Symmetry Adapted Basis Sets
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Symmetry Adapted Basis Sets
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Author : John Avery
language : en
Publisher: World Scientific
Release Date : 2012
Symmetry Adapted Basis Sets written by John Avery and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Science categories.
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.
Symmetry Adapted Basis Sets Automatic Generation For Problems In Chemistry And Physics
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Author : John Scales Avery
language : en
Publisher: World Scientific
Release Date : 2011-10-31
Symmetry Adapted Basis Sets Automatic Generation For Problems In Chemistry And Physics written by John Scales Avery and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-31 with Science categories.
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.
Generalized Sturmians And Atomic Spectra
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Author : John Scales Avery
language : en
Publisher: World Scientific
Release Date : 2006-11-14
Generalized Sturmians And Atomic Spectra written by John Scales Avery and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Science categories.
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.
Group Theoretical Methods And Applications To Molecules And Crystals
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Author : Shoon K. Kim
language : en
Publisher: Cambridge University Press
Release Date : 1999-06-24
Group Theoretical Methods And Applications To Molecules And Crystals written by Shoon K. Kim and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-24 with Mathematics categories.
From the pioneering author in the field, this book is ideal for condensed matter physicists and physical chemists.
Determination Of Liquid Water Structure
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Author : E. Clementi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Determination Of Liquid Water Structure written by E. Clementi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
One should distinguish between coordination numbers and hydration numbers. Following Bockris
Molecular Geometry
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Author : Alison Rodger
language : en
Publisher: Butterworth-Heinemann
Release Date : 2014-05-16
Molecular Geometry written by Alison Rodger and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-16 with Science categories.
Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and transition metal clusters. The last chapter tackles the consequences of small, local variations in geometry. The text will be of great use to chemists who primarily deal with the properties of molecules and atoms.
Introduction To Relativistic Quantum Chemistry
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Author : Kenneth G. Dyall
language : en
Publisher: Oxford University Press
Release Date : 2007-04-19
Introduction To Relativistic Quantum Chemistry written by Kenneth G. Dyall and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-19 with Science categories.
This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a good background in nonrelativistic theory. In addition to explaining the necessary theory in detail, at a level that the non-expert and the student should readily be able to follow, the book discusses the implementation of the theory and practicalities of its use in calculations. After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored. Four-component molecular methods are then developed: self-consistent field theory and the use of basis sets, double-group and time-reversal symmetry, correlation methods, molecular properties, and an overview of relativistic density functional theory. The emphases in this section are on the basics of relativistic theory and how relativistic theory differs from nonrelativistic theory. Approximate methods are treated next, starting with spin separation in the Dirac equation, and proceeding to the Foldy-Wouthuysen, Douglas-Kroll, and related transformations, Breit-Pauli and direct perturbation theory, regular approximations, matrix approximations, and pseudopotential and model potential methods. For each of these approximations, one-electron operators and many-electron methods are developed, spin-free and spin-orbit operators are presented, and the calculation of electric and magnetic properties is discussed. The treatment of spin-orbit effects with correlation rounds off the presentation of approximate methods. The book concludes with a discussion of the qualitative changes in the picture of structure and bonding that arise from the inclusion of relativity.
Computational Spectroscopy Of Polyatomic Molecules
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Author : Sergey Yurchenko
language : en
Publisher: CRC Press
Release Date : 2023-02-18
Computational Spectroscopy Of Polyatomic Molecules written by Sergey Yurchenko and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-18 with Science categories.
This book provides a detailed description of the modern variational methods available for solving the nuclear motion Schrödinger equation to enable accurate theoretical spectroscopy of polyatomic molecules. These methods are currently used to provide important molecular data for spectroscopic studies of atmospheres of astronomical objects including solar and extrasolar planets as well as cool stars. This book has collected descriptions of quantum mechanical methods into one cohesive text, making the information more accessible to the scientific community, especially for young researchers, who would like to devote their scientific career to the field of computational molecular physics. The book addresses key aspects of the high-accuracy computational spectroscopy of the medium size polyatomic molecules. It aims to describe numerical algorithms for the construction and solution of the nuclear motion Schrödinger equations with the central idea of the modern computational spectroscopy of polyatomic molecules to include the construction of the complex kinetic energy operators (KEO) into the computation process of the numerical pipeline by evaluating the corresponding coefficients of KEO derivatives on-the-fly. The book details key aspects of variational solutions of the nuclear motion Schrödinger equations targeting high accuracy, including construction of rotational and vibrational basis functions, coordinate choice, molecular symmetry as well as of intensity calculations and refinement of potential energy functions. The goal of this book is to show how to build an accurate spectroscopic computational protocol in a pure numerical manner of a general black-box type algorithm. This book will be a valuable resource for researchers, both experts and not experts, working in the area of the computational and experimental spectroscopy; PhD students and early-career spectroscopists who would like to learn basics of the modern variational methods in the field of computational spectroscopy. It will also appeal to astrophysicists and atmospheric physicists who would like to assess data and perform calculations themselves. Key features: Supported by the latest research and based on the state-of-the-art computational methods in high-accuracy computational spectroscopy of molecules. Authored by an authority in the field. Accessible to both experts and non-experts working in the area of computational and experimental spectroscopy, in addition to graduate students.
Hyperspherical Harmonics And Their Physical Applications
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Author : James Emil Avery
language : en
Publisher: World Scientific
Release Date : 2017-11-27
Hyperspherical Harmonics And Their Physical Applications written by James Emil Avery and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-27 with Science categories.
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.
A Handbook Of Magnetochemical Formulae
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Author : Roman Boca
language : en
Publisher: Elsevier
Release Date : 2012-02
A Handbook Of Magnetochemical Formulae written by Roman Boca and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02 with Science categories.
Magnetochemistry is concerned with the study of magnetic properties in materials. It investigates the relationship between the magnetic properties of chemical compounds and their atomic and molecular structure. This rapidly growing field has a number of applications, and the measuring and interpreting of magnetic properties is often conducted by scientists who are not specialists in the field. Magnetochemistry requires complex mathematics and physics and so can be daunting for those who have not previously studied it in depth. Aimed at providing a single source of information on magnetochemistry, this book offers a comprehensive and contemporary review of the mathematical background and formula for predicting or fitting magnetic data, including a summary of the theory behind magnetochemistry to help understand the necessary calculations. Along with tables listing the key formula, there is also a model of the magnetic functions showing the effect of individual magnetic parameters. The clear structure and comprehensive coverage of all aspects of magnetochemistry will make this an essential book for advanced students and practitioners. Provides comprehensive overview of the mathematical background of magnetochemistry Uses clear and accessible language so scientists in a variety of fields can utilize the information Detailed explanations of equations and formula