The correlation theory of the chemical bond. (arXiv:1605.06919v3 [quant-ph] UPDATED)

The quantum mechanical description of the chemical bond is generally given in
terms of delocalized bonding orbitals, or, alternatively, in terms of
correlations of occupations of localised orbitals. However, in the latter case,
multiorbital correlations were treated only in terms of two-orbital
correlations, although the structure of multiorbital correlations is far
richer; and, in the case of bonds established by more than two electrons,
multiorbital correlations represent a more natural point of view. Here, for the
first time, we introduce the true multiorbital correlation theory, consisting
of a framework for handling the structure of multiorbital correlations, a
toolbox of true multiorbital correlation measures, and the formulation of the
multiorbital correlation clustering, together with an algorithm for obtaining
that. These make it possible to characterise quantitatively, how well a bonding
picture describes the chemical system. As proof of concept, we apply the theory
for the investigation of the bond structures of several molecules. We show that
the non-existence of well-defined multiorbital correlation clustering provides
a reason for debated bonding picture.

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