Molecular modeling and experimental studies on structure and NMR parameters of 9-benzyl-3,6-diiodo-9H-carbazole

A combined experimental and theoretical study has been performed on 9-benzyl-3,6-diiodo-9H-carbazole. Experimental X-ray (100.0 K) and room-temperature 13C nuclear magnetic resonance (NMR) studies were supported by advanced density functional theory calculations. The non-relativistic structure optimization was performed and the 13C nuclear magnetic shieldings were predicted at the relativistic level of theory using the zeroth-order regular approximation. The changes in the benzene and pyrrole rings compared to the unsubstituted carbazole or the parent molecules were discussed in terms of aromaticity changes using the harmonic oscillator model of aromaticity and the nucleus independent chemical shift indexes. Theoretical relativistic calculations of chemical shifts of carbons C3 and C6, directly bonded to iodine atoms, produced a reasonable agreement with experiment (initial deviation from experiment of 41.57 dropped to 5.6 ppm). A good linear correlation between experimental and theoretically predicted structural and NMR parameters was observed.

derivatives are currently among the most widely studied materials [11][12][13][14][15]. It is known that the presence of heavy atoms (Cl and Br) decreases the relative quantum yield of fluorescence and increases phosphorescence in the carbazole derivatives [16]. Bonesi [17] observed the same effect in carbazole modified by Cl and Br at positions 3 and 3, 6 in a solid matrix. Finally, in a work of Safoula [18] an increase in conductivity by molecular doping with iodine was observed.
Experimental nuclear magnetic resonance (NMR) studies are widely used to characterize the geometrical and electronic structure of isolated compounds, their solutesolute and solute-solvent interactions in solution. Nowadays, the assignment of experimental spectra is often supported by molecular modeling of the relevant NMR parameters [19][20][21], as it is possible to predict satisfactory chemical shifts for several different nuclei including 13 C, 17 O, 15 N, and 19 F [19,[22][23][24][25] using density functional theory (DFT) calculations in combination with gauge including atomic orbitals (GIAOs [26,27]) and employing the Becke three-parameter, Lee-Yang-Parr (B3LYP [27,28]) or the hybrid half-and-half (BHandHLYP) exchange correlation functionals [29]. Several NMR reports on the simplest carbazoles are available [30][31][32][33]. However, systematic studies of the correlation between the molecular structure of carbazoles and their NMR parameters are lacking in the literature. The presence of a fairly heavy nucleus (here iodine) in a molecule affects the NMR properties of the neighboring light atom (close in space or directly connected H, C, N atoms). This effect was described by Pyykkö et al. [34] as the heavy-atom-on-lightatom (HALA) effect. Ziegler, Autschbach and Arcisauskaite [35][36][37][38][39][40][41] reported on several relativistic calculations of NMR shieldings. In the work of Pecul et al. [42] the importance of inclusion of the HALA effect on 13 C shielding constants in organomercury compounds and halogen derivatives was discussed. They observed large spin-orbit (SO) contributions to the HALA effects in the halogen substituted compounds, which were well reproduced using zeroth-order regular approximation with SO coupling (SO ZORA [43][44][45]) while these effects could not be recovered using relativistic effective core potentials (ECP [46]) on the halogen atoms. The study of Wodyński and Pecul [47] described the influence of heavy atom on the spin-spin coupling constants between two light nuclei in organometallic compounds and halogen derivatives.
Another main factor related to the structural and electronic parameters of carbazoles and resulting in their different chemical properties is aromaticity. This chemical property can be analyzed in several ways: via structurally (harmonic oscillator model of aromaticity), electronically (PDI-para-delocalization index), and magnetically (NICS) based indices. The work of Poater et al. [48] showed a clear divergence between the structural, electronic, and magnetic measures, so it is important to use different aromaticity indexes to quantify this property. The HOMA is a structurally based measure of aromaticity. It was defined by Kruszewski and Krygowski [49,50] as where n is the number of included bonds with bond lengths R i , and a is an empirical constant chosen in such a way that HOMA = 0 for a model non aromatic system, and HOMA = 1 for a system with all bonds equal to an optimal value R opt , assumed to be achieved for fully aromatic systems. The HOMA index has been found to be among the most effective structural indicators of aromaticity. Another way to show the aromaticity of a compound is the widely employed nucleus independent chemical shift (NICS), which was defined by Schleyer et al. [51] as the negative value of the absolute shielding computed at the ring center, or at some other interesting geometrical point of the system. In common use, there are three variants: NICS(0) calculated at the ring plane, NICS(1) calculated 1 Å above the plane, and its zz-tensor component, NICS(1) zz , where the z-axis is a normal to the plane. Rings with large negative NICS values are considered to be aromatic and the more negative the NICS value is the more aromatic the rings are. Keeping in mind the above facts, we aimed to synthesize and characterize a very specific carbazole derivative containing two iodo-substituents. Its crystal structure and NMR spectra are not yet described in the literature. This paper presents thus the first report on crystal structure of 9-benzyl-3,6-diiodo-9H-carbazole and its 13 C NMR parameters in CDCl 3 solution. We compare the experimental low temperature X-ray (100.0 K) and room-temperature NMR data with the DFT-calculated geometry of a single molecule in the gas phase and its carbon shifts calculated using standard non-relativistic and the relativistic ZORA approach. The changes in aromaticity in 9-benzyl-3,6-diiodo-9H-carbazole compared to free carbazole, benzene, and pyrrole are also discussed via the structural HOMA and magnetic NICS measures.
The crystals suitable for X-ray analysis of 9-benzyl-3,6diiodo-9H-carbazole were obtained by slow evaporation of a saturated solution in chloroform.

Characterization
The single crystals of 9-benzyl-3,6-diiodo-9H-carbazole were used for data collection at 100.0(1) K on a four-circle Oxford Diffraction Xcalibur diffractometer equipped with a two-dimensional area CCD detector with the graphite monochromatised MoKa radiation (k = 0.71073 Å ) and the x-scan technique. Integration of the intensities and correction for Lorenz and polarization effects were performed using the CrysAlis RED software [53]. Crystal structures were solved by direct methods and refined by a full-matrix least-squares method on F 2 using the SHELXL-97 program [54]. Complete crystallographic details are available as a supplementary material, and have been deposited at the Cambridge Crystallographic Data Centre (CCDC 990604) CCDC [55]. Any request to the CCDC for this material should quote the full literature citation. The room-temperature 13 C NMR spectra in CDCl 3 solution were measured using Bruker Ultrashield 400 MHz NMR spectrometer operating at 100.663 MHz for carbon nuclei at ambient temperature and referenced to tetramethylsilane (TMS) as internal standard.

Theoretical calculations
The geometric parameters of the isolated molecule were obtained from an unconstrained optimization using the B3LYP density functional [27,28,56] and a flexible 6-311++G(3df,2pd) basis set for C, N and H, and the smaller 6-311G** basis set for iodine. The subsequent vibrational analysis at the same level of theory showed no imaginary frequencies indicating a true energy minimum. These traditional non-relativistic calculations were carried out using Gaussian 09 [57]. In the subsequent steps, the non-relativistic geometry has been used both for typical non-relativistic shielding calculations with the BHandH-LYP half-and-half hybrid functional [29] and for the relativistic shielding calculations employing the zeroth-order regular approximation Hamiltonian, including the SO coupling term (SO ZORA) [58]. For consistence, all NMR parameters were obtained with Amsterdam density functional (ADF) program [59]. In this case, we employed the DZP-, TZ2P-, and QZ4P STO-type basis sets. However, we are aware that slightly better agreement between theoretical and experimental NMR parameters could be obtained using optimized structures at the same level of theory [60]. Theoretical chemical shifts (in ppm) were referenced to benzene calculated at the same level of theory.
The HOMA and NICS indexes of aromaticity were calculated in Gaussian 09 at the same level as the geometry optimization.

Crystal structure
The molecular structure of 9-benzyl-3,6-diiodo-9H-carbazole, the atomic numbering and ring labeling schemes are presented in Fig. 1. The packing arrangement in the crystal state is presented in Fig. 2. The molecular structure of 9-benzyl-3,6-diiodo-9H-carbazole consists of two units: the carbazole unit containing atoms C1-C9A and the benzyl unit containing atoms C10-C16.
The crystal data measured at 100 K and refinement parameters are summarized in Table 1. The interatomic distances between iodine atoms in neighboring molecules are given in Table 2 and selected bond lengths in Table 3. For brevity, all experimental bond distances, bond angles, and torsion angles within this compound are given in Tables S1, S2, and S3 in the Supplementary Material. The value of iodine-iodine distance coincides well with their van der Waals radius proposed by Bondi (1.98 Å [61]) or Bastanov (2.1 Å [62,63]). Thus, the intermolecular IÁÁÁI contact of 3.9558(3) Å in the crystal structure of the title compound is about twice the iodine van der Waals radius (see Table 2; Fig. 2). It is well known that X-ray crystallography determines accurately bond lengths between non-hydrogen atoms and significantly underestimates C-H bonds [64]. This is also apparent from Table S1. Therefore, we will limit the discussion of theoretical bond lengths to C-C, C-N, and C-I only (see Table 3). All measured bond lengths and angles are within normal ranges and fairly similar to distances reported earlier for 9-benzyl-9H-carbazole X-ray structure [65] (see Table 3). For better illustration of the quality of predictions in the gas phase, we compared in Fig. 3 the theoretical (non-relativistic) bond lengths with experimental values obtained from X-ray measurement at low temperature. A good agreement between theoretical and experimental interatomic distances of 9-benzyl-3,6-diiodo-9H-carbazole is apparent from a perfect linear correlation between theory and experiment (y = 1.0415x-0.0535, R 2 = 0.9998), see Fig. 3).
The structural parameters obtained at the ZORA (B3LYP/DZP/TZP level of theory) are of similar accuracy to the results of the non-relativistic calculations, but they are more time-consuming and we will not consider them in future studies. The differences between theoretical and experimental C-C and C-N bond lengths are in the range of 0.013-0.001 Å . For the C-I bond the difference is higher (in the range of 0.03-0.04 Å ). All geometric data for the studied carbazole derivative correlate also well with the corresponding values found in the crystal structure of the non-halogenated 9-benzyl-9H-carbazole [65] (see Table 3).   Table 4. It is apparent that a very significant HALA effect of about -42 ppm is only present for the C3 and C6 carbons directly bond to iodine atoms.
Thus, the non-relativistic calculations of C3 and C6 chemical shifts lead to significant errors with a root mean square deviation (RMS) of 12.85 ppm (for SO ZORA calculations RMS = 3.34 ppm, see Table 4 and Fig. 4). It is also apparent from Fig. 4 that the spin-orbit effects played a major role in the calculations of chemical shifts of carbon atoms directly attached to the halogen atom (here iodine). The observed HALA effects are very close to earlier results for halogen-substituted carbon atoms [15,35,42]. The other carbons, however, do practically not feel the presence of the heavy halogen atoms.

HOMA and NICS indexes
The calculated HOMA and NICS values are gathered in Table 5. HOMA indexes were calculated from Equation (1) using a = 257.7 and R opt (CC) = 1.388 Å [66] and bond lengths from B3LYP/6-311++G(3df,2pd) optimized geometries. For comparison, the corresponding HOMA values for benzene and pyrrole, calculated at the same level of theory are 0.998 and 0.772. The most aromatic ring within the studied molecule is the benzyl unit (D): HOMA = 0.996. The two benzene rings of the carbazole moiety (A and C) are very similar (0.960 and 0.962). The aromaticity of these rings is higher than in the parent unsubstituted carbazole molecule (HOMA = 0.919). The least aromatic is the pyrrolic unit (ring B). In comparison to the parent pyrrole, the five-membered ring B is significantly less aromatic (0.446) than in the pyrrole molecule (0.772) or in the unsubstituted carbazole (0.679).
Apart from HOMA, in Table 5 are also gathered the results for the three variants of the NICS parameter, No. of restrains 0 H-atom treatment H atoms treated by a mixture of independent and considered refinement 0.393, -0.379 Table 2 Experimental iodine-iodine distance (in Å ) for 9-benzyl-3,6-diiodo-9H-carbazole in the solid state at 100 K  Table 5; Fig. 5). Interestingly, examining the above results it is evident that the most sensitive marker of aromaticity is NICS(1) zz . Following the theory, that the more negative the NICS value the more aromatic the ring is, it is apparent from Fig. 5 that NICS(0) calculated for pyrrole, 9H-carbazole, and 9-benzyl-3,6-diiodo-9H-carbazole predicts more aromatic rings than for benzene. The other two variants NICS(1) and NICS(1) zz , however, show a different pattern. Based on NICS(1) zz only the pyrrole ring is more aromatic than benzene in complete contrast to the HOMA index. Also the zz-component of NICS (1) indicates that the addition of the benzyl ring and the two iodine atoms significantly affects the aromaticity of carbazole. In comparison to pristine carbazole, the aromaticity of the benzene rings (A and C) of 9-benzyl-3,6-diiodo-9H-carbazole are slightly different. This could reflect the effect of specific twisting of benzyl ring to one of the benzene ring of carbazole moiety. Fig. 3 Linear correlation between theoretical (predicted at B3LYP/6-311++G(3df,2pd) level, and 6-311G** for iodine atom) and experimental bond lengths for 9-benzyl-3,6-diiodo-9H-carbazole Table 3 Comparison of selected geometric data for 9-benzyl-3,6-diiodo-9Hcarbazole (Å ) and 9-benzyl-9Hcarbazole (Å ) obtained from X-ray measurements at 100 K and calculated via nonrelativistic (NR) B3LYP/6-311++G(3df,2pd)/6-311G** and relativistic ZORA/DZP/ TZP geometry optimizations RMS values are marked using bold font Bond X-ray NR DFT ZORA DFT 9-Benzyl-9H-carbazole (X-ray) [65] I (1)

Conclusions
A combined experimental and theoretical study has been performed on 9-benzyl-3,6-diiodo-9H-carbazole. For the first time its crystal structure was determined at 100 K and the room-temperature 13 C NMR spectrum in CDCl 3 solution was measured. The B3LYP/6-311++G(3df,2pd) calculated gas-phase geometry was close (not identical) to the X-ray measured structure in the solid state. The observed IÁÁÁI contact distances in the crystal structure were 3.9558(3) Å and no H-bonding was observed. It was essential to employ the relativistic SO ZORA approach in the chemical shift calculations to reproduce the experimental chemical shift of carbons C3 and C6 (a very large HALA effect of -42 ppm was calculated). Finally, we observed a good linear correlation between experimental and theoretically predicted structural and NMR parameters.
The aromaticity of individual rings was determined by calculations of structural (HOMA) and magnetic (NICS) Fig. 4 Deviation of theoretically calculated non-relativistic (NR) and relativistic (scalar ZORA and spin-orbit ZORA) 13 C chemical shifts (Dd in ppm) from experimental data measured for 9-benzyl-3,6diiodo-9H-carbazole in CDCl 3 solution at room temperature  indexes. The most aromatic ring was the benzyl unit (HOMA = 0.996). The least aromatic was the pyrrolic ring (HOMA = 0.446). The calculated NICS indexes showed all rings also to be aromatic, but there were significant differences in the predictions of the HOMA and NICS aromaticity indices for the individual rings.