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Author: John Avery
Publisher: World Scientific
ISBN: 9814350478
Category : Science
Languages : en
Pages : 239
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Book Description
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.
Author: John Avery
Publisher: World Scientific
ISBN: 9814350478
Category : Science
Languages : en
Pages : 239
Get Book Here
Book Description
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.
Author: John Avery
Publisher: World Scientific
ISBN: 981435046X
Category : Science
Languages : en
Pages : 239
Get Book Here
Book Description
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.
Author: ILYA KUPROV
Publisher: Springer Nature
ISBN: 3031056078
Category : Science
Languages : en
Pages : 400
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Book Description
This monograph is a fundamental reference for scientists and engineers who encounter spin processes in their work. The author, Ilya Kuprov, derives the concept of spin from basic symmetries and gives an overview of theoretical and computational aspects of spin dynamics: from Dirac equation and spin Hamiltonian, through coherent evolution and relaxation theories, to quantum optimal control, and all the way to practical implementation advice for parallel computers.
Author: Sergey Yurchenko
Publisher: CRC Press
ISBN: 0429531834
Category : Science
Languages : en
Pages : 235
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Book Description
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.
Author: Valerio Magnasco
Publisher: Elsevier
ISBN: 008046680X
Category : Science
Languages : en
Pages : 750
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Book Description
Elementary Methods of Molecular Quantum Mechanics shows the methods of molecular quantum mechanics for graduate University students of Chemistry and Physics. This readable book teaches in detail the mathematical methods needed to do working applications in molecular quantum mechanics, as a preliminary step before using commercial programmes doing quantum chemistry calculations.This book aims to bridge the gap between the classic Coulson's Valence, where application of wave mechanical principles to valence theory is presented in a fully non-mathematical way, and McWeeny's Methods of Molecular Quantum Mechanics, where recent advances in the application of quantum mechanical methods to molecular problems are presented at a research level in a full mathematical way. Many examples and mathematical points are given as problems at the end of each chapter, with a hint for their solution. Solutions are then worked out in detail in the last section of each Chapter.* Uses clear and simplified examples to demonstrate the methods of molecular quantum mechanics * Simplifies all mathematical formulae for the reader* Provides educational training in basic methodology
Author:
Publisher: ScholarlyEditions
ISBN: 1464963347
Category : Science
Languages : en
Pages : 6582
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Book Description
Issues in Chemistry and General Chemical Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Chemistry and General Chemical Research. The editors have built Issues in Chemistry and General Chemical Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Chemistry and General Chemical Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Chemistry and General Chemical Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Author: Peter Fulde
Publisher: Springer Science & Business Media
ISBN: 3642973094
Category : Science
Languages : en
Pages : 428
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Book Description
Quantum chemistry and solid-state theory are two important related fields of research that have grown up with almost no cross communication. This book bridges the gap between the two. In the first half, new concepts for treating weak and strong correlations are developed, and standard quantum-chemical methods, as well as density functional, Green's function, functional integral, and Monte Carlo methods are discussed. The second half discusses applications of the theory to molecules, semiconductors, homogeneous metallic systems, transition metals, and strongly correlated systems such as heavy-fermion systems and the new high-Tc superconducting materials.
Author: Robert G. Mortimer
Publisher: Academic Press
ISBN: 0080878598
Category : Technology & Engineering
Languages : en
Pages : 1415
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Book Description
In this third edition, core applications have been added along with more recent developments in the theories of chemical reaction kinetics and molecular quantum mechanics, as well as in the experimental study of extremely rapid chemical reactions.* Fully revised concise edition covering recent developments in the field* Supports student learning with step by step explanation of fundamental principles, an appropriate level of math rigor, and pedagogical tools to aid comprehension* Encourages readers to apply theory in practical situations
Author: Kenneth G. Dyall
Publisher: Oxford University Press
ISBN: 0190286377
Category : Science
Languages : en
Pages : 544
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Book Description
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.
Author: Eva Perlt
Publisher: Springer Nature
ISBN: 303067262X
Category : Science
Languages : en
Pages : 255
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Book Description
This book addresses the construction and application of the major types of basis sets for computational chemistry calculations. In addition to a general introduction, it includes mathematical basics and a discussion of errors arising from incomplete or inappropriate basis sets. The different chapters introduce local orbitals and orbital localization as well as Slater-type orbitals and review basis sets for special applications, such as those for correlated methods, solid-state calculations, heavy atoms and time-dependent adaptable Gaussian bases for quantum dynamics simulations. This detailed review of the purpose of basis sets, their design, applications, possible problems and available solutions provides graduate students and beginning researchers with information not easily obtained from the available textbooks and offers valuable supporting material for any quantum chemistry or computational chemistry course at the graduate and/or undergraduate level. This book is also useful as a guide for researchers who are new to computational chemistry but are willing to extend their research tools by applying such methods.
