I. Introduction: Conceptual vs Fundamental andComputational Aspects of DFT1793II. Fundamental and Computational Aspects of DFT 1795A. The Basics of DFT: The Hohenberg−KohnTheorems1795B. DFT as a Tool for Calculating Atomic andMolecular Properties: The Kohn−ShamEquations1796C. Electronic Chemical Potential andElectronegativity: Bridging Computational andConceptual DFT1797III. DFT-Based Concepts and Principles 1798A. General Scheme: Nalewajski’s ChargeSensitivity Analysis1798B. Concepts and Their Calculation 18001. Electronegativity and the ElectronicChemical Potential18002. Global Hardness and Softness 18023. The Electronic Fukui Function, LocalSoftness, and Softness Kernel18074. Local Hardness and Hardness Kernel 18135. The Molecular Shape FunctionsSimilarity 18146. The Nuclear Fukui Function and ItsDerivatives18167. Spin-Polarized Generalizations 18198. Solvent Effects 18209. Time Evolution of Reactivity Indices 1821C. Principles 18221. Sanderson’s Electronegativity EqualizationPrinciple18222. Pearson’s Hard and Soft Acids andBases Principle18253. The Maximum Hardness Principle 1829IV. Applications 1833A. Atoms and Functional Groups 1833B. Molecular Properties 18381. Dipole Moment, Hardness, Softness, andRelated Properties18382. Conformation 18403. Aromaticity 1840C. Reactivity 18421. Introduction 18422. Comparison of Intramolecular ReactivitySequences18443. Comparison of Intermolecular ReactivitySequences18494. Excited States 1857D. Clusters and Catalysis 1858V. Conclusions 1860VI. Glossary of Most Important Symbols andAcronyms1860VII. Acknowledgments 1861VIII. Note Added in Proof 1862IX. References 1865

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Conceptual density functional theory.

Density functional theory (DFT) is a (in principle exact) theory of electronic structure, based on the electron density distribution n(r), instead of the many-electron wave function Ψ(r1,r2,r3,...). Having been widely used for over 30 years by physicists working on the electronic structure of solids, surfaces, defects, etc., it has more recently also become popular with theoretical and computational chemists. The present article is directed at the chemical community. It aims to convey the basic concepts and breadth of applications:  the current status and trends of approximation methods (local density and generalized gradient approximations, hybrid methods) and the new light which DFT has been shedding on important concepts like electronegativity, hardness, and chemical reactivity index.

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Density Functional Theory of Electronic Structure

The theoretical description of charge distribution, and related properties, such as chemical reactivity descriptors of chemical compounds, has greatly benefited from the development of density functional theory (DFT) methods. Indeed, most concepts stemmed from DFT but, up to now, they have been used mostly within semiempirical MO methods, Hartree–Fock, or post-Hartree–Fock methods. During the last decade, however, DFT has enabled theoretical chemistry to predict accurately structures and energetics of clusters and molecules. Therefore, more attention should also now be paid to these reactivity descriptors determined directly from DFT calculations. In this work, chemical reactivity is explored in DFT through a functional Taylor expansion of energy that introduces various energy derivatives of chemical significance. This review summarizes their main features and examines the limitations of some indexes presently used for the characterization of reactivity. Also, several perspectives are given. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 129–154, 1999

Chemical reactivity indexes in density functional theory

The fundamental principles of density functional theory are applied to achieve a better understanding of various theoretical tools for describing chemical reactivity. Emphasis is given to the Fukui function, the central site reactivity index of density functional theory, which is approached through its own variational principle. A maximum hardness principle is then developed and discussed. To make contact with an earlier proof of a maximum hardness principle, changes in chemical potential are considered.

Variational Principles for Describing Chemical Reactions: The Fukui Function and Chemical Hardness Revisited

No wonder you activities are, reading will be always needed. It is not only to fulfil the duties that you need to finish in deadline time. Reading will encourage your mind and thoughts. Of course, reading will greatly develop your experiences about everything. Reading molecular biology of the gene is also a way as one of the collective books that gives many advantages. The advantages are not only for you, but for the other peoples with those meaningful benefits.

Molecular Biology of the Gene.

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Thermodynamics: Foundations and Applications

Thermionic conversion is a method for converting heat directly into electrical energy. Unlike the conventional indirect methods for generating electricity from heat sources, no intermediate form of energy is required, and no working fluid--except the flow of the electrical charges themselves--are involved in the process. And unlike other direct conversion methods, there is no need for access to natural light (as required for photocells) or special chemicals (as required for fuel cells)--there are many available sources of thermal energy that can be utilized.The phenomenon of thermionic emission has been known since the late nineteenth century, but for many decades only sporadic and disconnected efforts were made to harness it for useful work. In the past few years, however, its potential for practical application has been recognized, and much research has now been done that supports the prospect that thermionic energy conversion will find increasing utility over the coming years. The purpose of this volume--the first of two--is to summarize what is known about the process for the benefit of a wide audience of technical readers who are not familiar with its potentials as well as to serve as a reference for those already in the field. (The second volume, now in preparation, will develop the more advanced scientific aspects of the process, describe the experience with actual hardware now operational, and estimate the limits of parameters that are unlikely to be exceeded in the near future.)Volume One opens with an introductory chapter that classifies thermionic converters by type and specifies their performance characteristics. The second chapter investigates the devices on a theoretical level by analyzing the ideal performance of the simplest configuration, which consists of a heated electrode and a collector electrode connected to a heat sink, the two separated and enclosed in an evacuated or vapor-filled space, and connected externally through an electrical load.The final two chapters take up, respectively, vacuum and vapor converters. The vacuum devices considered are diode, magnetic triode, and electrostatic triode converters; the vapor devices taken up include such converter configurations as cesium diodes, low- and high-pressure diodes, cesium diodes with additives, supplemented vapor diodes, ion emission triodes, and arc triodes.

Thermionic energy conversion

A theoretical correlation is derived to account for the variation of the work function of refractory metals coated by metallic films for all degrees of coverage. This correlation is based on an extension of the concept of electronegativity to composite surfaces and use of Pauling's rule about electronegativity and dipole moment of complex molecules. A series of theoretical curves is given for different crystallographically ideal surfaces of refractory metals such as W, Mo, and Ta coated by Cs, Sr, Ba, and Th.The derived correlation is compared with available experimental data for which the experimenters specify the exact conditions under which the experiment is performed and excellent agreement between theory and experiment is established.It is shown for the first time that the maximum work function variation does not necessarily always occur either when a full monolayer is reached or at a definite fractional coverage. The exact position of the maximum variation is a function of the adsorbate and substrat...

Work Function Variation of Metals Coated by Metallic Films

(1) Introduction.-Rigorous definitions of electronegativity of atoms, neutral or ionized, and of atomic orbitals are given. The definitions are consistent with the rules of the statistics of ensembles and the quantum-mechanical picture of atomic structure. The definitions have been extended to atoms in a molecule and to atoms in a solid. The extensions, however, will be presented in future communications. The concept of electronegativity, \"the power of an atom in a molecule to attract electrons to itself,\"' has been found to be a useful tool for the correlation of a vast field of chemical knowledge and experience.2 But in spite of the great amount of literature on the subject, no rigorous definition of electronegativity has been suggested. The lack of definition has resulted in some confusion with respect to both the physical concept represented by electronegativity and the units of electronegativity.'-8 In the present communication, a free atom or a free ion is regarded as a thermodynamic system, and the electronegativity of such a system is identified with the negative of its electrochemical potential. The electrochemical potential of a component in a phase may be evaluated by means of the theory of statistical ensembles. This theory, whether related to classical or quantum mechanics, applies to thermodynamic systems of any size.9 Consequently, it is possible to find ensemble (thermodynamic) properties, such as the electrochemical potential, even of an atom representative of an ensemble of one-atom members. If the center of mass of each atom is fixed in space, both the one-atom members and the one-atom thermodynamic system representative of the ensemble may be regarded as open systems having one independent component, namely, electrons. Even when all the mechanical properties of an atom, such as the energy eigenvalues and the number of electrons, assume only discrete values, the thermodynamic properties of the one-atom system representative of the ensemble, such as the energy E and the number of electrons n, assume continuous values. Each of these properties may be expressed as a continuous function of two independent thermodynamic variables. The electrochemical potential M is defined as the partial derivative of E with respect to n at constant entropy. This derivative must be evaluated for the ensemble passing through equilibrium states because otherwise it is indeterminate. This fact in turn implies that in any calculation of ju, two independent thermodynamic variables, say, n and temperature T, must be considered even if the interest is in results at 00K. For example, if ,u is computed as the derivative mentioned above, in order to vary n at constant entropy while the ensemble

Quantum-thermodynamic definition of electronegativity.

A novel nonlinear equation of motion is proposed for quantum systems consisting of a single elementary constituent of matter. It is satisfied by pure states and by a special class of mixed states evolving unitarily. But, in general, it generates a nonunitary evolution of the state operator. It keeps the energy invariant and causes the entropy to increase with time until the system reaches a state of equilibrium or a limit cycle.

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Elias P. Gyftopoulos

Papers

Thermodynamics: Foundations and Applications

Thermionic energy conversion

Work Function Variation of Metals Coated by Metallic Films

Quantum-thermodynamic definition of electronegativity.

Quantum thermodynamics. A new equation of motion for a single constituent of matter