Direct (through‐space) and indirect (through‐bridge) components of the chemical bond multiplicities
Authors: Nalewajski Roman F. 
Published: September 2011

It is argued that the chemical bond concept embodies all types of dependencies between general basis functions, called “atomic orbitals” (AO), which are used to construct the bonding subspace of the occupied molecular orbitals (MOs), which in the single‐determinant LCAO MO type approach fully describes the bonding pattern of a molecule. The chemical interaction between the specified AO can be both of the direct and indirect origin: the former results from the explicit dependency between the interacting AO, due to their constructive interference in a molecule, and the latter has its roots in the implicit dependencies between basis functions in the molecular bonding subspace. The indirect (through‐bridge) contributions complement the familiar direct (through‐space) bond‐orders in the resultant pattern of bond multiplicities. The implicit components, realized via AO intermediates, are examined using the “quadratic” Wiberg approach to the localized bond‐orders and their information sources are investigated in the orbital communication theory of the chemical bond, in terms of the cascade communications between AO. The explicit and implicit dependencies between basis functions in the bonding subspace are linked to the relevant elements of the molecular charge‐and‐bond‐order matrix. The conditional probabilities of the direct and bridge (cascade) probability propagations (“communications”) between AO, which determine the associated molecular information channels, are derived and used to determine the information‐theoretic (IT) bond descriptors. These entropy/information indices of the bond covalency and ionicity accordingly reflect the average “noise” and the amount of the information flow in the molecular communications between AO. The multistage propagations involving full cascades of parallel AO bridges are shown to conserve the direct, stationary scattering probability between the given pair of terminal AO. This demonstrates the internal consistency of the bridge perspective on propagation of the electronic information in molecules. The associated Wiberg‐type (quadratic) bond‐order measures and IT bond multiplicities for these two types of interactions between AO are illustrated in the Hückel theory for selected π‐electron systems (benzene, butadiene, and linear polyenes). In all these representative molecular systems, the resultant bond indices, combining the direct and indirect multiplicity contributions, are shown to generate a more balanced bonding perspective compared with the corresponding patterns resulting from the direct (Wiberg) bond‐order approach alone. As illustrated for linear polyenes, the direct bonding can be realized at relatively short distances, while the indirect mechanism effectively extends the range of chemical interactions in molecular systems. The AO‐resolved communications have been examined in a general basis set case, and the “transition” communication system for the “promolecule” → molecule transformation has been proposed. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012