Bond order and valence indices: A personal account

Abstract

Abstract:The paper accounts for the author's activity in developing bond order and valence indices since the early 80s.These indices represent an important conceptual link between the physical description of molecules as systems of electrons and nuclei and the chemical picture of molecules consisting of atoms kept together by bonds. They are also useful for a systematization and interpretation of the results obtained in the quantum chemical calculations, by permitting to extract from the wave function different pieces of information that may be assigned chemical significance. In some cases they can have some predictive power, too. Historically, the prototypes of such indices were introduced in the semiempirical quantum chemistry; the most important developments were Coulson's charge-bond order matrix in the simple Hückel theory and the Wiberg index in the CNDO framework. (Valence indices were also introduced in the semiempirical theory.) The definition of the ab initio bond order index emerged from the asymptotic term of the exchange energy component of the partitioning performed in the framework of the author's so-called "chemical Hamiltonian approach" using a "mixed" second quantization formalism for overlapping basis sets. They can also be introduced by studying the exchange part of the two-particle density (or of the second-order density matrix). Some properties of the bond order indices are discussed and the author's (until now unpublished) proof is also presented, showing the sufficient conditions under which the bond order index of a homonuclear diatomics is equal to the "chemist's bond order," i.e., the half of the difference between the number of electrons occupying bonding and antibonding orbitals. The ab initio valence indices are also introduced and discussed, and it is stressed that for correlated wave function the same "exchange only" definition of the bond order and valence indices should be used, which was introduced for the SCF case. The recent concept of the "atomic decomposition of identity" is also discussed and it is utilized for introducing bond orders and valences in the framework of the "3D analysis," when atoms are defined not by their basis orbitals but as regions of the three-dimensional (3D) physical space. Two versions of the 3D analysis are considered-the AIM (atoms in molecules)-type decomposing the space into disjunct atomic domains and the "fuzzy atoms" scheme in which there are no sharp boundaries between the atoms but they exhibit a continuous transition from one to another.

Communication: Covalent nature of X⋯H2O (X = F, Cl, and Br) interactions

“…Further evidence in support of the 2c-3e bond is collected in Table I, with details of the calculations given in the supplementary material. 24 Specifically, it is shown that the bond lengths (R e ) in the halogen complexes are much shorter than the corresponding van der Waals distances (R vdW ), 40 and their fuzzy bond orders defined by Mayer 41 are also much larger than other complexes. Perhaps the most convincing evidence is the integrated half-spin densities, which exhibits substantial delocalization between the halogen and oxygen moieties in the pertinent complexes.…”

Hermitian “chemical” Hamiltonian: an alternative ab initio method

“…(36), owing to the fact that for the expectation values of the "mixed" pairs of creation and annihilation operators one has (in the single determinant case) [1,6] …”

One- and two-center physical space partitioning of the energy in the density functional theory

“…23 It was shown by Borisova and Semenov 25 for the Wiberg index 26 of the complete neglect of differential overlap ͑CNDO͒ theory and by one of us for the ab initio 27 that the bond order index calculated in the Hilbert-space framework may be considered as the effective number of electron pairs participating in the bonding between the atoms considered. 28 This should be applicable mutatis mutandis in the fuzzy atoms frame as well.…”