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Roby-Gould bond indices as a tool for understanding chemical bonding
from a mathematical and quantum mechanical perspective
بخشی از متن:In this paper we elaborate and evaluate the Roby-Gould bond index method (RGBI) for classifying and
interpreting the nature of chemical bonds [Gould et al., Theor. Chem. Acc., 2008, 119, 275]. We emphasize that
the RGBI method defines atoms as subspaces of a Hilbert space, represented as projection operators, and in
accord with basic mathematical requirements concerning the assignment of probabilities to such subspaces.
The definition of the bond indices between such atoms follows from simple set theoretical ideas concerning
the sharing of, and differences between, atomic electron populations; and from the geometric properties
associated with these subspaces—properties which are closely aligned with older chemical notions, which are
reviewed.We also introduce the Araki angle percentage ionicity of a bond,which is easily read off froma compact
two-dimensional representation of the chemical bond, which we call the bond dial diagram. Additionally we
explore the theory with defining atoms by the occupied natural atomic spinorbitals (NAOs) of Reed and
coworkers, instead of the atomic natural orbitals (ANOs) previously used. Bond indices from these ANO- and
NAO-based atoms are applied to a dataset of 353 molecules, including 27 first row molecules, 280 organic
molecules, and 46 semiochemical molecules, comprising 33 A–H bonds, where A are first and second row
elements, 1779 C–X, 3415 H–X bonds (X=C, N, O, S), and a few more other types of bonds. The bond indices
fromthe ANO-based atoms are much more in accordwith chemists' expectations as compared to those obtained
from NAO-based atoms provided that the excited triplet state defines the ANOs for group 2 atoms.
© 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://
