Modelling the properties of magnetic clusters with complex structures: how symmetry can help us

Boris Tsukerblat, Andrew Palii, Juan Modesto Clemente-Juan, Eugenio Coronado

Research output: Contribution to journalReview articlepeer-review

4 Scopus citations


The purpose of this article is to answer the question of how symmetry helps us to investigate and understand the properties of nanoscopic magnetic clusters with complex structures. The systems of choice will be the three types of polyoxometalates (POMs): (1) POMs containing localised spins; (2) reduced mixed-valence (MV) POMs; (3) partially delocalised POMs in which localised and delocalised subunits coexist and interact. The theoretical tools based on various kinds of symmetry are the following: (1) irreducible tensor operator (ITO) approach based on the so-called “spin-symmetry” and MAGPACK program; (2) group-theoretical assignment of the exchange multiplets based on spin- and point symmetries; (3) group-theoretical classification of the delocalised electronic and electron-vibrational states of MV POMs; (4) general approach (based on spin symmetry) to evaluate the energy levels of large MV clusters and the corresponding MVPACK program; (5) computational approach (employing point symmetry) to solve multidimensional non-adiabatic vibronic problems in the nanoscopic systems realized as VIBPACK software. We made it our goal to avoid a conventional deductive style of presentation. On the contrary, we first consider specially selected complex POMs and then show by what methods and in what way the theoretical problems arising in the description of the properties of these molecules can be properly solved.

Original languageEnglish
Pages (from-to)217-265
Number of pages49
JournalInternational Reviews in Physical Chemistry
Issue number2
StatePublished - 2 Apr 2020


  • Jahn–Teller effect
  • Molecular magnetism
  • antisymmetric exchange
  • double exchange
  • exchange interactions
  • irreducible tensor operators
  • magnetic anisotropy
  • magnetic clusters
  • mixed-valency
  • polyoxometalates
  • polyoxovanadates
  • spin frustration
  • spin rings
  • symmetry
  • vibronic coupling

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry


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