Skip to main content
SpringerLink
Log in

Beyond the Wade-Mingos Rules: Deviations from Sphericality in Metallaborane Structures

  • Chapter
  • First Online:
50th Anniversary of Electron Counting Paradigms for Polyhedral Molecules

Part of the book series: Structure and Bonding ((STRUCTURE,volume 187))

Abstract

Deviation from the most spherical closo deltahedral geometry can occur in metallaboranes and metallacarbaboranes because of the energetic preference of transition metal moieties for higher degree vertices than boron and/or carbon. The isocloso structures with a metal at a degree 6 vertex and two fewer skeletal electrons than the corresponding closo structures represent a minor deviation from such sphericity and are particularly favorable for 10-vertex systems. Spherical supraicosahedral deltahedra with 14 to 16 vertices, also known as Frank-Kasper deltahedra, necessarily have several degree 6 vertices and accordingly can have isocloso skeletal electron counts. More substantial deviations from sphericality occurs in the oblate ellipsoidal structures of the dirhenaboranes Cp2Re2Bn–2Hn–2 (8 ≤ n ≤ 12) with the rhenium atoms antipodally situated at degree 6 or 7 vertices of relatively low local curvature and the boron atoms situation at degree 4 and 5 vertices of relatively high local curvature. Species isoelectronic with the Cp2Re2Bn–2Hn–2 derivatives can also have closo or isocloso structures with surface metal–metal multiple bonds. The experimentally known icosahedral Cp2Cr2C2B8H10 was believed to be such a species with a surface Cr≣Cr quadruple bond. However, theoretical prediction of chromium–chromium distances suggest that a Cp2Cr2(μ-H)2C2B8H10 structure with a surface Cr≡Cr triple bond bridged by two “extra” hydrogen atoms is more likely. The tri- and tetrametallaboranes Cp*3W3(H)B8H8 and Cp*4Mo4B7H7 of the groups 6 metals molybdenum and tungsten provide examples of non-spherical 11-vertex deltahedra with metal atoms located at degree 6 and 7 vertices and boron atoms located at degree 4 and 5 vertices. The topology of the lowest energy Cp*4Mo4Bn–4Hn–4 (n = 10, 11, 12) deltahedra can be generated by capping n – 8 vertices of a central Mo4B4 cube and then drawing diagonals across the remaining uncapped faces.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Allard G (1932) X-ray study of some borides. Bull Soc Chim Fr 51:1213–1215

    CAS  Google Scholar 

  2. Pauling L, Weinbaum S (1943) The structure of calcium boride CaB6. Z Kristallog 7:181–182

    Google Scholar 

  3. Longuet-Higgins HC, de Roberts MV (1954) The electronic structure of the borides MB6. Proc Roy Soc (London) 224A:336–347

    Google Scholar 

  4. Longuet-Higgins HC, de Roberts MV (1955) The electronic structure of an icosahedron of boron atoms. Proc Roy Soc (London) 230A:110–119

    Google Scholar 

  5. Hawthorne MF, Pitochelli AR (1960) The isolation of the icosahedral B12H122− ion. J Am Chem Soc 82:3328–3329

    Google Scholar 

  6. Hawthorne MF, Pitochelli AR (1959) The reaction of bis acetonitrile decaborane with amines. J Am Chem Soc 81:5519–5519

    Article  CAS  Google Scholar 

  7. Boone JL (1964) Isolation of hexahydroclovohexaborate(2–) anion B6H62−. J Am Chem Soc 86:5036–5036

    Article  CAS  Google Scholar 

  8. Klanberg F, Muetterties EL (1966) New polyhedral borane anions B9H92− and B11H12−. Inorg Chem 5:1955–1960

    Article  CAS  Google Scholar 

  9. Klanberg F, Eaton DR, Guggenberger LJ, Muetterties EL (1967) New polyhedral borane anions B8H82−, B8H8−, and B7H72−. Inorg Chem 6:1271–1281

    Article  CAS  Google Scholar 

  10. Grimes RN (2011) Carboranes. Elsevier, Amsterdam

    Google Scholar 

  11. Williams RE (1971) Carboranes and boranes – polyhedral fragments. Inorg Chem 10:210–214

    Article  CAS  Google Scholar 

  12. Williams RE (1992) The polyborane, carborane, carbocation continuum – architectural patterns. Chem Rev 92:177–207

    Article  CAS  Google Scholar 

  13. King RB, Duijvestijn AJW (1990) The topological uniqueness of the deltahedra found in the boranes BnHn 2− ( 6 ≤ n ≤ 12). Inorg Chim Acta 178:55–57

    Article  CAS  Google Scholar 

  14. Frank FC, Kasper JS (1958) Complex alloy structures regarded as sphere packings. 1. Definitions and basic principles. Acta Crystallogr 11:184–190

    Article  CAS  Google Scholar 

  15. Wade K (1971) The structural significance of the number of skeletal bonding electron-pairs in carboranes, the higher boranes and borane anions, and various transition-metal carbonyl cluster compounds. J Chem Soc D Chem Commun:792

    Google Scholar 

  16. Rudolph RW, Pretzer WR (1972) Hückel-type rules and systematization of borane and heteroborane chemistry. Inorg Chem 11:1974–1978

    Article  CAS  Google Scholar 

  17. Rudolph RW (1976) Boranes and heteroboranes – paradigm for electron requirements of clusters. Acc Chem Res 9:446–452

    Article  CAS  Google Scholar 

  18. Mingos DMP (1972) A general theory for cluster and ring compounds of the main group and transition elements. Nat Phys Sci 236:99

    Article  CAS  Google Scholar 

  19. Mingos DMP (1984) Polyhedral skeletal electron pair approach. Acc Chem Res 17:311–319

    Article  CAS  Google Scholar 

  20. King RB, Rouvray DH (1977) A graph-theoretical interpretation of the bonding topology in polyhedral boranes, carboranes, and metal clusters. J Am Chem Soc 99:7834–7840

    Article  CAS  Google Scholar 

  21. Stone AJ, Alderton MJ (1982) A new model of structure and bonding in the boron hydrides. Inorg Chem 21:2297–2302

    Article  CAS  Google Scholar 

  22. Johnston RL, Mingos DMP (1986) The pairing theorem in tensor surface harmonic theory: definition of a general class of N atom polar deltahedra with N skeletal electron pairs. Polyhedron 5:2059–2061

    Article  CAS  Google Scholar 

  23. Johnston RL, Mingos DMP (1989) The classification of tensor surface harmonic functions for clusters and coordination compounds. Theor Chim Acta 75:11–32

    Article  CAS  Google Scholar 

  24. Aihara J-I (1978) 3-Dimensional aromaticity of polyhedral boranes. J Am Chem Soc 100:3339–3342

    Article  CAS  Google Scholar 

  25. King RB (2001) Three-dimensional aromaticity in polyhedral boranes and related molecules. Chem Rev 101:1119–1152

    Article  CAS  PubMed  Google Scholar 

  26. Callahan KP, Hawthorne MF (1976) Ten years of metallocarboranes. Adv Organometal Chem 14:145

    Article  CAS  Google Scholar 

  27. Grimes RN (1983) The role of metals in borane clusters. Acc Chem Res 16:22–26

    Article  CAS  Google Scholar 

  28. Rasmussen SC (2015) The 18-electron rule and electron counting in transition metal compounds: theory and application. Chem Texts 1. Article 10

    Google Scholar 

  29. Tolman CA (1972) The 16 and 18 electron rule in organometallic chemistry and homogenous catalysis. Chem Soc Rev 1:337–353

    Article  CAS  Google Scholar 

  30. Craig DP, Doggett G (1963) Theoretical basis of the “rare-gas rule”. J Chem Soc:4189–4198

    Google Scholar 

  31. Elian M, Hoffmann R (1975) Bonding capabilities of transition metal carbonyl fragments. Inorg Chem 14:1058–1076

    Article  CAS  Google Scholar 

  32. Elian M, Chen MML, Mingos DMP, Hoffmann R (1976) Comparative bonding study of conical fragments. Inorg Chem 15:1148–1155

    Article  CAS  Google Scholar 

  33. Barker GK, Godfrey MR, Green M, Parge HE, Stone FGA, Welch AJ (1983) Synthesis and molecular structures of nido-[9-(η-C5H5)-7,8,9-C2NiB8H11], nido-[9-(η-C5H5-μ10,11-(Ph3PAu)-7.8.9-C2NiB8H10], and closo-[1,3-(η-C5H5)2-1,2,3,4-CrCCrCB8H10]: evidence for a multiple metal-metal bond in a dimetallacarbaborane. Chem Commun 277–279

    Google Scholar 

  34. Jákó S, Lupan A, Kun A-Z, King RB (2019) Spherical closo deltahedra with surface metal-metal multiple bonding versus oblate deltahedra with internal metal-metal bonding in dichromadicarbaborane structures: the nature of Stone’s icosahedral dichromadicarbaborane. Inorg Chem 58:3825–3837

    Article  PubMed  Google Scholar 

  35. Callahan KP, Evans WJ, Lo FY, Strouse CE, Hawthorne MF (1975) Structures of metallocarboranes. V. Synthesis and crystal and molecular structure of the closo 20-electron bimetallocarborane 1,6-bis(η-cyclopentadienyl)-1,6-diferra-2,3-dicarba-closo-decaborane(8), 1,6-(η-C5H5)2-1,6,2,3-Fe2C2B6H8. J Am Chem Soc 97:296–302

    Article  CAS  Google Scholar 

  36. Hoel EL, Strouse CE, Hawthorne MF (1974) Crystal and molecular structure of 2,6-di-η-cyclopentadienyloctahydro-1,10-dicobalta-closo-decaborane at −150°, a bimetallocarborane with a metal-metal bond. Inorg Chem 13:1388–1392

    Article  CAS  Google Scholar 

  37. Bould J, Kennedy JD, Thornton-Pett M (1992) Ten-vertex metallaborane chemistry. Aspects of the iridadecaborane closo→isonido→isocloso structural continuum. J Chem Soc Dalton:563–576

    Google Scholar 

  38. Kennedy JD, Štibr B (1994) Kabalka GW (ed) Current topics in the chemistry of boron. Royal Society of Chemistry, Cambridge, pp 285–292

    Google Scholar 

  39. Kennedy JD (1998., ch. 3) Casanova J (ed) The borane-carborane-carbocation continuum. Wiley, New York, pp 85–116

    Google Scholar 

  40. Štibr B, Kennedy JD, Drdáková E, Thornton-Pett M (1994) Nine-vertex polyhedral iridamonocarbaborane chemistry. Products of thermolysis of [(CO)(PPh3)2IrCB7H8] and emerging alternative cluster-geometry patterns. J Chem Soc Dalton:229–236

    Google Scholar 

  41. Kennedy JD (1986) Structure and bonding in recently isolated metallaboranes. Inorg Chem 25:111–112

    Article  CAS  Google Scholar 

  42. Baker RT (1986) Hyper-closo metallaboranes. Inorg Chem 25:109–111

    Article  CAS  Google Scholar 

  43. Johnston RL, DMP M (1986) Molecular orbital calculations relevant to the hypercloso vs iso-closo controversy in metalloboranes. Inorg Chem 25:3321–3323

    Article  CAS  Google Scholar 

  44. Johnston RL, Mingos DMP, Sherwood P (1991) Bonding and electron counting in hyper closo metalloboranes and metallocarboranes. New J Chem 15:831–841

    CAS  Google Scholar 

  45. Lipscomb WN (1966) Framework rearrangements in boranes and carboranes. Science 153:373–378

    Article  CAS  PubMed  Google Scholar 

  46. King RB (1981) Degenerate edges as a source of inherent fluxionality in deltahedra. Inorg Chim Acta 49:237–240

    Article  CAS  Google Scholar 

  47. Lupan A, King RB (2011) Limited occurrence of isocloso deltahedra with 9 to 12 vertices in low-energy hypoelectronic diferradicarbaborane structures. Inorg Chem 50:9571–9577

    Article  CAS  PubMed  Google Scholar 

  48. Dunn S, Rosair GM, Thomas RL, Weller AS, Welch AJ (1997) Isolation of a nonicosahedral intermediate in the isomerization of an icosahedral metallacarborane. Angew Chem Int Ed 36:645–647

    Article  CAS  Google Scholar 

  49. Roy SK, Mondal B, Shankhari P, Anju RS, Geetharani K, Mobin SM, Ghosh S (2013) Supraicosahedral polyhedra in metallaboranes: synthesis and structural characterization of 12-, 15-, and 16-vertex rhodaboranes. Inorg Chem 52:6705–6712

    Article  CAS  PubMed  Google Scholar 

  50. King RB (1999) Topological aspects of the skeletal bonding in “isocloso” metallaboranes containing “anomalous” numbers of skeletal electrons. Inorg Chem 38:5151–5153

    Article  CAS  PubMed  Google Scholar 

  51. O’Neill ME, Wade K (1983) Closo clusters with unusual electron numbers: the significance of frontier orbital degeneracies and bonding characteristics. J Mol Struct (THEOCHEM) 103:259–268

    Article  Google Scholar 

  52. Morrison JA (1991) Chemistry of the polyhedral boron halides and the diboron tetrahalides. Chem Rev 91:35–48

    Article  CAS  Google Scholar 

  53. Corminboeuf C, Wodrich MW, King RB, Schleyer PVR (2008) Effects of halogen substitution on the properties of eight- and nine-vertex closo-boranes. Dalton Trans:1745–1751

    Google Scholar 

  54. Borthakur R, Mondal B, Nandi P, Ghosh S (2016) Hypoelectronic isomeric diiridaboranes [(Cp*Ir)2B6H6]: the “Rule-Breakers”(Cp* = η5-C5Me5). Chem Commun 52:3199–3202

    Article  CAS  Google Scholar 

  55. Roy DK, Borthakur R, Prakash R, Bhattacharya S, Jagan R, Ghosh S (2016) Hypoelectronic 8–11-vertex irida- and rhodaboranes. Inorg Chem 55:4764

    Article  CAS  PubMed  Google Scholar 

  56. Evans WJ, Hawthorne MF (1974) Synthesis of fourteen vertex metallocarboranes by polyhedral expansion. Chem Commun:38–39

    Google Scholar 

  57. McAnaw A, Lopez ME, Ellis D, Rosair GM, Welch AJ (2013) The synthesis and characterization of homo- and heterometallic 1,14,2,9- and 1,14,2,10-M2C2B10 14-vertex metallocarboranes. Dalton Trans 42:671–679

    Article  CAS  PubMed  Google Scholar 

  58. McAnaw A, Lopez ME, Ellis D, Rosair GM, Welch AJ (2014) Asymmetric 1,8/1,3,2,x-M2C2B10 14-vertex metallacarboranes by direct electrophilic insertion reactions, the VCD and BHD methods in critical analysis of cage C atom positions. Dalton Trans 43:5095–5105

    Article  CAS  PubMed  Google Scholar 

  59. Robertson APM, Beattie NA, Scott C, Man WY, Jones JJ, Macgregor SA, Rosair GM, Welch AJ (2016) 14-Vertex heteroboranes with 14 skeletal electron pairs: an experimental and computational study. Angew Chem Int Ed 55:8706–8710

    Article  CAS  Google Scholar 

  60. Szabolcs J, Lupan A, Kun A-Z, King RB (2020) Isocloso versus closo deltahedra in slightly hypoelectronic supraicosahedral 14-vertex dimetallaboranes with 28 skeletal electrons. New J Chem 44:16977–16984

    Article  Google Scholar 

  61. Attia AAA, Lupan A, King RB, Ghosh S (2019) The tetracapped truncated tetrahedron in 16-vertex tetrametallaborane structures: spherical aromaticity with an isocloso rather than a closo skeletal electron count. PhysChemChemPhys 21:22022–22030

    CAS  Google Scholar 

  62. For a review of much of the relevant chemistry from Fehlner’s group see Fehlner TP (2002) In: Shapiro PJ, Atwood DA (eds) Group 13 chemistry: from fundamentals to applications, American Chemical Society, Washington, pp 49–67

    Google Scholar 

  63. Ghosh S, Shang M, Li Y, Fehlner TP (2001) Synthesis of [(Cp*re)2BnHn] (n = 8–10): metal boride particles that stretch the cluster structure paradigms. Angew Chem Int Ed 40:1125–1128

    Article  CAS  Google Scholar 

  64. Wadepohl H (2002) Hypoelectronic dimetallaboranes. Angew Chem Int Ed 41:4220

    Article  CAS  Google Scholar 

  65. Le Guennic B, Jiao H, Kahlal S, Saillard J-Y, Halet J-F, Ghosh S, Shang M, Beatty AM, Rheingold AL, Fehlner TP (2004) Synthesis and characterization of hypoelectronic rhenaboranes analysis of the geometric and electronic structures of species following neither borane nor metal cluster electron-counting paradigms. J Am Chem Soc 126:3203–3217

    Article  PubMed  Google Scholar 

  66. King RB (2006) Oblate deltahedra in dimetallaboranes: geometry and chemical bonding. Inorg Chem 45:8211–8216

    Article  CAS  PubMed  Google Scholar 

  67. Lupan A, King RB (2012) Hypoelectronic dirhenaboranes having eight to twelve vertices: internal versus surface rhenium-rhenium bonding. Inorg Chem 51:7609–7616

    Article  CAS  PubMed  Google Scholar 

  68. Cotton FA, Harris CB (1965) Crystal and molecular structure of dipotassium octachlorodirhenate(3) dehydrate K2[Re2Cl8]·2H2O. Inorg Chem 4:330–333

    Article  CAS  Google Scholar 

  69. Lupan A, King RB (2013) Dimetallaboranes with polyhedral surface metal-metal multiple bonds: deltahedral dirhenaboranes with pentalenedirhenium vertices. Organometallics 32:4002–4008

    Article  CAS  Google Scholar 

  70. Cotton FA, Rice CE, Rice GW (1977) Crystal and molecular structure of anhydrous tetraacetatodichromium. J Am Chem Soc 99:4704–4707

    Article  CAS  Google Scholar 

  71. Evans WJ, Hawthorne MF (1971) An 11-atom polyhedral metallocarborane formed from 1,6-dicarba-closo-decaborane(10) by polyhedral expansion. J Am Chem Soc 93:3063–3064

    Article  Google Scholar 

  72. Timofeev SV, Lovanova IA, Petrovskii PV, Starikova ZA, Bregadze VI (2001) Electrophilic substitution in eleven-vertex metallacarborane 1,2,4-CpCoC2B8H10. Russ Chem Bull 50:1683–1688

    Article  CAS  Google Scholar 

  73. Weller AS, Shang M, Fehlner TP (1998) Synthesis and structure of the metallaborane Cp*3(μ-H)W3B8H8 from the thermolysis of Cp*H3WB4H8 (Cp* = η5-C5Me5). A close-packed 11-atom boron-rich cluster. J Am Chem Soc 120:8283–8284

    Article  CAS  Google Scholar 

  74. Thakur A, Sahoo S, Ghosh S (2011) A homometallic tricapped cubane cluster [(Cp*Mo)4B4H4(μ4-BH)3] (Cp* = η5-C5Me5). Inorg Chem 50:7940–7942

    Article  CAS  PubMed  Google Scholar 

  75. Attia AAA, Lupan A, King RB (2016) Novel non-spherical deltahedra in trirhenaborane structures. New J Chem 40:7564–7572

    Article  CAS  Google Scholar 

  76. Attia AAA, Lupan A, King RB (2020) Novel non-spherical deltahedra in tetramolybdaborane structures: generation of low-energy structures by capping Mo4B4 cubes. Polyhedron 187. article 114626

    Google Scholar 

  77. Cox DN, Mingos DMP, Hoffmann R (1981) Extended Hückel molecular-orbital calculations on dodecahedral metalloboranes which do not conform to the polyhedral skeletal electron-pair theory. J Chem Soc Dalton Trans:1788–1797

    Google Scholar 

Download references

Acknowledgments

Funding from the Romanian Ministry of Education and Research, (Grant PN-III-P4-ID-PCE-2016-0089) is gratefully acknowledged. Additional computational resources were provided by the high-performance computational facility MADECIP, POSCCE, COD SMIS 48801/1862 co-financed by the European Regional Development Fund of the European Union.

Author information

Authors and Affiliations

  1. Faculty of Chemistry and Chemical Engineering, Babeș-Bolyai University, Cluj-Napoca, Romania

    Alexandru Lupan, Amr A. A. Attia, Szabolcs Jákó & Attila-Zsolt Kun

  2. Department of Chemistry and Center for Computational Quantum Chemistry, University of Georgia, Athens, GA, USA

    R. Bruce King

Authors
  1. Alexandru Lupan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amr A. A. Attia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Szabolcs Jákó
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Attila-Zsolt Kun
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. R. Bruce King
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Alexandru Lupan or R. Bruce King .

Editor information

Editors and Affiliations

  1. Chemistry Department, University of Oxford, Oxford, UK

    D. Michael P. Mingos

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Lupan, A., Attia, A.A.A., Jákó, S., Kun, AZ., Bruce King, R. (2021). Beyond the Wade-Mingos Rules: Deviations from Sphericality in Metallaborane Structures. In: Mingos, D. (eds) 50th Anniversary of Electron Counting Paradigms for Polyhedral Molecules . Structure and Bonding, vol 187. Springer, Cham. https://doi.org/10.1007/430_2021_83

Download citation

Publish with us

Policies and ethics

Search

Navigation