The Unitary Group for the Evaluation of Electronic Energy Matrix Elements PDF Download
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Author: Jürgen Hinze
Publisher: Springer Science & Business Media
ISBN: 3642931634
Category : Science
Languages : en
Pages : 381
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Book Description
During the last thirty years, with the development of high speed electronic computers, methods have evolved, which permit an accurate and quantitative, ab initio determina tion of the electronic wavefunctions of atoms and molecules. Thus a detailed elucida tion of the electronic energy and structure of molecules has become possible using quantum mechanics directly. Ho\~ever, it is necessary, if such calculations are to yield accurate and reliable results, to include electron correlation explicitely, which requires in general . configuration mixing procedures with an extremely large 5 number of configurations, of the order of 10 configurations. With eigenvalue problems of this size, the limits of even the largest and fastest computers are reached rapidly, and their solution has become possible only, because direct methods have been deve~ loped which permit the determination of eigenvalues and eigenvectors for such large matrices iteratively without constructing the energy matrix explicitely. These direct methods had been limited to the description of closed shell systems, i. e. systems with a single dominant closed shell reference determinant. This limitation arose, because with an open shell reference or with several reference determinants, no procedures were known, which allowed a rapid calculation of the energy matrix elements between configurations with general and widely different spin couplings, which would be necessary. Recently such methods have been developed, based on early work of Gelfand, Biedenharn and Moshinski using a unitary group representation of different spin coupled states; Paldus achieved an extremely compact description.
Author: Jürgen Hinze
Publisher: Springer Science & Business Media
ISBN: 3642931634
Category : Science
Languages : en
Pages : 381
Get Book Here
Book Description
During the last thirty years, with the development of high speed electronic computers, methods have evolved, which permit an accurate and quantitative, ab initio determina tion of the electronic wavefunctions of atoms and molecules. Thus a detailed elucida tion of the electronic energy and structure of molecules has become possible using quantum mechanics directly. Ho\~ever, it is necessary, if such calculations are to yield accurate and reliable results, to include electron correlation explicitely, which requires in general . configuration mixing procedures with an extremely large 5 number of configurations, of the order of 10 configurations. With eigenvalue problems of this size, the limits of even the largest and fastest computers are reached rapidly, and their solution has become possible only, because direct methods have been deve~ loped which permit the determination of eigenvalues and eigenvectors for such large matrices iteratively without constructing the energy matrix explicitely. These direct methods had been limited to the description of closed shell systems, i. e. systems with a single dominant closed shell reference determinant. This limitation arose, because with an open shell reference or with several reference determinants, no procedures were known, which allowed a rapid calculation of the energy matrix elements between configurations with general and widely different spin couplings, which would be necessary. Recently such methods have been developed, based on early work of Gelfand, Biedenharn and Moshinski using a unitary group representation of different spin coupled states; Paldus achieved an extremely compact description.
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Languages : en
Pages : 0
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Book Description
Author: Jurgen Hinze
Publisher:
ISBN: 9783642931642
Category :
Languages : en
Pages : 384
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Book Description
Author: R. Pauncz
Publisher: CRC Press
ISBN: 1351094122
Category : Science
Languages : en
Pages : 260
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Book Description
This is the first book to provide comprehensive treatment of the use of the symmetric group in quantum chemical structures of atoms, molecules, and solids. It begins with the conventional Slater determinant approach and proceeds to the basics of the symmetric group and the construction of spin eigenfunctions. The heart of the book is in the chapter dealing with spin-free quantum chemistry showing the great interpretation value of this method. The last three chapters include the unitary group approach, the symmetric group approach, and the spin-coupled valence bond method. An extensive bibliography concludes the book.
Author: C.E. Dykstra
Publisher: Springer Science & Business Media
ISBN: 940096451X
Category : Science
Languages : en
Pages : 241
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Book Description
That there have been remarkable advances in the field of molecular electronic structure during the last decade is clear not only to those working in the field but also to anyone else who has used quantum chemical results to guide their own investiga tions. The progress in calculating the electronic structures of molecules has occurred through the truly ingenious theoretical and methodological developments that have made computationally tractable the underlying physics of electron distributions around a collection of nuclei. At the same time there has been consider able benefit from the great advances in computer technology. The growing sophistication, declining costs and increasing accessibi lity of computers have let theorists apply their methods to prob lems in virtually all areas of molecular science. Consequently, each year witnesses calculations on larger molecules than in the year before and calculations with greater accuracy and more com plete information on molecular properties. We can surely anticipate continued methodological develop ments of real consequence, and we can also see that the advance in computational capability is not about to slow down. The recent introduction of array processors, mUltiple processors and vector machines has yielded a tremendous acceleration of many types of computation, including operations typically performed in quantum chemical studies. Utilizing such new computing power to the ut most has required some new ideas and some reformulations of existing methods.
Author: Ron Shepard
Publisher: Springer
ISBN: 3662481480
Category : Science
Languages : en
Pages : 346
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Book Description
In this Festschrift dedicated to the late Isaiah Shavitt (1925-2012) , selected researchers in theoretical chemistry present research highlights on major developments in the field. Originally published in the journal Theoretical Chemistry Accounts, these outstanding contributions are now available in a hardcover print format, as well as a special electronic edition. This volume provides valuable content for all researchers in theoretical chemistry, and will especially benefit those research groups and libraries with limited access to the journal.
Author: Clyde A. Morrison
Publisher: Springer Science & Business Media
ISBN: 3642933769
Category : Science
Languages : en
Pages : 161
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Book Description
From December 1985 through March 1986 the text of this book formed the basis of an in-hours course taught by the author at Harry Diamond Laborato ries. Considerable assistance in revising and organizing the first draft was given by John Bruno. The original draft of these notes was based on a collection of lectures delivered at the Universidade Federal de Pernambuco, Recife, Brazil, between 2 November 1981 and 2 December 1981. The visit to Recife was a response to an invi tation of Professor Gilberto F. de Sa of the Physics Department. In the preparation of these notes I made many requests of my coworkers for earlier resul ts and recollections of our early work. Among those consul ted were Donald Wortman, Nick Karayianis, and Richard Leavitt. Further, a number of .suggestions from my Brazilian colleagues helped make the lectures more clear. Particular among these were Professor Oscar Malta and Professor Alfredo A. da Gama both of whom I wish to thank for their help. Encouragement and assistance with funding for much of this work came from Leon Esterowitz of the Naval Research Laboratory and Rudolph Buser and Albert Pinto of the center for Night Vision and Electro-Optics.
Author: Cesare Pisani
Publisher: Springer Science & Business Media
ISBN: 3642933858
Category : Science
Languages : en
Pages : 202
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Book Description
This book presents a computational scheme for calculating the electronic properties of crystalline systems at an ab-ini tio Hartree-Fock level of approximation. The first chapter is devoted to discussing in general terms the limits and capabilities of this approximation in solid state studies, and to examining the various options that are open for its implementation. The second chapter illustrates in detail the algorithms adopted in one specific computer program, CRYSTAL, to be submitted to QCPE. Special care is given to illustrating the role and in:fluence of computational parameters, because a delicate compromise must always be reached between accuracy and costs. The third chapter describes a number of applications, in order to clarify the possible use of this kind of programs in solid state physics and chemistry. Appendices A, B, and C contain various standard expressions, formulae, and definitions that may be useful for reference purposes; appendix D is intended to facilitate the interpretations of symbols, conventions, and acronyms that occur in the book. Thanks are due to all those who have contributed to the implementation and test of the CRYSTAL program, especially to V.R. Saunders and M. Causal, and to F. Ricca, E. Ferrero, R. Or lando, E. Ermondi, G. Angonoa, P. Dellarole, G. Baracco.
Author: S. Wilson
Publisher: Courier Corporation
ISBN: 0486150224
Category : Science
Languages : en
Pages : 305
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Book Description
Electron correlation effects are of vital significance to the calculation of potential energy curves and surfaces, the study of molecular excitation processes, and in the theory of electron-molecule scattering. This text describes methods for addressing one of theoretical chemistry's central problems, the study of electron correlation effects in molecules. Although the energy associated with electron correlation is a small fraction of the total energy of an atom or molecule, it is of the same order of magnitude as most energies of chemical interest. If the solution of quantum mechanical equations from first principles is to provide an accurate quantitative prediction, reliable techniques for the theoretical determination of the effect of electron correlation on molecular properties are therefore important. To that end, this text explores molecular electronic structure, independent electron models, electron correlation, the linked diagram theorem, group theoretical aspects, the algebraic approximation, and truncation of expansions for expectation values.
Author: Trygve Helgaker
Publisher: John Wiley & Sons
ISBN: 1119019559
Category : Science
Languages : en
Pages : 949
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Book Description
Ab initio quantum chemistry has emerged as an important tool in chemical research and is appliced to a wide variety of problems in chemistry and molecular physics. Recent developments of computational methods have enabled previously intractable chemical problems to be solved using rigorous quantum-mechanical methods. This is the first comprehensive, up-to-date and technical work to cover all the important aspects of modern molecular electronic-structure theory. Topics covered in the book include: * Second quantization with spin adaptation * Gaussian basis sets and molecular-integral evaluation * Hartree-Fock theory * Configuration-interaction and multi-configurational self-consistent theory * Coupled-cluster theory for ground and excited states * Perturbation theory for single- and multi-configurational states * Linear-scaling techniques and the fast multipole method * Explicity correlated wave functions * Basis-set convergence and extrapolation * Calibration and benchmarking of computational methods, with applications to moelcular equilibrium structure, atomization energies and reaction enthalpies. Molecular Electronic-Structure Theory makes extensive use of numerical examples, designed to illustrate the strengths and weaknesses of each method treated. In addition, statements about the usefulness and deficiencies of the various methods are supported by actual examples, not just model calculations. Problems and exercises are provided at the end of each chapter, complete with hints and solutions. This book is a must for researchers in the field of quantum chemistry as well as for nonspecialists who wish to acquire a thorough understanding of ab initio molecular electronic-structure theory and its applications to problems in chemistry and physics. It is also highly recommended for the teaching of graduates and advanced undergraduates.
