Revisiting the definition of local hardness and hardness kernel

A local measure of the electrophilicity has been recently proposed to analyze the chemical reactivity of several kinds of molecules. In this work a theoretical rationalization of the local extension is proposed following the quantitative definition of the molecular electrophilic power and a variational method for the distribution of the transferred charge. A condensation scheme to atoms or fragments follows from its relation to the Fukui function and the local softness. Differences between these quantities are discussed and they are tested in a model system. The analysis shows that the local electrophilicity is more appropriate to describe differences among a set of substituted molecules.

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Reply to the ‘Comment on “Revisiting the definition of local hardness and hardness kernel”’ by C. Morell, F. Guégan, W. Lamine, and H. Chermette, Phys. Chem. Chem. Phys., 2018, 20, DOI: 10.1039/C7CP04100D

Physical Chemistry Chemical Physics ◽

10.1039/c7cp07974e ◽

2018 ◽

Vol 20 (13) ◽

pp. 9011-9014 ◽

Cited By ~ 3

Author(s):

Marco Franco-Pérez ◽

Carlos A. Polanco-Ramírez ◽

José L. Gázquez ◽

Paul W. Ayers

Keyword(s):

General Procedure ◽

Chem Phys ◽

Chain Rule ◽

Local Hardness ◽

Functional Derivatives ◽

Non Local ◽

Definition Of ◽

Phys Chem Chem Phys

Starting from the chain rule for functional derivatives we develop a general procedure to define the local and non-local counterparts of a global reactivity indicator.

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Comment on “Revisiting the definition of local hardness and hardness kernel” by C. A. Polanco-Ramirez, M. Franco-Pérez, J. Carmona-Espíndola, J. L. Gázquez and P. W. Ayers, Phys. Chem. Chem. Phys., 2017, 19, 12355

Physical Chemistry Chemical Physics ◽

10.1039/c7cp04100d ◽

2018 ◽

Vol 20 (13) ◽

pp. 9006-9010 ◽

Cited By ~ 2

Author(s):

F. Guégan ◽

W. Lamine ◽

H. Chermette ◽

C. Morell

Keyword(s):

Taylor Expansion ◽

Chem Phys ◽

Local Hardness ◽

Definition Of ◽

Phys Chem Chem Phys

In this comment we show that the derivation proposed Polanco-Ramirez et al. appears naturally in the Taylor expansion of the energy, showing that their whole construction is not artificially built.

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An information-theoretic resolution of the ambiguity in the local hardness

Physical Chemistry Chemical Physics ◽

10.1039/c3cp52906a ◽

2014 ◽

Vol 16 (13) ◽

pp. 6019-6026 ◽

Cited By ~ 20

Author(s):

Farnaz Heidar Zadeh ◽

Patricio Fuentealba ◽

Carlos Cárdenas ◽

Paul W. Ayers

Keyword(s):

Information Theory ◽

Acid Base ◽

Information Theoretic ◽

Local Hardness ◽

Definition Of ◽

Soft Acid

A definition of the local hardness, suitable for application in the local hard/soft acid/base principle, is derived by applying information theory.

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Introductory paper

Symposium - International Astronomical Union ◽

10.1017/s0074180900053031 ◽

1966 ◽

Vol 24 ◽

pp. 3-5

Author(s):

W. W. Morgan

Keyword(s):

Line Intensity ◽

Classification Scheme ◽

Two Dimensional ◽

Spectral Classification ◽

Dimensional Array ◽

Rr Lyrae ◽

Metallic Line ◽

Introductory Paper ◽

Parameter Varying ◽

Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

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2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

International Astronomical Union Colloquium ◽

10.1017/s0252921100050867 ◽

1975 ◽

Vol 26 ◽

pp. 21-26

Keyword(s):

Coordinate System ◽

Working Group ◽

General Character ◽

Coordinate Systems ◽

Reference Coordinate System ◽

Group 2 ◽

Definition Of ◽

Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

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Symbiotic Stars at Optical, Infrared and Radio Wavelengths

International Astronomical Union Colloquium ◽

10.1017/s025292110007336x ◽

1979 ◽

Vol 46 ◽

pp. 125-149 ◽

Cited By ~ 3

Author(s):

David A. Allen

Keyword(s):

Temperature Regime ◽

Type Star ◽

Stellar Systems ◽

Symbiotic Stars ◽

Lower Excitation ◽

Definition Of ◽

Original Type

No paper of this nature should begin without a definition of symbiotic stars. It was Paul Merrill who, borrowing on his botanical background, coined the termsymbioticto describe apparently single stellar systems which combine the TiO absorption of M giants (temperature regime ≲ 3500 K) with He II emission (temperature regime ≳ 100,000 K). He and Milton Humason had in 1932 first drawn attention to three such stars: AX Per, CI Cyg and RW Hya. At the conclusion of the Mount Wilson Ha emission survey nearly a dozen had been identified, and Z And had become their type star. The numbers slowly grew, as much because the definition widened to include lower-excitation specimens as because new examples of the original type were found. In 1970 Wackerling listed 30; this was the last compendium of symbiotic stars published.

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Immunoferritin localization of intracellular antigens in positively stained frozen sections

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010008170x ◽

1978 ◽

Vol 36 (2) ◽

pp. 168-169

Author(s):

K. T. Tokuyasu

Keyword(s):

Surface Tension ◽

Water Surface ◽

Thin Layers ◽

The Other ◽

Positive Staining ◽

Frozen Sections ◽

The Past ◽

Ultrathin Frozen Sections ◽

Definition Of

During the past investigations of immunoferritin localization of intracellular antigens in ultrathin frozen sections, we found that the degree of negative staining required to delineate u1trastructural details was often too dense for the recognition of ferritin particles. The quality of positive staining of ultrathin frozen sections, on the other hand, has generally been far inferior to that attainable in conventional plastic embedded sections, particularly in the definition of membranes. As we discussed before, a main cause of this difficulty seemed to be the vulnerability of frozen sections to the damaging effects of air-water surface tension at the time of drying of the sections.Indeed, we found that the quality of positive staining is greatly improved when positively stained frozen sections are protected against the effects of surface tension by embedding them in thin layers of mechanically stable materials at the time of drying (unpublished).

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Initial Polymerization Sites Indicated During Mitochondrial Oxidation of Diaminobenzidine after Toluene Treatment

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100079498 ◽

1977 ◽

Vol 35 ◽

pp. 408-409

Author(s):

W. A. Shannon ◽

M. A. Matlib

Keyword(s):

Membrane Permeability ◽

Cytochrome Oxidase ◽

Rat Liver ◽

Precise Definition ◽

Cytochemical Localization ◽

Oxidative Reaction ◽

Mitochondrial Oxidation ◽

Definition Of ◽

Exogenous Substrates

Numerous studies have dealt with the cytochemical localization of cytochrome oxidase via cytochrome c. More recent studies have dealt with indicating initial foci of this reaction by altering incubation pH (1) or postosmication procedure (2,3). The following study is an attempt to locate such foci by altering membrane permeability. It is thought that such alterations within the limits of maintaining morphological integrity of the membranes will ease the entry of exogenous substrates resulting in a much quicker oxidation and subsequently a more precise definition of the oxidative reaction.The diaminobenzidine (DAB) method of Seligman et al. (4) was used. Minced pieces of rat liver were incubated for 1 hr following toluene treatment (5,6). Experimental variations consisted of incubating fixed or unfixed tissues treated with toluene and unfixed tissues treated with toluene and subsequently fixed.

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