Advertisement

Pythagorean Harmony in the World of Metal Oxygen Clusters of the Mo11 Type: Giant Wheels and Spheres both Based on a Pentagonal Type Unit

  • Achim Müller
  • Paul Kögerler
  • Hartmut Bögge
Chapter
Part of the Structure and Bonding book series (STRUCTURE, volume 96)

Abstract

“[...]; since, again, they (the Pythagoreans) saw that the attributes and the ratios of the musical scales were expressible in numbers; since, then, all other things seemed in their whole nature to be modeled after numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number.” (Aristotle Metaphysics 1, 985b 31 ff).

Polyoxometalate systems provide excellent models for the study of unusual molecular growth processes based on Mo11-type building motifs/blocks leading to unusual giant spherical and ring-shaped structures with stoichiometry Mo11 n (n = 12, 14, 16)-a Pythagorean harmony.

Keywords

Clusters Polyoxometalates Building Blocks 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1. a)
    Müller A, Peters F, Pope MT, Gatteschi D (1998) Chem Rev 98: 239CrossRefGoogle Scholar
  2. 1. b)
    Pope MT, Müller A (1991) Angew Chem Int Ed Engl 30: 34CrossRefGoogle Scholar
  3. 1. c)
    Pope MT, Müller A (eds) (1994) Polyoxometalates: From Platonic Solids to Anti-Retroviral Activity. Kluwer, DordrechtGoogle Scholar
  4. 1. d)
    Pope MT (1983) Heteropoly and Isopoly Oxometalates. Springer, Berlin Heidelberg New YorkGoogle Scholar
  5. 2.
    Voet D, Voet JG (1995) Biochemistry, 2nd edn. Wiley, New York, p 1076Google Scholar
  6. 3.
    First reports on the three-fragment Mo57V6cluster appeared in 1993, see a) Zhang S, Huang G, Shao M, Tang Y (1993) J Chem Soc Chem Commun 37Google Scholar
  7. 3. b)
    Müller A, Krickemeyer E, Dillinger S, Bögge H, Proust A, Plass W, Rohlfing R (1993) Naturwissenschaften 80: 560. Other related clusters (such as the two-fragment Mo36 cluster) were published later and errors concerning the formula in the first publications were corrected, seeCrossRefGoogle Scholar
  8. 3. c)
    Müller A, Krickemeyer E, Dillinger S, Bögge H, Plass W, Proust A, Dloczik L, Menke C, Meyer J, Rohlfing R (1994) Z Anorg Allg Chem 620: 599CrossRefGoogle Scholar
  9. 3. d)
    Müller A, Plass W, Krickemeyer E, Dillinger S, Bögge H, Armatage A, Beugholt C, Bergmann U (1994) Monatsh Chem 125: 525CrossRefGoogle Scholar
  10. 3. e)
    Müller A, Plass W, Krickemeyer E, Dillinger S, Bögge H, Armatage A, Proust A, Beugholt C, Bergmann U (1994) Angew Chem Int Ed Engl 33: 849CrossRefGoogle Scholar
  11. 3. f)
    Müller A, Bögge H, Krickemeyer E, Dillinger S (1994) Bull Pol Acad Sci Chem 42: 291Google Scholar
  12. 3. g)
    Müller A, Reuter H, Dillinger S (1995) Angew Chem Int Ed Engl 34: 2311. For details on the relevant basic Mo8 groups see alsoCrossRefGoogle Scholar
  13. 3. h)
    Müller A, Beugholt C (1996) Nature 383: 296. For the two-fragment isopolyoxomolybdate Mo36-type cluster with [MoO] instead of [MoNO] groups see alsoCrossRefGoogle Scholar
  14. 3. i)
    Tytko K-H, Schönfeld B, Buss B, Glemser O (1973) Angew Chem Int Ed Engl 12: 330 and with the corrected formulaCrossRefGoogle Scholar
  15. 3. j)
    Krebs B, Stiller S, Tytko K-H, Mehmke J (1991) Eur J Solid Inorg Chem 28: 883Google Scholar
  16. 4. a)
    Krätschmer W, Schuster H (eds) (1996) Von Fuller bis zu Fullerenen, Beispiele einer interdisziplinären Forschung. Vieweg, BraunschweigGoogle Scholar
  17. 4. b)
    Coxeter HSM (1969) Introduction to Geometry. Wiley, New YorkGoogle Scholar
  18. 5.
    Chae HK, Klemperer WG, Marquart TA (1993) Coord Chem Rev 128: 209CrossRefGoogle Scholar
  19. 6.
    Müller A, Krickemeyer E, Bögge H, Schmidtmann M, Peters F (1998) Angew Chem Int Ed 37: 3360Google Scholar
  20. 7.
    Liljas L, Strandberg B (1984) In: Jurnak FA, McPherson A (eds) Biological Macromolecules and Assemblies, vol 1, Virus Structures. Wiley, New York, p 97Google Scholar
  21. 8. a)
    Voet D, Voet JG (1995) Biochemistry, 2nd edn. Wiley, New YorkGoogle Scholar
  22. 8. b)
    Alberts B, Bray D, Lewis J, Raff M, Roberts K, Watson JD (1994) Molecular Biology of the Cell, 3rd edn. Garland, New YorkGoogle Scholar
  23. 8. c)
    Davies BD, Dulbecco R, Eisen HN, Ginsberg HS (1980) Microbiology, 3rd edn. Harper and Row, PhiladelphiaGoogle Scholar
  24. 8. d)
    Harrison SC (1984) Trends Biochem Sci 9: 345CrossRefGoogle Scholar
  25. 9.
    Müller A, Fedin VP, Kuhlmann C, Bögge H, Schmidtmann M (1999) Chem Commun 927Google Scholar
  26. 10. a)
    Kepler J (1596) Mysterium Cosmographicum; see alsoGoogle Scholar
  27. 10. b)
    Kemp M (1998) Nature 393: 123CrossRefGoogle Scholar
  28. 11.
    Müller A, Sarkar S, Bögge H, Schmidtmann M, Sarkar Sh, Kögerler P, Hauptfleisch B, Shah SQN, Trautwein A, Schünemann V (1999) Angew Chem Int Ed 38: 3238CrossRefGoogle Scholar
  29. 12.
    Müller A, Krickemeyer E, Meyer J, Bögge H, Peters F, Plass W, Diemann E, Dillinger S, Nonnenbruch F, Randerath M, Menke C (1995) Angew Chem Int Ed Engl 34: 2122CrossRefGoogle Scholar
  30. 13.
    Bradley D (1995) New Scientist 148 (2003): 18Google Scholar
  31. 14. a)
    Müller A, Krickemeyer E, Bögge H, Schmidtmann M, Beugholt C, Kögerler P, Lu C (1998) Angew Chem Int Ed 37: 1220CrossRefGoogle Scholar
  32. 14. b)
    Jiang C, Wei Y, Liu Q, Zhang S, Shao M, Tang Y (1998) Chem Commun 1937Google Scholar
  33. 15.
    Müller A, Eimer W, Diemann E, Serain C, to be publishedGoogle Scholar
  34. 16.
    Müller A, Krickemeyer E, Bögge H, Schmidtmann M, Beugholt C, Das SK, Peters F (1999) Chem Eur J 5: 2114CrossRefGoogle Scholar
  35. 17.
    Müller A, Koop M, Bögge H, Schmidtmann M, Beugholt C (1998) Chem Commun 1501Google Scholar
  36. 18.
    Müller A, Krickemeyer E, Bögge H, Schmidtmann M, Peters F, Menke C, Meyer J (1997) Angew Chem Int Ed Engl 36: 484CrossRefGoogle Scholar
  37. 19.
    Müller A, Das SK, Bögge H, Beugholt C, Schmidtmann M (1999) Chem Commun 1035Google Scholar
  38. 20.
    Müller A, Das SK, Fedin VP, Krickemeyer E, Beugholt C, Bögge H, Schmidtmann M, Hauptfleisch B (1999) Z Anorg Allg Chem 625: 1187CrossRefGoogle Scholar
  39. 21. a)
    Müller A, Shah SQN, Bögge H, Schmidtmann M (1999) Nature 397: 48CrossRefGoogle Scholar
  40. 21. b)
    Ball P (1998) Nature 395: 745CrossRefGoogle Scholar
  41. 22. a)
    Cotton FA, Wilkinson G (1980) Advanced Inorganic Chemistry, 4th ed. Wiley, New York, p 847Google Scholar
  42. 22. b)
    Kihlborg L (1963) Arkiv Kemi 21: 427Google Scholar
  43. 22. c)
    Müller A, Hauptfleisch B, in preparationGoogle Scholar
  44. 23.
    Müller A et al. (1999) in preparationGoogle Scholar
  45. 24.
    Müller A, Koop M, Bögge H, Schmidtmann M, Peters F, Kögerler P (1999) Chem Commun 1885Google Scholar
  46. 25. a)
    (1935) Gmelins Handbuch der Anorganischen Chemie, Molybdän. Verlag Chemil, Berlin, p 134Google Scholar
  47. 25. b)
    (1987) Gmelin Handbook of Inorganic Chemistry, Molybdenum Suppl., vol B3a, 8th edn. Springer, Berlin Heidelberg New York. See alsoGoogle Scholar
  48. 25. c)
    Müller A, Meyer J, Krickemeyer E, Diemann E (1996) Angew Chem Int Ed Engl 35: 1206CrossRefGoogle Scholar
  49. 26.
    Horgan J (1995) Scientific American, June Issue 74Google Scholar
  50. 27.
    Müller A, Meyer J, Krickemeyer E, Beugholt C, Bögge H, Peters F, Schmidtmann M, Kögerler P, Koop MJ (1998) Chem Eur J 4: 1000CrossRefGoogle Scholar
  51. 28. a)
    Khan MI, Müller A, Dillinger S, Bögge H, Chen Q, Zubieta J (1993) Angew Chem Int Ed Engl 32: 1780CrossRefGoogle Scholar
  52. 28. b)
    Müller A, Dillinger S, Krickemeyer E, Bögge H, Plass W, Stammler A, Haushalter RC (1997) Z Naturforsch 52b: 1301Google Scholar
  53. 28. c)
    Khan MI, Zubieta J (1992) J Am Chem Soc 114: 10058CrossRefGoogle Scholar
  54. 28. d)
    Khan MI, Chen Q, Salta J, O’Connor CJ, Zubieta J (1996) Inorg Chem 35: 1880CrossRefGoogle Scholar
  55. 29. a)
    Krautscheid H, Fenske D, Baum G, Semmelmann M (1993) Angew Chem Int Ed Engl 32: 1303CrossRefGoogle Scholar
  56. 29. b)
    Fenske D, Zhu N, Langetepe T (1998) Angew Chem Int Ed 37: 2640Google Scholar
  57. 30.
    Ecker A, Weckert E, Schnöckel H (1997) Nature 387: 379CrossRefGoogle Scholar
  58. 31.
    Wassermann K, Dickman MH, Pope MT (1997) Angew Chem Int Ed Engl 36: 1445CrossRefGoogle Scholar
  59. 32.
    Mackay AL (1990) In: Hargittai I (ed) Quasicrystals, Networks, and Molecules of Fivefold Symmetry. VCH, WeinheimGoogle Scholar
  60. 33.
    Müller A, Polarz S, Das SK, Krickemeyer E, Bögge H, Schmidtmann M, Hauptfleisch B (1999) Angew Chem Int Ed 38: 3241CrossRefGoogle Scholar
  61. 34.
    Müller A et al., to be publishedGoogle Scholar

Copyright information

© Springer Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Achim Müller
    • 1
  • Paul Kögerler
    • 1
  • Hartmut Bögge
    • 1
  1. 1.Faculty of ChemistryUniversity of BielefeldBielefeldGermany

Personalised recommendations