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Bonding features in Appel's salt from the orbital-free quantum crystallographic perspective

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aResearch Laboratory of Multiscale Modelling, South Ural State University, Lenin prospect, 76, Chelyabinsk, 454080, Russian Federation, bA.N. Nesmeyanov Institute of Organoelement Compounds RAS, Moscow, 119991, Russian Federation, cN.D. Zelinsky Institute of Organic Chemistry Russian Academy of Sciences, Moscow, 119991, Russian Federation, and dQuantum Chemistry Department, D.I. Mendeleev University of Chemical Technology, Miusskaya sq., Moscow, 125047, Russian Federation
*Correspondence e-mail: bartashevichev@susu.ru

Edited by P. Macchi, Politecnico di Milano, Italy (Received 30 April 2021; accepted 8 June 2021; online 22 July 2021)

Bonding properties in the crystal of 4,5-di­chloro-l,2,3-di­thia­zolium chloride (Appel's salt) were studied using a combination of single-crystal high-resolution X-ray diffraction data and the orbital-free quantum crystallography approach. A QTAIM-based topological model shows the proximity of S—C and S—N bonds to the sesquialteral type and establishes the low S—S bond order in the l,2,3-di­thia­zolium heterocycle. It is found that the electrostatic potential carries the traces of a common positive area on the junction of interatomic zero-flux surfaces of S1 and S2 atomic basins; meanwhile the exchange energy density per particle shows perfectly here two separate minima through which the two bond paths run. Thus, the pair intermolecular interactions Cl⋯S1 and Cl⋯S2 formed by the common chloride anion placed near the center of the S—S bond are categorized as chalcogen bonds.

1. Introduction

The study of electronic properties and charge density distribution in crystals of five-membered heterocycles, such as thia­zoles, 1,2,3-di­thia­zoles and 1,2,3,5-di­thia­diazoles, is important because of their predisposition to form stable radicals (Hicks, 2010[Hicks, R. G. (2010). In Stable Radicals: Fundamentals and Applied Aspects of Odd-Electron Compounds, pp. 317-380. John Wiley & Sons, Ltd.]; Rakitin, 2011[Rakitin, O. A. (2011). Russ. Chem. Rev. 80, 647-659.]). They also exhibit some biological activity (Asquith et al., 2019[Asquith, C. R. M., Meili, T., Laitinen, T., Baranovsky, I. V., Konstantinova, L. S., Poso, A., Rakitin, O. A. & Hofmann-Lehmann, R. (2019). Bioorg. Med. Chem. Lett. 29, 1765-1768.]). The early works dealing with the synthesis of 1,2,3-di­thia­zolyl radical salts mainly used the data of standard X-ray diffraction and electron paramagnetic resonance (EPR) spectroscopy studies (Barclay, Beer et al., 1999[Barclay, T. M., Beer, L., Cordes, A. W., Haddon, R. C., Itkis, M. I., Oakley, R. T., Preuss, K. E. & Reed, R. W. (1999). J. Am. Chem. Soc. 121, 6657-6663.]; Fairhurst et al., 1983[Fairhurst, S. A., Pilkington, R. S. & Sutcliffe, L. H. (1983). J. Chem. Soc. Faraday Trans. 1, 79, 439-452.]; Rees et al., 2002[Rees, C. W., Sivadasan, S., White, A. J. P. & Williams, D. J. (2002). J. Chem. Soc. Perkin Trans. 1, pp. 1535-1542.]). The S—S and S—N bonds and S⋯S interactions in derivatives of the 1,2,3-di­thia­zolium salt have attracted great attention due to their effect on dimerization processes, stabilization of radical states and the impact on conducting properties in the solid state (Beer et al., 2002[Beer, L., Cordes, W. A., Haddon, R. C., Itkis, M. E., Oakley, R. T., Reed, R. W. & Robertson, C. M. (2002). Chem. Commun. pp. 1872-1873.], 2004[Beer, L., Britten, J. F., Clements, O. P., Haddon, R. C., Itkis, M. E., Matkovich, K. M., Oakley, R. T. & Reed, R. W. (2004). Chem. Mater. 16, 1564-1572.]; Brusso et al., 2004[Brusso, J. L., Clements, O. P., Haddon, R. C., Itkis, M. E., Leitch, A. A., Oakley, R. T., Reed, R. W. & Richardson, J. F. (2004). J. Am. Chem. Soc. 126, 8256-8265.]; Leitch et al., 2007[Leitch, A. A., Reed, R. W., Robertson, C. M., Britten, J. F., Yu, X., Secco, R. A. & Oakley, R. T. (2007). J. Am. Chem. Soc. 129, 7903-7914.]). More recent studies tend to proceed from the interatomic distances to deeper understanding of the bonding properties by analysing electronic characteristics in the framework of orbital and quantum-topological schemes. Electronic characteristics of the S—S bond in benzodi­thiol-3-one based on experimental electron density (Shukla et al., 2020[Shukla, R., Dhaka, A., Aubert, E., Vijayakumar-Syamala, V., Jeannin, O., Fourmigué, M. & Espinosa, E. (2020). Cryst. Growth Des. 20, 7704-7725.]) revealed the features of this bond, as well as the ability of sulfur atoms to form intermolecular chalcogen bonds. A deep study of the nature of S–S bonding from the simple two-center two-electron (2c-2e) and three-center four-electron (3c-4e) models and up to complicated four-center six-electron (4c-6e) organization was performed by Gleiter & Haberhauer, (2017[Gleiter, R. & Haberhauer, G. (2017). Coord. Chem. Rev. 344, 263-298.]). The conclusion from the orbital viewpoint is that the loss of electron density by the divalent sulfide form could lead to trivalent sulfur centers.

Accurate X-ray diffraction studies of N,S-heterocycles have been made long ago (Hübschle et al., 2008[Hübschle, C. B., Dittrich, B., Grabowsky, S., Messerschmidt, M. & Luger, P. (2008). Acta Cryst. B64, 363-374.]; Bodar-Houillon et al., 1999[Bodar-Houillon, F., Elissami, Y., Marsura, A., Ghermani, N. E., Espinosa, E., Bouhmaida, N. & Thalal, A. (1999). Eur. J. Org. Chem. 1999, 1427-1440.]; Tafipolsky et al., 2002[Tafipolsky, M., Scherer, W., Öfele, K., Artus, G., Pedersen, B., Herrmann, W. A. & McGrady, G. S. (2002). J. Am. Chem. Soc. 124, 5865-5880.]). Recent studies (Gleiter & Haberhauer, 2017[Gleiter, R. & Haberhauer, G. (2017). Coord. Chem. Rev. 344, 263-298.], 2014[Gleiter, R. & Haberhauer, G. (2014). J. Org. Chem. 79, 7543-7552.]) considered the complicated cases of bonding between chalcogen atoms, including two-, three- and four-center bonds. The other studies covered aspects of bonding in biologically important molecules such as the drug metronidazole with a diazole heterocycle in its structure (Kalaiarasi et al., 2019[Kalaiarasi, C., George, C., Gonnade, R. G., Hathwar, V. R. & Poomani, K. (2019). Acta Cryst. B75, 942-953.]), polymorphs of famotidine based on a thia­zole ring (Overgaard & Hibbs, 2004[Overgaard, J. & Hibbs, D. E. (2004). Acta Cryst. A60, 480-487.]) and (2-oxo-1,3-benzoxazol-3(2H)-yl) acetic acid (Wang et al., 2016[Wang, A., Ashurov, J., Ibragimov, A., Wang, R., Mouhib, H., Mukhamedov, N. & Englert, U. (2016). Acta Cryst. B72, 142-150.]). The electron density point of view on halogen bonds has been thoroughly presented in the recent works dealing with the N⋯I bond (Wang et al., 2018[Wang, R., Hartnick, D. & Englert, U. (2018). Z. Kristallogr. Cryst. Mater. 233, 733-744.]), interactions in tetra­fluoro­diiodo­benzene (Wang et al., 2019[Wang, R., George, J., Potts, S. K., Kremer, M., Dronskowski, R. & Englert, U. (2019). Acta Cryst. C75, 1190-1201.]) and short Cl⋯Cl bonding (Wang et al., 2012[Wang, R., Dols, T. S., Lehmann, C. W. & Englert, U. (2012). Chem. Commun. 48, 6830-6832.], 2017[Wang, A., Wang, R., Kalf, I., Dreier, A., Lehmann, C. W. & Englert, U. (2017). Cryst. Growth Des. 17, 2357-2364.]). The bonding in 3-alk­oxy-4-methyl­thia­zole-2(3H)-thione (Vénosová et al., 2020[Vénosová, B., Koziskova, J., Kožíšek, J., Herich, P., Lušpai, K., Petricek, V., Hartung, J., Müller, M., Hübschle, C. B., van Smaalen, S. & Bucinsky, L. (2020). Acta Cryst. B76, 450-468.]), which is one of the most frequently used progenitors of oxygen radicals, is discussed with the main focus on the features of the N—O bond involved in radical generation.

1,2,3,5-Di­thia­diazole derivatives, capable of forming stable radical salts, were characterized at the atomic level by Gleiter & Haberhauer (2014[Gleiter, R. & Haberhauer, G. (2014). J. Org. Chem. 79, 7543-7552.]) and Campo et al. (2006[Campo, J., Luzón, J., Palacio, F. & Rawson, J. (2006). In Carbon Based Magnetism: an Overview of the Magnetism of Metal Free Carbon-Based Compounds and Materials, ch. 7, pp. 159-188. Elsevier.]). 1,2,3-Di­thia­zole stable radicals were thoroughly studied using X-ray diffraction, EPR, electrochemical and spectroscopic methods (Lekin et al., 2010[Lekin, K., Winter, S. M., Downie, L. E., Bao, X., Tse, J. S., Desgreniers, S., Secco, R. A., Dube, P. A. & Oakley, R. T. (2010). J. Am. Chem. Soc. 132, 16212-16224.]; Beer et al., 2004[Beer, L., Britten, J. F., Clements, O. P., Haddon, R. C., Itkis, M. E., Matkovich, K. M., Oakley, R. T. & Reed, R. W. (2004). Chem. Mater. 16, 1564-1572.]; Barclay, Cordes et al., 1999[Barclay, T. M., Cordes, W. A., Beer, L., Oakley, R. T., Preuss, K. E., Taylor, N. J. & Reed, R. W. (1999). Chem. Commun. pp. 531-532.]; Smithson et al., 2016[Smithson, C. S., MacDonald, D. J., Matt Letvenuk, T., Carello, C. E., Jennings, M., Lough, A. J., Britten, J., Decken, A. & Preuss, K. E. (2016). Dalton Trans. 45, 9608-9620.]; Barclay et al., 2001[Barclay, T. M., Beer, L., Cordes, A. W., Oakley, R. T., Preuss, K. E., Reed, R. W. & Taylor, N. J. (2001). Inorg. Chem. 40, 2709-2714.]). But unlike 1,2,3,5-di­thia­diazole derivatives (Domagała & Haynes, 2016[Domagała, S. & Haynes, D. A. (2016). CrystEngComm, 18, 7116-7125.]; Domagała et al., 2014[Domagała, S., Kosc, K., Robinson, S. W., Haynes, D. A. & Woźniak, K. (2014). Cryst. Growth Des. 14, 4834-4848.]), the bonding features in 1,2,3-di­thia­zole-containing systems have been estimated from bond-length analysis and calculated electronic characteristics (Konstantinova et al., 2016[Konstantinova, L. S., Baranovsky, I. V., Irtegova, I. G., Bagryanskaya, I. Y., Shundrin, L. A., Zibarev, A. V. & Rakitin, O. A. (2016). Molecules, 21, 596.]; Bol'shakov et al., 2017[Bol'shakov, O. I., Yushina, I. D., Bartashevich, E. V., Nelyubina, Y. V., Aysin, R. R. & Rakitin, O. A. (2017). Struct. Chem. 28, 1927-1934.], 2020[Bol'shakov, O. I., Yushina, I. D., Stash, A. I., Aysin, R. R., Bartashevich, E. V. & Rakitin, O. A. (2020). Struct. Chem. 31, 1729-1737.]). However, the bond-length approach may be insufficient for the cases with unclear bond orders and intermediate sesquialteral bonds which is correct for the 1,2,3-di­thia­zole system. Therefore, the details of bonding properties based on experimentally observed electron density in such systems are still not established.

To provide a deeper insight into this problem, we address in this work the features of covalent bonding in 1,2,3-di­thia­zole systems, together with different types of noncovalent bonds such as chalcogen (ChB) (Aakeroy et al., 2019[Aakeroy, C. B., Bryce, D. L., Desiraju, G. R., Frontera, A., Legon, A. C., Nicotra, F., Rissanen, K., Scheiner, S., Terraneo, G., Metrangolo, P. & Resnati, G. (2019). Pure Appl. Chem. 91, 1889-1892.]) and halogen bonds (HaB) (Desiraju et al., 2013[Desiraju, G. R., Ho, P. S., Kloo, L., Legon, A. C., Marquardt, R., Metrangolo, P., Politzer, P., Resnati, G. & Rissanen, K. (2013). Pure Appl. Chem. 85, 1711-1713.]) which are capable of forming such heterocycles in crystals. The aim of our study is to characterize the bonding features on the level of electron density for Appel's salt (4,5-dichloro-l,2,3-dithiazolium chloride) (Appel et al., 1985[Appel, R., Janssen, H., Siray, M. & Knoch, F. (1985). Chem. Ber. 118, 1632-1643.]; Rabe & Müller, 1999[Rabe, S. & Müller, U. (1999). Z. Kristallogr. NCS, 214, 68.]; Rees et al., 2002[Rees, C. W., Sivadasan, S., White, A. J. P. & Williams, D. J. (2002). J. Chem. Soc. Perkin Trans. 1, pp. 1535-1542.]), the important representative of 1,2,3-di­thia­zole systems. We are going to discuss the insights that it can give for synthetic purposes and organic routes of obtaining stable radicals, as although Appel's salt itself does not demonstrate any radical properties, it is still extremely efficient in obtaining stable radical salts upon dimerization. The clue to this process lies in the bonding features of Appel's salt, which are the center of attention in the present work. Our approach is based on orbital-free quantum crystallography (Tsirelson & Ozerov, 1996[Tsirelson, V. G. & Ozerov, R. P. (1996). Electron Density and Bonding in Crystals. Bristol, Philadelphia: IOP.]; Tsirelson & Stash, 2004[Tsirelson, V. & Stash, A. (2004). Acta Cryst. A60, 418-426.]; Tsirelson, 2018[Tsirelson, V. (2018). J. Comput. Chem. 39, 1029-1037.]; Tsirelson & Stash, 2020[Tsirelson, V. & Stash, A. (2020). Acta Cryst. B76, 769-778.], 2021[Tsirelson, V. G. & Stash, A. I. (2021). Acta Cryst. B77, 467-477.]), when the molecular properties of interest are presented in the framework of orbital-free density functional theory (DFT) (Feynman et al., 1949[Feynman, R. P., Metropolis, N. & Teller, E. (1949). Phys. Rev. 75, 1561-1573.]; Lignères & Carter, 2005[Lignères, V. L. & Carter, E. A. (2005). In Handbook of Materials Modeling, edited by S. Yip, pp. 137-148. Dordrecht: Springer Netherlands.]) and then are expressed via experimental electron density and its derivatives. The latter were obtained using the combination of an experimental high-resolution X-ray diffraction method and a computational ab initio study of a solid under the periodic boundary conditions.

2. Materials and methods

2.1. Synthesis and crystallization

Di­chloro­methane (analytical grade, Ecros Ltd), sulfur monochloride (Merck, Darmstadt) and chloro­aceto­nitrile (99%, Sigma–Aldrich) were used as received. Appel's salt single crystals were obtained according to method of Appel et al. (1985[Appel, R., Janssen, H., Siray, M. & Knoch, F. (1985). Chem. Ber. 118, 1632-1643.]). Chloroaceto­nitrile (3.02 g, 40 mmol) and sulfur monochloride (27 g, 0.20 mol) were mixed in di­chloro­methane (15 ml) at room temperature and left for 18 h without stirring. The resulting precipitate was washed with di­chloro­methane (50 ml) three times and dried in vacuum to obtain black–green crystals (6.66 g, 32 mmol, 80% yield), which were used for analysis.

2.2. Single-crystal X-ray diffraction experiment and spherical atom refinement

For X-ray diffraction analysis, a black–green block-like crystal [C2Cl2NS2]+·Cl (I) with an approximate size (mm) 0.110 × 0.120 × 0.580 was selected. Data were collected at 100 K using a Bruker Quest D8 diffractometer with a Photon III detector with an Oxford Cryojet low-temperature attachment (graphite monochromator, Mo Kα, λ = 0.71073 Å, ω-scan). A total of 20 637 frames were collected over 108.5 h.

Data collection, determination of unit-cell parameters, integration and reflection index were carried out using the software packages APEX3 (Bruker, 2019[Bruker (2019). APEX3, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]) and SAINT (V8.38A; Bruker, 2019[Bruker (2019). APEX3, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]). The data set was corrected for X-ray absorption of the crystal using the multi-scan method (SADABS-2016/2; Bruker, 2019[Bruker (2019). APEX3, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]).

The structure was solved and refined in the orthorhombic space group P212121 using the Bruker SHELXTL software package APEX3 (Bruker, 2019[Bruker (2019). APEX3, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]; Sheldrick, 2015[Sheldrick, G. M. (2015). Acta Cryst. A71, 3-8.]), with Z = 4 for the empirical formula C2Cl3NS2. The final refinement of the structure was carried out using full-matrix least-squares on F2 in the anisotropic harmonic approximation of the displacement parameters of atoms. Extinction in the sample was accounted for in the SHELXTL method.

2.3. Multipole model refinement

We used the structural multipole model by Hansen & Coppens (1978[Hansen, N. K. & Coppens, P. (1978). Acta Cryst. A34, 909-921.]). It was limited to the hexadecapole level for all atoms. Atomic Macchi and Coppens (2001[Macchi, P. & Coppens, P. (2001). Acta Cryst. A57, 656-662.]) wavefunctions were used in the model. A set of symmetry-independent structure factors for refining the multipole model was obtained by averaging equivalent reflections in the SADABS program. Refinement of the model parameters was carried out using the XD2016 program (Volkov et al., 2016[Volkov, A., Macchi, P., Farrugia, L. J., Gatti, C., Mallinson, P., Richter, T. & Koritsanszky, T. (2016). XD2016. University at Buffalo, State University of New York, NY, USA; University of Milan, Italy; University of Glasgow, UK; CNRISTM, Milan, Italy; Middle Tennessee State University, TN, USA; and Freie Universität, Berlin, Germany.]).

In the first step, the set of spherical atom harmonic atomic displacement parameters was extended to fourth-order anharmonic parameters. They were refined together with atomic positions using X-ray reflections with sin(θ/λ) > 0.7 Å−1. The anharmonic displacements of nitro­gen and carbon atoms turned out to be statistically insignificant (< 3σ). Therefore, the positional and displacement parameters for Cl and S atoms were refined in the anharmonic approximation for atomic vibrations, while the anisotropic harmonic approximation was kept for N and C atoms.

In the second step, the electron populations and extension/contraction parameters of the multipoles and the extension/contraction atomic κ-parameters were alternately refined over the whole reflection set. The scale factor was refined at all stages. During the refinement, the condition of electroneutrality of the unit cell and the non-negativity of the electron density were monitored.

The residual Fourier maps characterizing the electron density not covered by the multipole model and the experimental `noise' in the data were calculated over the whole array of reflections. They showed a scatter of values from −0.116 to 0.133 e Å−3 with an e.s.d. = 0.032 e Å−3. The latter value can serve as an estimate of the electron density accuracy in this work. Crystal data, data collection and details of structure refinement are shown in Table 1[link]. All calculations concerning the experimental functions were performed using WinXPRO (Stash & Tsirelson, 2002[Stash, A. & Tsirelson, V. (2002). J. Appl. Cryst. 35, 371-373.], 2005[Stash, A. I. & Tsirelson, V. G. (2005). Crystallogr. Rep. 50, 177-184.], 2014[Stash, A. I. & Tsirelson, V. G. (2014). J. Appl. Cryst. 47, 2086-2089.]; Tsirelson & Stash, 2020[Tsirelson, V. & Stash, A. (2020). Acta Cryst. B76, 769-778.]).

Table 1
Experimental details

  (I)
Crystal data
Chemical formula C2Cl2NS2+·Cl
Mr 208.50
Crystal system, space group Orthorhombic, P212121
Temperature (K) 100
a, b, c (Å) 5.90947 (10), 10.22455 (16), 10.97838 (18)
V3) 663.33 (2)
Z 4
Radiation type, wavelength λ (Å) Mo Kα, 0.71073
μ (mm−1) 1.89
Crystal size (mm) 0.58 × 0.12 × 0.11
 
Data collection
Diffractometer Bruker Quest D8 diffractometer with Photon III detector
Absorption correction Multi-scan (SADABS2016/2; Bruker, 2019[Bruker (2019). APEX3, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.])
Tmin, Tmax 0.566, 0.724
No. of measured, independent and observed [I > 2σ(I)] reflections 102 642, 12 761, 12 387
Rint 0.024
(sin θ/λ)max−1) 1.335
 
Spherical atom refinement
R[F > 2σ(F)], wR(F), S 0.014, 0.040, 1.07
Weighting scheme, w a1 = 0.0193, a2 = 0.0166
No. of reflections 12 761
No. of parameters 73
Δρmax, Δρmin (e Å−3) 0.49, −0.55
   
Multipole and anharmonicity model refinement
R[F > 2σ(F)], wR(F), S 0.0085, 0.0110, 1.403
Weighting scheme, w a1 = 0.01, a2 = 0.0
No. of reflections [I > 3σ(I), sin θ/λ ≤ 1.20] 9426
No. of parameters 414
Δρmax, Δρmin, RMS (e Å−3) 0.133, −0.116, 0.032
Absolute structure xFlack determined using 5383 quotients [(I+)−(I)]/[(I+)+(I)] (Parsons et al., 2013[Parsons, S., Flack, H. D. & Wagner, T. (2013). Acta Cryst. B69, 249-259.])
Absolute structure parameter 0.273 (7)
w = [σ2 + (a1P)2 + (a2P)]−1, where P = 0.3333 Fo2 + 0.66667 Fc2.

2.4. Calculations

Parameters of the crystalline Appel's salt obtained from high-resolution X-ray diffraction data were used for Kohn–Sham calculations as coded in the CRYSTAL17 program package (Dovesi et al., 2018[Dovesi, R., Erba, A., Orlando, R., Zicovich-Wilson, C. M., Civalleri, B., Maschio, L., Rérat, M., Casassa, S., Baima, J., Salustro, S. & Kirtman, B. (2018). WIREs Comput. Mol. Sci. 8, e1360.]). The calculations were carried out using PBE0 functional (Perdew et al., 1996[Perdew, J. P., Ernzerhof, M. & Burke, K. (1996). J. Chem. Phys. 105, 9982-9985.]) and TZVP basis set (Peintinger et al., 2013[Peintinger, M. F., Oliveira, D. V. & Bredow, T. (2013). J. Comput. Chem. 34, 451-459.]). The SHRINK parameter, which determines the number of k-points in reciprocal space, at which the Kohn–Sham matrix is diagonalized, was set to 8 in the Monkhorst net and 16 in the Gilat net resulting in 125 k-points in the irreducible part of the Brillouin zone. The optimization of the structure was performed so that only the shift of atomic positions was allowed, while the experimental unit-cell parameters were held constant. After geometry optimization, the calculation of the Hessian matrix showed that all IR vibrational frequencies are real. It is evident that the obtained crystal structure corresponds to the minimum on potential energy surface.

Quantum topological analysis of electron density (Bader, 1990[Bader, R. F. W. (1990). Atoms in Molecules. A Quantum Theory. New York: Oxford University Press.], 1991[Bader, R. F. W. (1991). Chem. Rev. 91, 893-928.]), based on the wavefunctions obtained from CRYSTAL17, was performed using the TOPOND (Gatti et al., 1994[Gatti, C., Saunders, V. R. & Roetti, C. (1994). J. Chem. Phys. 101, 10686-10696.]; Casassa et al., 2015[Casassa, S., Erba, A., Baima, J. & Orlando, R. (2015). J. Comput. Chem. 36, 1940-1946.]) program. Geometry optimization and atomic charges calculation for isolated cation (C2Cl2NS2+) were performed at the UB3LYP/TZVP level using the Gaussian09 (Frisch et al., 2016[Frisch, M. J., Trucks, G. W., Schlegel, H. B., Scuseria, G. E., Robb, M. A., Cheeseman, J. R., Scalmani, G., Barone, V., Petersson, G. A., Nakatsuji, H., Li, X., Caricato, M., Marenich, A., Bloino, J., Janesko, B. G., Gomperts, R., Mennucci, B., Hratchian, H. P., Ortiz, J. V., Izmaylov, A. F., Sonnenberg, J. L., Williams-Young, D., Ding, F., Lipparini, F., Egidi, F., Goings, J., Peng, B., Petrone, A., Henderson, T., Ranasinghe, D., Zakrzewski, V. G., Gao, J., Rega, N., Zheng, G., Liang, W., Hada, M., Ehara, M., Toyota, K., Fukuda, R., Hasegawa, J., Ishida, M., Nakajima, T., Honda, Y., Kitao, O., Nakai, H., Vreven, T., Throssell, K., Montgomery, J. A., Jr., Peralta, J. E., Ogliaro, F., Bearpark, M., Heyd, J. J., Brothers, E., Kudin, K. N., Staroverov, V. N., Keith, T., Kobayashi, R.,Normand, J., Raghavachari, K., Rendell, A., Burant, J. C., Iyengar, S. S., Tomasi, J., Cossi, M., Millam, J. M., Klene, M., Adamo, C., Cammi, R., Ochterski, J. W., Martin, R. L., Morokuma, K., Farkas, O., Foresman, J. B. & Fox, D. J. (2016). Gaussian 09, Rev. A.03. Gaussian Inc., Wallingford, CT, USA.]) program.

To provide a comparison with the experiment, the calculated electron density was expressed in terms of the same multipole model of Hansen & Coppens (1978[Hansen, N. K. & Coppens, P. (1978). Acta Cryst. A34, 909-921.]). The kinetic energy density of electrons was calculated by Kirzhnits (1957[Kirzhnits, D. (1957). Sov. Phys. JETP, 5, 64-71.]) approximation, and the exchange density was obtained using the local-density approximation (Barth & Hedin, 1972[Barth, U. & Hedin, L. (1972). J. Phys. C. Solid State Phys. 5, 1629-1642.]) in the WinXPRO (Stash & Tsirelson, 2002[Stash, A. & Tsirelson, V. (2002). J. Appl. Cryst. 35, 371-373.], 2005[Stash, A. I. & Tsirelson, V. G. (2005). Crystallogr. Rep. 50, 177-184.], 2014[Stash, A. I. & Tsirelson, V. G. (2014). J. Appl. Cryst. 47, 2086-2089.]; Tsirelson & Stash, 2020[Tsirelson, V. & Stash, A. (2020). Acta Cryst. B76, 769-778.]) program. Graphic representation of 3D functions was performed in the 3DPlot (Stash & Tsirelson, 2020[Stash, A. I. & Tsirelson, V. G. (2020). WinXPRO, 3DPlot and TrajPlot: Computer Software for Orbital-free Quantum Crystallography. Quantum Crystallography Online Meeting 2020, August, 27-29, CentraleSupélec (CS), France. P. 34.]) program.

3. Results and discussion

3.1. Electronic properties of the 1,2,3-di­thia­zolium ring

According to the various approaches to atomic charges estimation (Table S1), the most prominent positive charge in Appel's salt belongs to S2 atom. The charge of Bader's atomic basin Ω(S2), estimated from experimental electron density is almost twice as high as the Ω(S1) charge. This fact is in accordance with the possibility of nucleophilic attack at S2 in the 1,2,3-di­thia­zolium ring (Appel et al., 1985[Appel, R., Janssen, H., Siray, M. & Knoch, F. (1985). Chem. Ber. 118, 1632-1643.]; Konstantinova & Rakitin, 2008[Konstantinova, L. S. & Rakitin, O. A. (2008). Russ. Chem. Rev. 77, 521-546.]), which happens when the substituent at C2(C5) sterically hinders nucleophilic attack at S1. The charge of the chloride anion Ω(Cl) is less negative than for nitro­gen, Ω(N); however, the absolute value of Ω(Cl) = −0.45 e is significantly lower than the formal negative charge usually written in the organic synthetic schemes. Between the two carbon atoms, the more negative is C2(C5); this is consistent with the dimerization of 1,2,3-di­thia­zolium radicals in solution via the fifth position leading to the formation of tetra­thiadi­aza­fulvalene (Barclay, Beer et al., 1999[Barclay, T. M., Beer, L., Cordes, A. W., Haddon, R. C., Itkis, M. I., Oakley, R. T., Preuss, K. E. & Reed, R. W. (1999). J. Am. Chem. Soc. 121, 6657-6663.]) and other aza­lidene derivatives (Jeon & Kim, 1999[Jeon, M.-K. & Kim, K. (1999). Tetrahedron, 55, 9651-9667.]; Emayan et al., 1997[Emayan, K. F., English, R. A., Koutentis, P. & Rees, W. (1997). J. Chem. Soc. Perkin Trans. 1, pp. 3345-3350.]).

To clarify the bond orders in the structure of the cation, we used the QTAIM-based (topological) bond order model (Howard & Lamarche, 2003[Howard, S. T. & Lamarche, O. (2003). J. Phys. Org. Chem. 16, 133-141.]; Tsirelson et al., 2007[Tsirelson, V. G., Bartashevich, E. V., Stash, A. I. & Potemkin, V. A. (2007). Acta Cryst. B63, 142-150.]), which included the electron density at the bond critical points, ρ(rb), and the eigenvalues of Hessian of electron density at these points. We applied the fitting parameters of this model developed for N,S-heterocycles (Bartashevich et al., 2021[Bartashevich, E. V., Muhitdinova, S. E. & Tsirelson, V. G. (2021). Mendeleev Commun. 31. In the press.]).

In Appel's salt, the S—S bond length is 2.034 (2) Å and it is shorter than the common di­sulfide bond, but it is a little longer than in pure delocalized 1,2,3-di­thia­zole ring where it reaches less than 2.03 Å (Rees et al., 2002[Rees, C. W., Sivadasan, S., White, A. J. P. & Williams, D. J. (2002). J. Chem. Soc. Perkin Trans. 1, pp. 1535-1542.]; Konstantinova & Rakitin, 2008[Konstantinova, L. S. & Rakitin, O. A. (2008). Russ. Chem. Rev. 77, 521-546.]; Rakitin, 2011[Rakitin, O. A. (2011). Russ. Chem. Rev. 80, 647-659.]). The estimated bond order, ntopo(S—S), is significantly lower than it was expected from gas-phase calculations for the C2Cl2NS2+ cation (Fig. 1[link]). Nevertheless, decreased S—S bond order is indeed proved by its easy breaking during the Boulton–Katritzky rearrangement (Clarke et al., 1998[Clarke, D., Emayan, K. & Rees, W. (1998). J. Chem. Soc. Perkin Trans. 1, pp. 77-82.]). The highest topological bond orders based on the electron density values, ntopo, belong to S—C and S—N bonds, which have similar values and are relatively close to sesquialteral bonds. Still, in a crystal ntopo(S—C) is greater than ntopo(S—N). In 1,2,3-di­thia­zole derivatives, such as ilidenes or 5-thio­nes, C—N bonds, as a rule, are treated as double bonds and there is no doubt as their bond length is 1.276–1.279 Å. Whereas in Appel's salt, the C—N bond is longer at 1.319 Å. Topological bond order, ntopo(C—N), shows that C—N bond does not reach the sesquialteral type, and ntopo(C—N) < ntopo(S—N). Thus, among covalent bonds of the 1,2,3-di­thia­zolium ring, topological bond orders estimated from experimental electron density decrease in the order of bonds S—C > S—N > C—N > C—C > S—S.

[Figure 1]
Figure 1
Topological bond orders in Appel's salt cation. Top line is the estimation based on experimental electron density, the gas-phase calculations are given in italics.

3.2. Exchange energy density per electron

We compared the features of covalent bonds in the 1,2,3-di­thia­zolium ring in Appel's salt using the exchange energy density per electron,

[\varepsilon_{x}({\bf r})= - {3 \over 4}{\bigg({3 \over \pi }\bigg)^{1/3}}{{\rho}}{({\bf{r}} )^{1/3}}.]

It is connected to the exchange energy as Ex = ∫ɛx(r)ρ(r)dr and is easily derived from experimental electron density, ρ(r). Local density approximation has been used (Barth & Hedin, 1972[Barth, U. & Hedin, L. (1972). J. Phys. C. Solid State Phys. 5, 1629-1642.]). Let us consider the behavior of ɛx(r) along the covalent and noncovalent bonds (Fig. 2[link]), taking into account that electron exchange is responsible for bonding.

[Figure 2]
Figure 2
Profiles of the exchange electron energy density per electron, ɛx(r) along the interatomic lines: (a) covalent bonds in the 1,2,3-di­thia­zolium heterocycle of Appel's salt; (b) ChBs (chalcogen bonds) Cl⋯S1 and Cl⋯S2, HaB (halogen bond) Cl⋯Cl2(−x, −½ + y, [3\over 2]z), TtB (tetrel bond) Cl⋯C2(1 − x, −½ + y, [3\over 2]z) formed by Cl with atoms in cation.

For any type of bond, the density ɛx(r) is deeply negative around the atomic nuclei and goes to a slightly negative area near the 1D maximum showing the energy barrier between neighboring atomic basins for the same-spin electrons. Note that beyond local density approximation, the 1D maximum of ɛx(r) along the interatomic line does not coincide with the position of the bond critical point in electron density. The more prominent negative values of ɛx(r) between bound atoms are, the more stabilizing exchange energy is for this bond. Among covalent bonds of the 1,2,3-di­thia­zolium ring this barrier increases (becomes less negative) in the order C—N < C—C < S—N < C—S < S—S and does not exceed −0.40 a.u. The most prominent stabilization effect due to the electron exchange is observed for the C1—N1 bond, while the weakest effect is for the S1—S2 bond. This sequence does not match the sequence of topological bond orders despite the fact that both descriptors were obtained from the same experimental electron density. Thus, we can conclude that the exchange energy density per electron, ɛx(r), usefully complements the information based on topological bond orders.

3.3. Properties mapped on van der Waals surface

We turn now to the predisposition of a separate (C2NS2C12)+ cation participating in noncovalent interactions as it follows from manifestations of electrostatic effects on the van der Waals surface ρ(r) = 0.001 a.u. The electrostatic potential, φESP(r), mapped on this surface, reveals the most prominent electrophilic site located near the center of the S—S bond. Thus, the σ-hole is not located here on the extension of a covalent bond (Politzer & Murray, 2019[Politzer, P. & Murray, J. S. (2019). Crystals, 9, 165.]; Politzer et al., 2017[Politzer, P., Murray, J. S., Clark, T. & Resnati, G. (2017). Phys. Chem. Chem. Phys. 19, 32166-32178.]; Nayak et al., 2017[Nayak, S. K., Kumar, V., Murray, J. S., Politzer, P., Terraneo, G., Pilati, T., Metrangolo, P. & Resnati, G. (2017). CrystEngComm, 19, 4955-4959.]). The most evident in (C2NS2C12)+ is an `united' σ-hole with a common maximal value, VS,max(S—S), due to merged positive areas of the electrostatic potential generated by S1 and S2 atoms. The latter significantly exceeds the VS,max values of other σ-holes in this molecule (Fig. 3[link]). π-holes, above and below the heterocyclic plane near its center, show lesser VS,max values. The overlapping positive regions of increased electrostatic potential due to the contributions of five atoms of the 1,2,3-di­thia­zolium ring are also seen.

[Figure 3]
Figure 3
Separate cation C2NS2C12+: electrostatic potential (a.u.) mapped on the surface of electron density of 0.001 a.u.; gas-phase calculations, UB3LYP/TZVP; (a) and (b) show alternative views.

Note that the π-hole above the center of the ring is at the outlying position from the concentration of electron density. The lowest values of VS,max correspond to the typical σ-holes of Cl atoms; the electrophilic site of the Cl1 atom, which is opposite to the S—S bond, shows the lowest VS,max value.

Moving on to noncovalent interactions, we can indicate that the most pronounced positions of VS,max, originating from σ- and π-holes in an isolated cation, roughly correspond to the positions of Cl anions around the cation in crystalline Appel's salt. Corresponding noncovalent interactions form typical HaB or ChB bonds. The highest positive value VS,max(S—S) leads to the shortest contacts S1⋯Cl and S2⋯Cl. However, quantitative correlation between VS,max and the lengths of HaBs and ChBs bonds in the crystal of Appel's salt is not observed. The obstacle here is the steric factor. In the crystal structure the S2 atom, having a much lower VS,max(S2) value in the isolated cation, forms a typical S2⋯Cl(½ + x, ½ − y, 1 − z) chalcogen bond of length 3.1585 (2) Å strictly on the extension of the S1—S2 bond. At the same time, atom S1 showing much higher VS,max(S1) value, does not participate in a ChB with Cl. It is because the Cl2 atom on the side of the S1 atom creates the electrostatic repulsive area which does not allow the Cl anion to form a chalcogen bond with atom S1. This situation is similar to that previously observed for chalcogen bonds in 3H-1,2-benzodi­thiol-3-ones and their selenium analogs studied by Shukla et al. (2020[Shukla, R., Dhaka, A., Aubert, E., Vijayakumar-Syamala, V., Jeannin, O., Fourmigué, M. & Espinosa, E. (2020). Cryst. Growth Des. 20, 7704-7725.]), where the thione group hinders the formation of strong ChBs for the adjoining sulfur atom in the thiol group.

Next, we consider the features of electrophilic sites on the C2NS2C12+ cation in the actual crystal, when the noncovalent interactions have already formed a stable structure. A few functions based on experimental charge density and distributed on the surfaces of Bader's atomic basins (Bader, 1990[Bader, R. F. W. (1990). Atoms in Molecules. A Quantum Theory. New York: Oxford University Press.]) are of interest (Bartashevich et al., 2014[Bartashevich, E. V., Yushina, I. D., Stash, A. I. & Tsirelson, V. G. (2014). Cryst. Growth Des. 14, 5674-5684.]). Commonly, the electrostatic potential is intended to illustrate the predisposition of an isolated molecule to interactions with nucleophiles and electrophiles. However, in a crystal, another function is more suitable: that is potential acting on an electron belonging to a molecule, φPAEM(r), which takes into account already realized electrostatic interactions and accounts for the electronic exchange: φPAEM(r) = −φESP(r) + φx(r) (Yang & Davidson, 1997[Yang, Z. Z. & Davidson, E. R. (1997). Int. J. Quantum Chem. 62, 47-53.]; Zhao & Yang, 2014[Zhao, D.-X. & Yang, Z.-Z. (2014). J. Comput. Chem. 35, 965-977.]; Zhao, 2002[Zhao, D. (2002). Chin. Sci. Bull. 47, 635.], 2005[Zhao, D.-X., Gong, L.-D. & Yang, Z.-Z. (2005). J. Phys. Chem. A, 109, 10121-10128.]; Bartashevich & Tsirelson, 2018[Bartashevich, E. V. & Tsirelson, V. G. (2018). J. Comput. Chem. 39, 573-580.]). Here the exchange potential is φx(r) = δEx[ρ]/δρ, where Ex[ρ] is an exchange energy functional. An important advantage of this function is that it can be directly derived from experimental electron density by using the methods of the orbital-free quantum crystallography (Tsirelson et al., 2007[Tsirelson, V. G., Bartashevich, E. V., Stash, A. I. & Potemkin, V. A. (2007). Acta Cryst. B63, 142-150.]; Tsirelson, 2018[Tsirelson, V. (2018). J. Comput. Chem. 39, 1029-1037.]; Tsirelson & Stash, 2020[Tsirelson, V. & Stash, A. (2020). Acta Cryst. B76, 769-778.]).

The function φPAEM(r) mapped on the interatomic zero-flux surface (ZFS) in a crystal [Fig. 4[link](c)] distinctly carries the traces of σ-holes which have been observed in the isolated cation (C2NS2C12+). The most prominent trace may be associated with the electrophilic site near the center of the S—S bond, the place of the junction of ZFS of S1 and S2 atomic basins. Also, the trace of a slightly less pronounced negative area of φPAEM(r) for the typical ChB S2⋯Cl(½ + x, ½ − y, 1 − z) bond is seen [Fig. 4[link](c)]. The presented picture can be interpreted in a following way. PAEM along the interatomic line characterizes the potential barrier, which electrons moving between the basins of the bound atoms should overcome. We can expect that the lower the barrier is, the easier electrons exchange goes on, the stronger the formed bond is. For each pair of chalcogen bonds, S1⋯Cl and S2⋯Cl, formed by the same Cl atom, placed opposite the center of the S1—S2 bond, the φPAEM(r) barrier is lower than for the typical ChB S2⋯Cl(½ + x, ½ − y, 1 − z) on the extension of the S1—S2 bond.

[Figure 4]
Figure 4
(a) The Bader atomic basins of C2NS2C12+ in Appel's salt; the functions mapped on interatomic zero-flux surface of experimental charge density, (b) electrostatic potential, φESP(r), (c) potential acting on an electron in a molecule, φPAEM(r) and (d) exchange energy density per electron, ɛx(r).

The electrostatic potential with a negative sign is a dominating contribution of the potential acting on an electron in a molecule. Thus, it illustrates the similar picture with the traces of σ-holes on ZFS [Fig. 4[link](b)]. One common maximum of φESP(r) still remains at the junction of ZFS of S1 and S2 atoms. A completely different picture is obtained using the exchange energy density per one electron, ɛx(r). There are the two separated minima of decreased negative values of ɛx(r), which are perfectly shown on ZFSs of S1 and S2 atoms [Fig. 4[link](d)]. This is an argument for the importance of the electronic exchange for the pair of relatively strong chalcogen bonds formed by a Cl anion located opposite the S—S bond center. Negative minima of ɛx(r) on ZFS reflect the slices of two `exchange channels' formed by two chalcogen bonds. Note that the two bond paths, S1⋯Cl and S2⋯Cl, run inside such channels. The next minimum of ɛx(r) is clearly seen for the typical ChB S2⋯Cl(½ + x, ½ − y, 1 − z), which is on the elongation of the S1—S2 bond. However, in this case the region of decreased ɛx(r) values on ZFS of S2 is less pronounced. The typical chalcogen bond S2⋯Cl on the elongation of the di­sulfide group is weakened for two reasons at once: a competitive factor and the poor polarization due to low bond order and the weakness of the S1—S2 bond in the 1,2,3-di­thia­zolium ring.

Manifestation of the electronic exchange may be revealed using the distributions of partial exchange charge density, qx(r) (Tsirelson et al., 2010[Tsirelson, V. G., Stash, A. I. & Liu, S. (2010). J. Chem. Phys. 133, 114110.]); qx(r) = − [1/(4π)]∇2φx(r), where φx(r) is exchange potential. The function qx(r) represents the contribution from the static exchange effect to electron density, experimental and theoretical. It allows us to analyze the exchange potential by considering the extremes and inflection points of qi(r). We used the local density approximation (Barth & Hedin, 1972[Barth, U. & Hedin, L. (1972). J. Phys. C. Solid State Phys. 5, 1629-1642.]) to compute qx(r) (Fig. 5[link]).

[Figure 5]
Figure 5
Experimental results of (a) 2D map of the partial exchange charge density, qx(r), of the S1—S2—Cl1 plane of the 1,2,3-di­thia­zolium ring; (b) 3D representation of qx(r) with isosurface −0.03 a.u.; the lines between atoms are the bond paths; line thicknesses are proportional to the magnitude of the electron density at the bond critical points.

2D and 3D distributions (Fig. 5[link]) of the partial exchange charge density, qx(r), illustrate a pronounced peak with low negative values for the nitro­gen atom N1. This peak is in the plane of the 1,2,3-di­thia­zolium ring, and it can be associated with the lone pair position. It is interesting that the common contours with values of qx(r) < −0.030 a.u., and therefore with more pronounced contributions of electronic exchange density, are inherent only for C1—C2 and C1—N1 bonds. Both S1 and S2 atoms are not characterized by low values of qx(r) on the centers of covalent bonds, instead they have the several separate minima around them. 3D representation [Fig. 5[link](b)] led to the more detailed picture of qx(r) extremes. We observe four similar but not identical peaks located around sulfur atoms: two peaks are oriented towards each other with a slight shift relative to the interatomic line of the S1—S2 bond; the next pair of similar peaks are located on opposite sides on the elongation of the S1—S2 bond. The regions limited by the isosurface −0.03 a.u. include two minima which are placed slightly above and below the plane of the 1,2,3-di­thia­zolium ring. These minima of qx(r) are also slightly shifted towards the elongation of C1—S1 and N1—S2 covalent bonds. All those minima are influenced by the nonequivalence of two sulfur atoms. Moreover, their small but noticeable differences give rise to the inequality of the two planes of the 1,2,3-di­thia­zolium ring. Note that bond paths for relatively strong ChB do not cross these regions of decreased qx(r), whereas bond paths for weak van der Waals interactions follow through them directly. These features of the partial exchange charge density are worth systematic investigations.

3.4. Noncovalent bonds and their properties

A compelling fact is that the electrophilic sites of sulfur and chlorine atoms in crystalline Appel's salt can be involved in the formation of halogen (HaB) and chalcogen (ChB) bonds. To check this issue, let us analyze the superposition of gradient fields of electron density and electrostatic potential (Bartashevich et al., 2017[Bartashevich, E., Yushina, I., Kropotina, K., Muhitdinova, S. & Tsirelson, V. (2017). Acta Cryst. B73, 217-226.], 2019[Bartashevich, E., Mukhitdinova, S., Yushina, I. & Tsirelson, V. (2019). Acta Cryst. B75, 117-126.]), as well as the mutual position of minima of these functions along the lines connecting the nuclei of bound atoms. Along the typical HaB Cl⋯Cl2(1 − x, −½ + y, [3\over 2]z) [Fig. 6[link](c)] and ChB Cl⋯S2(½ + x, ½ − y, 1 − z) [Fig. 6[link](c)], the positions of ρ- and φ-minima are located at significant distances from each other. This is evidence of high electrostatic contribution to the interaction attributed in the first case to HaB and in the second case to ChB. In such cases, we can univocally find the direction of electron attraction belonging to the basin of Cl to the nuclei of halogen or chalcogen. Figs. 6[link] and 7[link](b) illustrate these directions with arrows. A similar picture is observed for the Cl⋯C2(1 − x, −½ + y, [3\over 2]z) interaction [Figs. 6[link](b) and 7[link](b)], which can be reliably attributed to the tetrel bond, TtB, as the carbon atom in this case provides its electrophilic site for noncovalent bonding. Here we can speculate about the fact that neither a unified σ-hole on the center of the S—S bond, nor a π-hole due to the cooperative effect of bound atoms in a heterocycle can prevent the analysis of a particular noncovalent bond formed by the atoms with common interatomic surface. That means that the considered electronic properties prove the existence of ChB, HaB and TtB.

[Figure 6]
Figure 6
Profiles of electron density, ρ(r) and electrostatic potential φ(r) along the interatomic line for (a) HaB Cl⋯Cl2(−x, −½ + y, [3\over 2]z); (b) TtB Cl⋯C2(1 − x, −½ + y, [3\over 2]z); (c) ChB S2⋯Cl(½ + x, ½ − y, 1 − z); (d) van der Waals interaction Cl2⋯S1(−x, ½ + y, [3\over 2]z). Arrows point to the electrophilic sites.
[Figure 7]
Figure 7
Atomic basins and bond paths for (a) cation⋯Cl interactions in the plane of the heterocycle; (b) superposition of gradient fields of electron density (ρ-basins) and electrostatic potential (φ-basins) and their boundaries in the plane of C2NS2C12+. Arrows show the attraction of electron density to electrophilic sites for ChBs and HaBs.

Let us note that some interactions in the Appel's salt crystal are difficult to attribute to the typical group-named bonds, although they do not differ significantly in the values of electron density at the bond critical point (BCP), ρ(rBCP), kinetic energy density, G(rBCP), potential energy density of electrons, V(rBCP). Among them, there is, for example, a rather weak interaction Cl2⋯S1(−x, ½ + y, [3\over 2]z) (0.009 a.u.) [Fig. 6[link](d)], which does not show the `Lp→σ-hole' orientation of neighboring atoms. The coincidence of ρ- and φ-minima along the Cl2⋯S1(−x, ½ + y, [3\over 2]z) line [Fig. 6[link](d)] means that such a noncovalent interaction can be attributed neither to ChB nor to HaB; it is just a weak van der Waals interaction.

For noncovalent bonds formed by the Cl anion, the stabilization due to electron exchange is approximately half than for covalent bonds; it follows from comparison of ɛx(r) maxima along bond lines (Fig. 2[link]). The low value of exchange contribution, ɛx(r), is evidence of the noncovalent character of interactions of Cl with atoms of the 1,2,3-di­thia­zolium ring. For all typical ChB and HaB bonds, the maxima of exchange energy density per electron, ɛx(r), lie in the rather narrow range of −0.20 ± 0.02 a.u. The most significant stabilization due to electron exchange and the lowest barrier of exchange interaction is observed for the pair of chalcogen bonds S1⋯Cl⋯S2. We note that ɛx(r) reveals slight differences due to chemical inequivalence of S1 and S2 atoms. At the same time, for Cl located above the plane of the heterocycle, signs of the typical tetrel bond Cl⋯C2(1 − x, −½ + y, [3\over 2]z) are observed. At least, the value of exchange energy density ɛx(r) for the Cl⋯C2(1 − x, −½ + y, [3\over 2]z) interaction is comparable with ChB and HaB bonds observed in this crystal.

The characteristics derived from the experimental electron density show that the C2NS2C12+ cation forms the relatively strong noncovalent bonds lying in the plane of the heterocycle [Fig. 7[link](a)]. Positions of bond critical points in electron density and superposition of gradient fields of electron density (ρ-basins) and electrostatic potential (φ-basins) are shown in Fig. 7[link](b). The bond characteristics show good agreement of experimental and theoretical data for both covalent and noncovalent bonds (Table S1).

In the absence of direct methods, we estimated the energy of noncovalent bonds in a crystal (EHaB, EChB) indirectly, see Table S2, relying on parametric correlation (Espinosa et al., 1998[Espinosa, E., Molins, E. & Lecomte, C. (1998). Chem. Phys. Lett. 285, 170-173.]) between quantum-topological properties at BCPs and the binding energy of molecules obtained for complexes with halogen and chalcogen bonds in cluster approximation. We also took into account that quantitative models for HaB, as well as for ChB, require specifically chosen parameters for each bond type (Bartashevich & Tsirelson, 2014[Bartashevich, E. V. & Tsirelson, V. G. (2014). Russ. Chem. Rev. 83, 1181-1203.]; Vener et al., 2013[Vener, M. V., Shishkina, A. V., Rykounov, A. A. & Tsirelson, V. G. (2013). J. Phys. Chem. A, 117, 8459-8467.]). In order to estimate the energy of bonding (EHaB, EChB), we found out the parameters previously designed for the series of ChB (Bartashevich et al., 2020[Bartashevich, E. V., Matveychuk, Y. V., Mukhitdinova, S. E., Sobalev, S. A., Khrenova, M. G. & Tsirelson, V. G. (2020). Theor. Chem. Acc. 139, 26.]) and used models obtained for charged-assisted HaBs [(A)nC—Cl⋯Cl] (Kuznetsov, 2019a[Kuznetsov, M. L. (2019a). Int. J. Quantum Chem. 119, e25869.]) and for HaBs formed by the pair of halogen atoms [(A)nY—Cl⋯Cl—Z(B)m] (Kuznetsov, 2019b[Kuznetsov, M. L. (2019b). Molecules, 24, 2733.]). Certainly, such estimation is not completely reliable and is applicable only for relative comparison of weak noncovalent bonds.

Among relatively strong interactions there are two ChB formed by the same chloride anion S1⋯Cl [0.025 a.u., −5.8 kcal mol−1 (1 kcal mol−1 = 4.184 kJ mol−1)] and S2⋯Cl (0.02 a.u., −5.0 kcal mol−1). Here and further on the values of ρ(rBCP) and bonding energy, EXB, X = Ha, Ch, averaged over different parametric models are shown in brackets. There is also the typical chalcogen bond S2⋯Cl(½ + x, ½ − y, 1 − z) (0.016 a.u., −3.2 kcal mol−1) formed on the elongation of the S1—S2 line. Among HaBs, the highest electron density at BCP has Cl⋯Cl2(−x, −½ + y, [3\over 2] − z) interaction (0.015 a.u., −3.6 kcal mol−1). Similar electronic characteristics are observed for noncovalent bond Cl⋯C2(1 − x, −½ + y, [3\over 2]z) (0.011 a.u.), which is located almost perpendicular to the plane of the heterocycle. For relatively weak interactions, we find the typical HaB bond between the atoms of neighboring cations. According to our estimations, the energy of such interactions is very low, for example, the interaction in which atom N1 serves as the acceptor of HaB: Cl1⋯N1 (0.007 a.u., −1.4 kcal mol−1). Nevertheless, this bond is stronger than Cl1⋯Cl(x, 1 + y, z) (0.005 a.u., −0.6 kcal mol−1). Thus, estimations using quantum-topological characteristics of electron density prove that two chalcogen bonds S1⋯Cl⋯S2 are formed in Appel's salt: they are close in energy, but still nonequivalent; they do not weaken each other, but remain the strongest noncovalent bonds in this structure. Besides, the most prominent in energies are for chalcogen bond S2⋯Cl and halogen bond Cl2⋯Cl(−x, ½ + y, [3\over 2]z).

4. Conclusions

We discussed the bonding properties in an Appel's salt crystal using the results from the combination of the single-crystal high-resolution X-ray diffraction method and the orbital-free quantum crystallography approach.

Considering the features of electrostatic potential on the van der Waals surface around the 4,5-di­chloro-l,2,3-di­thia­zolium cation, we faced a conceptual question: should noncovalent interactions associated with the common maximum of electrostatic potential near the center of the S—S bond be treated as chalcogen bonds? Considering such interactions in the Appel's salt crystal in terms of the density of exchange energy per electron, we arrived at an affirmative answer. Another argument in favor of this conclusion is the existence of the two chalcogen bond paths: S1⋯Cl and S2⋯Cl. It is worth noting that the position of the common maximum of electrostatic potential on ZFSs of S1 and S2 basins almost never coincides with the points where bond paths cross this ZFS. Nevertheless, the bond paths of two chalcogen bonds pass through the minima of the exchange energy density per electron. The conclusion that each sulfur atom delivers the electrophilic sites for chalcogen bonds is based on the analysis of the superposition of gradient fields of electron density (ρ-basins) and electrostatic potential (φ-basins) and on the dispositions of ρ- and φ-minima along the bond line.

The same tools allow one to categorize the interaction between Cl located above the 1,2,3-di­thia­zolyl heterocycle and the carbon atom C2 as a tetrel bond. The comparison of QTAIM-based descriptors of bonding energy confirms that each of the chalcogen bonds, S1⋯Cl and S2⋯Cl, with a common electron donor, is stronger than the typical chalcogen bond S2⋯Cl on the elongation of the di­sulfide group. Such specificity of interactions provides a very low S—S bond order equal to only 0.912 according to the topological bond orders model. The remaining halogen bonds in the crystal are weaker than observed chalcogen bonds.

Supporting information


Computing details top

Cell refinement: SAINT V8.38A (Bruker AXS Inc., 2013) for (I). Data reduction: SAINT V8.38A (Bruker AXS Inc., 2013) for (I). Program(s) used to solve structure: SHELXT-2018/3 (Sheldrick, 2018) for (I). Program(s) used to refine structure: SHELXL2013/8 (Sheldrick, 2018) for (I); Volkov et al., (2006) for Appel_mult. Molecular graphics: Bruker SHELXTL (Bruker AXS Inc., 2013) for (I); Volkov et al., (2006) for Appel_mult. Software used to prepare material for publication: Volkov et al., (2006) for Appel_mult.

(I) top
Crystal data top
C2Cl2NS2·ClDx = 2.088 Mg m3
Mr = 208.50Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, P212121Cell parameters from 9877 reflections
a = 5.90947 (10) Åθ = 2.7–39.7°
b = 10.22455 (16) ŵ = 1.89 mm1
c = 10.97838 (18) ÅT = 100 K
V = 663.33 (2) Å3Block-like, dark brown
Z = 40.58 × 0.12 × 0.11 mm
F(000) = 408
Data collection top
Bruker Quest D8
diffractometer with Photon III detector
12387 reflections with I > 2σ(I)
ω–scanRint = 0.024
Absorption correction: multi-scan
SADABS-2016/2 - Bruker AXS area detector scaling and absorption correction
θmax = 71.6°, θmin = 2.7°
Tmin = 0.566, Tmax = 0.724h = 1415
102642 measured reflectionsk = 2627
12761 independent reflectionsl = 2929
Refinement top
Refinement on F20 restraints
Least-squares matrix: full w = 1/[σ2(Fo2) + (0.0193P)2 + 0.0166P]
where P = (Fo2 + 2Fc2)/3
R[F2 > 2σ(F2)] = 0.014(Δ/σ)max = 0.003
wR(F2) = 0.040Δρmax = 0.49 e Å3
S = 1.07Δρmin = 0.55 e Å3
12761 reflectionsAbsolute structure: Flack x determined using 5383 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons, Flack and Wagner, Acta Cryst. B69 (2013) 249-259).
73 parametersAbsolute structure parameter: 0.273 (7)
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Cl10.28475 (3)0.74344 (2)0.60078 (2)0.01886 (2)
Cl20.03886 (2)0.53741 (2)0.75136 (2)0.01531 (1)
Cl30.48426 (2)0.08785 (2)0.59885 (2)0.01301 (1)
S10.27725 (2)0.33636 (2)0.67299 (2)0.01203 (1)
S20.54906 (2)0.37393 (2)0.56445 (2)0.01248 (1)
N10.51415 (6)0.53003 (3)0.55287 (3)0.01376 (3)
C10.33891 (6)0.57994 (3)0.60914 (3)0.01276 (4)
C20.19775 (6)0.49364 (3)0.67624 (3)0.01212 (3)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Cl10.02390 (4)0.01003 (2)0.02265 (4)0.00335 (2)0.00101 (4)0.00118 (2)
Cl20.01380 (3)0.01544 (3)0.01668 (3)0.00184 (2)0.00185 (2)0.00338 (2)
Cl30.01313 (2)0.01159 (2)0.01431 (2)0.00126 (2)0.00119 (2)0.00060 (2)
S10.01314 (3)0.00975 (2)0.01320 (2)0.00035 (2)0.00160 (2)0.00013 (2)
S20.01325 (3)0.00998 (2)0.01422 (3)0.00051 (2)0.00215 (2)0.00003 (2)
N10.01559 (9)0.01034 (6)0.01534 (8)0.00005 (6)0.00207 (7)0.00064 (6)
C10.01502 (9)0.00973 (7)0.01352 (9)0.00078 (6)0.00014 (7)0.00002 (6)
C20.01295 (8)0.01117 (7)0.01224 (8)0.00074 (6)0.00017 (7)0.00139 (6)
Geometric parameters (Å, º) top
Cl1—C11.7045 (3)S2—N11.6143 (3)
Cl2—C21.6838 (4)N1—C11.3094 (5)
S1—C21.6757 (3)C1—C21.4203 (5)
S1—S22.0366 (1)
C2—S1—S293.014 (13)C2—C1—Cl1121.80 (3)
N1—S2—S197.570 (13)C1—C2—S1114.87 (3)
C1—N1—S2116.70 (3)C1—C2—Cl2125.21 (3)
N1—C1—C2117.84 (3)S1—C2—Cl2119.89 (2)
N1—C1—Cl1120.36 (3)
(Appel_mult) top
Crystal data top
a = Åα = °
b = Åβ = °
c = Åγ = °
Data collection top
h = l =
k =
Refinement top
Refinement on F29426 reflections
Least-squares matrix: full414 parameters
R[F2 > 2σ(F2)] = 0.0090 restraints
wR(F2) = 0.011 w2 = q/[s2(Fo2) + (0.01 P)2 + 0.00 P + 0.00 + 0.00 sin(th)]
where P = (0.3333 Fo2 + 0.6667 Fc2) q = 1.0
S = 1.40(Δ/σ)max < 0.001
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Cl(1)0.28457 (7)0.74324 (2)0.60055 (4)0.019
Cl(2)0.03844 (5)0.53756 (3)0.75118 (2)0.016
Cl(3)0.48423 (4)0.08786 (2)0.59881 (2)0.013
S(1)0.27720 (4)0.33636 (2)0.67291 (2)0.012
S(2)0.54893 (4)0.37393 (2)0.56454 (2)0.013
N(1)0.51412 (3)0.529971 (16)0.552909 (18)0.014
C(1)0.33882 (4)0.580022 (17)0.609172 (19)0.013
C(2)0.19767 (3)0.493656 (18)0.676274 (18)0.012
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Cl(1)0.02510 (11)0.01005 (6)0.02313 (10)0.00356 (6)0.00106 (9)0.00108 (6)
Cl(2)0.01443 (7)0.01575 (7)0.01701 (7)0.00192 (5)0.00180 (6)0.00347 (6)
Cl(3)0.01360 (6)0.01152 (5)0.01460 (6)0.00132 (4)0.00135 (5)0.00060 (5)
S(1)0.01368 (7)0.00971 (5)0.01347 (6)0.00036 (5)0.00160 (5)0.00017 (5)
S(2)0.01384 (7)0.00994 (5)0.01443 (6)0.00054 (5)0.00221 (5)0.00009 (5)
N(1)0.01572 (5)0.01029 (4)0.01568 (5)0.00001 (3)0.00242 (4)0.00073 (3)
C(1)0.01503 (5)0.00968 (4)0.01378 (5)0.00083 (3)0.00000 (4)0.00006 (4)
C(2)0.01309 (5)0.01107 (4)0.01247 (4)0.00079 (3)0.00035 (4)0.00131 (3)
 

Acknowledgements

The authors declare no competing financial interests.

Funding information

The following funding is acknowledged: This research was funded by the Ministry of Science and Higher Education of the Russian Federation (project No. FENU-2020-0019).

References

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