are clearly shown by the deformation map of the electron density distribution 48 . Deformation map of electron density shows the electron density variation during the formation of a molecule, which is actually molecular electron density minus electron densities of each atom in free-state. As expected, a significant amount of electron density concentrates towards C-C bonding regions that correspond to typical covalent bonds. For covalent bonds, the local energy density at   Table 1. AIM parameters, electron density (ρ(r)), Laplacian ∇ 2 ρ(r), density of the total energy of the electron (H(r)), kinetic electron energy density (G(r)), potential electron energy density (V(r)) for LCPs of the complexes and the delocalization index (DI).
the site of maximum concentration of electron density is always negative (blue line), however, for ionic bonds, H bonds, or Van der Waals bonds, electron density are always positive (black line). The ionic character of the Os-C bonds is observed (Fig. 3).
In order to further determine the bonding type, the Quantum Theory of Atoms (QTAIM) 49 rigorously provides the nature of the interaction between two atoms (whether covalent, coordinate, and/or ionic) by electron density ρ(r) topologies and its derivatives in the line critical point (LCP) 50 . As for the ∇ 2 ρ(r) value, the negative value of ∇ 2 ρ(r) indicates the shared electron (covalent) interactions. However, a positive value of ∇ 2 ρ(r) means the closed-shell interactions. Therefore, the bond between Os and C was not pure covalent bond. The evaluation of the local kinetic energy density, G(r), and the local potential energy density V(r) have also been listed in Table 1. The values of the total electron energy density (H), H(r) = G(r) + V(r), V(r) < 0 by definition and G(r) > 0 also by definition, reveal the characteristics of the interactions. One can also use the ratio |V(r)|/G(r) as another useful description; |V(r)|/G(r) < 1 is characteristic of a typical ionic interaction and |V(r)|/G(r) > 2 is defined as a "classical" covalent interaction. Taking all these criteria into consideration, the topological properties at LCPs indicate a mixed (partially ionic and partially covalent) character of these coordination bonds because of 1 < |V(r)|/G(r) < 2 51 . As shown in Table 1, for all complexes, the Os-C bonding interactions are characteristic of partially ionic and partially covalent owing to 1 < |V(r)|/G(r) < 2. The delocalization index (DI) 52 measures the number of shared electrons between two atoms and is unity for an equally shared pair of electrons. It is correlated to bond order listed in Table S1.
The energies of the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) of 1-6*[M] were shown in Figures S4-S7 Aromatic properties. For the sake of exploring the nature of the chemical bonding and aromaticity in these complexes, we show here that a qualitative bonding analysis of the canonical molecular orbitals (CMOs) for the complexes (Fig. 4), which is the most fundamental tool in elucidating aromaticity of a molecular system. It shows that the planar metallacycle 1*[Os] has extended Möbius aromaticity arising from 8-center-8-electron (8c-8e) d π -p π π-conjugation which is in conformity with the literature results 26 . In this complex, the 5coordinated Os center possesses three electrons in its two unhybridized d π atomic orbitals (AOs). The 7-center carbon chain ligand contributes 7 unpaired electrons 9 . A distribution of electrons among metal fragment and carbon chain is only a formal analogy and not without ambiguity. These π-AOs constitute seven occupied π molecular orbitals (MOs) of 1*[Os]. In the same way, 2*[Os] have extended Möbius aromaticity. The delocalized plane carbon-carbon single bond could be attributed to the σ-aromaticity and π-aromaticity are shown in its three-membered and five-membered rings, respectively 27 . For 3*[Os], π orbital diagram of HOMO-12 reveals the 10c-10e π-conjugation. The metal fragment decreases the antiaromaticity in cyclobutadiene and pentalene simultaneously. The four membered ring is antiaromaticity while two fused five-membered rings are aromaticity. The aromaticity of 4*[Os] arise from three aromatous five-membered rings. For 5*[Os], the aromaticity arising from 12c-12e architecture. Similar to 5*[Os], 6*[Os] shows that the five coordinated carbons lie in the equatorial plane, representing the highest carbon coordination number for a metal atom in a planar geometry 30 .
Complementary analyses (such as NICS calculations and other aromaticity indexes) offer additional or independent support for the assessment of CMO analysis. It is emphasized here that the CMO analyses and electron counting are the most fundamental tools in elucidating aromaticity. Complementary analyses (such as NICS calculations) only offer additional or independent support for the assessment. Since NICS as a criterion of aromaticity has been documented to fail in a number of cases (in particular in metal clusters) 53-56 , we are inclined to state that the aromaticity of these complexes on account of negative NICS values. With the aim of quantitatively evaluating the aromatic character of these novel metal-bridged aromatic systems, the nucleus-independent chemical shift (NICS) values were calculated. NICS is commonly studied at some special points (e.g. ring center), and can be investigated by scanning its value in a line (1D) or in a plane (2D). On the other hand, the so-called iso-chemical shielding surface (ICSS) actually is the isosurface of NICS, which clearly exhibits the distribution of NICS and thus presents a very intuitive picture on aromaticity. Present function is used to generate grid data and visualize isotropic ICSS, anisotropic ICSS, ICSS XX , ICSS YY and ICSS ZZ , they correspond to the isosurface of NICS, NICS ani , NICS XX , NICS YY and NICS ZZ , respectively. For planar systems, the component form of ICSS must be more meaningful and useful than ICSS, just like NICS ZZ has conspicuous advantage over NICS. Thus, we chose to generate ICSS ZZ for the purpose of NICS ZZ . The cut-plane map representations are perpendicular to the z axis with a distance of 1 Å from the xy plane, which represent NICS(1) ZZ (Figs 5, 6, S8 and S9). Aromaticity is colored by green-yellow-red, while antiaromaticity is shown in cyan-light blue-dark blue. The line charts present the variation of -NICS(1) ZZ values with increasing perpendicular distance from xy plane, specifically, the ring centers.
In general, negative values of NICS(1) zz indicate aromaticity and positive values are antiaromaticity. The NICS(1) zz values at the centres of rings a and b in 1*[Os] are −23.7 and −16.7 ppm, respectively, which is in keeping with the cut-plane which shows that aromaticity of ring a is more obvious (Fig. 5). The NICS (1)   . A general rule can be obtained, that is, for the metal compounds in the same period, the aromaticity presents a roughly weakening trend with the decrease of metal radius.
To ensure the accuracy of the results, we performed calculations using the quantum theory of atoms-in-molecules (QTAIM). Here, the Multiwfn program is used to generate the para-delocalization index (PDI), the multicenter bond order aromaticity index (MCBD) 57 Table S7. Larger PDI and MCBO value corresponds to stronger aromaticity. The smaller the SA index, the more aromatic is the molecule. The range of 0.003 < SA < 0.005 is chosen as the boundary of aromaticity/antiaromaticity in original paper. The more negative the curvature, the stronger the aromaticity. The results of these aromaticity indexes verify the results of NICS and ICSS on the side.

UV-vis absorption spectrum and electron transition.
The absorption spectra of these complexes in two solvents show that the spectra in dichloromethane and methanol are exactly similar (Figs 7 and S10-S12), thus we choose the former of 1-6*[Os] to study the absorption spectra (Fig. 8). The absorption maximum of complex 2*[Os] in the low-energy absorption band located at 385 nm, which is a little red-shifted by 13 nm compared with that of 1*[Os] (λ max = 372 nm) due to that the additionally coordinate C2 atom in 2*[Os] was not involved in the effective conjugation of surface. Remarkably, the low-energy absorption band (λ max = 612 nm) of 3*[Os] is red-shifted by 227 nm with respect to that of 1*[Os], which results from the increased delocalized π electrons and the enlargement of conjugate surface. Similarly, the low-energy absorption band (λ max = 669 nm)   intensity as well as oscillator strength were increased. As shown in the electron density difference maps, there are unconspicuous intramolecular charge transfer (CT), including CT from metal to ligand, ligand to metal, or intramolecular CT within ligands. And, of course, they also have a small amount of π-π* of electron transition, which is the main reason for the organic molecules with large NLO response.
The liner and nonlinear optical properties. In order to guarantee the reliability of the results, three methods have been used to calculated the α values. The results (Fig. 9a) show that the α values are not sensitive to methods. The results of CAM-B3LYP were chosen to discuss in detail. The liner optical response data shows that the orders of α values for these four kinds of metal organic complexes are semblable (Fig. 9b). Taking  (2.51 × 10 2 a.u.) shown in Tables S8-S11. In order to provide an original understanding of the α values, we focused on the relative electronic spatial extent 〈R 2 〉. To the best of our knowledge, the 〈R 2 〉 is a physical property that characterizes the electron density volume around the molecule 60  The third-order NLO properties of the complexes were measured by the second hyperpolarizability (γ tot ). As is well known that the γ values are sensitive to the methods, thus, CAM-B3LYP, BHandHLYP and M06-2X have been employed. From the Fig. 9c, the γ tot trends of three methods are consistent with each other. The CAM-B3LYP has been employed with success in prediction of (hyper)polarizabilities. Therefore, the results of CAM-B3LYP were chosen to discuss following. The orders of γ tot values for these four kinds of metal organic complexes are also semblable (Fig. 9d) values with respect to that of others. Combining with the above conclusion of the aromaticity, a novel relation between aromaticity and third order NLO response can be created that the metal-bridged polycyclic complex with better aromaticity is expected to exhibit larger third order NLO responses. To have an insight into the origin of third-order NLO responses, two-level model of the γ tot is considered for the studied complexes, which is the linkage between the γ tot and electronic transition(s) in low-lying crucial excited states. Therefore, using the two-level models 61 is a reliable way to analyze second hyperpolarizabilities and the expression is as follows: f 2 /E 5 . where f the oscillator strength, and E the transition energy. In the two-level expression, the γ tot value is proportional to the quadratic power of f but inversely proportional to the fifth power of E. f 2 /E 5 of low-lying crucial excited states have been calculated as  (Table S16). Particularly noteworthy is that the γ tot values of different kinds of metal organic complexes increase as 6*[Fe] (2.50 × 10 4 a.u.) < 6*[Re] (3.39 × 10 4 a.u.) < 6*[Ir] (5.62 × 10 4 a.u.) < 6*[Os] (6.62 × 10 4 a.u.).

Conclusions
Overall, for metal-bridged polcyclic complex, the aromaticity was attributed to Craig-Möbius topology which favours 4n π-electron conjugation counts. The introduction of a metal fragment is an efficient strategy to stabilize cyclic alkynes by reducing ring strain. The current study showed the atomic radius of center metal greatly influence the bond, aromaticity. Specifically, smaller metal radius is conducive to the formation of the bond. With regard to the metal compounds in the same period, the aromaticity decreases and might even become the antiaromaticity as the decrease of metal radius. It reveals useful information for scientists to develop new applications of metal regulatory mechanism. The α values increase with the increasing number of conjugated C atoms, which is in well accordance with the increasing order of the electronic spatial extent values. Significantly, a novel relationship between aromaticity and third order NLO response can be concluded that the metal-bridged polycyclic complex with better aromaticity will exhibit larger third order NLO responses, which opens new perspectives to discriminate and design improved NLO materials.