Relativistic Quantum Theory of Atoms and Molecules

Theory and Computation

Author: Ian P Grant

Publisher: Springer Science & Business Media

ISBN: 0387350691

Category: Science

Page: 800

View: 7774

This book is intended for physicists and chemists who need to understand the theory of atomic and molecular structure and processes, and who wish to apply the theory to practical problems. As far as practicable, the book provides a self-contained account of the theory of relativistic atomic and molecular structure, based on the accepted formalism of bound-state Quantum Electrodynamics. The author was elected a Fellow of the Royal Society of London in 1992.
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Relativistic Quantum Chemistry

The Fundamental Theory of Molecular Science

Author: Markus Reiher,Alexander Wolf

Publisher: John Wiley & Sons

ISBN: 352766758X

Category: Science

Page: 750

View: 5069

Einstein proposed his theory of special relativity in 1905. For a long time it was believed that this theory has no significant impact on chemistry. This view changed in the 1970s when it was realized that (nonrelativistic) Schr?dinger quantum mechanics yields results on molecular properties that depart significantly from experimental results. Especially when heavy elements are involved, these quantitative deviations can be so large that qualitative chemical reasoning and understanding is affected. For this to grasp the appropriate many-electron theory has rapidly evolved. Nowadays relativistic approaches are routinely implemented and applied in standard quantum chemical software packages. As it is essential for chemists and physicists to understand relativistic effects in molecules, the first edition of "Relativistic Quantum Chemistry - The fundamental Theory of Molecular Science" had set out to provide a concise, comprehensive, and complete presentation of this theory. This second edition expands on some of the latest developments in this fascinating field. The text retains its clear and consistent style, allowing for a readily accessible overview of the complex topic. It is also self-contained, building on the fundamental equations and providing the mathematical background necessary. While some parts of the text have been restructured for the sake of clarity a significant amount of new content has also been added. This includes, for example, an in-depth discussion of the Brown-Ravenhall disease, of spin in current-density functional theory, and of exact two-component methods and its local variants. A strength of the first edition of this textbook was its list of almost 1000 references to the original research literature, which has made it a valuable reference also for experts in the field. In the second edition, more than 100 additional key references have been added - most of them considering the recent developments in the field. Thus, the book is a must-have for everyone entering the field, as well as for experienced researchers searching for a consistent review.
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Introduction to the Theory of Collisions of Electrons with Atoms and Molecules

Author: S.P. Khare

Publisher: Springer Science & Business Media

ISBN: 1461506115

Category: Science

Page: 353

View: 3187

An understanding of the collisions between micro particles is of great importance for the number of fields belonging to physics, chemistry, astrophysics, biophysics etc. The present book, a theory for electron-atom and molecule collisions is developed using non-relativistic quantum mechanics in a systematic and lucid manner. The scattering theory is an essential part of the quantum mechanics course of all universities. During the last 30 years, the author has lectured on the topics presented in this book (collisions physics, photon-atom collisions, electron-atom and electron-molecule collisions, "electron-photon delayed coincidence technique", etc.) at many institutions including Wayne State University, Detroit, MI, The University of Western Ontario, Canada, and The Meerut University, India. The present book is the outcome of those lectures and is written to serve as a textbook for post-graduate and pre-PhD students and as a reference book for researchers.
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Theoretical Chemistry and Physics of Heavy and Superheavy Elements

Author: U. Kaldor,Stephen Wilson

Publisher: Springer Science & Business Media

ISBN: 9401701059

Category: Science

Page: 565

View: 7382

Quantum mechanics provides the fundamental theoretical apparatus for describing the structure and properties of atoms and molecules in terms of the behaviour of their fundamental components, electrons and nudeL For heavy atoms and molecules containing them, the electrons can move at speeds which represent a substantial fraction of the speed of light, and thus relativity must be taken into account. Relativistic quantum mechanics therefore provides the basic formalism for calculating the properties of heavy-atom systems. The purpose of this book is to provide a detailed description of the application of relativistic quantum mechanics to the many-body prob lem in the theoretical chemistry and physics of heavy and superheavy elements. Recent years have witnessed a continued and growing interest in relativistic quantum chemical methods and the associated computa tional algorithms which facilitate their application. This interest is fu elled by the need to develop robust, yet efficient theoretical approaches, together with efficient algorithms, which can be applied to atoms in the lower part of the Periodic Table and, more particularly, molecules and molecular entities containing such atoms. Such relativistic theories and computational algorithms are an essential ingredient for the description of heavy element chemistry, becoming even more important in the case of superheavy elements. They are destined to become an indispensable tool in the quantum chemist's armoury. Indeed, since relativity influences the structure of every atom in the Periodic Table, relativistic molecular structure methods may replace in many applications the non-relativistic techniques widely used in contemporary research.
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Relativistic Quantum Mechanics

Author: Hartmut Pilkuhn

Publisher: Springer Science & Business Media

ISBN: 366205275X

Category: Science

Page: 240

View: 6941

In this book, quantum mechanics is developed from the outset on a relativistic basis, using the superposition principle, Lorentz invariance and gauge invariance. Nonrelativistic quantum mechanics appears as a special case, and classical relativistic mechanics as another one. These special cases are important for giving plausible names to operators, for example "orbital angular momentum", "spin" or "magnetic moment". A subject which is treated for the first time in this book is the theory of binaries in terms of differential equations which have the mathematical structure of the corresponding one-body equations (Klein--Gordon for two spin- less particles, Dirac for two spinor particles).
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New Trends in Quantum Systems in Chemistry and Physics

Volume 1 Basic Problems and Model Systems Paris, France, 1999

Author: Jean Maruani,Christian Minot,R. McWeeny,Y.G. Smeyers,Stephen Wilson

Publisher: Springer Science & Business Media

ISBN: 0792367081

Category: Science

Page: 424

View: 7094

These two volumes collect thirty-eight selected papers from the scientific contributions presented at the Fourth European Workshop on Quantum Systems in Chemistry and Physics (QSCP-IV), held in Marly-le-Roi (France) in April 22-27, 1999, A total ofone hundred and fifteen scientists attended the workshop, 99 from Europe and 16 from the rest ofthe world. They discussed the state of the art, new trends, and future evolution of the methods and applications. The workshop was held in the old town of Marly-le-Roi, which lies to the West of Paris between the historic centres of Saint-Germain-en-Laye and Versailles. Participants were housed at the National Youth Institute, where over sixty lectures were given by l- ding members ofthe scientific community; in addition, over sixty posters were presented in two very animated sessions. We are grateful to the oral speakers and to the poster p- senters for making the workshop such an stimulating experience. The social programme was also memorable - and notjust for the closing banquet, which was held at the French Senate House. We are sure that participants will long remember their visit to the 'Musée des Antiquités Nationales': created by Napoleon III at the birthplace ofLouis XIV, this museum boasts one ofthe world finest collections ofarcheological artifacts. The Marly-le-Roi workshop followed the format established at the three previous meetings, organized by Prof.
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Computational Chemistry

Reviews of Current Trends

Author: Jerzy Leszczynski

Publisher: World Scientific

ISBN: 9789810225728

Category: Science

Page: 271

View: 7824

This book presents an overview of recent progress in computational techniques as well as examples of the application of existing computational methods in different areas of chemistry, physics, and biochemistry. Introductory chapters cover a broad range of fundamental topics, including: state-of-the-art basis set expansion methods for computing atomic and molecular electronic structures based on the use of relativistic quantum mechanics; the most recent developments in Hartree-Fock methods, particularly in techniques suited for very large systems; the current analysis of the solute-solvent free energy of interaction and the physical bases used to evaluate the electrostatic, cavitation, and dispersion terms; an introduction to the additive fuzzy electron density fragmentation scheme within various ab initio Hartree-Fock quantum-chemical computational schemes, which has provided the means for generating representative molecular fragment densities characteristic to their local environment within a molecule. This book also features a review of recent ab initio calculations on the structure and interactions of DNA bases, a chapter on computational approaches to the design of safer drugs and their molecular properties, and a systematic conceptual study on a route which allows one to stuff fullerenes.
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Relativistic Many-Body Theory

A New Field-Theoretical Approach

Author: Ingvar Lindgren

Publisher: Springer Science & Business Media

ISBN: 9781441983091

Category: Science

Page: 366

View: 3582

This book gives a comprehensive account of relativistic many-body perturbation theory, based upon field theory. After some introductory chapters about time-independent and time dependent many-body perturbation theory (MBPT), the standard techniques of S-matrix and Green’s functions are reviewed. Next, the newly introduced covariant-evolution-operator method is described, which can be used, like the S-matrix method, for calculations in quantum electrodynamics (QED). Unlike the S-matrix method, this has a structure that is similar to that of MBPT and therefore can serve as basis for a unified theory. Such an approach is developed in the final chapters, and its equivalence to the Bethe-Salpeter equation is demonstrated. Possible applications are discussed and numerical illustrations given.
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Quantum Theory of Tunneling

Author: Mohsen Razavy

Publisher: World Scientific

ISBN: 9814525030

Category: Science

Page: 792

View: 1945

In this revised and expanded edition, in addition to a comprehensible introduction to the theoretical foundations of quantum tunneling based on different methods of formulating and solving tunneling problems, different semiclassical approximations for multidimensional systems are presented. Particular attention is given to the tunneling of composite systems, with examples taken from molecular tunneling and also from nuclear reactions. The interesting and puzzling features of tunneling times are given extensive coverage, and the possibility of measurement of these times with quantum clocks are critically examined. In addition, by considering the analogy between evanescent waves in waveguides and in quantum tunneling, the times related to electromagnetic wave propagation have been used to explain certain aspects of quantum tunneling times. These topics are treated in both non-relativistic as well as relativistic regimes. Finally, a large number of examples of tunneling in atomic, molecular, condensed matter and nuclear physics are presented and solved. Contents:A Brief History of Quantum TunnelingSome Basic Questions Concerning Quantum TunnelingSimple Solvable ProblemsTime-Dependence of the Wave Function in One-Dimensional TunnelingSemiclassical ApproximationsGeneralization of the Bohr–Sommerfeld Quantization Rule and Its Application to Quantum TunnelingGamow's Theory, Complex Eigenvalues, and the Wave Function of a Decaying StateTunneling in Symmetric and Asymmetric Local Potentials and Tunneling in Nonlocal and Quasi-Solvable BarriersClassical Descriptions of Quantum TunnelingTunneling in Time-Dependent BarriersDecay Width and the Scattering TheoryThe Method of Variable Reflection Amplitude Applied to Solve Multichannel Tunneling ProblemsPath Integral and Its Semi-Classical Approximation in Quantum TunnelingHeisenberg's Equations of Motion for TunnelingWigner Distribution Function in Quantum TunnelingDecay Widths of Siegert States, Complex Scaling and Dilatation TransformationMultidimensional Quantum TunnelingGroup and Signal VelocitiesTime-Delay, Reflection Time Operator and Minimum Tunneling TimeMore About Tunneling TimeTunneling of a System with Internal Degrees of FreedomMotion of a Particle in a Waveguide with Variable Cross Section and in a Space Bounded by a Dumbbell-Shaped ObjectRelativistic Formulation of Quantum TunnelingInverse Problems of Quantum TunnelingSome Examples of Quantum Tunneling in Atomic and Molecular PhysicsSome Examples in Condensed Matter PhysicsAlpha Decay Readership: Graduate students and researchers in theoretical, mathematical, condensed matter and nuclear physics, as well as theoretical chemistry. Keywords:Quantum Tunneling;Quantum Clocks;Electromagnetic Wave Propagation;Semiclassical Approximations
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Problems in Structural Inorganic Chemistry

Author: Wai-Kee Li,Yu-San Cheung,Kendrew Kin Wah Mak,Thomas Chung Wai Mak

Publisher: OUP Oxford

ISBN: 0191633054

Category: Science

Page: 328

View: 8905

This book consists of over 300 problems (and their solutions) in structural inorganic chemistry at the senior undergraduate and beginning graduate level. The topics covered comprise Atomic and Molecular Electronic States, Atomic Orbitals, Hybrid Orbitals, Molecular Symmetry, Molecular Geometry and Bonding, Crystal Field Theory, Molecular Orbital Theory, Vibrational Spectroscopy, and Crystal Structure. The central theme running through these topics is symmetry, molecular or crystalline. The problems collected in this volume originate in examination papers and take-home assignments that have been part of the teaching of the book's two senior authors' at The Chinese University of Hong Kong over the past four decades. The authors' courses include Chemical Bonding, Elementary Quantum Chemistry, Advanced Inorganic Chemistry, X-Ray Crystallography, etc. The problems have been tested by generations of students taking these courses.
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Relativistic Theory of Atoms and Molecules III

A Bibliography 1993–1999

Author: Pekka Pyykkö

Publisher: Springer Science & Business Media

ISBN: 3642518850

Category: Science

Page: 354

View: 4387

Relativistic effects are of major importance for understanding the properties of heavier atoms and molecules. Volumes I-III of Relativistic Theory of Atoms and Molecules constitute the only available bibliography on related calculations. In Volume III, 3792 new references covering 1993-1999 are added to the database. The material is characterized by an analysis of the respective papers. The volume gives the user a comprehensive bibliography on relativistic atomic and molecular calculations, including studies on the Dirac equation and related solid-state work.
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Mathematical Concepts of Quantum Mechanics

Author: Stephen J. Gustafson,Israel Michael Sigal

Publisher: Springer Science & Business Media

ISBN: 3642218660

Category: Mathematics

Page: 382

View: 6916

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory.
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Relativistic Electronic Structure Theory

Part 2. Applications

Author: N.A

Publisher: Elsevier

ISBN: 9780080540474

Category: Science

Page: 804

View: 9875

The field of relativistic electronic structure theory is generally not part of theoretical chemistry education, and is therefore not covered in most quantum chemistry textbooks. This is due to the fact that only in the last two decades have we learned about the importance of relativistic effects in the chemistry of heavy and superheavy elements. Developments in computer hardware together with sophisticated computer algorithms make it now possible to perform four-component relativistic calculations for larger molecules. Two-component and scalar all-electron relativistic schemes are also becoming part of standard ab-initio and density functional program packages for molecules and the solid state. The second volume of this two-part book series is therefore devoted to applications in this area of quantum chemistry and physics of atoms, molecules and the solid state. Part 1 was devoted to fundamental aspects of relativistic electronic structure theory whereas Part 2 covers more of the applications side. This volume opens with a section on the Chemistry of the Superheavy Elements and contains chapters dealing with Accurate Relativistic Fock-Space Calculations for Many-Electron Atoms, Accurate Relativistic Calculations Including QED, Parity-Violation Effects in Molecules, Accurate Determination of Electric Field Gradients for Heavy Atoms and Molecules, Two-Component Relativistic Effective Core Potential Calculations for Molecules, Relativistic Ab-Initio Model Potential Calculations for Molecules and Embedded Clusters, Relativistic Pseudopotential Calculations for Electronic Excited States, Relativistic Effects on NMR Chemical Shifts, Relativistic Density Functional Calculations on Small Molecules, Quantum Chemistry with the Douglas-Kroll-Hess Approach to Relativistic Density Functional Theory, and Relativistic Solid State Calculations. - Comprehensive publication which focuses on new developments in relativistic quantum electronic structure theory - Many leaders from the field of theoretical chemistry have contributed to the TCC series - Will no doubt become a standard text for scientists in this field.
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Relativistic Quantum Mechanics of Leptons and Fields

Author: W.T. Grandy

Publisher: Springer Science & Business Media

ISBN: 9401133026

Category: Science

Page: 438

View: 2393

The material contained in this work concerns relativistic quantum mechanics, and as such pertains to classical fields. On the one hand it is meant to serve as a text on the subject, a desire stemming from the author's fruitless searches for an adequate, up-to-date reference when lecturing on these topics. At times the supplementary material was found to exceed by far that in the assigned text. On the other hand, there is some flavor of a monograph to what follows, most particularly in the later chapters, for a major goal is to demonstrate just how far we can advance our understanding of the behavior of stable particles and their interactions without introducing quantized fields. Those wishing to describe the world in this way may view the result as a point of departure, despite the fact that their wish remains unfulfilled. Confirmed quantum-field theorists, however, will doubtless view it as a summary of just why they feel compelled to quantize the fields. Approximately half the book is devoted to the single-particle Dirac equation and its solutions. A great deal of detail is provided in this respect, and the discus sion is reasonably comprehensive. The Dirac equation is extraordinarily important in its own right, particularly as a basis for quantum electrodynamics (QED), and is thus worthy of extensive study.
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Philosophical Problems of Space and Time

Second, enlarged edition

Author: Adolf Grünbaum

Publisher: Springer Science & Business Media

ISBN: 940102622X

Category: Science

Page: 884

View: 9248

It is ten years since Adolf Griinbaum published the first edition of this book. It was promptly recognized to be one of the few major works in the philosophy of the natural sciences of this generation. In part, this is so because Griinbaum has chosen a problem basic both to philosophy and to the natural sciences - the nature of space and time; and in part, this is so because he so admirably exemplifies that Aristotelian devotion to the intimate and mutual dependence of actual science and philosophical understanding. More than this, however, the quality of his work derives from his achievement in combining detail with scope. The problems of space and time have been among the most difficult in contemporary and classical thought, and Griinbaum has been responsible to the full depth and complexity of these difficulties. This revised and enlarged second edition is a work in progress, in the tradition of reflective analysis of modern science of such figures as Ehrenfest and Reichenbach. In publishing this work among the Boston Studies in the Philosophy of Science, we hope to contribute to and encourage that broad tradition of natural philosophy which is marked by the close collaboration of philoso phers and scientists. To this end, we have published the proceedings of our Colloquia, of meetings and conferences here and abroad, as well as the works of single authors.
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Advanced Molecular Quantum Mechanics

An Introduction to Relativistic Quantum Mechanics and the Quantum Theory of Radiation

Author: R. Moss

Publisher: Springer Science & Business Media

ISBN: 9400956886

Category: Science

Page: 300

View: 8785

This book is primarily intended for graduate chemists and chemical physicists. Indeed, it is based on a graduate course that I give in the Chemistry Depart ment of Southampton University. Nowadays undergraduate chemistry courses usually include an introduction to quantum mechanics with particular reference to molecular properties and there are a number of excellent textbooks aimed specifically at undergraduate chemists. In valence theory and molecular spectroscopy physical concepts are often encountered that are normally taken on trust. For example, electron spin and the anomalous magnetic moment of the electron are usually accepted as postulates, although they are well understood by physicists. In addition, the advent of new techniques has led to experimental situations that can only be accounted for adequately by relatively sophisticated physical theory. Relativis tic corrections to molecular orbital energies are needed to explain X-ray photo electron spectra, while the use oflasers can give rise to multiphoton transitions, which are not easy to understand using the classical theory of radiation. Of course, the relevant equations may be extracted from the literature, but, if the underlying physics is not understood, this is a practice that is at best dissatisfy ing and at worst dangerous. One instance where great care must be taken is in the use of spectroscopically determined parameters to test the accuracy of elec tronic wave functions.
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Handbook of Relativistic Quantum Chemistry

Author: Wenjian Liu

Publisher: Springer

ISBN: 9783642407659

Category: Science

Page: 1200

View: 3076

This handbook covers new methodological developments and applications of relativistic quantum chemistry. It also pays attention to the foundation of relativistic quantum mechanics and addresses a number of fundamental issues that have not been covered by any book. For instance, what is the appropriate relativistic many-electron Hamiltonian? How to do relativistic explicit/local correlation? How to formulate relativistic properties? How to combine double-group and time-reversal symmetries? How to do QED calculations for molecules? Just to name a few. This book aims to establish the big picture of relativistic molecular quantum mechanics, ranging from pedagogic introduction for uninitiated readers, advanced methodologies and efficient algorithms for experts, to possible future perspectives, such that the reader knows when/how to apply/develop the methodologies. This self-contained two-volume book can be regarded as a supplement to the three-volume "Handbook of Computational Chemistry", which contains no relativity at all. It is to be composed of 6 sections with different chapters (will be further expanded), each of which is to be written by the most active experts, who will be invited upon approval of this proposal.
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