Charge, bond order and valence in the AB initio SCF theory

Mayer, I.

doi:10.1016/0009-2614(83)80005-0

Cited by 2,014 publications

(1,034 citation statements)

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“…Then, as it is easy to see, (12) which means that the annihilation operatorφ − ν defined with respect to the biorthogonal basis of spin-orbitals is that operator which acts in the nonorthogonal case exactly in the same manner as the usual annihilation operators do in the orthogonal case. Note that we invoke the biorthogonal basis {ϕ ν } only to define the true annihilation operatorsφ − ν corresponding to the creation operatorsχ + µ in the nonorthogonal case, and no other reference to the biorthogonal basis is necessary.…”

Section: The "Mixed" Second Quantization Formalismmentioning

confidence: 99%

“…In my previous papers 10,12 I had given two independent proofs (one for the single determinant wave functions, another-see Appendix A-for the general case) for the expectation value of the operator stringχ…”

Section: The Operator Of Atomic Populationmentioning

confidence: 99%

“…(There is a full analogy also in the sense that the CNDO energy partitioning mentioned in the work of Fischer and Kollmar 18 also exhibits an exchange energy component proportional to the Wiberg index. 12 ) Thus I had arrived at the definition of the ab initio bond order index in terms of spin-orbitals:…”

Section: Expectation Value Ofĥ Point Ab and The Bond Order Indexmentioning

confidence: 99%

“…After publication of my paper, 12 I got a letter from Ms. Giambiagi (Rio de Janeiro) with a copy of their paper 19 in which essentially the same definition (46) was proposed for the "all valence electron" semiempirical theories with overlap (practically extended Hückel) as a formal generalization of the Wiberg index. Their paperprobably because of the use of unusual and rather cumbersome notations and too lapidary a presentation-did not receive the proper attention in the literature.…”

Section: Expectation Value Ofĥ Point Ab and The Bond Order Indexmentioning

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: The "Mixed" Second Quantization Formalismmentioning

confidence: 99%

Section: The Operator Of Atomic Populationmentioning

confidence: 99%

Section: Expectation Value Ofĥ Point Ab and The Bond Order Indexmentioning

confidence: 99%

Section: Expectation Value Ofĥ Point Ab and The Bond Order Indexmentioning

confidence: 99%

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Bond order and valence indices: A personal account

2006

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“…Atomic charges and bond order indices were obtained from the generalized MP2 density matrix in GAMESS. [27][28][29] …”

Section: Methodsmentioning

confidence: 99%

Computational Study of Sulfur Atom-Transfer Reactions from Thiiranes to ER₃(E = As, P; R = CH₃, Ph)

2005

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Computational estimates have been made for the PS and AsS bond strengths in triphenylphosphine sulfide and triphenylarsine sulfide, on the basis of G3 calculations for the methyl analogues and isodesmic-exchange reactions. Also, with the performance of the G3 method level for related compounds taken into consideration, the best estimates are 82 and 68 kcal/mol, respectively. While the value for triphenylarsine sulfide is within 2 kcal/mol of the single experimental estimate, that for triphenylphosphine sulfide is lower by 6 kcal/mol. Computational estimates have been made for the PdS and AsdS bond strengths in triphenylphosphine sulfide and triphenylarsine sulfide, on the basis of G3 calculations for the methyl analogues and isodesmic-exchange reactions. Also, with the performance of the G3 method level for related compounds taken into consideration, the best estimates are 82 and 68 kcal/mol, respectively. While the value for triphenylarsine sulfide is within 2 kcal/mol of the single experimental estimate, that for triphenylphosphine sulfide is lower by 6 kcal/mol. (Capps, K. B.; Wixmerten, B.; Bauer, A.; Hoff, C. D. Inorg. Chem. 1998, 37, 2861−2864.) Despite virtually identical electronegativities of P and As, it is found that there is greater charge separation in the PdS bond. It is found that S atom transfer from thiiranes to arsines is exothermic.

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