Density Functional Theory (DFT) first established it's theoretical footing in the 1960s from the framework of Hohenberg-Kohn theorems. DFT has since seen much development in evaluation techniques as well as application in solving problems in Physics, Mathematics and Chemistry.This review volume, part of the IMS Lecture Notes Series, is a collection of contributions from the September 2019 Workshop on the topic, held in the Institute for Mathematical Sciences, National University of Singapore.With contributions from prominent Mathematicians, Physicists, and Chemists, the volume is a blend of comprehensive review articles on the Mathematical and the Physicochemical aspects of DFT and shorter contributions on particular themes, including numerical implementations.The book will be a useful reference for advanced undergraduate and postgraduate students as well as researchers.

Density Functional Theory is a rapidly developing branch of many-particle physics that has found applications in atomic, molecular, solid-state and nuclear physics. This book describes the conceptual framework of density functional theory and discusses in detail the derivation of explicit functionals from first principles as well as their application to Coulomb systems. Both non-relativistic and relativistic systems are treated. The connection of density functional theory with other many-body methods is highlighted. The presentation is self-contained; the book is, thus, well suited for a graduate course on density functional theory.

Density Functional Theory (DFT) first established it's theoretical footing in the 1960s from the framework of Hohenberg-Kohn theorems. DFT has since seen much development in evaluation techniques as well as application in solving problems in Physics, Mathematics and Chemistry.This review volume, part of the IMS Lecture Notes Series, is a collection of contributions from the September 2019 Workshop on the topic, held in the Institute for Mathematical Sciences, National University of Singapore.With contributions from prominent Mathematicians, Physicists, and Chemists, the volume is a blend of comprehensive review articles on the Mathematical and the Physicochemical aspects of DFT and shorter contributions on particular themes, including numerical implementations.The book will be a useful reference for advanced undergraduate and postgraduate students as well as researchers.

Density Functional Theory (DFT) has firmly established itself as the workhorse for atomic-level simulations of condensed phases, pure or composite materials and quantum chemical systems. This work offers a rigorous and detailed introduction to the foundations of this theory, up to and including such advanced topics as orbital-dependent functionals as well as both time-dependent and relativistic DFT. Given the many ramifications of contemporary DFT, the text concentrates on the self-contained presentation of the basics of the most widely used DFT variants: this implies a thorough discussion of the corresponding existence theorems and effective single particle equations, as well as of key approximations utilized in implementations. The formal results are complemented by selected quantitative results, which primarily aim at illustrating the strengths and weaknesses of particular approaches or functionals. The structure and content of this book allow a tutorial and modular self-study approach: the reader will find that all concepts of many-body theory which are indispensable for the discussion of DFT - such as the single-particle Green's function or response functions - are introduced step by step, along with the actual DFT material. The same applies to basic notions of solid state theory, such as the Fermi surface of inhomogeneous, interacting systems. In fact, even the language of second quantization is introduced systematically in an Appendix for readers without formal training in many-body theory.

Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H. Lieb has discovered a host of inequalities that are enormously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.

Density functional methods form the basis of a diversified and very active area of present days computational atomic, molecular, solid state and even nuclear physics. A large number of computational physicists use these meth ods merely as a recipe, not reflecting too much upon their logical basis. One also observes, despite of their tremendeous success, a certain reservation in their acceptance on the part of the more theoretically oriented researchers in the above mentioned fields. On the other hand, in the seventies (Thomas Fermi theory) and in the eighties (Hohenberg-Kohn theory), density func tional concepts became subjects of mathematical physics. In 1994 a number of activities took place to celebrate the thirtieth an niversary of Hohenberg-Kohn-Sham theory. I took this an occassion to give lectures on density functional theory to senior students and postgraduates in the winter term of 1994, particularly focusing on the logical basis of the the ory. Preparing these lectures, the impression grew that, although there is a wealth of monographs and reviews in the literature devoted to density func tional theory, the focus is nearly always placed upon extending the practical applications of the theory and on the development of improved approxima tions. The logical foundadion of the theory is found somewhat scattered in the existing literature, and is not always satisfactorily presented. This situation led to the idea to prepare a printed version of the lecture notes, which resulted in the present text.

This book is a rigorous, unified account of the fundamental principles of the density-functional theory of the electronic structure of matter and its applications to atoms and molecules. Containing a detailed discussion of the chemical potential and its derivatives, it provides an understanding of the concepts of electronegativity, hardness and softness, and chemical reactivity. Both the Hohenberg-Kohn-Sham and the Levy-Lieb derivations of the basic theorems are presented, and extensive references to the literature are included. Two introductory chapters and several appendices provide all the background material necessary beyond a knowledge of elementary quantum theory. The book is intended for physicists, chemists, and advanced students in chemistry.

Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2. DFT overcomes this problem by 1) reformulating the N-body problem involving functions of 3N variables in terms of the density, a function of 3 variables, 2) approximating it by a pioneering hybrid approach which keeps important ab initio contributions and re-models the remainder in a data-driven way. This book intends to be an accessible, yet state-of-art text on DFT for graduate students and researchers in applied and computational mathematics, physics, chemistry, and materials science. It introduces and reviews the main models of DFT, covering their derivation and mathematical properties, numerical treatment, and applications.

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