Theory of the Inhomogeneous Electron Gas
Theory of the Inhomogeneous Electron Gas

Author: Stig Lundqvist

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 405

ISBN-13: 1489904158

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The theory of the inhomogeneous electron gas had its origin in the Thomas Fermi statistical theory, which is discussed in the first chapter of this book. This already leads to significant physical results for the binding energies of atomic ions, though because it leaves out shell structure the results of such a theory cannot reflect the richness of the Periodic Table. Therefore, for a long time, the earlier method proposed by Hartree, in which each electron is assigned its own personal wave function and energy, dominated atomic theory. The extension of the Hartree theory by Fock, to include exchange, had its parallel in the density description when Dirac showed how to incorporate exchange in the Thomas-Fermi theory. Considerably later, in 1951, Slater, in an important paper, showed how a result similar to but not identical with that of Dirac followed as a simplification of the Hartree-Fock method. It was Gombas and other workers who recognized that one could also incorporate electron correlation consistently into the Thomas-Fermi-Dirac theory by using uniform electron gas relations locally, and progress had been made along all these avenues by the 1950s.

Conceptual Density Functional Theory and Its Application in the Chemical Domain
Conceptual Density Functional Theory and Its Application in the Chemical Domain

Author: Nazmul Islam

Publisher: CRC Press

Published: 2018-06-13

Total Pages: 362

ISBN-13: 135136023X

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In this book, new developments based on conceptual density functional theory (CDFT) and its applications in chemistry are discussed. It also includes discussion of some applications in corrosion and conductivity and synthesis studies based on CDFT. The electronic structure principles—such as the electronegativity equalization principle, the hardness equalization principle, the electrophilicity equalization principle, and the nucleophilicity equalization principle, along studies based on these electronic structure principles—are broadly explained. In recent years some novel methodologies have been developed in the field of CDFT. These methodologies have been used to explore mutual relationships between the descriptors of CDFT, namely electronegativity, hardness, etc. The mutual relationship between the electronegativity and the hardness depend on the electronic configuration of the neutral atomic species. The volume attempts to cover almost all such methodology. Conceptual Density Function Theory and Its Application in the Chemical Domain will be an appropriate guide for research students as well as the supervisors in PhD programs. It will also be valuable resource for inorganic chemists, physical chemists, and quantum chemists. The reviews, research articles, short communications, etc., covered by this book will be appreciated by theoreticians as well as experimentalists.

Many-body Theory of a Rapidly Varying Inhomogeneous Electron Gas
Many-body Theory of a Rapidly Varying Inhomogeneous Electron Gas

Author: John William Gadzuk

Publisher:

Published: 1968

Total Pages: 100

ISBN-13:

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The case of an inhomogeneous electron gas within which the density variation is significant over a spatial range of the order of a Fermi wave-length is considered in this report. It is seen that for most systems of physical interest, this sort of non-uniformity is a result of diffraction effects. This is a fundamentally different phenomenon than can reasonably be treated by the density gradient method of Kohn for slowly varying inhomogeneous electron gases. Several sample cases are treated. The first considerations are directed towards the problem of a weak periodic potential in an interacting electron gas. The momentum-dependent self-energy is calculated for an electron propagating in the many-body medium of an electron gas plus a periodic lattice pseudo-potential. This is the equivalent of a quasi-particle energy spectrum and thus an orthogonalized plane wave energy band. It does not appear that the lattice drastically changes qualitative aspects of plane wave many-body theory. A dielectric formulation for a general inhomogeneous electron gas is presented. By introducing a new image technique, the dielectric function within the random phase approximation, which is valid in the surface region of an electron gas, is obtained. A Green's function formalism is developed for treating the static dielectric screening of a point impurity in an electron gas. The surface dielectric function is used with the impurity screening formalism to treat the problem of impurity screening in the surface region. This is an idealized model of ionic adsorption on metal surface. Screening charge densities resulting from volume polarization effects are calculated. From these results, it is seen why unjustifiable application of classical image forces in previous adsorption theories has fortunately produced reasonable results. A new method for obtaining the appropriate plasmon contribution to the electron self-energy in the surface region is developed. With these results, the electron gas surface potentials calculated by Loucks and Cutler are then improved.

Condensed Matter Theories
Condensed Matter Theories

Author: Jouko Arponen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 395

ISBN-13: 1461309719

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This book is the third volume in an approximately annual series which comprises the proceedings of the International Workshops on Condensed Matter Theories. The first of these meetings took place in 1977 in Sao Paulo, Brazil, and successive workshops have been held in Trieste, Italy (1978), Buenos Aires, Argentina (1979), Caracas, Venezuela (1980), Mexico City, Mexico (1981), St. Louis, USA (1982), Altenberg, Federal Republic of Germany (1983), Granada, Spain (1984), San Francisco, USA (1985), and Argonne, USA (1986). The present volume contains the proceedings of the Eleventh Workshop which took place in Qulu, Finland during the period 27 July - 1 August, 1987. The original motivation and the historical evolution of the series of Workshops have been amply described in the preface to the first volume in the present series. An important objective throughout has been to work against the ever-present trend for physics to fragment into increasingly narrow fields of specialisation, between which communication is difficult. The Workshops have traditionally sought to emphasise the unity of physics. By bringing together scientists working in many different areas of condensed matter theory, for the dual purpose of fostering collaborations between them and promoting the exchange of ideas between various disciplines, a common language has been exposed and developed. The Editor of the first volume in the series, F. B.

Many-Body Approach to Electronic Excitations
Many-Body Approach to Electronic Excitations

Author: Friedhelm Bechstedt

Publisher: Springer

Published: 2014-12-01

Total Pages: 596

ISBN-13: 366244593X

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The many-body-theoretical basis and applications of theoretical spectroscopy of condensed matter, e.g. crystals, nanosystems, and molecules are unified in one advanced text for readers from graduate students to active researchers in the field. The theory is developed from first principles including fully the electron-electron interaction and spin interactions. It is based on the many-body perturbation theory, a quantum-field-theoretical description, and Green's functions. The important expressions for ground states as well as electronic single-particle and pair excitations are explained. Based on single-particle and two-particle Green's functions, the Dyson and Bethe-Salpeter equations are derived. They are applied to calculate spectral and response functions. Important spectra are those which can be measured using photoemission/inverse photoemission, optical spectroscopy, and electron energy loss/inelastic X-ray spectroscopy. Important approximations are derived and discussed in the light of selected computational and experimental results. Some numerical implementations available in well-known computer codes are critically discussed. The book is divided into four parts: (i) In the first part the many-electron systems are described in the framework of the quantum-field theory. The electron spin and the spin-orbit interaction are taken into account. Sum rules are derived. (ii) The second part is mainly related to the ground state of electronic systems. The total energy is treated within the density functional theory. The most important approximations for exchange and correlation are delighted. (iii) The third part is essentially devoted to the description of charged electronic excitations such as electrons and holes. Central approximations as Hedin's GW and the T-matrix approximation are discussed.(iv) The fourth part is focused on response functions measured in optical and loss spectroscopies and neutral pair or collective excitations.

Elementary Excitations in Solids, Molecules, and Atoms
Elementary Excitations in Solids, Molecules, and Atoms

Author: Jozef T. Devreese

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 379

ISBN-13: 1468428209

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The Advanced Study Institute on 'Elementary Excitations in Solids, Molecules, and Atoms' was held at the University of Antwerp (U.I.A.) from June 18th till June 30th 1973. The In stitute was sponsored by NATO. Co-sponsors were: Agfa-Gevaert N.V. (Mortsel - Belgium), Bell Telephone Mfg. Co. (Antwerp Belgium), the National Science Foundation (Washington D.C. - U.S.A.) and the University of Antwerp (U.I.A.). A total of 120 lecturers and participants attended the Institute. Over the last few years, substantial progress has been made in the description of the elementary excitations of the elec tronic and vibrational systems and their interactions. Parallel with this, the experimentalists have obtained outstanding re sults, partly as a result of availability of coherent light sour ces from the far infrared through the visible region, and partly because of the availability of synchrotron radiation sources in the soft X-ray region. The results of today will lead to fur ther progress over the next years. It was the purpose of this NATO Advanced Study Institute to present astate of the art, namely a survey of experiment and theory.

First Principles Approaches to Spectroscopic Properties of Complex Materials
First Principles Approaches to Spectroscopic Properties of Complex Materials

Author: Cristiana Di Valentin

Publisher: Springer

Published: 2014-09-26

Total Pages: 397

ISBN-13: 3642550681

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The series Topics in Current Chemistry presents critical reviews of the present and future trends in modern chemical research. The scope of coverage is all areas of chemical science including the interfaces with related disciplines such as biology, medicine and materials science. The goal of each thematic volume is to give the non-specialist reader, whether in academia or industry, a comprehensive insight into an area where new research is emerging which is of interest to a larger scientific audience. Each review within the volume critically surveys one aspect of that topic and places it within the context of the volume as a whole. The most significant developments of the last 5 to 10 years are presented using selected examples to illustrate the principles discussed. The coverage is not intended to be an exhaustive summary of the field or include large quantities of data, but should rather be conceptual, concentrating on the methodological thinking that will allow the non-specialist reader to understand the information presented. Contributions also offer an outlook on potential future developments in the field. Review articles for the individual volumes are invited by the volume editors. Readership: research chemists at universities or in industry, graduate students.

A Trajectory Description of Quantum Processes. II. Applications
A Trajectory Description of Quantum Processes. II. Applications

Author: Ángel S. Sanz

Publisher: Springer

Published: 2013-09-13

Total Pages: 345

ISBN-13: 3642179746

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Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of "classical" concepts. Beginning as an introductory level suitable for students, this two-volume monograph presents (1) the fundamentals and (2) the applications of the trajectory description of basic quantum processes. This second volume is focussed on simple and basic applications of quantum processes such as interference and diffraction of wave packets, tunneling, diffusion and bound-state and scattering problems. The corresponding analysis is carried out within the Bohmian framework. By stressing its interpretational aspects, the book leads the reader to an alternative and complementary way to better understand the underlying quantum dynamics.