Overlap populations, bond orders and valences for ‘fuzzy’ atoms

Mayer, I.; Salvador, P.

doi:10.1016/j.cplett.2003.11.048

Cited by 350 publications

(326 citation statements)

References 27 publications

Supporting

Mentioning

309

Contrasting

Order By: Relevance

“…It follows from this result that (P σ µ S µ ) 12 (P σ µ S µ ) 21 = 1 4 , and by substituting into the definition (44) we see that the orbital φ b µ contributes 1 2 to the bond order B AB if it is occupied once. (There is a common factor of 2 in the equation.)…”

Section: Bond Orders In Homonuclear Diatomicsmentioning

confidence: 84%

“…(44) or, introducing the spin-density matrix P s = P α − P β , as (47) and not as eq. (46), which is valid in the closed-shell case only (The corrections (44) and (47) had been published 20 as an "addendum" to my paper. 12 )…”

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

confidence: 99%

“…However, for basis sets of reasonably atomic nature the use of definitions eqs. (44) or (47) is clearly preferable.…”

Section: Some Properties Of the Ab Initio Bond Order Indexmentioning

confidence: 99%

“…Recently we have proposed to use Becke's weight function 43 for calculating bond order and valence indices, 44 as well as to use it in energy partitioning. 45 Becke originally proposed that function for performing effectively the numerical integrations necessary in the DFT framework.…”

Section: The Aim Casementioning

confidence: 99%

“…This is a relatively simple algebraic function, which is calculated in an iterative manner. We shall not repeat here the algorithm, which is almost easier to program 46 than to describe (see the original paper 43 and the appendix in our paper 44 ), but only mention that it satisfies requirements (87) and has the value strictly equal to 1 at the position of "own" nucleus (therefore the weight functions corresponding to all the other atoms vanish there). The nature of the atoms is introduced by the use of empirical atomic radii; actually only the ratio of the radii of atoms that are close to each other is of importance.…”

Section: The Aim Casementioning

confidence: 99%

See 4 more Smart Citations

Bond order and valence indices: A personal account

2006

View full text Add to dashboard Cite

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.

show abstract

Section: Bond Orders In Homonuclear Diatomicsmentioning

confidence: 84%