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.

Department of Chemical and Biological Engineering University of Wisconsin Madison 1415 Engineering Drive Madison Wisconsin 53706 United States

Department of Inorganic and Analytical Chemistry Budapest University of Technology and Economics H 1111 Budapest Szent Gellért tér 4 Hungary

J Heyrovský Institute of Physical Chemistry Academy of Sciences of the Czech Republic CZ 18223 Prague Czech Republic

Strongly Correlated Systems Lendület Research Group Institute for Solid State Physics and Optics MTA Wigner Research Centre for Physics H 1121 Budapest Konkoly Thege Miklós út 29 33 Hungary

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