Skip to main content
SpringerLink
Log in

General Theory of Superexchange in Molecules

  • Chapter
  • First Online:
Single-Molecule Magnets and Related Phenomena

Part of the book series: Structure and Bonding ((STRUCTURE,volume 122))

Abstract

After recalling the basic physical backgrounds, we examine the concept of magnetic orbital, which is very useful for treating the mechanism of superexchange. Then we recall the general broad lines of the first historical model proposed by Anderson. In a second step, we develop a new general treatment for superexchange, in the case of the centrosymmetrical model AXB. A and B are 3d 1 metal cations characterized by σ-type bonds on both sides of the diamagnetic bridge X without the presence of a π-type orbital (with here A = B or A ≠ B). The cationic orbitals are of the d-type, whereas that of diamagnetic ligand is of the s- or p-type. This treatment allows one to retrieve the expression of exchange energy J vs key molecular integrals, as respectively proposed by several authors such as Anderson, on the one hand, Hay, Thibeault and Hoffmann, on the other one, and, finally, Kahn and Briat. This toy model may be easily generalized to 3d n ions (with n > 1) with or without transfer between both cations, with A ≠ B . Under these conditions we show that this general treatment allows one to calculate superexchange interactions in any type of molecule.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Curie P (1895) Ann Chim Phys (Paris) 5:289

    Google Scholar 

  2. Langevin P (1905) J Phys (Paris) 4:678

    Google Scholar 

  3. Langevin P (1905) Ann Chim Phys (Paris) 5:70

    CAS  Google Scholar 

  4. Weiss P (1906) Comptes Rendus Acad Sci (Paris) 143:1136

    CAS  Google Scholar 

  5. Weiss P (1907) J Phys (Paris) 6:661

    Google Scholar 

  6. Weiss P (1908) Physik Z 9:358

    CAS  Google Scholar 

  7. Debye P (1925) In: Marx E (ed) Handbuch der Radiologie, vol IV. Akad Verlagsges, Leipzig, p 597

    Google Scholar 

  8. Weiss P (1914) Ann Phys (Paris) 1(9):134

    Google Scholar 

  9. Rozansky D (1926) Physik Z 27:779

    CAS  Google Scholar 

  10. Heisenberg W (1926) Z Physik 38:411

    Article  Google Scholar 

  11. Dirac PAM (1926) Proc Roy Soc A112:661

    Article  CAS  Google Scholar 

  12. Hund F (1927) In: Linienspektren und periodisches System der Elemente. Springer, Berlin

    Google Scholar 

  13. Hund F (1925) Z Physik 33:855

    Article  CAS  Google Scholar 

  14. Heisenberg W (1926) Z Physik 39:499

    Article  CAS  Google Scholar 

  15. Néel L (1932) In: Ph D Thesis, chap VIII. Masson, Paris

    Google Scholar 

  16. Kramers HA (1934) Physica 1:182

    Article  CAS  Google Scholar 

  17. Van Vleck JH (1934) In: The Theory of Electric and Magnetic Susceptibilities, chap XI. Oxford University Press, London and New York

    Google Scholar 

  18. Anderson PW (1959) Phys Rev 115:2

    Article  CAS  Google Scholar 

  19. Anderson PW (1963) Solid State Phys 14:99

    Article  CAS  Google Scholar 

  20. Kanamori J (1957) Prog Theor Physics 17:197

    Article  CAS  Google Scholar 

  21. Van Vleck JH (1962) Revista de Matematicas y Fisica Teorica (Tucuma, Argentina) 14:189

    Google Scholar 

  22. Lévy PM (1964) Phys Rev 135A:155

    Google Scholar 

  23. Lévy PM (1966) Phys Rev 147:311

    Article  Google Scholar 

  24. Curély J (2005) Monatshefte für Chemie, 136(6):1013

    Article  CAS  Google Scholar 

  25. Herring C (1966) In: Rado, Suhl (eds) Magnetism, vol IIB. Wiley, New York, p 1

    Google Scholar 

  26. Kahn O (1987) Structure and Bonding 68:89

    CAS  Google Scholar 

  27. Jahn HA, Teller E (1937) Proc Roy Soc (London) A161:220

    Article  CAS  Google Scholar 

  28. Bates CA (1978) Phys Rep 35:187

    Article  CAS  Google Scholar 

  29. Hartmann-Boutron F (1968) J Phys (Paris) 29:212

    CAS  Google Scholar 

  30. Heitler W, London F (1927) Z Physik 44:455

    Article  CAS  Google Scholar 

  31. Heitler W (1927) Z Physik 46:47

    Article  Google Scholar 

  32. Heitler W (1928) Z Physik 47:835

    Article  CAS  Google Scholar 

  33. Heitler W (1928) Z Physik 51:805

    Article  CAS  Google Scholar 

  34. London F (1928) Z Physik 46:455

    Article  CAS  Google Scholar 

  35. London F (1928) Z Physik 50:24

    Article  CAS  Google Scholar 

  36. Born M, Oppenheimer JR (1927) Ann Physik 84:457

    Article  CAS  Google Scholar 

  37. Sugiura Y (1927) Z Physik 45:484

    Article  CAS  Google Scholar 

  38. Courant R, Hilbert D (1931) In: Methoden der Mathematischen Physik, 2nd ed. Springer, Berlin

    Google Scholar 

  39. Courant R, Hilbert D (1953) In: Methods of Mathematical Physics. Wiley, New York

    Google Scholar 

  40. Van Vleck JH (1934) Phys Rev 45:405

    Article  Google Scholar 

  41. Silvi B, Fourré I, Alikhani ME (2005) Monatshefte für Chemie 136(6):855

    Article  CAS  Google Scholar 

  42. Bocǎ R, Linert W (2005) Monatshefte für Chemie 136(6):881

    Article  CAS  Google Scholar 

  43. Dirac PAM (1928) Proc Roy Soc (London) A117:610

    Article  Google Scholar 

  44. Dirac PAM (1930) Proc Roy Soc (London) A126:360

    Article  CAS  Google Scholar 

  45. Boča R (1999) In: Theoretical Foundations of Molecular Magnetism, chap IV and references therein. Elsevier, Amsterdam

    Google Scholar 

  46. Curély J (2005) Monatshefte für Chemie 136(6):987

    Article  CAS  Google Scholar 

  47. Moriya T (1962) In: Rado, Suhl (eds) Magnetism, vol I. Wiley, New York, p 85

    Google Scholar 

  48. Dzialoshinski IE (1957) Sov Phys JETP 6:821

    Google Scholar 

  49. Dzialoshinski IE (1957) Sov Phys JETP 6:1259

    Google Scholar 

  50. Moriya T (1960) Phys Rev 120:91

    Article  CAS  Google Scholar 

  51. Kahn O (1985) In: Willet, Gatteschi, Kahn (eds) Magneto-Structural Correlations in Exchange Coupled Systems. NATO ASI Series C: Mathematical and Physical Sciences, vol 140. Reidel, Dordrecht, p 37

    Google Scholar 

  52. Kahn O (1993) In: Molecular Magnetism. VCH Publishers, New York

    Google Scholar 

  53. Girerd JJ, Journaux Y, Kahn O (1981) Chem Phys Lett 82:534

    Article  CAS  Google Scholar 

  54. Anderson PW (1963) In: Rado, Suhl (eds) Magnetism, vol I. Wiley, New York, p 25

    Google Scholar 

  55. Kahn O, Charlot MF (1980) Nouv J Chim 4:567

    CAS  Google Scholar 

  56. Charlot MF, Kahn O, Drillon M (1982) Chem Phys 70:177

    Article  CAS  Google Scholar 

  57. Löwdin PO (1950) J Chem Phys 18:365

    Article  Google Scholar 

  58. Shull CG, Strauser WA, Wollan EO (1951) Phys Rev 83:333

    Article  CAS  Google Scholar 

  59. Anderson PW (1950) Phys Rev 79:350

    Article  Google Scholar 

  60. Tinkham M (1956) Proc Roy Soc (London) A236:535

    Article  CAS  Google Scholar 

  61. Shulman RG, Jaccarino V (1956) Phys Rev 103:1126

    Article  CAS  Google Scholar 

  62. Jaccarino V, Shulman RG (1957) Phys Rev 107:1196

    Article  CAS  Google Scholar 

  63. Shulman RG, Jaccarino V (1957) Phys Rev 108:1219

    Article  CAS  Google Scholar 

  64. Kondo J (1957) Prog Theor Phys 18:541

    Article  Google Scholar 

  65. Blount EI (1962) Solid State Phys 13:305

    Article  CAS  Google Scholar 

  66. Goodenough JB (1960) Phys Rev 117:1442

    Article  CAS  Google Scholar 

  67. Goodenough JB (1955) Phys Rev 100:564

    Article  CAS  Google Scholar 

  68. Goodenough JB (1958) J Phys Chem Solids 6:287

    Article  CAS  Google Scholar 

  69. Kanamori J (1959) J Phys Chem Solids 10:87

    Article  CAS  Google Scholar 

  70. Wollan EO, Child HR, Koehler WC, Wilkinson MK (1958) Phys Rev 112:1132

    Article  CAS  Google Scholar 

  71. Georges R (1992) In: Proceedings of Primera Escuela Nacional de Materiales Moleculares, vol II, Peñiscola, Spain

    Google Scholar 

  72. Hay PJ, Thibeault JC, Hoffmann R (1975) J Am Chem Soc 97:4884

    Article  CAS  Google Scholar 

  73. Hatfield WE (1985) In: Willet, Gatteschi, Kahn (eds) Magneto-Structural Correlations in Exchange Coupled Systems. NATO ASI Series C: Mathematical and Physical Sciences, vol 140. Reidel, Dordrecht, p 555

    Google Scholar 

  74. Kahn O, Briat B (1976) J Chem Soc Faraday II 72:1968

    Google Scholar 

  75. Kahn O, Pei Y, Journaux Y (1989) Mol Cryst Liq Cryst 176:429

    Article  CAS  Google Scholar 

  76. Kahn O, Galy J, Journaux Y, Jaud J, Morgenstern-Badarau I (1982) J Am Chem Soc 104:2165

    Article  CAS  Google Scholar 

  77. Journaux Y, Kahn O, Zarembowitch J, Galy J, Jaud J (1983) J Am Chem Soc 105:7585

    Article  CAS  Google Scholar 

  78. Mataga N (1968) Theor Chim Acta (Berlin) 10:372

    Article  CAS  Google Scholar 

  79. Ovchinnikov AA (1978) Theor Chim Acta (Berlin) 47:297

    Article  CAS  Google Scholar 

  80. Bencini A, Benelli C, Caneschi A, Carlin RL, Dei A, Gatteschi D (1985) J Am Chem Soc 107:8128

    Article  CAS  Google Scholar 

  81. Pei Y, Journaux Y, Kahn O (1988) Inorg Chem 27:399

    Article  CAS  Google Scholar 

  82. Dixon DA, Miller JS (1989) Mol Cryst Liq Cryst 176:211

    Article  CAS  Google Scholar 

  83. Miller JS, Epstein AJ (1989) Mol Cryst Liq Cryst 176:347

    Article  CAS  Google Scholar 

  84. Epstein AJ, Miller JS (1989) Mol Cryst Liq Cryst 176:359

    Article  CAS  Google Scholar 

  85. Tyutyulkov N, Karabunarliev S, Ivano C (1989) Mol Cryst Liq Cryst 176:139

    Article  CAS  Google Scholar 

  86. Buchachenko AL (1989) Mol Cryst Liq Cryst 176:307

    Article  CAS  Google Scholar 

  87. McConnell HM (1967) Proc R A Welch Found Conf Chem Res 11:144

    Google Scholar 

  88. Breslow R (1982) Pure Appl Chem 54:927

    Article  CAS  Google Scholar 

  89. Torrance JB, Oostra A, Nazzal A (1987) Synth Met 19:709

    Article  CAS  Google Scholar 

  90. Breslow R (1989) Mol Cryst Liq Cryst 176:211

    Article  Google Scholar 

  91. Julve M, Verdaguer M, Charlot MF, Kahn O, Claude R (1984) Inorg Chim Acta 82:5

    Article  CAS  Google Scholar 

  92. Pei Y, Verdaguer M, Kahn O, Sletten J, Renard JP (1986) J Am Chem Soc 108:7428

    Article  CAS  Google Scholar 

  93. Gadet V, Mallah T, Castro I, Verdaguer M, Veillet P (1992) J Am Chem Soc 114:9213

    Article  CAS  Google Scholar 

  94. Eyert V, Siberchicot B, Verdaguer M (1997) Phys Rev B56:8959

    Article  CAS  Google Scholar 

  95. Arrio MA, Scuiller A, Sainctavit P, Cartier dit Moulin C, Mallah T, Verdaguer M (1999) J Amer Chem Soc 121:6414

    Article  CAS  Google Scholar 

  96. Verdaguer M, Bleuzen A, Marvaud V, Vaissermann J, Seuleiman M, Desplanches C, Scuiller A, Train C, Garde R, Gelly G, Lomenech C, Rosenman I, Veillet P, Cartier dit Moulin C, Villain F (1999) Coord Chem Rev 190:1023

    Article  Google Scholar 

  97. Vostrikova KE, Luneau D, Wernsdorfer W, Rey P, Verdaguer M (2000) J Am Chem Soc 122:718

    Article  CAS  Google Scholar 

  98. Verdaguer M (2001) Polyhedron 20:1115

    Article  CAS  Google Scholar 

  99. Andrés R, Brissard M, Gruselle M, Train C, Vaissermann J, Malézieux B, Jamet JP, Verdaguer M (2001) Inorg Chem 40:4633

    Article  CAS  Google Scholar 

  100. Lescouëzec R, Vaissermann J, Lloret F, Julve M, Verdaguer M (2002) Inorg Chem 41:5943

    Article  CAS  Google Scholar 

  101. Tiron R, Wernsdorfer W, Tuyeras F, Scuiller A, Marvaud V, Verdaguer M (2003) Polyhedron 22:2427

    Article  CAS  Google Scholar 

  102. Verdaguer M, Girolami G (2005) In: Miller JS, Drillon M (eds) Magnetoscience: molecules to materials, vol V. Wiley (Interscience), New York, p 283

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre de Physique Moléculaire Optique et Hertzienne (C.P.M.O.H.), Université Bordeaux 1, 351 Cours de la Libération, 33405, Talence Cedex, France

    Jacques Curély

  2. Laboratoire L. Néel, CNRS, B.P. 166, 38042, Grenoble Cedex 09, France

    Bernard Barbara

Authors
  1. Jacques Curély
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bernard Barbara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jacques Curély .

Editor information

Richard Winpenny

Rights and permissions

Reprints and permissions

About this chapter

Cite this chapter

Curély, J., Barbara, B. General Theory of Superexchange in Molecules. In: Winpenny, R. (eds) Single-Molecule Magnets and Related Phenomena. Structure and Bonding, vol 122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/430_033

Download citation

Publish with us

Policies and ethics

Search

Navigation