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A Hierarchical set of one electron functions in real space

A hierarchical set of one-electron functions obtained from domain-averaged cummulant density matrices is presented. The first family in this set, constructed from the second order cummulant density (or exchange-correlation density) coincides with the domain natural orbitals obtained by diagonalizing Ponec's Domain-Averaged Fermi hole [1]. Similarly, the second and third families define two-, and three-center bond functions, respectively. It is shown how each of these functions add up additively to the appropriate multi-center delocalization index [2]. Two- and three-center examples are shown for simple molecular systems ​
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