Valency. I. A quantum chemical definition and properties

Gopinathan, M. S.; Jug, Karl

doi:10.1007/bf00552652

Cited by 61 publications

(74 citation statements)

References 9 publications

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“…However, if the overlap matrix of the spin-orbital basis {χ µ } is not a unit matrix, i.e., χ µ |χ ν = S µν = δ µν (8) then the operatorχ − ν = (χ + ν ) † is only formally an annihilation operator, because its anticommutator with the creation operatorχ + µ is not δ µν as it were the case for an orthonormalized basis, but…”

Section: The "Mixed" Second Quantization Formalismmentioning

confidence: 99%

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 Some properties of the bond order indices are discussed and the author's (until now unpublished) proof is also presented, showing the sufficient conditions under which the bond order index of a homonuclear diatomics is equal to the "chemist's bond order,"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: The "Mixed" Second Quantization Formalismmentioning

confidence: 99%

Bond order and valence indices: A personal account

2006

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“…A similar description follows [1][2][3] from the Wiberg-type bond-multiplicities formulated in the MO theory [4,[14][15][16][17][18][19][20][21][22][23]. In MO description the chemical interaction between, say, two (valence) AO or general basis functions originating from different atoms is strongly influenced by their direct overlap and interaction, which both condition the bonding effect experienced by electrons occupying their bonding combination in the molecule, compared to the non-bonding reference of electrons on separated AO.…”

Section: R F Nalewajski (B)mentioning

confidence: 99%

Chemical bonds from through-bridge orbital communications in prototype molecular systems

Nalewajski

2010

J Math Chem

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The indirect components of chemical interactions between atomic orbitals are explored within the Orbital Communication Theory of the chemical bond. The conditional probabilities for such through-bridge probability propagation and the associated entropy/information measures of the bond covalency are examined. The illustrative example of the bridge components of the chemical bonds between bridgehead carbons in small propellanes is discussed using the hybrid-orbital model. The bridge π -bonds in benzene and butadiene from the inter-orbital communications involving the single intermediate atomic orbitals are probed within the Hückel description and selected higher-orders of orbital bridges, involving several orbital intermediaries, are investigated.

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“…Because of immense debt which chemistry owes to the classical model of molecule as composed of directionally oriented and well localized chemical bonds, it is not surprising that a lot of effort was and still is devoted to its reconciliation with the quantum mechanical description in terms of delocalized wave functions. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] One of the promising procedures which indeed seem to provide the desired link between the classical and quantum chemical description of chemical bonding is the approach based on the so-called electron localization function (ELF). [19][20][21][22] This function allows the unique partitioning of the molecule into disjunct domains, which indeed are reminiscent of classical chemical bonds.…”

Section: Introductionmentioning

confidence: 99%

Electron pairing and chemical bonds: Pair localization in ELF domains from the analysis of domain averaged Fermi holes

Ponec

Chaves

2006

J Comput Chem

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This article reports the application of a recently proposed formalism of domain averaged Fermi holes to the problem of the localization of electron pairs in electron localization function (ELF) domains and its possible implications for the electron pair model of chemical bond. The main focus was on the systems, such as H 2 O or N 2 , in which the ''unphysical'' population of ELF domains makes the parallel between these domains and chemical bond questionable. On the basis of the results of the Fermi-hole analysis, we propose that the above problems could be due to the fact that in some cases the boundaries of the ELF domains need not be determined precisely enough.

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Valency. I. A quantum chemical definition and properties

Cited by 61 publications

References 9 publications

Bond order and valence indices: A personal account

Bond order and valence indices: A personal account

Chemical bonds from through-bridge orbital communications in prototype molecular systems

Electron pairing and chemical bonds: Pair localization in ELF domains from the analysis of domain averaged Fermi holes

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