Correlation of bond metallicity measures to electronegativity for binary oxides

We have investigated alkali, alkaline‐earth, and rutile binary oxides within density functional theory (DFT) and Bader's atoms‐in‐molecules theory, focusing on properties of bond and ring critical points, and their relations to band gap and Pauling electronegativity. We find linear relations of kinetic energy density, electron density, and the gap divided by kinetic energy density at the bond critical points to the difference of Pauling electronegativities of the cation and oxygen anion. At the ring critical points of rutile compounds, we also find that some bond metallicity measures are linearly related to the difference of electronegativities. This study extends our knowledge about the relations between bond critical points, band gap, and electronegativity, but also shows for the first time a quantitative relation between quantities at the ring critical points and global properties of the compounds.     

Molecular electronegativity in density functional theory (II) --Direct calculation of group electronegativity and the atomic charges in a group

On the basis of a more precise expression of the atomic effective electronegativity deduced from the density functional theory and electronegativity equalization principle, a new scheme for calculating the group electronegativity and the atomic charges in a group is proposed and programed, and various parameters of electronegativity and hardness are given for some common atoms. Through calculation, analysis and comparison of more than one hundred groups, it is shown that the results from this scheme are reasonable and may be extended.     

原子-键电负性均衡方法参数的确定与探讨

原子-键电负性均衡方法(ABEEM)是以密度泛函理论(DFT)和电负性均衡原理为基础发展而来，它明确地考虑了化学键是不引入任何实验数据的带纯理论性和计算的方法．使用统一标准并具有代表性和全面性地选择了200多个模型分子，利用可得到较准确结构的MP2／6-31G*优化结构，心／STO-3G单点计算得到Mulliken重叠布居，再用最小二乘法拟合得到许多主族元素在分子体系中的诸原子(包括单、双和叁键等不同成键状态)和化学键的ABEEM参数．所得到的原子的价态电负性可与已提出的其他电负性标度相比拟，计算CO得到的电荷负端为C(与从头计算的结果相反)，结果与实验相符，且原子电荷的正负不完全由原子电负性决定．     

Chemistry and electronegativity

This article addresses the chemical aspects of electronegativity: (1) What is its present status in the chemical community? (2) What are the necessary chemical criteria for a quantitative definition? (3) To what extent do contemporary proposals satisfy these criteria? (4) What connection can be made between the traditional free-atom scales and an in situ electronegativity appropriate for a particular atom in a specific molecule or solid? A longstanding special feature of electronegativity has been the seeming inability to measure it in the laboratory and this aspect proves to be a key to its definition. © 1994 John Wiley & Sons, Inc.     

Molecular orbital electronegativity

The molecular orbital electronegativities of a representative set of free radicals of Be, BC, N and O have been calculated for the first time using the transition operator method within the semi-empirical CNDO LCAO MO theory. The significance of the effect of delocalization on electronegativity is discussed.     

Ab initio calculations, electronegativity equalisation and group electronegativity

A correspondence betweenab initio calculations, the principle of electronegativity equalisation and group electronegativity has been established within the framework of Mulliken population analysis. Using this we have calculated electronegativities of some 37 groups/atoms. These electronegativities show excellent linear correlation with¹ J _CC coupling constants in monosubstituted benzenes and Inamoto’si scale and a satisfactory one with Wells’ group electronegativity data. The correspondence however required a scaling of charge (obtained byab initio calculations) and a proportionality between the electronegativity of the neutral group and its hardness. It is shown that using these electronegativity values it is possible to calculate group charges in molecules where groups under consideration interact with each other through σ bond only.     

Generalization of electronegativity concept

A generalization of the original method introduced by Hinze and Jaffé for calculating the orbital electronegativities is proposed. This generalization is based on a new energy partitioning scheme within the framework of CNDO approximation and permits the orbital electronegativities to be calculated for atoms in actual valence states in which they occur in real molecules.     

Systematic formulations for electronegativity and hardness and their atomic scales within density functional softness theory

A unified Mulliken valence with Parr ground‐state electronegativity picture is presented. It provides a useful analytical tool on which the absolute hardness as well ionization potential and electron affinity functionals are based. For all these chemical reactivity indices, systematic approximate density functionals are formulated within density functional softness theory and are applied to atomic systems. For the absolute hardness, a special relationship with the new electronegativity ansatz and a particular atomic trend paralleling the absolute electron affinity are established that should complement and augment the earlier finite‐difference energetic approach. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Group electronegativity of radicals

A method for calculating the group electronegativity of a radical has been suggested. Group electronegativities of a large number of radicals were obtained by using a modified Gordy's relation and using the new group electronegativity values, the ionic character in the bonds and the percentage s-hybridization of the halogen bonding orbitals have been calculated.     

Optimized and parallelized implementation of the electronegativity equalization method and the atom-bond electronegativity equalization method

The most common way to calculate charge distribution in a molecule is ab initio quantum mechanics (QM). Some faster alternatives to QM have also been developed, the so-called "equalization methods" EEM and ABEEM, which are based on DFT. We have implemented and optimized the EEM and ABEEM methods and created the EEM SOLVER and ABEEM SOLVER programs. It has been found that the most time-consuming part of equalization methods is the reduction of the matrix belonging to the equation system generated by the method. Therefore, for both methods this part was replaced by the parallel algorithm WIRS and implemented within the PVM environment. The parallelized versions of the programs EEM SOLVER and ABEEM SOLVER showed promising results, especially on a single computer with several processors (compact PVM). The implemented programs are available through the Web page http://ncbr.chemi.muni.cz/~n19n/eem_abeem.     

On the electronegativity nonlocality paradox

The electronegativity equalization principle states that, in its ground state, the electronegativity of every component in a system is the same. A paradox then arises: molecular fragments that are very far apart must still have the same electronegativity, which seems to contradict the common assumption that spatially separated molecular species can be described independently. Density-functional theory provides the tools needed to analyze this paradox at a fundamental level, and a resolution is found from the properties of the exact Hohenberg–Kohn functional. Specifically, there is no paradox because the electronegativity is not uniquely defined for separated systems. Instead, there is an “apparent electronegativity” that preserves locality. This may have implications for the treatment of charge-transfer excited states. A model for the energy as a function of the number of electrons is also presented. This model gives some insight into the utility of the grand canonical ensemble formulation (at nonzero temperature) and, unlike most previous models, this model recovers the appropriate behavior in the limits of infinitely separated and/or weakly interacting subsystems.     

Molecular dipole moments and electronegativity

As suggested by acharge-transfer model based on Mulliken's definition of electronegativity, the dipole moments of various diatomic molecules and certain photoemission chemical shifts are shown to depend on the normalized electronegativity differences, [(x_B ? x_A)/$\text{x}$], and not simply on (x_B ? x_A).     

关于电负性均恒原理

9分子中某原子实际所具有的电负性, 可确定如下:计算结果表明, 据电负性均恒原理分子中一个键两边的基甲电负性相等, 并不是分子中所有原子的电负性都会相等.     

About the Mulliken electronegativity in DFT

In the framework of density functional theory, a new formulation of electronegativity that recovers the Mulliken definition is proposed and its reliability is checked by computing electronegativity values for a large number of elements. It is found that the obtained values, which are compared with previously proposed electronegativity scales, fulfill the main periodic criteria.     

Correlation of photosensitive electrode properties with electronegativity

The ability of semiconducting electrodes to photoelectrolyze water without any external bias is an important criterion for satisfactory conversion of solar energy to chemical energy. Here we correlate this ability with the electronegativities of the constituent atoms.     

On the pauling electronegativity scales—II

From the analysis of the electrostatic potential near the core-valence boundary in an atom, it is shown that the Pauling electronegativity scale χ_p is approximately given by the formula,

where N_v is the valence electron number and f(n) is some function of the periodic number in the periodic table. It is also shown in detail that the Pauling electronegativity scale is closely related to the Wang-Parr electronegativity scale which is determined as the negative of the chemical potential in density functional theory. Correlation between the Pauling and Mulliken electronegativities is briefly discussed.     

On the Pauling electronegativity scales—I

It is shown that the Pauling electronegativity scale χ is closely related to the electrostatic potential near the physical meaningful boundary between the core and valence regions in an atom, and is well reproduced by the relationship:

where N_ν is the valence electron number and the factor f(n) is empirically given by

n being the periodic number.     

A molecular orbital approach to electronegativity equalization

From the basic premises of Molecular orbital theory it is shown that the various electronegativity equalization theories, at present in the literature, are fundamentally the same, and are expressable in a unified theory, developed herein. General relationships are established for calculating equilibrated electronegativities, electron densities and extra ionic resonance energies. The Equalization method is related to other methods for calculating the properties of localized bonds in molecules.

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Zusammenfassung Auf der Grundlage der MO-Theorie werden die verschiedenen bekannten Theorien des ElektronegativitÄtsausgleichs im Rahmen einer Theorie dargestellt. Allgemeine Regeln zur Berechnung ausgeglichener ElektronegativitÄten, Elektronendichten und der zusÄtzlichen ionischen Resonanzenergien werden angegeben. Die Methode des ElektronegativitÄtsausgleichs wird mit anderen Methoden zur Berechnung der Eigenschaften lokalisierter Bindungen in Molekülen verknüpft.

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Résumé On montre, à partir des fondements de la théorie des orbitales moléculaires, que les diverses théories d'égalisation de l'électronégativité, qui ont actuellement cours, sont essentiellement les mÊmes et peuvent Être exprimées dans une théorie unifiée développée ci-après. Des relations générales sont établies pour calculer les électronégativités égalisées, les densités électroniques et oes énergies de résonance ionique supplémentaires. La méthode d'égalisation est reliée aux autres méthodes de calcul des propriétés des liaisons localisées dans les molécules.

     

Hammett equation and generalized Pauling's electronegativity equation

Substituent interaction energy (SIE) was defined as the energy change of the isodesmic reaction X-spacer-Y + H-spacer-H --> X-spacer-H + H-spacer-Y. It was found that this SIE followed a simple equation, SIE(X,Y) = -ksigma(X)sigma(Y), where k was a constant dependent on the system and sigma was a certain scale of electronic substituent constant. It was demonstrated that the equation was applicable to disubstituted bicyclo[2.2.2]octanes, benzenes, ethylenes, butadienes, and hexatrienes. It was also demonstrated that Hammett's equation was a derivative form of the above equation. Furthermore, it was found that when spacer = nil the above equation was mathematically the same as Pauling's electronegativity equation. Thus it was shown that Hammett's equation was a derivative form of the generalized Pauling's electronegativity equation and that a generalized Pauling's electronegativity equation could be utilized for diverse X-spacer-Y systems. In addition, the total electronic substituent effects were successfully separated into field/inductive and resonance effects in the equation SIE(X,Y) = -k(1)F(X)F(Y) - k(2)R(X)R(Y) - k(3)(F(X)R(Y) + R(X)F(Y)). The existence of the cross term (i.e., F(X)R(Y) and R(X)F(Y)) suggested that the field/inductive effect was not orthogonal to the resonance effect because the field/inductive effect from one substituent interacted with the resonance effect from the other. Further studies on multi-substituted systems suggested that the electronic substituent effects should be pairwise and additive. Hence, the SIE in a multi-substituted system could be described using the equation SIE(X1, X2, ..., Xn) = Sigma(n-1)(i=1)Sigma(n)(j=i+1)k(ij)sigma(X)isigma(X)j.     

Group electronegativity for prediction of materials hardness

We have developed a method to predict the hardness of materials containing ultrastrong anionic polyhedra, dense atomic clusters, and layers stacked through van der Waals bonds on the basis of group electronegativity. By considering these polyhedra, clusters, and layers as groups that behave as rigid unities like superatoms bonding to other atoms or groups, the hardness values of materials such as oxysalts, T-carbon, and graphite were quantitatively calculated, and the results are consistent with the available experiments. We found that the hardness of materials containing these artificial groups is determined by the bonds between the groups and other atoms or groups, rather than by the weakest bonds. This work sheds light on the nature of materials hardness and the design of novel inorganic crystal materials.