Bond indices and valency

Armstrong, David R.; Perkins, P. G.; Stewart, James J. P.

doi:10.1039/dt9730000838

Cited by 244 publications

(99 citation statements)

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“…The CNDO definition of valence index had been introduced independently by Borisova and Semenov 5 and Armstrong et al 6 with a few months priority of the former authors. Unfortunately, Borisova and Semenov published their very important papers in a journal with a limited circulation, and so I became aware of them only thanks to a favor by Dr. Obis Castaño-who was their former graduate student-after I had already published my first papers in the field.…”

Section: Introductionmentioning

confidence: 99%

“…Summing up the parameters b µ for all the orbitals of the atom, but extracting the intraatomic partial Wiberg indices lacking a chemical significance, 6 we arrive to the valence of atom A:…”

Section: Introductionmentioning

confidence: 99%

“…It follows from the idempotency of the density matrix that for closed-shell determinant wave functions the valence of an atom equals to the sum of its Wiberg indices: 5,6 …”

Section: Introductionmentioning

confidence: 99%

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Bond order and valence indices: A personal account

2006

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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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bond order and valence indices: A personal account

2006

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“…Despite this, the bond index has found widespread use. Armstrong et al [19] explored some of the applications of the Wiberg bond index. Natiello and Medrano [20] extended the bond index to ab initio calculations.…”

Section: Introduction: Bond Orders and Theorymentioning

confidence: 99%

Toward an experimental bond order

Jules

Lombardi

2003

Journal of Molecular Structure: THEOCHEM

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By inverting the Guggenheimer formula relating force constant to internuclear distance we derive an experimental expression for bond order, which can be applied throughout the periodic table to diatomic molecules as well as polyatomic molecules. Only two adjustable parameters are required except they must be modified somewhat for polar molecules, most hydrides, and certain triplet ground state molecules. An alternative, suggested by Bader, depends only on the electron density at the bond critical point. It is modified to make it more generally applicable and compatible with experimental results and we compare the two approaches. q

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“…40 Note that tight-binding descriptions are consistent with the trans-influence. Indeed, we show in Appendix B that the bond order 65 for the AB dimer from Eq. (4) is approximately given by the expression:…”

Section: Ppσ-bonded Semiconductors: the Role Of The Secondary Ppσmentioning

confidence: 99%

Electronic structure and the glass transition in pnictide and chalcogenide semiconductor alloys. I. The formation of the ppσ-network

Zhugayevych

Lubchenko

2010

The Journal of Chemical Physics

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Semiconductor glasses exhibit many unique optical and electronic anomalies. We have put forth a semi-phenomenological scenario (J. Chem. Phys. 132, 044508 (2010)) in which several of these anomalies arise from deep midgap electronic states residing on high-strain regions intrinsic to the activated transport above the glass transition. Here we demonstrate at the molecular level how this scenario is realized in an important class of semiconductor glasses, namely chalcogen and pnictogen containing alloys. Both the glass itself and the intrinsic electronic midgap states emerge as a result of the formation of a network composed of σ-bonded atomic p-orbitals that are only weakly hybridized. Despite a large number of weak bonds, these ppσ-networks are stable with respect to competing types of bonding, while exhibiting a high degree of structural degeneracy. The stability is rationalized with the help of a hereby proposed structural model, by which ppσ-networks are symmetry-broken and distorted versions of a high symmetry structure. The latter structure exhibits exact octahedral coordination and is fully covalently-bonded. The present approach provides a microscopic route to a fully consistent description of the electronic and structural excitations in vitreous semiconductors.

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Bond indices and valency

Cited by 244 publications

References 0 publications

Bond order and valence indices: A personal account

Bond order and valence indices: A personal account

Toward an experimental bond order

Electronic structure and the glass transition in pnictide and chalcogenide semiconductor alloys. I. The formation of the ppσ-network

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