Local Density Approximations in Quantum Chemistry and Solid State Physics

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Publisher : Springer Science & Business Media
ISBN 13 : 1489921427
Total Pages : 848 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Local Density Approximations in Quantum Chemistry and Solid State Physics by : Jens Peder Dahl

Download or read book Local Density Approximations in Quantum Chemistry and Solid State Physics written by Jens Peder Dahl and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: The· simplest picture of an atom, a molecule or a solid is the picture of its distribution of charge. It is obtained by specifying the positions of the atomic nuclei and by showing how the density, p(E), of the electronic charge-cloud varies from place to place. A much more detailed picture is provided by the many-electron wavefunction. This quantity shows not only the arrangement of the electrons with respect to the nuclei, but also the arrangement of the electrons with respect to each other, and it allows the evaluation of the total energy and other properties. The many-electron wavefunction is in principle obtained by solving the many-electron Schrodinger equation for the motion of the interacting electrons under the influ ence of the nuclei, but in practice the equation is unsolvable, and it is necessary to proceed by methods of approximation. Needless to say, .such methods will as a rule depend on the complexity of the system considered.

Energy Density Functional Theory of Many-Electron Systems

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Publisher : Springer Science & Business Media
ISBN 13 : 9400919700
Total Pages : 862 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Energy Density Functional Theory of Many-Electron Systems by : Eugene S. Kryachko

Download or read book Energy Density Functional Theory of Many-Electron Systems written by Eugene S. Kryachko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 862 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quantal Density Functional Theory II

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Publisher : Springer Science & Business Media
ISBN 13 : 3540922296
Total Pages : 426 pages
Book Rating : 4.5/5 (49 download)

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Book Synopsis Quantal Density Functional Theory II by : Viraht Sahni

Download or read book Quantal Density Functional Theory II written by Viraht Sahni and published by Springer Science & Business Media. This book was released on 2009-10-16 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: In my original proposal to Springer for a book on Quantal Density Functional Theory, I had envisaged one that was as complete in its presentation as possible, describing the basic theory as well as the approximation methods and a host of applications. However,after workingon the bookforabout ?ve years, I realizedthat the goal was too ambitious, and that I would be writing for another ?ve years for it to be achieved. Fortunately,there was a natural breakin the material, and I proposed to my editor, Dr. Claus Ascheron, that we split the book into two components: the ?rst on the basic theoretical framework, and the second on approximation methods and applications. Dr. Ascheron consented, and I am thankful to him for agreeing to do so. Hence, we published Quantal Density Functional Theory in 2004, and are now publishing Quantal Density Functional Theory II: Approximation Methods and Applications. One signi?cant advantage of this, as it turns out, is that I have been able to incorporate in each volume the most recent understandings available. This volume, like the earlier one, is aimed at advanced undergraduates in physics and chemistry, graduate students and researchers in the ?eld. It is written in the same pedagogical style with details of all proofs and numerous ?gures provided to explain the physics. The book is independent of the ?rst volume and stands on its own. However, proofs given in the ?rst volume are not repeated here.

Density Functional Methods in Chemistry

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Publisher : Springer Science & Business Media
ISBN 13 : 1461231361
Total Pages : 444 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Density Functional Methods in Chemistry by : Jan K. Labanowski

Download or read book Density Functional Methods in Chemistry written by Jan K. Labanowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Predicting molecular structure and energy and explaining the nature of bonding are central goals in quantum chemistry. With this book, the editors assert that the density functional (DF) method satisfies these goals and has come into its own as an advanced method of computational chemistry. The wealth of applications presented in the book, ranging from solid state sys tems and polymers to organic and organo-metallic molecules, metallic clus ters, and biological complexes, prove that DF is becoming a widely used computational tool in chemistry. Progress in the methodology and its imple mentation documented by the contributions in this book demonstrate that DF calculations are both accurate and efficient. In fact, the results of DF calculations may pleasantly surprise many chem ists. Even the simplest approximation of DF, the local spin density method (LSD), yields molecular structures typical of ab initio correlated methods. The next level of theory, the nonlocal spin density method, predicts the energies of molecular processes within a few kcallmol or less. Like the Hartree-Fock (HF) and configuration interaction (CI) methods, the DF method is based only on fundamental physical constants. Therefore, it does not require semiempirical parameters and can be applied to any molecular system and to metallic phases. However, DF's greatest advantage is that it can be applied to much larger systems than those approachable by tradition al ab initio methods, especially when compared with correlated ab initio methods.

Advances in Quantum Chemistry

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Publisher : Academic Press
ISBN 13 : 008058246X
Total Pages : 420 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Advances in Quantum Chemistry by :

Download or read book Advances in Quantum Chemistry written by and published by Academic Press. This book was released on 1990-10-25 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Quantum Chemistry

Quantum Chemistry Approaches to Chemisorption and Heterogeneous Catalysis

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Publisher : Springer Science & Business Media
ISBN 13 : 9401728259
Total Pages : 379 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Quantum Chemistry Approaches to Chemisorption and Heterogeneous Catalysis by : F. Ruette

Download or read book Quantum Chemistry Approaches to Chemisorption and Heterogeneous Catalysis written by F. Ruette and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of "high-tech" materials in contemporary industries is deeply related to a detailed understanding of specific surface properties of catalysts which make particular reactions possible. But this understanding presupposes that there exists a body of theory capable of explaining situations not easily accessible to experimental methods and of relating experimental findings among themselves and with theoretical constructs. For these reasons, theoretical developments in surface physics and surface chemistry of transition metal compounds have been of paramount importance in promoting progress in catalysis, electronic devices, corrosion, etc. Although a great variety of spectroscopic methods for analyzing solids and surfaces at molecular scale have been introduced in recent years, nevertheless, many questions about the adsorption sites and intermediates, the effect of promoters, the poisoning of active sites, the nature of segregation of impurities, the process of surface reconstruction, the mechanisms of reactions, etc. have remained unanswered simply because of the great complexity of surface phenomena. It is in this sense that quantum mechanical method- combined with experimental data - may shed some light on the microscopic properties of new surface materials.

Ab Initio Methods in Quantum Chemistry, Volume 69, Part 2

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Publisher : John Wiley & Sons
ISBN 13 : 047014338X
Total Pages : 600 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis Ab Initio Methods in Quantum Chemistry, Volume 69, Part 2 by : K. P. Lawley

Download or read book Ab Initio Methods in Quantum Chemistry, Volume 69, Part 2 written by K. P. Lawley and published by John Wiley & Sons. This book was released on 2009-09-08 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.

Ab Initio Methods in Quantum Chemistry, Volume 67, Part 1

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Publisher : John Wiley & Sons
ISBN 13 : 0470143371
Total Pages : 568 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis Ab Initio Methods in Quantum Chemistry, Volume 67, Part 1 by : K. P. Lawley

Download or read book Ab Initio Methods in Quantum Chemistry, Volume 67, Part 1 written by K. P. Lawley and published by John Wiley & Sons. This book was released on 2009-09-08 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.

Reviews of Modern Quantum Chemistry

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Publisher : World Scientific
ISBN 13 : 9812775706
Total Pages : 1882 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Reviews of Modern Quantum Chemistry by : Kali Das Sen

Download or read book Reviews of Modern Quantum Chemistry written by Kali Das Sen and published by World Scientific. This book was released on 2002 with total page 1882 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book collects together stateOCoofOCotheOCoart reviews of diverse topics covering almost all the major areas of modern quantum chemistry. The current focus in the discipline of chemistry OCo synthesis, structure, reactivity and dynamics OCo is mainly on control . A variety of essential computational tools at the disposal of chemists have emerged from recent studies in quantum chemistry. The acceptance and application of these tools in the interfacial disciplines of the life and physical sciences continue to grow. The new era of modern quantum chemistry throws up promising potentialities for further research. Reviews of Modern Quantum Chemistry is a joint endeavor, in which renowned scientists from leading universities and research laboratories spanning 22 countries present 59 inOCodepth reviews. Along with a personal introduction written by Professor Walter Kohn, Nobel laureate (Chemistry, 1998), the articles celebrate the scientific contributions of Professor Robert G Parr on the occasion of his 80th birthday. List of Contributors: W Kohn, M Levy, R Pariser, B R Judd, E Lo, B N Plakhutin, A Savin, P Politzer, P Lane, J S Murray, A J Thakkar, S R Gadre, R F Nalewajski, K Jug, M Randic, G Del Re, U Kaldor, E Eliav, A Landau, M Ehara, M Ishida, K Toyota, H Nakatsuji, G Maroulis, A M Mebel, S Mahapatra, R CarbOCoDorca, u Nagy, I A Howard, N H March, SOCoB Liu, R G Pearson, N Watanabe, S TenOCono, S Iwata, Y Udagawa, E Valderrama, X Fradera, I Silanes, J M Ugalde, R J Boyd, E V Ludea, V V Karasiev, L Massa, T Tsuneda, K Hirao, J-M Tao, J P Perdew, O V Gritsenko, M Grning, E J Baerends, F Aparicio, J Garza, A Cedillo, M Galvin, R Vargas, E Engel, A HAck, R N Schmid, R M Dreizler, J Poater, M Sola, M Duran, J Robles, X Fradera, P K Chattaraj, A Poddar, B Maiti, A Cedillo, S Guti(r)rrezOCoOliva, P Jaque, A ToroOCoLabb(r), H Chermette, P Boulet, S Portmann, P Fuentealba, R Contreras, P Geerlings, F De Proft, R Balawender, D P Chong, A Vela, G Merino, F Kootstra, P L de Boeij, R van Leeuwen, J G Snijders, N T Maitra, K Burke, H Appel, E K U Gross, M K Harbola, H F Hameka, C A Daul, I Ciofini, A Bencini, S K Ghosh, A Tachibana, J M CabreraOCoTrujillo, F Tenorio, O Mayorga, M Cases, V Kumar, Y Kawazoe, A M KAster, P Calaminici, Z Gmez, U Reveles, J A Alonso, L M Molina, M J Lpez, F Dugue, A Maanes, C A Fahlstrom, J A Nichols, D A Dixon, P A Derosa, A G Zacarias, J M Seminario, D G Kanhere, A Vichare, S A Blundell, ZOCoY Lu, HOCoY Liu, M Elstner, WOCoT Yang, J Muoz, X Fradera, M Orozco, F J Luque, P Tarakeshwar, H M Lee, K S Kim, M Valiev, E J Bylaska, A Gramada, J H Weare, J Brickmann, M Keil, T E Exner, M Hoffmann & J Rychlewski. Contents: Volume I: Applications of the Automorphisms of SO(8) to the Atomic f Shell (B R Judd & E Lo); Probability Distributions and Valence Shells in Atoms (A Savin); Information Theoretical Approaches to Quantum Chemistry (S R Gadre); Quantum Chemical Justification for Clar''s Valence Structures (M Randic); Functional Expansion Approach in Density Functional Theory (S-B Liu); Normconserving Pseudopotentials for the Exact Exchange Functional (E Engel et al.); Volume II: Chemical Reactivity and Dynamics within a Density-based Quantum Mechanical Framework (P K Chattaraj et al.); Fukui Functions and Local Softness (H Chermette et al.); The Nuclear Fukui Function (P Geerlings et al.); Causality in Time-Dependent Density-Functional Theory (M K Harbola); Theoretical Studies of Molecular Magnetism (H F Hameka); Melting in Finite-Sized Systems (D G Kanhere et al.); Density Functional Theory (DFT) and Drug Design (M Hoffmann & J Rychlewski); and other papers. Readership: Researchers and academics in computational, physical, fullerene, industrial, polymer, solid state and theoretical/quantum chemistry; nanoscience, superconductivity & magnetic materials, surface science; atomic, computational and condensed matter physics; and thermodynamics."

Density Functional Theory of Molecules, Clusters, and Solids

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Publisher : Springer Science & Business Media
ISBN 13 : 9401104875
Total Pages : 321 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Density Functional Theory of Molecules, Clusters, and Solids by : D.E. Ellis

Download or read book Density Functional Theory of Molecules, Clusters, and Solids written by D.E. Ellis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rapid advances are taking place in the application of density functional theory (DFT) to describe complex electronic structures, to accurately treat large systems and to predict physical and chemical properties. Both theoretical content and computational methodology are developing at a pace which offers researchers new opportunities in areas such as quantum chemistry, cluster science, and solid state physics. This volume contains ten contributions by leading scientists in the field and provides an authoritative overview of the most important developments. The book focuses on the following themes: determining adequate approximations for the many-body problem of electronic correlations; how to transform these approximations into computational algorithms; applications to discover and predict properties of electronic systems; and developing the theory. For researchers in surface chemistry, catalysis, ceramics and inorganic chemistry.

Electronic Structure and Properties of Transition Metal Compounds

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Publisher : John Wiley & Sons
ISBN 13 : 0470920858
Total Pages : 658 pages
Book Rating : 4.4/5 (79 download)

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Book Synopsis Electronic Structure and Properties of Transition Metal Compounds by : Isaac B. Bersuker

Download or read book Electronic Structure and Properties of Transition Metal Compounds written by Isaac B. Bersuker and published by John Wiley & Sons. This book was released on 2010-12-01 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: With more than 40% new and revised materials, this second edition offers researchers and students in the field a comprehensive understanding of fundamental molecular properties amidst cutting-edge applications. Including ~70 Example-Boxes and summary notes, questions, exercises, problem sets, and illustrations in each chapter, this publication is also suitable for use as a textbook for advanced undergraduate and graduate students. Novel material is introduced in description of multi-orbital chemical bonding, spectroscopic and magnetic properties, methods of electronic structure calculation, and quantum-classical modeling for organometallic and metallobiochemical systems. This is an excellent reference for chemists, researchers and teachers, and advanced undergraduate and graduate students in inorganic, coordination, and organometallic chemistry.

Condensed Matter Theories

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Publisher : Springer Science & Business Media
ISBN 13 : 1461309719
Total Pages : 395 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Condensed Matter Theories by : Jouko Arponen

Download or read book Condensed Matter Theories written by Jouko Arponen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advances in Chemical Reaction Dynamics

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Publisher : Springer Science & Business Media
ISBN 13 : 9400947348
Total Pages : 608 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Advances in Chemical Reaction Dynamics by : Peter M. Rentzepis

Download or read book Advances in Chemical Reaction Dynamics written by Peter M. Rentzepis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the formal lectures and contributed papers presented at the NATO Advanced Study Institute on. the Advances in Chemical Reaction Dynamics. The meeting convened at the city of Iraklion, Crete, Greece on 25 August 1985 and continued to 7 September 1985. The material presented describes the fundamental and recent advances in experimental and theoretical aspects of, reaction dynamics. A large section is devoted to electronically excited states, ionic species, and free radicals, relevant to chemical sys tems. In addition recent advances in gas phase polymerization, formation of clusters, and energy release processes in energetic materials were presented. Selected papers deal with topics such as the dynamics of electric field effects in low polar solutions, high electric field perturbations and relaxation of dipole equilibria, correlation in picosecond/laser pulse scattering, and applications to fast reaction dynamics. Picosecond transient Raman spectroscopy which has been used for the elucidation of reaction dynamics and structural changes occurring during the course of ultrafast chemical reactions; propagation of turbulent flames and detonations in gaseous· energetic systems are also discussed in some detail. In addition a large portion of the program was devoted to current experimental and theoretical studies of the structure of the transition state as inferred from product state distributions; translational energy release in the photodissociation of aromatic molecules; intramolecu lar and intraionic dynamic processes.

Quantum Chemistry of Solids

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Publisher : Springer Science & Business Media
ISBN 13 : 3642303560
Total Pages : 745 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Quantum Chemistry of Solids by : Robert A. Evarestov

Download or read book Quantum Chemistry of Solids written by Robert A. Evarestov and published by Springer Science & Business Media. This book was released on 2013-01-19 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Chemistry of Solids delivers a comprehensive account of the main features and possibilities of LCAO methods for the first principles calculations of electronic structure of periodic systems. The first part describes the basic theory underlying the LCAO methods applied to periodic systems and the use of Hartree-Fock(HF), Density Function theory(DFT) and hybrid Hamiltonians. The translation and site symmetry consideration is included to establish connection between k-space solid –state physics and real-space quantum chemistry. The inclusion of electron correlation effects for periodic systems is considered on the basis of localized crystalline orbitals. The possibilities of LCAO methods for chemical bonding analysis in periodic systems are discussed. The second part deals with the applications of LCAO methods for calculations of bulk crystal properties, including magnetic ordering and crystal structure optimization. In the second edition two new chapters are added in the application part II of the book. Chapter 12 deals with the recent LCAO calculations and illustrates the efficiency of the scalar-relativistic LCAO method for solids, containing heavy atoms. Chapter 13 deals with the symmetry properties and the recent applications of LCAO method to inorganic nanotubes. New material is added to chapter 9 devoted to LCAO calculations of perfect-crystal properties. The possibilities of LCAO method for calculation of the high-frequency dielectric constants of crystals and the description of phase transitions in solids are discussed. The efficiency of LCAO method in the quantum-mechanics-molecular dynamics approach to the interpretation of x-ray absorption and EXAFS spectra is illustrated. A new section is devoted to recent LCAO calculations of electronic, vibrational and magnetic properties of tungstates MeWO4 (Me: Fe,Co,Ni,Cu,Zn,Cd).

Applied Quantum Chemistry

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Publisher : Springer Science & Business Media
ISBN 13 : 9400947461
Total Pages : 440 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Applied Quantum Chemistry by : Vedene H. Smith Jr.

Download or read book Applied Quantum Chemistry written by Vedene H. Smith Jr. and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the proceedings of the Nobel Laureate Symposium on Applied Quantum Chemistry held during the International Chemical Congress of Pacific Basin Societies, 16-21 December 1984, in Honolulu, Hawaii. The Symposium was held in honour of the five Nobel Laureates who have contributed so extensively to the development of Applied Quantum Chemistry. K. Fukui, G. Herzberg, R. Hoffmann, W.N. Lipscomb and R.S. Mulliken. Professors Fukui, Hoffmann and Lipscomb attended and presented plenary lectures to the Symposium. Their lectures and the other invited papers and invited poster presentations brought into focus the current state of Applied Quantum Chemistry and showed the importance of the interaction between quantum theory and experiment. We are indebted to the Subdivision of Theoretical Chemistry and the Division of Physical Chemistry of the American Chemical Society, the Division of Physical Chemistry of the Chemical Institute of Canada, Energy Conversion Devices, Inc., the IBM Corporation, and the Congress for their financial support which helped to make the Symposium possible. We would like to thank Dr. Philip Payne for making some of the local arrangements, and Mrs. Betty McIntosh for her assistance in arranging the Symposium and in the preparation of these proceedings for publication.

Density-Functional Theory of Atoms and Molecules

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Publisher : Oxford University Press
ISBN 13 : 0195357736
Total Pages : 344 pages
Book Rating : 4.1/5 (953 download)

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Book Synopsis Density-Functional Theory of Atoms and Molecules by : Robert G. Parr

Download or read book Density-Functional Theory of Atoms and Molecules written by Robert G. Parr and published by Oxford University Press. This book was released on 1994-05-26 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Matrices and Density Functionals

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Publisher : Springer Science & Business Media
ISBN 13 : 9400938551
Total Pages : 718 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Density Matrices and Density Functionals by : R.M. Erdahl

Download or read book Density Matrices and Density Functionals written by R.M. Erdahl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt: THE COLEMAN SYMPOSIUM This collection of papers is dedicated to Albert John Coleman for his enthusiastic devotion to teaching and research and his many scientific accomplishments. John was born in Toronto on May 20, 1918 and 21 years later graduated from the University of Toronto in mathematics. Along the way he teamed up with Irving Kaplansky and Nathan Mendelson to win the first William Lowell Putnam Mathematical Competition in 1938. He earned his M.A. at Princeton in 1942 and then his Ph.D. at Toronto in 1943 in relativistic quantum mechanics under the direction of Leopold Infeld. During this period he was secretary of the Student Christian Movement in Toronto. Later, in 1945, he became traveling secretary of the World's Student Christian Federation in Geneva and in this capacity visited some 100 universities in 20 countries in the next four years. He spent the 50's as a member of the faculty at the University of Toronto and for 20 years, starting in 1960, he served as Dupuis Professor of Mathematics and Head of the Department at Queen's University. Since 1983 he has been Professor Emeritus at Queen's.