The Construction Of Spin Eigenfunctions
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| Author | : Ruben Pauncz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 193 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 146154291X |
The author wrote a monograph 20 years ago on the construction of spin eigen functions; the monograph was published by Plenum. The aim of that mono graph was to present all aspects connected with the construction of spin eigen functions and its relation to the use of many-electron antisymmetric wavefunc tions. The present book is an introduction to these subjects, with an emphasis on the practical side. After the theoretical treatment, there will be many exam ples and exercises which will illustrate the different methods. The theory of the symmetric group and its representations generated by the different spin eigen functions is an other subject, this is closely related to the quantum chemical applications. Finally we will survey the calculation of the matrix elements of the Hamiltonian, using the different constructions of the spin functions. The closing chapter will deal with a new method that gained much importance recently; the spin-coupled valence bond method. Since the publication of Spin Eigenfunctions, nearly 20 years ago there have been many interesting developments in the subject; there are quite a few new algorithms for the construction of spin eigenfunctions. Moreover the use of the spin-coupled valence bond method showed the importance of using different constructions for the spin functions. The subject matter of this book has been presented in a graduate course in the Technion. The author is obliged to the graduate students Averbukh Vitali, Gokhberg Kirill, and Narevicius Edvardas for many helpful comments.
| Author | : Ruben Pauncz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 374 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1468485261 |
The aim of this book is to give a comprehensive treatment of the different methods for the construction of spin eigenfunctions and to show their interrelations. The ultimate goal is the construction of an antisymmetric many-electron wave function that has both spatial and spin parts and the calculation of the matrix elements of the Hamiltonian over the total wave function. The representations of the symmetric group playa central role both in the construction of spin functions and in the calculation of the matrix elements of the Hamiltonian, so this subject will be treated in detail. We shall restrict the treatment to spin-independent Hamiltonians; in this case the spin does not have a direct role in the energy expression, but the choice of spin functions influences the form of spatial functions through the antisymmetry principle; the spatial functions determine the energy of the system. We shall also present the "spin-free quantum chemistry" approach of Matsen and co-workers, in which one starts immediately with the construction of spatial functions that have the correct permutational symmetries. By presenting both the conventional and the spin-free approach, one gains a better understanding of certain aspects of the elec tronic correlation problem. The latest advance in the calculation of the matrix elements of the Hamiltonian is the use of the representations of the unitary group, so this will be the last subject. It is a pleasant task to thank all those who helped in writing this book.
| Author | : Frank L. Pilar |
| Publisher | : Courier Corporation |
| Total Pages | : 646 |
| Release | : 2001-01-01 |
| Genre | : Science |
| ISBN | : 9780486414645 |
Useful introductory course and reference covers origins of quantum theory, Schrödinger wave equation, quantum mechanics of simple systems, electron spin, quantum states of atoms, Hartree-Fock self-consistent field method, more. 1990 edition.
| Author | : R. Pauncz |
| Publisher | : CRC Press |
| Total Pages | : 343 |
| Release | : 2018-05-04 |
| Genre | : Science |
| ISBN | : 1351085670 |
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 | : J. Maruani |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 421 |
| Release | : 2006-04-11 |
| Genre | : Science |
| ISBN | : 0306469510 |
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.
| Author | : John E. Harriman |
| Publisher | : Academic Press |
| Total Pages | : 416 |
| Release | : 2013-10-22 |
| Genre | : Science |
| ISBN | : 1483191664 |
Theoretical Foundations of Electron Spin Resonance deals with the theoretical approach to electron paramagnetic resonance. The book discusses electron spin resonance in applications related to polyatomic, probably organic, free radicals in condensed phases. The book also focuses on essentially static phenomena, that is, the description and determination of stationary-state energy levels. The author reviews the Dirac theory of the electron in which a four-component wave function is responsible for the behavior of the electron. The author then connects this theory with the nonrelativistic wave function theory. The book also addresses the relationship between spin Hamiltonian parameters and observable energy levels, as well as the expressions for specific spin Hamiltonian parameters concerning operators and wave functions. The book discusses wave- functions for open-shell systems; as well as how to extract values of spin Hamiltonian from information related to wave functions. The author then examines empirically adjusted parameters that can determine the wave function itself. This book can prove valuable for scientists involved with nuclear physics, molecular physics, and researchers in chemical physics.
| Author | : Caio Lima Firme |
| Publisher | : CRC Press |
| Total Pages | : 445 |
| Release | : 2019-08-28 |
| Genre | : Science |
| ISBN | : 1351205773 |
A novel proposal for teaching organic chemistry based on a broader and simplified use of quantum chemistry theories and notions of some statistical thermodynamic concepts aiming to enrich the learning process of the organic molecular properties and organic reactions. A detailed physical chemistry approach to teach organic chemistry for undergraduate students is the main aim of this book. A secondary objective is to familiarize undergraduate students with computational chemistry since most of illustrations of optimized geometries (plus some topological graphs) and information is from quantum chemistry outputs which will also enable students to obtain a deeper understanding of organic chemistry.
| Author | : Ruben Pauncz |
| Publisher | : |
| Total Pages | : 208 |
| Release | : 2000-06-30 |
| Genre | : |
| ISBN | : 9781461542926 |
The current volume is a very practical book, consisting primarily of many examples and exercises. In particular, The Construction of Spin Eigenfunctions presents all aspects connected with the construction of spin eigenfunctions, and their relationship with many-electron antisymmetric wave functions. This book treats new aligorithms in a way that no previous books have. The Construction of Spin Eigenfunctions opens with a brief theoretical introduction. Due to the increasing importance of spin eigenfunctions in quantum chemistry, Dr. Pauncz has followed up with two helpful chapters on the symmetric group and its representations. The author has also calculated matrix elements of the Hamiltonian using spin eigenfunctions. Dr. Pauncz wraps up the book with an important new technique: the spin-coupled valence bond method. This book should be very useful to graduate students working in the field of molecular quantum mechanics. It also could be used as a text for a one-semester graduate course in physics or in chemistry.
| Author | : Frank L. Pilar |
| Publisher | : Courier Corporation |
| Total Pages | : 646 |
| Release | : 2013-08-22 |
| Genre | : Science |
| ISBN | : 0486143872 |
As the author notes in the Preface to this valuable text, experimental chemists have moved past studying the average behavior of atoms or molecules "to probe the step-by-step behavior of individual atoms and molecules as they collide, form 'transition states,' and ultimately form products." In such experiments, quantum mechanical computations do two useful tasks: They fill in the observational gaps and help to interpret what has been observed. This introductory course — developed by the former chairman of the chemistry department at the University of New Hampshire — covers, among other topics, the origins of the quantum theory, the Schrödinger wave equation, the quantum mechanics of simple systems, the rigid rotator, the hydrogen atom, electron spin and many-electron systems, the quantum states of atoms, the Hartree-Fock self-consistent field method, the electronic structure of molecules, and semi-empirical molecular orbital methods. One of the great values of the course is its calculations and diagrams, which were created specifically for this text and which students will be able to replicate on their home computers. The text will be most useful for advanced undergraduate or beginning graduate students who have had calculus and at least a year of undergraduate physics. A knowledge of differential equations, linear algebra, and atomic physics is helpful but not essential. Seven appendices give a concise exposition of mathematical and physical material that may not be part of the students' background.
| Author | : K. P. Lawley |
| Publisher | : John Wiley & Sons |
| Total Pages | : 600 |
| Release | : 2009-09-08 |
| Genre | : Science |
| ISBN | : 047014338X |
The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.
