Electronegativity Equalization Principle Research Articles

A closer look to the bispericyclic transition structure leading to 4 + 2 and 2 + 4 cycloadducts in the endo dimerization of cyclopentadiene

AbstractThis work delves into the study presented by Caramella and co‐workers (J. Am. Chem. Soc. 2002, 124, 7) on the cyclopentadiene dimerization. We have reperformed the calculations of this work using updated methodologies, obtaining the structures of the reactants and transition states, as well as new energy profiles. Additionally, we have obtained new insights that were not included in the previous work, such as bond structures from NBO analysis, QTAIM theory, and spin density. Reactivity indices of the principal NBOs responsible for the reaction have also been obtained using a recently developed model based on conceptual DFT and Sanderson's principle of electronegativity equalization and the new results obtained have allowed us to propose reaction mechanisms that satisfactorily justify all reaction stages. This work is a study of the mechanism of the cyclopentadiene dimerization reaction, but it is also an example of applying the new model for calculating reactivity indices for NBOs. Additionally, it demonstrates the combined use of these descriptors with other types of analyses that also employ NBOs or provide a description of the molecular bonding structure. As shown in this work, the collective use of all these methodologies generally provides an adequate description of the chemical reactivity of the studied processes.

Local reactivity descriptors of the important atoms in chelotropic reactions provide insight into their global variants along the reaction path

AbstractChelotropic reactions are widely used in organic synthesis. These reactions are of the pericyclic type where a π bond and a lone pair are transformed into a pair of sigma bonds; with both sigma bonds added to the same atom. This work presents an analysis of several representative chelotropic reactions. To study the reaction path, we have divided it into two parts, from the reactants to the transition state and from the transition state to the products which has allowed us to compare the behavior of the reactants in these two ranges of the path. To perform the analysis, global reactivity descriptors based on the conceptual‐density functional theory (DFT), such as electrophilicity and global softness, have been calculated. To analyze these descriptors, the corresponding local descriptors have been used. A model based on Sanderson's principle (electronegativity equalization principle), developed previously, has been used to calculate the local reactivity descriptors (atomic). The statistical methodology of multiple regression analysis has been used to determine which local variables are the most relevant for the global parameter under study (softness, and electrophilicity), also the principal component analysis has been used as a guide to estimate the number of variables to take into account in the analysis, finally this has led us to important correlations between global and local parameters which has allowed us to analyze the reactions of the study. Transition states of the reactions are aromatic as obtained from the nucleus independent chemical shift (NICS) and gauge including magnetically induced ring current (GIMIC) analysis.

Theoretical Base of Pseudo Chemical Potential (PCP) Method

Pseudo chemical potential (PCP) method is a novel one based on the thermodynamic formalization, and the purpose of this work is to clarify theoretical base of PCP method and to perfect PCP method into a novel method for molecular calculation. Therefore, it is very important to clarify validity of thermodynamic formalization that becomes principle and methodology of this method for achievement of its purpose. The thermodynamic formalization in molecular calculation is to achieve molecular calculation by using principle and methodology of thermodynamics. In order to apply the method of thermodynamic formalization in molecular calculation, it must be clarified that molecule (atom) electron system, computational object of PCP method, can be considered to be “thermodynamic system”. In this paper, we have clarified the temperature zero limit (TZL) state of a finite temperature thermal equilibrium system, as physical base of the pseudo chemical potential (PCP) method, having thermodynamic properties and therefore being the research object of thermodynamic formalism. Furthermore, we have proved an existence of energy minimization principle, as the theoretical base of PCP method, and from it derived the variation equation and defined the electron charge distribution equation, and on the basis of it analyzed theoretically the electronegativity equalization principle. Resultantly, herein we have demonstrated theoretical validity of PCP method, as a novel method for calculation of molecular energies and charge distributions.

An FSGO based Electronegativity Scale invoking the Electrophilicity Index

AbstractElectronegativity is an important chemical construct that plays a pivotal role to explain several chemical, biochemical and physicochemical phenomena. The study of this periodic descriptor is still considered an active domain of research, and a number of scientists are involved to propose different scales of electronegativity based on experimental findings and theoretical concepts. In this study, we have proposed a model to compute atomic electronegativity values of 103 elements based on the Floating Spherical Gaussian Orbital approach invoking the atomic electrophilicity index as a descriptor. The computed electronegativity scale observes the periodic trend and justifies many chemical phenomena. Molecular electronegativity values have also been computed using the computed atomic electronegativity data and utilized to justify the Electronegativity Equalization Principle. In order to validate our proposed model, internuclear bond distances for some molecules have been deduced in terms of our computed atomic electronegativity data. A strong correlation with experimental counterparts proves the efficacy of our proposed model.

From Density Functional Theory to Conceptual Density Functional Theory and Biosystems.

The position of conceptual density functional theory (CDFT) in the history of density functional theory (DFT) is sketched followed by a chronological report on the introduction of the various DFT descriptors such as the electronegativity, hardness, softness, Fukui function, local version of softness and hardness, dual descriptor, linear response function, and softness kernel. Through a perturbational approach they can all be characterized as response functions, reflecting the intrinsic reactivity of an atom or molecule upon perturbation by a different system, including recent extensions by external fields. Derived descriptors such as the electrophilicity or generalized philicity, derived from the nature of the energy vs. N behavior, complete this picture. These descriptors can be used as such or in the context of principles such as Sanderson’s electronegativity equalization principle, Pearson’s hard and soft acids and bases principle, the maximum hardness, and more recently, the minimum electrophilicity principle. CDFT has known an ever-growing use in various subdisciplines of chemistry: from organic to inorganic chemistry, from polymer to materials chemistry, and from catalysis to nanotechnology. The increasing size of the systems under study has been coped with thanks to methodological evolutions but also through the impressive evolution in software and hardware. In this flow, biosystems entered the application portfolio in the past twenty years with studies varying (among others) from enzymatic catalysis to biological activity and/or the toxicity of organic molecules and to computational peptidology. On the basis of this evolution, one can expect that “the best is yet to come”.

Introducing a new model based on electronegativity equalization principle for the analysis of the natural bond orbital reactivity in the c‐DFT background

AbstractPrevious studies presented two independent models based on the equalization of electronegativity and on an alternative operative formula for the Fukui function. The current paper presents modifications to these models to obtain a new model for calculating the local energy derivatives (electronic chemical potential, local electronic hardness and local hypersoftness) and density (Fukui and dual descriptor indices) in natural bond orbitals for the study of chemical reactivity from the perspective of these orbitals (local electrophilicity and local maximum charge variation have also been deduced). We have radically changed the way of partitioning the electron density because the atomic model cannot distinguish between bonding and non‐bonding electron pairs, or between electrons with different types of bonds, however, this is possible with the model based on bond orbitals. In this respect, this model is ideal for organic reactions because of their correspondence with Lewis structures, which are simple but very useful for representing reaction mechanisms.

Structural and Compositional Characteristics of Ball-Milled Lepidocrocite Alkali Titanate and the Correlation to Its Surface Acidic-Basic Properties.

The studies on mechanical treatments of layered alkali metal oxides are limited despite their diverse compositions/structures and potential for property tuning. In this work, we vibratory mill Cs0.7Zn0.35Ti1.65O4, K0.8Zn0.4Ti1.6O4, and Cs2Ti6O13 for up to 4 h, during which the lepidocrocite-type structure and the plate-like morphology are well preserved. X-ray diffraction (XRD) indicates a tiny (≤0.6 Å) interlayer expansion accompanied by the enhancement of the preferred orientation along the stacking direction. Chemical analyses across multiple length scales suggest Cs deintercalation, elemental redistributions, and bulk-to-surface (or crystal edge) Cs migration. This ball-milling-induced Cs-rich moiety partially blocks the surface acid sites, although the solids still show a dominating acidic character. The ball-milled samples Cs0.7-pZn0.35-qTi1.65O4-δ contain vacancies between the sheets (p) and at the sheets (q and δ). It is deduced from Sanderson's electronegativity equalization principle and experimentally verified by X-ray photoelectron spectroscopy (XPS) that ball milling increases (decreases) the partial charge at the surface acidic Ti4+/Zn2+ (basic O2-) sites. These nonporous solids (≤20 m2·g-1) contain water sorbed on the external surface as high as 1.1 mol·mol-1, which is comparable to that in a water-intercalated sample. Our work expands the current understanding of the reactivity vs robustness in layered alkali titanates under physically demanding conditions, complementing knowledge gathered via the soft chemistry approach.

A Scale of Atomic Electronegativity Based on Floating Spherical Gaussian Orbital Approach

AbstractElectronegativity (χ) is an old yet valuable concept having multidisciplinary applications. To advance the understanding of this concept, an electronegativity model has been proposed based on polarizability within the context of Floating Spherical Gaussian Orbital (FSGO) approach. The model provides atomic electronegativity scale for 120 elements. The calculated electronegativity presents marked periodicity and relates well with other electronegativity scales. Further, Electronegativity Equalization Principle is validated by the computed electronegativity data. The proposed scale has also been successfully applied to compute Fermi energy for some metal oxides. In accordance with the literature, this is the first FSGO‐polarizability based model of electronegativity.

Neutron Diffraction Study of Significant sp3 and sp2 C-H Bond Shortening in a Fluorinated Pyridinium Saccharinate.

We have experimentally shown by neutron diffraction significant shortening of both sp3- and sp2-hybridized C-H bonds to 1.092(2) and 1.081(1) Å in a hydrogen-bonded crystal of a difluorinated compound, 4-((2,2-difluoroethoxy)methyl)pyridinium saccharinate. Both MP2 and DFT calculations affirmed the C-H bond shrinkages. Sanderson's electronegativity equalization principle provides insight into the shortening of the C-H covalent bond lengths for both sp3- and sp2-hybridized carbon atoms. To the best of our knowledge, this neutron diffraction study has revealed the largest extents of sp3 and sp2 C-H bond shrinkages with a 3-sigma rule being satisfied.

Theorems and rules connecting bond energy and bond order with electronegativity equalization and hardness maximization

Bond orders are attributed a new role in rationalizing the electronegativity equalization (ENE) and maximum hardness (MH) rules. The following rules and theorems are formulated for chemical species (atoms, groups, molecules), X, Y, XY, their ionization energies, I, electron affinities, A, electronegativity, χ = ½(I + A), and chemical hardness, η = ½ (I − A). Rule 1 Sanderson’s principle of electronegativity equalization is supported (individual deviations < 10%) by association reactions, X + Y → XY, if the ionic bond dissociation energies are equal, D (XY+) = D (XY−), or, equivalently, if the relative bond orders are equal, BOrel (XY+) = BOrel (XY−). Rule 2 Sanderson’s principle of electronegativity equalization is supported (individual deviations < 10%) by association reactions, X + Y → XY, if the formal bond orders, FBO, of the ions are equal, FBO (XY+) = FBO (XY−). Theorem 1 The electronegativity is not equalized by association reactions, X + Y → XY, if the formal bond orders of the ions differ, FBO (XY+) − FBO (XY−) ≠ 0. Theorem 2 The chemical hardness is increased by nonpolar bond formation, 2X → X2, if (and for atomic X: if and only if) the sum BOrel (X2+) + BOrel (X2−) < 2. Rule 3 The chemical hardness is decreased, thus the “maximum hardness principle” violated by association reactions, X + Y → XY, if (but not only if) BOrel (XY+) + BOrel (XY−) > 2. The theorems are proved, and the rules corroborated with the help of elementary thermochemical cycles according to the first law of thermodynamics. They place new conditions on the “structural principles” ENE and MH. The performances of different electronegativities and hardness scales are compared with respect to ENE and MH. The scales based on valence-state energies perform consistently better than scales based on ground-state energies. The present work provides the explanation for the order of magnitude better performance of valence-state ENE compared to that of the ground-state ENE. We here show by a new approach that the combination of several fuzzy concepts clarifies the situation and helps in defining the range of validity of rules and principles derived from such concepts.

Generalized Stress-Redox Equivalence: A Chemical Link between Pressure and Electronegativity in Inorganic Crystals.

The crystal structure of many inorganic compounds can be understood as a metallic matrix playing the role of a host lattice in which the nonmetallic atomic constituents are located, the Anions in Metallic Matrices (AMM) model stated. The power and utility of this model lie in its capacity to anticipate the actual positions of the guest atoms in inorganic crystals using only the information known from the metal lattice structure. As a pertinent test-bed for the AMM model, we choose a set of common metallic phases along with other nonconventional or more complex structures (face-centered cubic (fcc) and simple cubic Ca, CsCl-type BaSn, hP4-K, and fcc-Na) and perform density functional theory electronic structure calculations. Our topological analysis of the chemical pressure (CP) scalar field, easily derived from these standard first-principles electronic computations, reveals that CP minima appear just at the precise positions of the nonmetallic elements in typical inorganic crystals presenting the above metallic subarrays: CaF2, rock-salt and CsCl-type phases of CaX (X = O, S, Se, Te), BaSnO3, K2S, and NaX (X = F, Cl, Br, I). A theoretical basis for this correlation is provided by exploring the equivalence between hydrostatic pressure and the oxidation (or reduction) effect induced by the nonmetallic element on the metal structure. Indeed, our CP analysis leads us to propose a generalized stress-redox equivalence that is able to account for the two main observed phenomena in solid inorganic compounds upon crystal formation: (i) the expansion or contraction experienced by the metal structure after hosting the nonmetallic element while its topology is maintained and (ii) the increasing or decreasing of the effective charge associated with the anions in inorganic compounds with respect to the charge already present in the interstices of the metal network. We demonstrate that a rational explanation of this rich behavior is provided by means of Pearson-Parr's electronegativity equalization principle.

Unconventional Look at the Diameters of Quantum Systems: Could the Characteristic Atomic Radius Be Interpreted as a Reactivity Measure?

Decoding of atomic and ionic radii of transition metals in terms of energy response against changes in electron number and external potential variation has been considered. Energy as a functional of electron density by means of its derivatives is linked to response density and the electron detachment process. Employing charge sensitivity analysis and the electronegativity equalization principle, we interpret the electronic structure transformations (electron-following/preceding perspectives) into atomic diameters. Additionally, qualitative associations described within hard/soft acid/base theory and the approximate correlations of respective conceptual density functional theory reactivity descriptors were considered to meet postulates of the correspondence principle, giving the characteristic radius the attribute of latent variable related to quantum mechanical observables. By means of local density approximation, an insight from statistical analysis of frontier electron density complements the picture of...

Comments on Electronegativity Equalization with Pauling Units

Objective: It is known that the electronegativities of functional groups can be significantly to used predict the reaction mechanisms and to explain inductive effects of chemical compounds. Method: Bratsch equation is one of the most important equations used to calculate the electronegativities of functional groups. Conclusion: In the present study, some important comments and contributions related to Bratsch's group electronegativity equation are presented. In addition, it is proposed that absolute electronegativity should be considered in comparison of inductive effects of functional groups. Keywords: Bratsch equation, chemical hardness, conceptual density functional theory, electronegativity, group electronegativity, sanderson's electronegativity equalization principle.

Flotation of a new chelate collector on fine refractory iron ore-containing carbonate

A suitable and efficient flotation collector at normal atmospheric temperature for Donganshan iron ore was developed. A new chelate collector W-2 was synthesized. At 30 °C, condition flotation tests on mixed magnetic concentrate of Donganshan sintering plant established the best reagent system. With the optimum reagent system, one direct flotation and one reverse flotation including one roughing, one cleaning and two scavenging stages have been conducted. After closed-circuit flotation, excellent indices were obtained with grade of siderite concentrate of 36.49%, recovery rate of 10.65%, and loss on ignition of 11.17%, and the grade of hematite concentrate reached 66.27%, with recovery rate of 78.25%, tailing grade of 16.22%, and recovery rate of 11.10%. To analyze the mechanism of action from W-2 to quartz and siderite, zeta potential and FTIR spectra were detected. Results showed that after reaction with W-2, the zeta potential of quartz and siderite evidently changed, which resulted from hydrogen bond between quartz and W-2, and a certain chemical action between siderite and W-2. In addition, the electronegativity equalization principle was used to calculate electronegativity of active adsorption sites and analysis on reagent molecular structure showed that W-2 molecule had five active adsorption sites. Results showed that the electronegativity of atoms N and O in W-2 presented a substantial increase, and the synergy of atomic sites allowed considerable enhancement of collecting ability.

The nucleophilicity equalization principle and new algorithms for the evaluation of molecular nucleophilicity

In this work, we have attempted to explore whether the nucleophilicity equalization principle can be conceived analogous to the well-established electronegativity, hardness, and electrophilicity equalization principle. Based on our new definitions of hardness and electronegativity and relying upon the geometric mean principle we proposed a new electronic structure principle, namely the nucleophilicity equalization principle. This approach provides a unified and useful procedure to calculate the nucleophilicity of molecules and groups assuming that nucleophilicity equalization principle is operative and justifiably valid. The results shown here indicate a close resemblance between theory and experiment.

Simulating an Applied Voltage in Molecular Dynamics Using Charge Optimized Many Body (COMB3) Potentials

Technological development of energy sources such as fuel cells and batteries has been enhanced by the progress of computational models and simulations used to study these electrochemical systems, more specifically, the electrode/electrolyte interface. Here, we present a methodology for applying a voltage during a dynamic charge molecular dynamics (MD) simulation. Our method is developed within the third generation charge optimized many body (COMB3) potential [1] framework and implemented in the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software package [2]. The COMB3 potential incorporates the electronegativity-equalization (EE) principle in its dynamic charge equilibration scheme. The EE principle requires the electronegativity at all atomic sites be equal, assuming fixed atomic positions. The partial charge on each atom is dynamically equilibrated by solving Euler-Lagrange equations of motion, a method developed by Rick et al. [3]. Only changes in the charge equations of motion are shown for brevity, but a complete description of the charge equilibration steps in COMB3 can be found in ref. 1. Electrode COMB3 (ECOMB3) development includes a simplistic view of varying the atomic charge equations of motion during the charge equilibration steps to simulate an applied voltage for various electrochemical systems. In ECOMB3, the mean electronegativities at the cathode and anode differ by an applied voltage, V. This electronegativity imbalance generates a new set of charge equations of motion for the anode and cathode while the electrolyte (non-electrode) equation of motion remains unchanged. Using the ECOMB3 method, we simulate an applied voltage for a system of liquid water between two Cu electrodes. The aim of these simulations is to study the differing dynamical and structural properties of water molecules at the Cu/H2O interface as opposed to molecules in the bulk. More specifically, we analyze the charge density distribution across the interface to demonstrate the practicality of using a charge transfer scheme in such a simulation. We also report density distribution profiles for atomic oxygen and hydrogen in water, indicating the ordering of molecules near the interface.

A new equation based on ionization energies and electron affinities of atoms for calculating of group electronegativity

In particular, in organic chemistry, the electronegativity of functional groups are taken into consideration significantly to predict reaction mechanism and to explain inductive effects of functional groups. In the present study, considering the relationship with charge of the electronic energy for atoms, Sanderson’s electronegativity equalization principle and Density Functional Theory (DFT), we have obtained a new equation by which group electronegativity can be calculated from ionization energies (I) and electron affinities (A) of atoms that constitute the group, where the results obtained were compared with equation of Sanderson who proposed that group electronegativity is the geometric mean of atomic electronegativities. For a large number of groups, it was found to be a very close agreement with a standard deviation of 0.12. The advantage of the present equation is that it can be used for ionic groups. In addition, the derived equation can be used to calculate Mulliken and Pauling electronegativities of molecules.

ChemInform Abstract: Recent Progress in Quantifying Substituent Effects

AbstractReview: 152 refs.

Critical Study of the Charge Transfer Parameter for the Calculation of Interaction Energy Using the Local Hard–Soft Acid–Base Principle

Local hard-soft acid-base (HSAB) principle is semiquantitative in nature due to the presence of an ad hoc charge transfer parameter. The accuracy of HSAB principle significantly depends on the definition of this ad hoc parameter. In this paper, for the first time we have introduced the second-order approximation of ΔN (ΔNsecond) as an ad hoc parameter for charge transfer to calculate interaction energies of multiple site based interactions using local hard soft acid base principle. The second-order approximation of ΔN has been derived from Sanderson's electronegativity equalization principle. To validate our approach, we have studied interaction energies of some prototype molecules. The interaction energies obtained from our approach have been further compared with the interaction energies of those obtained using other charge transfer parameters (ΔNfirst and λ) and the conventional methods. We have also discussed the advantages and limitations of the approach.

Protophilicity index and protofelicity equalization principle: new measures of Brønsted-Lowry-Lewis acid–base interactions

The simultaneous contributions of proton and electron transfer to the Brønsted-Lowry and Lewis acid-base properties of a set of p-substituted phenols are reported in this work. As a result of the analysis, a novel protophilicity index considered as the second-order energy change of a Brønsted-Lowry base as it is saturated with protons, a combined Brønsted-Lowry-Lewis acidity index (with a corresponding basicity index), and a protofelicity equalization principle (a parallel of the electronegativity equalization principle) are presented.