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

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 non-physical 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 defined for isoelectronic systems of a fixed number N of nuclei, where each nucleus is replaced by a possibly fictive 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.