Relations between real molecules through abstract molecules: the reference cluster approach

  • Paul G. MezeyEmail author
Part of the Highlights in Theoretical Chemistry book series (HITC, volume 12)


Replacing integer atomic numbers representing nuclear charges by continuous variables has already provided some rigorous quantum chemical relations between real molecules, using a formal interpolation through nonphysical abstract molecules of continuously varying nuclear charges. Extending this approach to the more general “universal molecule” model, where all discrete parameters of molecules are generalized and replaced by continuous variables, provides further relations, actually interconnecting all real molecules through abstract, non-physical “molecules,” involving, for example, non-integer number of electrons. One simplifying idea of this model is the so-called “reference cluster,” originally defi ned for isoelectronic systems of a fixed number N of nuclei, where each nucleus is replaced by a possibly fi ctive nucleus with a nuclear charge equal to the average of the N nuclear charges. Based on the earlier results, some new relations are derived interrelating energies and some other properties of some real molecules, and also providing a unifying framework for the utilization of both symmetry and energy relations of the universal molecule model.


Nuclear charge space Electronic energy inequalities Reference cluster Universal molecule model 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Scientific Modeling and Simulation Laboratory (SMSL), Department of Chemistry and Department of Physics and Physical OceanographyMemorial University of NewfoundlandSt. John’sCanada
  2. 2.Institute of ChemistryEötvös UniversityBudapestHungary
  3. 3.Institute of ChemistryBabes-Bolyai UniversityCluj-NapocaRomania

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