View PDF Version
 
DOI: 10.1039/D5CC03041B (Communication) Chem. Commun., 2025, Advance Article

A planar pentacoordinate sulfur atom†

Palash J. Thakuria, Kangkan Sarmah, Siddharth K. Purkayastha, Amit Das and Ankur K. Guha*
Advanced Computational Chemistry Centre, Cotton University, Panbazar, Guwahati, Assam 781001, India. E-mail: ankurkantiguha@gmail.com

Received 30th May 2025 , Accepted 2nd July 2025

First published on 2nd July 2025

Abstract

Planar pentacoordinate sulfur atoms (ppS) are rare, with only one example experimentally verified to date. Herein, we report a planar pentacoordinate sulfur atom (ppS) as the global minimum [Mg5S6]2− cluster. Despite dianionic nature, it is stable towards spontaneous electron detachment making it a suitable candidate for experimental detection. The global minimum of this cluster features perfect D5h symmetry. Detailed electronic structure calculations reveal the presence of significant covalency in the Mg–S bonds.

Planar hypercoordinate atoms (phA) have fascinated chemists for decades.1–5 In this regard, planar tetracoordinate carbon (ptC) serves as an enchanting example which challenged the tetrahedral paradigm of carbon chemistry. Many ptCs6–21 were predicted to be global energy minima (GEMs) and some of them were experimentally synthesized or detected.9–16 Planar hypercoordination has also been extended to other main group elements and even to transition metals. Except for Ne, all main group elements in the second period,22–27 as well as some elements from subsequent periods, have been predicted to form phA structures.28–38

Extending the coordination of the carbon atom in a plane from four to five4 and six has also been predicted.22,23 Planar pentacoordinate atoms (ppA) other than carbon have also been predicted to be GEMs.25,35–39 This included planar pentacoordinate nitrogen (ppN),25 planar pentacoordinate hydrogen (ppH),35 planar pentacoordinate beryllium (ppBe),36 planar pentacoordinate s-block metals (ppM)37 and planar pentacoordinate halogens (ppX).38 Very recently, planar pentacoordinate oxygen (ppO)39 has been predicted to be the GEM in an experimentally observed [Be5O6]2− cluster.40

Interestingly, the [Be5O6]2− cluster is the first example of ppO in an experimentally detected and computationally predicted cluster, although a high energy linear isomer was computationally predicted earlier.41 Recently, Merino et al. have predicted 35 global minimum geometries containing planar tetracoordinate oxygen atoms (ptO) stabilized by group 13 elements.42 Despite sulfur being in the same group of the periodic table, planar tetra or pentacoordination of sulfur is very rare. Herein, we propose a planar pentacoordinate sulfur atom (ppS) as the GEM of the [Mg5S6]2− cluster. To the best of our knowledge, only one experimental report (by Müller and Henkel) of ppS in the complex [Ni5S(StBu)5]− is there in the literature,43 although some examples of computationally designed ppS in the hydrometal complexes, Ag5H5S2+ and Au5H5S2+ are there in the literature.44 But it is unclear whether they are GEMs or not3 and hence, their experimental detection is still a matter of question.

The potential energy surface of the [Mg5S6]2− cluster was explored using the TPSS-D3(BJ)/def2-SVP level45–48 in combination with the ABCluster code.49,50 Low energy isomers were then re-optimized at the TPSS-D3(BJ)/aug-cc-pVTZ level. Harmonic frequency calculations reveal that all the structures are local minima. Low energy isomers were then energetically refined using single point calculations at the CCSD(T)/aug-cc-pVTZ51 level on top of TPSS-D3(BJ) optimized geometries. All these calculations were performed using the Gaussian 16 suite of programs.52 Electronic structure was analyzed using the adaptive natural density partitioning (AdNDP)53 scheme implemented in the Multiwfn program code.54

Fig. 1 shows the optimized GEM geometry of the [Mg5S6]2− cluster, which adopts D5h symmetry in the singlet ground state. Low lying isomers are shown in Fig. S1 (ESI†). All the structures have shown reliable T1 diagnostic values (<0.02)55 suggesting negligible multi-reference character. The closest isomer lies 10.1 kcal mol−1 higher in energy at the CCSD(T)/aug-cc-pVTZ//TPSS-D3(BJ)/aug-cc-pVTZ level. The lowest energy triplet state lies 58.3 kcal mol−1 higher in energy. The Mg–Scentral (Scentral means the central S atom) bond length is 2.60 Å with Mayer bond order of 0.28, while the terminal Mg–S distance is 2.33 Å with Mayer bond order of 0.67. The calculated Mayer bond order of 0.28 for the Mg–Scentral bond indicates significant covalency. The Mg–Mg distance is 3.06 Å with Mayer bond order of 0.14. The calculated Hirshfeld charge at the central S atom is −0.35 e, while Mg carries positive charge of 0.28 e. This indicates that significant electrostatic interaction is also present in the GEM of the [Mg5S6]2− cluster.


image file: d5cc03041b-f1.tif
Fig. 1 TPSS-D3(BJ)/aug-cc-pVTZ optimized global minimum geometry of the [Mg5S6]2− cluster. Bond lengths are in Å and Hirshfeld charges (in red font) are in electrons.

The electronic stability of the dianion was assessed through the calculation of its vertical detachment energy (VDE) using the outer valence Green's function (OVGF) method at the OVGF/aug-cc-pVTZ level.56 The calculated first VDE is found to be positive (2.48 eV with a pole strength of 0.87) indicating that the dianion is stable towards spontaneous electron detachment. Similar positive VDE was also computed for the ppO [Be5O6]2− cluster,39 an experimentally detected dianion.40 Furthermore, the electronic structure was analyzed using the adaptive natural density partitioning scheme (AdNDP) at the TPSS-D3(BJ)/def2-TZVP level. This analysis provides a description of the electron distribution in nc-ne bonds and is a very important tool to analyse the electronic structure having unusual chemical bonds. As shown in Fig. 2, AdNDP recovers five 1c-2e S lone pairs, ten 2c-2e Mg–S σ bonds and five 3c-2e S–Mg–S π bonds (set A). All these orbitals have significant occupation numbers (1.95–1.98 |e|). In set B, one 1c-2e lone pair orbital at the central S atom was recovered with an occupation number of 1.90 |e|. In set C, three 1c-2e lone pairs at the central sulfur atom were recovered. However, their occupation numbers are significantly less (1.76–1.83 |e|). Note that the difference of 0.23–0.16 |e| between the occupancies of the lone pairs and 6c-2e bonds is not negligible. The lower occupation numbers in set C indicate that it may not be an adequate description of the electronic structure. An alternative scheme is also shown (set D) where three 6c-2e σ bonds are recovered with significant occupation number (1.99 |e|). Therefore, the alternative scheme (set D) is more appropriate description of the electronic structure. This is also in tune with the computed Mayer bond order of 0.28 for the Mg–Scentral bond, which indicated covalency. Moreover, the delocalization index – an atoms in molecules (AIM)57 – based indicator of covalency computed for the Mg–Scentral bond is significant (0.49), further supporting significant covalency.


image file: d5cc03041b-f2.tif
Fig. 2 Bonds recovered using the AdNDP scheme. Occupation numbers are in |e|.

To investigate the nature of interaction, the GEM structure has been further analysed using natural orbital for chemical valence extended to transition state (ETS-NOCV)58 using Multiwfn program code at the TPSS-D3(BJ)/def2-TZVP level. For this, the S2− dianion and neutral Mg5S5 fragments have been considered as interacting fragments. Fig. 3 shows the deformation densities corresponding to ΔEorb(n) along with the eigen values |νn| of charge transfer (from yellow to green). Significant orbital interactions have been observed where charge transfer taking place from the central S atom to Mg atoms has been observed (Fig. 3), suggesting covalency in the Mg–S bonds.


image file: d5cc03041b-f3.tif
Fig. 3 Deformation densities and orbital interaction energies (kcal mol−1) along with eigen values |ν| of charge transfer. Charge transfer is from yellow to green.

In summary, the present quantum chemical establishes a planar pentacoordinate sulfur atom as the global minimum of the [Mg5S6]2− cluster. Despite being dianionic in nature, it is stable towards spontaneous electron detachment as revealed by its positive vertical detachment energy. Detailed electronic structure study reveals significant covalency in the Mg–S bonds. The presence of three 6c-2e σ bonds renders stability to the global minimum. We feel that owing to the binary nature of the cluster, its experimental detection is quite likely.

Conflicts of interest

The authors declare no conflict of interest.

Data availability

All data are provided in the ESI.†

Notes and references

  1. R. Keese, Chem. Rev., 2006, 106, 4787–4808 CrossRef CAS PubMed .
  2. R. Hoffmann, R. W. Alder and C. F. Wilcox, J. Am. Chem. Soc., 1970, 92, 4992–4993 CrossRef CAS .
  3. L. Yang, E. Ganz, Z. Chen, Z. Wang and P. V. R. Schleyer, Angew. Chem., Int. Ed., 2015, 54, 9468–9501 CrossRef CAS PubMed .
  4. R. V. Vassilev-Galindo, S. Pan, K. J. Donald and G. Merino, Nat. Rev. Chem., 2018, 2, 0114 CrossRef .
  5. Y. Wang, Y. Li and Z. Chen, Acc. Chem. Res., 2020, 53, 887–895 CrossRef CAS PubMed .
  6. J. B. Collins, D. Dill, E. D. Jemmis, Y. Apeloig, P. V. R. Schleyer, R. Seeger and J. A. Pople, J. Am. Chem. Soc., 1976, 98, 5419–5427 CrossRef CAS .
  7. Z. Cui, M. Contreras, Y. Ding and G. Merino, J. Am. Chem. Soc., 2011, 133, 13228–13231 CrossRef CAS PubMed .
  8. P. V. R. Schleyer and A. I. Boldyrev, J. Chem. Soc., Chem. Commun., 1991, 21, 1536–1538 RSC .
  9. F. A. Cotton and M. Millar, J. Am. Chem. Soc., 1977, 99, 7886–7891 CrossRef CAS .
  10. M. Albrecht, G. Erker and C. Krüger, Synlett, 1993, 441–448 CrossRef CAS .
  11. D. Röttger and G. Erker, Angew. Chem., Int. Ed. Engl., 1997, 36, 812–827 CrossRef .
  12. S. K. Nayak, B. K. Rao, P. Jena, X. Li and L.-S. Wang, Chem. Phys. Lett., 1999, 301, 379–384 CrossRef CAS .
  13. X. Li, L.-S. Wang, A. I. Boldyrev and J. Simons, J. Am. Chem. Soc., 1999, 121, 6033–6038 CrossRef CAS .
  14. L.-S. Wang, A. I. Boldyrev, X. Li and J. Simons, J. Am. Chem. Soc., 2000, 122, 7681–7687 CrossRef CAS .
  15. X. Li, H.-F. Zhang, L.-S. Wang, G. D. Geske and A. I. Boldyrev, Angew. Chem., Int. Ed., 2000, 112, 3776–3778 CrossRef .
  16. X. Li, H.-J. Zhai and L.-S. Wang, Chem. Phys. Lett., 2002, 357(5–6), 415–419 CrossRef CAS .
  17. A. I. Boldyrev and J. Simons, J. Am. Chem. Soc., 1998, 120, 7967–7972 CrossRef CAS .
  18. J. O. C. Jimenez-Halla, Y.-B. Wu, Z.-X. Wang, R. Islas, T. Heine and G. Merino, Chem. Commun., 2009, 8776 Search PubMed .
  19. A. C. Castro, M. Audiffred, J. M. Mercero, J. M. Ugalde, M. A. Méndez-Rojas and G. Merino, Chem. Phys. Lett., 2012, 519–520, 29–33 CrossRef CAS .
  20. R. Grande-Aztatzi, J. L. Cabellos, R. Islas, I. Infante, J. M. Mercero, A. Restrepo and G. Merino, Phys. Chem. Chem. Phys., 2015, 17, 4620–4624 RSC .
  21. Z. Cui, Y. Ding, J. L. Cabellos, E. Osorio, R. Islas, A. Restrepo and G. Merino, Phys. Chem. Chem. Phys., 2015, 17, 8769–8775 RSC .
  22. K. Exner and P. V. R. Schleyer, Science, 2000, 290, 1937–1940 CrossRef CAS PubMed .
  23. L. L. Parra, L. Diego, O. Yaňez, D. Inostroza, J. Barroso, A. V. Espinal, G. Merino and W. Tiznado, Angew. Chem., Int. Ed., 2021, 60, 8700–8704 CrossRef PubMed .
  24. A. J. Kalita, S. S. Rohman, C. Kashyap, S. S. Ullah, I. Baruah and A. K. Guha, Chem. Commun., 2020, 56, 12597–12599 RSC .
  25. A. J. Kalita, S. S. Rohman, C. Kashyap, S. S. Ullah, I. Baruah and A. K. Guha, Inorg. Chem., 2020, 59, 17880–17883 CrossRef CAS PubMed .
  26. K. Sarmah, A. J. Kalita and A. K. Guha, Phys. Chem. Chem. Phys., 2024, 26, 6678–6682 RSC .
  27. G. Castillo-Toraya, M. Orozco-Ic, E. Dzib, X. Zarate, F. Ortíz-Chi, Z. Cui, J. Barroso and G. Merino, Chem. Sci., 2021, 12, 6699–6704 RSC .
  28. X. Liu, W. Tiznado, L.-J. Cui, J. Barroso, L. L. Parra, L. Miao, H. Zhang, S. Pan, G. Merino and Z.-H. Cui, J. Am. Chem. Soc., 2024, 146, 16689–16697 CrossRef CAS PubMed .
  29. X. B. Liu, W. Tiznado, L.-J. Cui, J. Barroso, L. L. Parra, L.-H. Miao, H.-Y. Zhang, S. Pan, G. Merino and Z.-H. Cui, J. Am. Chem. Soc., 2024, 146, 16689–16697 CrossRef CAS PubMed .
  30. M. Wang, C. Chen, S. Pan and Z. Cui, Chem. Sci., 2021, 12, 15067–15076 RSC .
  31. C. Chen, M. Wang, L.-Y. Feng, L.-Q. Zhao, J.-C. Guo, H.-J. Zhai, Z. Cui, S. Pan and G. Merino, Chem. Sci., 2022, 13, 8045–8051 RSC .
  32. B. Jin, X. Guan, M. Yan, Y. Wang and Y. Wu, Chem. – Eur. J., 2023, 29, e202302672 CrossRef CAS PubMed .
  33. G. Yan, Y. Liu, X. Liu, M. Wang, Z. Cui and S. Pan, J. Chem. Phys., 2023, 159, 054301 CrossRef CAS PubMed .
  34. A. J. Kalita, S. S. Rohman, P. P. Sahu and A. K. Guha, Angew. Chem., Int. Ed., 2024, 63, e202317312 CrossRef CAS PubMed .
  35. K. Sarmah, A. J. Kalita, S. Purkayastha and A. K. Guha, Angew. Chem., Int. Ed., 2024, 63, e202318741 CrossRef CAS PubMed .
  36. C. Chen, Y.-Q. Liu and Z.-H. Cui, Inorg. Chem., 2021, 60, 16053–16058 CrossRef CAS PubMed .
  37. M.-H. Wang, A. J. Kalita, M. Orozco-Ic, G.-R. Yan, C. Chen, B. Yan, G. Castillo-Toraya, W. Tiznado, A. K. Guha, S. Pan, G. Merino and Z.-H. Cui, Chem. Sci., 2023, 14, 8785–8791 RSC .
  38. L.-J. Cui, L.-H. Miao, M. Orozco-Ic, L. Li, S. Pan, G. Merino and Z.-H. Cui, Angew. Chem., Int. Ed., 2025, 137, e202416057 CrossRef .
  39. R. Sun, Y. Yang, X. Wu, H. J. Zhai, C. Yuan and Y. B. Wu, Chem. Sci., 2025 10.1039/D5SC02361K .
  40. K. Franzreb and P. Williams, Chem. Phys. Lett., 2006, 419, 379–384 CrossRef CAS .
  41. A. Dreuw, Chem. Phys. Lett., 2006, 419, 385–389 CrossRef CAS .
  42. G. C. Toraya, F. O. Chi, J. Barroso, M. Orozco-Ic, L. L. Parra and G. Merino, Angew. Chem., Int. Ed., 2025, 64, e202500292 CrossRef PubMed .
  43. A. Müller and G. Henkel, Chem. Commun., 1996, 1005–1006 RSC .
  44. S. D. Li and C. Q. Miao, J. Phys. Chem. A, 2005, 109, 7594–7597 CrossRef CAS PubMed .
  45. J. Tao, J. P. Perdew, V. N. Staroverov and G. E. Scuseria, Phys. Rev. Lett., 2003, 91, 146401 CrossRef PubMed .
  46. F. Weigend and R. Ahlrichs, Phys. Chem. Chem. Phys., 2005, 7, 3297–3305 RSC .
  47. S. Grimme, S. Ehrlich and L. Goerigk, J. Comput. Chem., 2011, 32, 1456–1465 CrossRef CAS PubMed .
  48. A. D. Becke and E. R. Johnson, J. Chem. Phys., 2005, 123, 154101 CrossRef PubMed .
  49. J. Zhang and M. Dolg, Phys. Chem. Chem. Phys., 2015, 17, 24173–24181 RSC .
  50. J. Zhang and M. Dolg, Phys. Chem. Chem. Phys., 2015, 17, 24173–24181 RSC .
  51. K. Raghavachari, G. W. Trucks, J. A. Pople and M. Head-Gordon, Chem. Phys. Lett., 1989, 157, 479–483 CrossRef CAS .
  52. M. J. Frisch, et al., Gaussian 16, Revision B.01, Gaussian, Inc., Wallingford CT, 2016 Search PubMed . See ESI† for complete citation.
  53. D. Y. Zubarev and A. I. Boldyrev, Phys. Chem. Chem. Phys., 2008, 10, 5207–5217 RSC .
  54. T. Lu and F. Chen, J. Comput. Chem., 2012, 33, 580 CrossRef CAS .
  55. T. J. Lee and P. R. Taylor, Int. J. Quantum Chem., 2009, 36, 199–207 CrossRef .
  56. J. V. Ortiz, V. G. Zakrzewski and O. Dolgounircheva, Conceptual Perspectives in Quantum Chemistry, Kluwer Academic, 1997 Search PubMed .
  57. R. W. F. Bader, Atoms in Molecules: A Quantum Theory, Oxford Univ. Press, Oxford, 1990 Search PubMed .
  58. M. P. Miroraj, A. Michalak and T. Ziegler, J. Chem. Theory Comput., 2009, 5, 962–976 CrossRef PubMed .

Footnote

† Electronic supplementary information (ESI) available: It contains complete citation of ref. 51, Fig. S1 and Cartesian coordinates of the optimized geometries. See DOI: https://doi.org/10.1039/d5cc03041b
This journal is © The Royal Society of Chemistry 2025
Click here to see how this site uses Cookies. View our privacy policy here.