Bond orders and valences from ab initio wave functions

Mayer, I.

doi:10.1002/qua.560290320

Cited by 451 publications

(261 citation statements)

References 15 publications

(5 reference statements)

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“…It appears that the authors of ref. 35 misunderstood the message of my paper, 25 and assumed that I am proposing the use of the relationship (49) and have overlooked that I had proved there its inadequacy. Essentially the "exchange only" scheme has been rediscovered also in ref.…”

Section: Correlated Wave Functionsmentioning

confidence: 99%

“…In my opinion, the most important argument against using a bond order definition based on the relationships (49) or (68) is the fact 25 that such a definition gives the value 0.39 for Weinbaum's classical wave function for H 2 . This wave function represents the solution of the full CI problem for the minimal basis of Slatertype orbitals with optimized exponents.…”

Section: Correlated Wave Functionsmentioning

confidence: 99%

“…In one of my papers 25 I had proposed to connect bond order index with only the exchange part of the second-order density matrix which is formally constructed from the first-order density matrix exactly in the same manner as in the single determinant case. The same can be done for the simpler entity, the exchange density, used in Figure 1.…”

Section: Correlated Wave Functionsmentioning

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: Correlated Wave Functionsmentioning

confidence: 99%

Section: Correlated Wave Functionsmentioning

confidence: 99%

Section: Correlated Wave Functionsmentioning

confidence: 99%

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Bond order and valence indices: A personal account

2006

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“…Natiello and Medrano [20] extended the bond index to ab initio calculations. Mayer [21] applied the bond index to open shell SCF wavefunctions and generalized it to include correlation effects. This work emphasized the need to account for the contribution of non-classical exchange energy to bonding.…”

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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“…where q k is the resulting CM4 charge on atom k, q k 0 is the input Class II partial atomic charge, and T kk´ is a quadratic function of the Mayer bond order [44][45][46] (B kk´) :…”

Section: Theorymentioning

confidence: 99%

Charge Model 4 and Intramolecular Charge Polarization

Olson

Marenich

Cramer

et al. 2007

J. Chem. Theory Comput.

110

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Abstract. Partial atomic charges provide the most widely used model for molecular charge polarization, and Charge Model 4 (CM4) is designed to provide partial atomic charges that correspond to an accurate charge distribution, even though they may be calculated with polarized double zeta basis sets with any density functional. Here we extend CM4 to six additional basis sets, and we present a model (CM4M) that is individually optimized for the M06 suite of density functionals for ten basis sets. These charge models yield class IV partial atomic charges by mapping from those obtained with Löwdin or redistributed Löwdin population analyses of density functional electronic charge distributions.CM4M/M06-2X/6-31G(d)//M06-2X/6-31+G(d,p) partial atomic charges are calculated for ethylene, CH n Cl 4-n (n = 0 -4), benzene, nitrobenzene, phenol, and fluoromethanol and used to discuss gas-phase polarization effects.

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Bond orders and valences from ab initio wave functions

Cited by 451 publications

References 15 publications

Bond order and valence indices: A personal account

Bond order and valence indices: A personal account

Toward an experimental bond order

Charge Model 4 and Intramolecular Charge Polarization

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