Electronegativity Scale Research Articles

N-dependence of electronic energies in atoms and molecules: Mulliken and exponential interpolations

The unphysical artifact of the Mulliken (parabolic) interpolation of the dependence of the electronic energy of atoms and molecules on the system average number of electrons N is identified. To remedy this shortcoming a smooth exponential interpolation between the energies of the neutral system, its cation and anion is suggested. The trends exhibited by the associated electronegativity and chemical hardness scales are examined.

Computation of the dipole moments of some heteronuclear diatomic molecules in terms of the revised electronegativity scale of Gordy

Recently, we have critically analyzed the electronegativity scale of Gordy and found that the philosophical basis of designing the scale as the electrostatic energy of attraction between the screened nucleus and the valence electron is scientifically valid. We have calculated the electronegativity of the atoms of 103 elements of the periodic table using the ansatz suggested by Gordy by carefully allaying the dimensional mismatch seemingly prevalent in previous calculations. But the electronegativity is a conundrum and occurs in mind. It is neither a physical observable nor a quantum mechanically determinable quantity and for this reason there is no bench mark to perform any validity test of any scale of electronegativity. But the concept of electronegativity has extremely useful applications in the real world. The bond energies, bond polarities and the dipole moments, force constants and the internuclear distance between the atoms of a heteronuclear diatomic molecules can only be conceived in terms of the concept of electronegativity. In this report, we have calculated the dipole moments of as many as 31 molecules of widely diverse nature starting from strongly ionic to strongly covalent type of molecules using the electronegativity values computed by us. We have performed a comparative study of computed dipole moments vis-à-vis the available experimental dipole moments of the corresponding molecules. The results demonstrate that the scale of electronegativity of Gordy can be used realistically in representing the physical descriptors like dipole moments of heteronuclear molecules.

The electronegativity scale of Allred and Rochow: revisited

A new scale of electronegativity (χ), based on the view that χ is an atomic property and electronegativity is the force exerted by the screened nucleus on an electron at the periphery of an atom, has been designed and framed. The necessary ansatz used was suggested by Allred and Rochow, χ = Force = e 2 (Z eff)/r 2 where e is the electronic charge (esu), Z eff is the effective nuclear charge and r is the absolute (most probable) radius. The electronegativity is calculated in appropriate force unit. We have posited that the absolute (most probable) and not the covalent radii should be the appropriate size descriptor in evaluating electronegativity of atoms. It has been also demonstrated that all previous calculations of electronegativities using Allred and Rochow ansatz suffer from dimension mismatch. We have computed the electronegativities of 103 elements of the periodic table in force (dynes/electron) unit by invoking the electronegativity ansatz of Allred and Rochow, using the absolute radii and effective nuclear charge of Ghosh et al. The new scale of electronegativity satisfies all the sine qua non of a scale of electronegativity.

Gordy’s electrostatic scale of electronegativity revisited

Gordy identified electronegativity of an atom with the electrostatic potential felt by one of its valence electrons and suggested an ansatz, χ = Z eff/ r cov where χ is the electronegativity, Z eff is the effective nuclear charge and r cov is the radial distance equal to atom’s single bond covalent radius. In this report we have elucidated that the use of covalent radius in evaluating the electronegativity, ( χ), of atoms through Gordy’s formula, χ = Z eff/ r cov, is not justified. Armed with this knowledge and relying upon the electronegativity equalization principle, we have argued that the most probable radius (Slater radius), and not the covalent radius, is the fundamental size descriptor of atoms in mathematical formulation of electronegativity property of atoms. We have also suggested that the electronegativity, χ, is not equal to Z eff/ r according to Gordy’s original formula rather it is proportional to Z eff/ r and the new electronegativity ansatz is χ = [ a( Z eff/ r) + b], where a and b are constants and r is the Slater (most probable) radius of atoms. We have taken care so that the electronegativity is evaluated in proper unit i.e. energy unit. We have computed the electronegativity of 103 elements of the periodic table through the new suggested ansatz and using Slater radii and effective nuclear charge computed by us. The evaluated new electronegativities are found to satisfy the sine qua non of a reasonable scale of electronegativity by exhibiting periodicity of periods and groups, and observing silicon rule and correlating many physico-chemical properties of elements. The intrinsic inertness of Hg atom is revealed in the present scale.

Scale of Element Electronegativity by Intensive Electrostatic Potential of Atomic Nucleus and Quantity of Electricity of Atomic Valence Shell

According to the relationship between gravitational potential and electrostatic potential, as well as considering the physical meaning of the contrastive mass-to-electricity (mass per unit quantity of electricity) a definition of intensive electrostatic potential of the system(the electrostatic potential per unit mass) was proposed. Our research indicates that the electronegativity of elements (XSc) varied with the intensive electrostatic potential of atomic nucleus Vic and the quantity of electricity of atomic valence shell qcj. A formula for non-dimensional synthetic electronegativity was obtained by multiple regression analysis. The correlation coefficient (R=0.9844) and test of significance (Sig.= 0.0000) showed that XSc was closely related to Vic and qcj. The average absolute error of the 77 determined elemental electronegativities was 0.084, compared with Pauling electronegativities. The electronegativity of all elements except H may be calculated conveniently and accurately with our formula, and thus it is a new method for calculating the electronegativity of ions and groups.

Acidity Scale for Metal Oxides and Sanderson's Electronegativities of Lanthanide Elements

Metal oxides are widely used in industry and academia. As their electron-acceptor or acidic strengths play vital roles in their applications, there needs to be a general scale that can quantitatively compare their relative acidic strengths. Conventionally, calorimetric heat measurements during adsorption of probe molecules, infrared spectroscopic analyses of adsorbed bases or acids, application of indicator dyes, and temperature-programmed desorption of the pre-adsorbed bases are standard methods for the analyses of their acidic strengths. However, these methods are not suitable for a quantitative comparison. Thus, unlike metal ions in solution, no such scales have been available for metal oxides. One of the important types of interaction between adsorbates and metal oxides is the formation of coordinate covalent bonding between adsorbates and the surface metal ions. For instance, in the case of TiO2, those compounds that have enediol, carboxylate, and nitrile groups have been shown to form coordinate covalent bonding with the surface Ti ions. In this type of interaction, the adsorbateto-metal charge-transfer interaction is often the lowestenergy electronic transition. However, in the case of alizarin (Figure 1a, inset) on TiO2, a theoretical study has suggested that the intramolecular charge-transfer (IMCT) band from the catechol moiety to the entire ring system is the lowestenergy transition. Electronegativity (EN) is one of the most important fundamental properties of an atom, which represents “the power of an atom in a compound to attract electrons to itself”. Among various EN scales that have been developed, Sanderson s scale and the associated EN equalization principle are successful in calculating the bond energies of various compounds , elucidating the acidic and basic properties of zeolites, and establishing the relationship between the reactivity and the composition of the zeolite that served as the guideline for the preparation of optimum zeolite catalysts. These methods have also been used for various other purposes. However, owing to a lack of experimental data, Sanderson s EN scale has not been extended to lanthanides (Ln) during the last five decades, despite the fact that lanthanide-containing compounds are widely used. Herein, we report that the IMCT transition of alizarin is still the lowest-energy transition when it is adsorbed on various metal oxides and sulfides, regardless of the nature of the metal ion. The charge-transfer transition serves as a highly sensitive and accurate probe for the quantitative comparison of the acidic strengths of the metal oxides and sulfides. We also report the factors that govern the surface acidity, which allows us to assign for the first time the important Sanderson s EN values of Ln ions (SLn3+) and Ce . To experimentally verify the IMCT nature of the lowestenergy electronic transition from the catechol moiety to the entire ring, we also synthesized 4-methoxyalizarin (Figure 1a, inset; Supporting Information, SI-1). The UV/Vis spectra of the two compounds (Figure 1a) show that the lowest-energy transition (2.856 eV) shifts to the lower energy region (2.617 eV) upon introducing a methoxy group at the 4 position; that is, upon increasing the donor strength of the catechol moiety, which verifies the IMCT nature of the transition. The IMCT bands of alizarin and 4-methoxyalizarin adsorbed on various metal oxides and sulfides are shown in Figure 1b, with the order of energy increasing from bottom to top. The IMCT bands appear at 2.322–2.713 eV for alizarin and 2.288–2.536 eV for 4-methoxyalizarin (Supporting Information, Table SI-2). The red-shift from alizarin to 4-methoxyalizarin also suggests that the lowest-energy transition of the adsorbed alizarin is IMCT. Furthermore, the IMCT bands of alizarin and 4-methoxyalizarin are red-shifted when they are adsorbed onto oxides and sulfides. Such coordination-induced redshifts were also observed in solution. The IMCT band of alizarin (2.398 eV) red-shifts upon coordinating to Mg in ethanol relative to its uncoordinated state (2.856 eV; Supporting Information, Figure SI-3). We attribute the red shift to a decrease in the degree of electron withdrawal of the two phenoxide groups as a result of the replacement of the two strongly electron-withdrawing protons by a less strongly electron-withdrawing metal cation (Figure 1d, inset). In this context, the gradual blue shift of the IMCT band of the adsorbed alizarin and 4-methoxyalizarin on going from MgO to Ta2O5 is attributed to the increase in the degree of electron withdrawal from the two phenoxide ligands to a surface metal ion in the following order: MgO<PbO<Y2O3<ZnO< ZnS<HfO2<Ga2O3<ZrO2<TiO2< SnO2<Ta2O5. The IMCT energies do not correlate with Sanderson s partial charges of the metal ions (dM) in metal oxides and sulfides (Figure 1c), which are expressed by Equation (1) for metal chalcogenides MxChy (Ch= chalcogen): [32] [*] N. C. Jeong, Dr. J. S. Lee, Dr. E. L. Tae, Y. J. Lee, Prof. Dr. K. B. Yoon Center for Microcrystal Assembly, Center for Nanoporous Materials, Department of Chemistry, and Program of Integrated Biotechnology, Sogang University, Seoul 121-742 (Korea) Fax: (+82)2-706-4269 E-mail: yoonkb@sogang.ac.kr

Bond dissociation energies from a new electronegativity scale

The bond dissociation energies of some diatomic molecules (in both covalent and ionic forms) are estimated from different formulas and using a new scale of electronegativity. The calculated bond dissociation energies are compared with those which are obtained from the other commonly used electronegativity scales such as Pauling and Allred–Rochow. The best linear correlation is observed between the obtained bond dissociation energies from new electronegativity scale and experimental data. Comparison between the corrected results, which are calculated from the linear relationship equations for different scales, shows that in both covalent and ionic bonds the new scale of electronegativity represents a better correlation with the experimental data than the others. This indicates the reliability of the obtained results from the new scale.

Electronegativities of Elements in Covalent Crystals

A new electronegativity table of elements in covalent crystals with different bonding electrons and the most common coordination numbers is suggested on the basis of covalent potentials of atoms in crystals. For a given element, the electronegativity increases with increasing number of bonding electrons and decreases with increasing coordination number. Particularly, the ionicity of a covalent bond in different environments can be well-reflected by current electronegativity values; that is, the ionicity of chemical bonds increases as the coordination number of the bonded atoms increases. We show that this electronegativity scale can be successfully applied to predict the hardness of covalent and polar covalent crystals, which will be very useful for studying various chemical and physical properties of covalent materials.

Atomic sizes and atomic properties

We examine the dependence of atomic properties on a new atomic size, rcnZ, that has been rigorously defined by the presence of an interaction without depending on the strength or nature of the interaction. We have thus related the static dielectric polarizability radius, rα, the inverse of the first ionization potential, I−1, the inverse of Pauling electronegativity scale, χ−1P and the size CR of atoms that contribute to interatomic distance involving atoms of the main group elements in the periodic table. There is a linear relationship between rcnZ and a size-dependent atomic property P of the form P = CPratom + DP, where ratom is a simple and transparent function of rcnZ and DP is simply related to the property of the hydrogen atom, except for P = I−1 when DP is a property of the occupancy of the valence s- and p-electrons. We find a strict criterion for metallicity in elements based on atomic sizes and show how this criterion can be used to account for changes in descriptions of interatomic distance for gas-phase MX compounds of metallic elements.

A New Scale of Electronegativity Based on Electrophilicity Index

By calculating the energies of neutral and different ionic forms (M2+, M+, M, M-, and M2-) of 32 elements (using B3LYP/6-311++G** level of theory) and taking energy (E) to be a Morse-like function of the number of electrons (N), the electrophilicity values (omega) are calculated for these atoms. The obtained electrophilicities show a good linearity with some commonly used electronegativity scales such as Pauling and Allred-Rochow. Using these electrophilicities, the ionicities of some diatomic molecules are calculated, which are in good agreement with the experimental data. Therefore, these electrophilicities are introduced as a new scale for atomic electronegativity, chi(omega)0. The same procedure is also performed for some simple polyatomic molecules. It is shown that the new scale successfully obeys Sanderson's electronegativity equalization principle and for those molecules which have the same number of atoms, the ratio of the change in electronegativity during the formation of a molecule from its elements to the molecular electronegativity (Delta chi/chi omega) is the same.

Bonding Study in All-Metal Clusters Containing Al4 Units

The nature of the bonding of a series of gas-phase all-metal clusters containing the Al4 unit attached to an alkaline, alkaline earth, or transition metal is investigated at the DFT level using Mulliken, quantum theory of atoms in molecules (QTAIM), and Hirshfeld iterative (Hirshfeld-I) atomic partitionings. The characterization of ionic, covalent, and metallic bonds is done by means of charge polarization and multicenter electron delocalization. This Article uses for the first time Hirshfeld-I multicenter indices as well as Hirshfeld-I based atomic energy calculations. The QTAIM charges are in line with the electronegativity scale, whereas Hirshfeld-I calculations display deviations for transition metal clusters. The Mulliken charges fail to represent the charge polarization in alkaline metal clusters. The large ionic character of Li-Al and Na-Al bonds results in weak covalent bonds. On the contrary, scarcely ionic bonds (Be-Al, Cu-Al and Zn-Al) display stronger covalent bonds. These findings are in line with the topology of the electron density. The metallic character of these clusters is reflected in large 3-, 4- and 5-center electron delocalization, which is found for all the molecular fragments using the three atomic definitions. The previously reported magnetic inactivity (based on means of magnetic ring currents) of the pi system in the Al42- cluster contrasts with its large pi electron delocalization. However, it is shown that the different results not necessary contradict each other.

Structural investigation and electronic properties of the nickel ferriteNiFe2O4: a periodic density functional theory approach

Periodic density functional theory (DFT) calculations using plane-wavebasis sets were performed in order to study the bulk of nickel ferriteNiFe2O4. The local spin density approximation (LSDA) and the generalized gradient approximation(GGA) formalism were used, and it appeared that the LSDA failed to describe themagnetic structure of this compound. However, the GGA formalism gave reliable results ingood agreement with experimental data for the lattice parameters, the electronicproperties and the bulk modulus. In addition, the calculated density of states of themetallic species d block as well as their local magnetic moments were correlated tothe crystal-field theory. Then, a charge deformation map was computed and, asexpected from the electronegativity scale, the electron excess is localized aroundoxygen atoms along the bond axes. The formation energies of metallic vacancies arein good agreement with the inverse spinel structure experimentally observed.

Molecular Structural Formulas as One-Electron Density and Hamiltonian Operators: The VIF Method Extended

The valency interaction formula (VIF) method is given a broader and more general interpretation in which these simple molecular structural formulas implicitly include all overlaps between valence atomic orbitals even for interactions not drawn in the VIF picture. This applies for VIF pictures as one-electron Hamiltonian operators as well as VIF pictures as one-electron density operators that constitute a new implementation of the VIF method simpler in its application and more accurate in its results than previous approaches. A procedure for estimating elements of the effective charge density-bond order matrix, Pmunu, from electron configurations in atoms is presented, and it is shown how these lead to loop and line constants in the VIF picture. From these structural formulas, one finds the number of singly, doubly, and unoccupied molecular orbitals, as well as the number of molecular orbitals with energy lower, equal, and higher than -1/2Eh, the negative of the hydrogen atom's ionization energy. The VIF results for water are in qualitative agreement with MP2/6311++G3df3pd, MO energy levels where the simple VIF for water presented in the earlier literature does not agree with computed energy levels. The method presented here gives the simplest accurate VIF pictures for hydrocarbons. It is shown how VIF can be used to predict thermal barriers to chemical reactions. Insertion of singlet carbene into H2 is given as an example. VIF pictures as one-electron density operators describe the ground-state multiplicities of B2, N2, and O2 molecules and as one-electron Hamiltonian operators give the correct electronegativity trend across period two. Previous implementations of VIF do not indicate singly occupied molecular orbitals directly from the pictorial VIF rules for these examples. The direct comparison between structural formulas that represent electron density and those that represent energy is supported by comparison of a simple electronegativity scale, chiD=N/n2, with well-known electronegativity scales of Pauling, Mulliken, and Allen. This scale comes from the method used to calculate Pmumu for sp3 hybridized period-two elements and is comparable to electronegativity because it has the same form as <1/r> for hydrogenic orbitals. It therefore provides a physical basis for the representation of one electron density and Hamiltonian operators by the same VIF picture.

SEMICLASSICAL ELECTRONEGATIVITY AND CHEMICAL HARDNESS

The semiclassical path integral approach is undertaken to develop new definitions and atomic scales of electronegativity and chemical hardness. The considered quantum probability amplitude up to the fourth-order expansion provides intrinsic electronegativity and chemical hardness analytical expressions in terms of principal quantum number of the concerned valence shell and of the effective atomic charge including screening effects. The present electronegativity scale strikes on different orders of magnitude down groups of the periodic table, while still satisfying the main required acceptability criteria regarding the finite difference–based scale. The actual chemical hardness scale improves the trend across periods of the periodic system, avoiding the usual irregularities within the old-fashioned energetic picture. The current quest introduces the electronegativity of an element as the power by which the frontier electrons are attracted to the center of the atom being a stability measure of the atomic system as a whole.

POTENTIAL UNUSUAL CHEMICAL BONDING IN MIXED METAL STRUCTURES OF THE 3d TRANSITION SERIES CONTAINING THE ELEMENTNi

A heuristic proposal is made in this communication that involves potentially unusual chemical bonding between the 3d transition series element Ni and the 3d transition series metals preceding it in the Periodic Table. The bonding in such mixed metal dimers, and their potential realizations as some simple three-dimensional (3D) extended structures in a one-to-one stoichiometry, as sphaelerite, rocksalt or CsCl structure-types, is proposed to include two principal components that involve either covalent or ionic contributions. Ordinary covalent contributions from a σ bond (or band) formed from overlap of singly occupied 4s atomic orbitals on each metal center are proposed to be operative in these molecules (or their extended realizations). However, in addition to this 4s–4s σ bond (band), an unprecedented transfer of a d electron from the incomplete, open 3d9subshell of the transition metal involved in the bonding that precedes Ni in the Periodic Table, into the 3d9subshell on the Ni center, which results in completion of this 3d subshell in Ni , is here implicated as a further driving force for the formation of these species. The resulting molecular and extended structures MNi , where M is a 3d transition metal preceding Ni in the Periodic Table (i.e. M = Sc , Ti , V , Cr , Mn , Fe and Co ), are therefore proposed to be bonded together by a combination of covalent and ionic forces, such that the Ni center acts as an anion of charge 1-, a so-called nickelide anion Ni-, while its counterpart is a univalent cation M+. This proposal is consistent with commonly employed electronegativity scales of chemical bonding, and with considerations of the relative orbital energies of the 3d subshells of the elements across the 3d transition series period, as well as with known trends in covalent and ionic bonding in the Periodic Table of the elements. It is also found to be in agreement with the spin multiplicities calculated in the nickel dimers MNi ( M = Sc , Ti , V , Cr , Mn , Fe and Co ) if Hund's rule is assumed to be operative.

A new set of electronegativity scale for trivalent lanthanides

A new set of electronegativity (EN) scale for all trivalent lanthanides (Ln) is proposed on the basis of effective ionic potential, from which the electron-attracting power of trivalent Ln can be well differentiated. This new scale can be used to qualitatively explain the valence stability and valence change of some typical trivalent Ln. Furthermore, the good linear relationships of the charge-transfer energy of Ln3+ and the first dehydroxylation temperature in the agardite to the current EN scale of Ln3+ show us the further reasonableness of our new EN scale. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Charge Redistribution and Phonon Entropy of Vanadium Alloys

The effects of alloying on the lattice dynamics of vanadium were investigated using inelastic neutron scattering. Phonon densities of states were obtained for bcc solid solutions of V with 3d, 4d, and 5d transition metal solutes, from which vibrational entropies of alloying were obtained. A good correlation is found between the vibrational entropy of alloying and the electronegativity of transition metal solutes across the 3d row and down columns of the periodic table. First-principles calculations on supercells matching the experimental compositions predicted a systematic charge redistribution in the nearest-neighbor shell around the solute atoms, also following the Pauling and Watson electronegativity scales. The systematic stiffening of the phonons is interpreted in terms of the modified screening properties of the electron density around the solutes.

A NEW SCALE OF ELECTRONEGATIVITY OF 54 ELEMENTS OF PERIODIC TABLE BASED ON POLARIZABILITY OF ATOMS

A polarizability (α) based new scale of electronegativity (χ) is proposed. The basic algorithm is suggested by exploiting the fact that both polarizability and electronegativity are periodic properties and they are connected by an inverse relationship. Relying upon their express behavior along the periods of the periodic table, a general and straightforward relation between χ and α is suggested as χ = m(1/α)1/3 + c, where m and c are constants. The constants m and c are evaluated by least square fitting by plotting χ vs. (1/α)1/3 for each period separately. Thereafter, the suggested equation is used to evaluate the electronegativity, χ, of 54 elements from H to Xe in terms of least square fitted m and c, and a new set of atomic polarizabilities are computed by Ghosh and Biswas. The evaluated electronegativities exhibit periodicity of groups and periods and reproduce the silicon rule and the expected trend of variation of the electronegativities of d block transition metals. The evaluated electronegativities of the present semiempirical method are quite comparable with those computed by the rigorous mathematical method of Robles and Bartolotti. The efficacy of the new scale is also tested by computing the bond energy of a number of compounds. We have proposed a new formula relating the bond energy with the electronegativity difference. The proposed relation is given by D AB - 〈D AB 〉= 3.8866Δχ + 0.0422, where 〈D AA 〉 = (D AA D BB )1/2, Δχ represents the electronegativity difference, and D AA , D BB , and D AB are the bond energies of homonuclear A–A, B–B, and hetero-nuclear A–B molecules. A comparative study of bond energies evaluated through the proposed relation, determined experimentally, and evaluated through other relations is also furnished. It is demonstrated that the proposed relation of computing the bond energy in terms of Δχ yields good bond energy values. Results demonstrate that the new polarizability based empirical scale of electronegativity is a fairly successful venture.

Surface energy of talc and chlorite: Comparison between electronegativity calculation and immersion results

The surface energies of talc and chlorite is computed using a simple model, which uses the calculation of the electrostatic energy of the crystal. It is necessary to calculate the atomic charges. We have chosen to follow Henry's model of determination of partial charges using scales of electronegativity and hardness. The results are in correct agreement with a determination of the surface energy obtained from an analysis of the heat of immersion data. Both results indicate that the surface energy of talc is lower than the surface energy of chlorite, in agreement with observed behavior of wettability. The influence of Al and Fe on this phenomenon is discussed. Surface energy of this type of solids seems to depend more strongly on the geometry of the crystal than on the type of atoms pointing out of the surface; i.e., the surface energy depends more on the physics of the system than on its chemistry.

Effect of electron-acceptor strength of zeolite on the luminescence decay rate of Ru(bpy)32+ incorporated within zeolites

We carried out time-resolved luminescence and transient absorption studies of tris(2,2'-bipyridine)ruthenium(ii) complex, Ru(bpy)3(2+) assembled in the supercages of zeolites X and Y exchanged with various alkali metal cations. The average lifetime of the luminescence decay, a measure of the photoinduced electron transfer (PET) rate, of Ru(bpy)3(2+)* was found to decrease with increasing the electron-acceptor strength of the host which is represented by the Sanderson's electronegativity scale. This result strongly suggests that the zeolite host plays the role of electron acceptor for Ru(bpy)3(2+)*. However, we could not detect Ru(bpy)3(3+) in the transient absorption spectra, most likely due to very low absorption coefficient of Ru(bpy)3(3+) and to the low efficiency of net PET. For the above observation to be made, it is essential to employ the dehydrated zeolite hosts to allow direct interaction between the guest Ru(ii) complex and the host framework. The present study demonstrates the active role of the zeolite hosts during the PET of incorporated Ru(bpy)3(2+) under the carefully controlled experimental conditions. This report demonstrates the fact that the zeolite hosts can serve as electron acceptors although in the past zeolites were shown to play the role of electron donors.