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Generalized Sturmians And Atomic Spectra
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Book Synopsis Generalized Sturmians And Atomic Spectra by : John Scales Avery
Download or read book Generalized Sturmians And Atomic Spectra written by John Scales Avery and published by World Scientific. This book was released on 2006-11-14 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the generalized Sturmian method, which offers a fresh approach to the calculation of atomic spectra. Generalized Sturmians are isoenergetic solutions to an approximate many-electron Schrödinger equation with a weighted potential. The weighting factors are chosen in such a way as to make all of the solutions correspond to a given energy. The advantage of such an isoenergetic basis set is that every basis function has the correct turning point behavior needed for efficient synthesis of the wave function.The book also discusses methods for automatic generation of symmetry-adapted basis sets. Calculations using the generalized Sturmian method are presented and compared with experimental results from the NIST database. The relationship of Sturmians to harmonic polynomials and hyperspherical harmonics is also described. Methods for treating angular functions and angular integrals by means of harmonic projection are discussed, and these methods are shown to be especially useful for relativistic calculations. A final chapter discusses application of the generalized Sturmian method to the calculation of molecular spectra.
Book Synopsis Symmetry-Adapted Basis Sets by : John Scales Avery
Download or read book Symmetry-Adapted Basis Sets written by John Scales Avery and published by World Scientific. This book was released on 2011-10-31 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: In theoretical physics, theoretical chemistry and engineering, one often wishes to solve partial differential equations subject to a set of boundary conditions. This gives rise to eigenvalue problems of which some solutions may be very difficult to find. For example, the problem of finding eigenfunctions and eigenvalues for the Hamiltonian of a many-particle system is usually so difficult that it requires approximate methods, the most common of which is expansion of the eigenfunctions in terms of basis functions that obey the boundary conditions of the problem. The computational effort needed in such problems can be much reduced by making use of symmetry-adapted basis functions. The conventional method for generating symmetry-adapted basis sets is through the application of group theory, but this can be difficult. This book describes an easier method for generating symmetry-adapted basis sets automatically with computer techniques. The method has a wide range of applicability, and can be used to solve difficult eigenvalue problems in a number of fields. The book is of special interest to quantum theorists, computer scientists, computational chemists and applied mathematicians. Contents:General ConsiderationsExamples from Atomic PhysicsExamples from Quantum ChemistryGeneralized Sturmians Applied to AtomsMolecular Orbitals Based on SturmiansAn Example from AcousticsAn Example from Heat ConductionSymmetry-Adapted Solutions by Iteration Readership: Researchers in quantum physics, theoretical/quantum chemistry and numerical and computational mathematics. Keywords:Group Theory;Quantum Theory;Configuration Interaction;Computational Algorithms;Generalized SturmiansKey Features:The book describes easy algorithms for automatic generation of symmetry-adapted basis functionsIt also discusses the Generalized Sturmian Method and its applications to both atomic and molecular calculations. The method leads to automatic scaling of basis functionsA new method is introduced which applies hyperspherical harmonic theory to the rapid calculation of interelectron repulsion integrals involving exponential-type orbitals
Download or read book Advances in Quantum Chemistry written by and published by Academic Press. This book was released on 2015-01-29 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Quantum Chemistry presents surveys of current topics in this rapidly developing field one that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology. It features detailed reviews written by leading international researchers. In this volume the readers are presented with an exciting combination of themes. Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology Features detailed reviews written by leading international researchers
Book Synopsis State of The Art of Molecular Electronic Structure Computations: Correlation Methods, Basis Sets and More by :
Download or read book State of The Art of Molecular Electronic Structure Computations: Correlation Methods, Basis Sets and More written by and published by Academic Press. This book was released on 2019-09-07 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: State of the Art of Molecular Electronic Structure Computations: Correlation Methods, Basis Sets and More, Volume 79 in the Advances in Quantum Chemistry series, presents surveys of current topics in this rapidly developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry and biology. Chapters in this new release include Computing accurate molecular properties in real space using multiresolution analysis, Self-consistent electron-nucleus cusp correction for molecular orbitals, Correlated methods for computational spectroscopy, Potential energy curves for the NaH molecule and its cation with the cock space coupled cluster method, and much more. Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry and biology Features detailed reviews written by leading international researchers
Book Synopsis Proceedings of MEST 2012: Exponential Type Orbitals for Molecular Electronic Structure Theory by :
Download or read book Proceedings of MEST 2012: Exponential Type Orbitals for Molecular Electronic Structure Theory written by and published by Academic Press. This book was released on 2013-11-19 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Quantum Chemistry presents surveys of current topics in this rapidly developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology. It features detailed reviews written by leading international researchers. This volume focuses on the theory of heavy ion physics in medicine. Advances in Quantum Chemistry presents surveys of current topics in this rapidly developing field and this volume focuses on the theory of heavy ion physics in medicine
Book Synopsis Novel Electronic Structure Theory: General Innovations and Strongly Correlated Systems by :
Download or read book Novel Electronic Structure Theory: General Innovations and Strongly Correlated Systems written by and published by Academic Press. This book was released on 2018-01-03 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Novel Electronic Structure Theory: General Innovations and Strongly Correlated Systems, Volume 76, the latest release in the Advances in Quantum Chemistry series presents work and reviews of current work in quantum chemistry (molecules), but also includes scattering from atoms and solid state work of interest in physics. Topics covered in this release include the Present Status of Selected Configuration Interaction with Truncation Energy Error, Recent Developments in Asymptotic Expansions from Numerical Analysis and Approximation Theory, The kinetic energy Pauli enhancement factor and its role in determining the shell structure of atoms and molecules, Numerical Hartree-Fock and Many-Body Calculations for Diatomic Molecules, and more. Provides reports on current work in molecular and atomic quantum mechanics Contains work reported by many of the best scientists in the field Presents the latest release in the Advances in Quantum Chemistry series
Book Synopsis Solving the Schrodinger Equation by : Paul L. A. Popelier
Download or read book Solving the Schrodinger Equation written by Paul L. A. Popelier and published by World Scientific. This book was released on 2011 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Schrodinger equation is the master equation of quantum chemistry. The founders of quantum mechanics realised how this equation underpins essentially the whole of chemistry. However, they recognised that its exact application was much too complicated to be solvable at the time. More than two generations of researchers were left to work out how to achieve this ambitious goal for molecular systems of ever-increasing size. This book focuses on non-mainstream methods to solve the molecular electronic Schrodinger equation. Each method is based on a set of core ideas and this volume aims to explain these ideas clearly so that they become more accessible. By bringing together these non-standard methods, the book intends to inspire graduate students, postdoctoral researchers and academics to think of novel approaches. Is there a method out there that we have not thought of yet? Can we design a new method that combines the best of all worlds?
Author :David Michael P. Mingos Publisher :Springer Science & Business Media ISBN 13 :3642273785 Total Pages :247 pages Book Rating :4.6/5 (422 download)
Book Synopsis Molecular Electronic Structures of Transition Metal Complexes II by : David Michael P. Mingos
Download or read book Molecular Electronic Structures of Transition Metal Complexes II written by David Michael P. Mingos and published by Springer Science & Business Media. This book was released on 2012-01-11 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: T. Ziegler: A Chronicle About the Development of Electronic Structure Theories for Transition Metal Complexes.- J. Linderberg: Orbital Models and Electronic Structure Theory.- J.S. and J.E. Avery: Sturmians and Generalized Sturmians in Quantum Theory.- B.T Sutcliffe: Chemistry as a “Manifestation of Quantum Phenomena” and the Born–Oppenheimer Approximation?- A.J. McCaffery: From Ligand Field Theory to Molecular Collision Dynamics: A Common Thread of Angular Momentum.- M. Atanasov, D. Ganyushin, K. Sivalingam and F. Neese: A Modern First-Principles View on Ligand Field Theory Through the Eyes of Correlated Multireference Wavefunctions.- R.S. Berry and B.M. Smirnov: The Phase Rule: Beyond Myopia to Understanding.
Book Synopsis Hyperspherical Harmonics and Generalized Sturmians by : John S. Avery
Download or read book Hyperspherical Harmonics and Generalized Sturmians written by John S. Avery and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explores the connections between the theory of hyperspherical harmonics, momentum-space quantum theory and generalized Sturmian basis functions. It also introduces methods which may be used to solve many-particle problems directly, without the use of the self-consistent-field approximation.; The method of many-electron Sturmians offers an interesting alternative to the usual SCF-CI methods for calculating atomic and molecular structure. When many-electron Sturmians are used, and when the basis potential is chosen to be the attractive potential of the nuclei in the system, the following advantages are offered: the matrix representation of the nuclear attraction potential is diagonal; the kinetic energy term vanishes from the secular equation; the Slater exponents of the atomic orbitals are automatically optimized; convergence is rapid; a correlated solution to the many-electron problem can be obtained directly, without the use of the SCF approximation; and excited states can be obtained with good accuracy.; The text should be of interest to advanced students and research workers in theoretical chemistry, physics and mathematics.
Book Synopsis Dynamical Symmetry by : Carl Wulfman
Download or read book Dynamical Symmetry written by Carl Wulfman and published by World Scientific. This book was released on 2011 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whenever systems are governed by continuous chains of causes and effects, their behavior exhibits the consequences of dynamical symmetries, many of them far from obvious. Dynamical Symmetry introduces the reader to Sophus Lie's discoveries of the connections between differential equations and continuous groups that underlie this observation. It develops and applies the mathematical relations between dynamics and geometry that result. Systematic methods for uncovering dynamical symmetries are described, and put to use. Much material in the book is new and some has only recently appeared in research journals. Though Lie groups play a key role in elementary particle physics, their connection with differential equations is more often exploited in applied mathematics and engineering. Dynamical Symmetry bridges this gap in a novel manner designed to help readers establish new connections in their own areas of interest. Emphasis is placed on applications to physics and chemistry. Applications to many of the other sciences illustrate both general principles and the ubiquitousness of dynamical symmetries.
Book Synopsis Advances in Quantum Chemistry by : Erkki J. Brändas
Download or read book Advances in Quantum Chemistry written by Erkki J. Brändas and published by Elsevier. This book was released on 2004-12-01 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Quantum Chemistry presents surveys of current developments in this rapidly developing field that falls between the historically established areas of mathematics, physics, and chemistry. With invited reviews written by leading international researchers, as well as regular thematic issues, each volume presents new results and provides a single vehicle for following progress in this interdisciplinary area. Volume 47 is a tribute in honor of Professor Osvaldo Goscinski. The volume will look at the accomplishments of a man who has led a remarkable development within the field and developed and strengthened scientific networks in Quantum Chemistry and Chemical Physics. Provides a tribute in honor of Professor Osvaldo Goscinski, a man who has led a remarkable development within the field
Book Synopsis Hyperspherical Harmonics Expansion Techniques by : Tapan Kumar Das
Download or read book Hyperspherical Harmonics Expansion Techniques written by Tapan Kumar Das and published by Springer. This book was released on 2015-11-26 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a generalized theoretical technique for solving the fewbody Schrödinger equation. Straight forward approaches to solve it in terms of position vectors of constituent particles and using standard mathematical techniques become too cumbersome and inconvenient when the system contains more than two particles. The introduction of Jacobi vectors, hyperspherical variables and hyperspherical harmonics as an expansion basis is an elegant way to tackle systematically the problem of an increasing number of interacting particles. Analytic expressions for hyperspherical harmonics, appropriate symmetrisation of the wave function under exchange of identical particles and calculation of matrix elements of the interaction have been presented. Applications of this technique to various problems of physics have been discussed. In spite of straight forward generalization of the mathematical tools for increasing number of particles, the method becomes computationally difficult for more than a few particles. Hence various approximation methods have also been discussed. Chapters on the potential harmonics and its application to Bose-Einstein condensates (BEC) have been included to tackle dilute system of a large number of particles. A chapter on special numerical algorithms has also been provided. This monograph is a reference material for theoretical research in the few-body problems for research workers starting from advanced graduate level students to senior scientists.
Book Synopsis Hyperspherical Harmonics And Their Physical Applications by : Avery James Emil
Download or read book Hyperspherical Harmonics And Their Physical Applications written by Avery James Emil and published by World Scientific. This book was released on 2017-11-27 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hyperspherical harmonics are extremely useful in nuclear physics and reactive scattering theory. However, their use has been confined to specialists with very strong backgrounds in mathematics. This book aims to change the theory of hyperspherical harmonics from an esoteric field, mastered by specialists, into an easily-used tool with a place in the working kit of all theoretical physicists, theoretical chemists and mathematicians. The theory presented here is accessible without the knowledge of Lie-groups and representation theory, and can be understood with an ordinary knowledge of calculus. The book is accompanied by programs and exercises designed for teaching and practical use. Contents: PrefaceHarmonic FunctionsGeneralized Angular MomentumGegenbauer PolynomialsFourier Transforms in d DimensionsFock's Treatment of Hydrogenlike Atoms and Its GeneralizationD-Dimensional Hydrogenlike Orbitals in Direct SpaceGeneralized SturmiansChoosing Appropriate Hyperspherical RepresentationsMolecular Integrals from Hyperspherical HarmonicsLagrangians for Particles and FieldsCoordinate Transformations for N BodiesSome Illustrative ExamplesAppendices: The D-Dimensional Harmonic OscillatorMolecular Integrals for Slatertype OrbitalsBibliographyIndex Readership: Scientists and researchers in theoretical physics, theoretical chemistry, and mathematics. Keywords: Harmonic Functions;Reactive Scattering Theory; Nuclear Physics;Gegenbauer Polynomials;Generalized Sturmians;Slatertype OrbitalsReview: Key Features: Exercises are included at the end of each chapterThe e-version of the exercises and solutions can be found in the supplementary tab
Download or read book Dynamical Symmetry written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advances in the Theory of Quantum Systems in Chemistry and Physics by : Philip E. Hoggan
Download or read book Advances in the Theory of Quantum Systems in Chemistry and Physics written by Philip E. Hoggan and published by Springer Science & Business Media. This book was released on 2011-11-16 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in the Theory of Quantum Systems in Chemistry and Physics is a collection of 32 selected papers from the scientific contributions presented at the 15th International Workshop on Quantum Systems in Chemistry and Physics (QSCP-XV), held at Magdalene College, Cambridge, UK, from August 31st to September 5th, 2010. This volume discusses the state of the art, new trends, and the future of methods in molecular quantum mechanics and their applications to a wide range of problems in chemistry, physics, and biology. The breadth and depth of the scientific topics discussed during QSCP-XV are gathered in seven sections: I. Fundamental Theory; II. Model Atoms; III. Atoms and Molecules with Exponential-Type Orbitals; IV. Density-Oriented Methods; V. Dynamics and Quantum Monte-Carlo Methodology; VI. Structure and Reactivity; VII. Complex Systems, Solids, Biophysics. Advances in the Theory of Quantum Systems in Chemistry and Physics is written for research students and professionals in Quantum systems of chemistry and physics. It also constitutes and invaluable guide for those wishing to familiarize themselves with research perspectives in the domain of quantum systems for thematic conversion or simply to gain insight into the methodological developments and applications to physics chemistry and biology that have actually become feasible by the end of 2010.
Book Synopsis Electron Correlation in Molecules – ab initio Beyond Gaussian Quantum Chemistry by :
Download or read book Electron Correlation in Molecules – ab initio Beyond Gaussian Quantum Chemistry written by and published by Academic Press. This book was released on 2016-01-28 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electron Correlation in Molecules – ab initio Beyond Gaussian Quantum Chemistry presents a series of articles concerning important topics in quantum chemistry, including surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology. Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology Features detailed reviews written by leading international researchers The volume includes review on all the topics treated by world renown authors and cutting edge research contributions.
Book Synopsis Computational Science and Its Applications -- ICCSA 2013 by : Beniamino Murgante
Download or read book Computational Science and Its Applications -- ICCSA 2013 written by Beniamino Murgante and published by Springer. This book was released on 2013-06-22 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: The five-volume set LNCS 7971-7975 constitutes the refereed proceedings of the 13th International Conference on Computational Science and Its Applications, ICCSA 2013, held in Ho Chi Minh City, Vietnam, in June 2013. Apart from the general track, ICCSA 2013 also include 33 special sessions and workshops, in various areas of computational sciences, ranging from computational science technologies, to specific areas of computational sciences, such as computer graphics and virtual reality. There are 46 papers from the general track, and 202 in special sessions and workshops.
