Author: Simon L. Altmann
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 396

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Author: R. Mirman
Publisher: World Scientific
ISBN: 9789810237325
Category : Science
Languages : en
Pages : 768

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Book Description
This book is by far the most comprehensive treatment of point and space groups, and their meaning and applications. Its completeness makes it especially useful as a text, since it gives the instructor the flexibility to best fit the class and goals. The instructor, not the author, decides what is in the course. And it is the prime book for reference, as material is much more likely to be found in it than in any other book; it also provides detailed guides to other sources.Much of what is taught is folklore, things everyone knows are true, but (almost?) no one knows why, or has seen proofs, justifications, rationales or explanations. (Why are there 14 Bravais lattices, and why these? Are the reasons geometrical, conventional or both? What determines the Wigner-Seitz cells? How do they affect the number of Bravais lattices? Why are symmetry groups relevant to molecules whose vibrations make them unsymmetrical? And so on). Here these analyses are given, interrelated, and in-depth. The understanding so obtained gives a strong foundation for application and extension. Assumptions and restrictions are not merely made explicit, but also emphasized.In order to provide so much information, details and examples, and ways of helping readers learn and understand, the book contains many topics found nowhere else, or only in obscure articles from the distant past. The treatment is (often completely) different from those elsewhere. At least in the explanations, and usually in many other ways, the book is completely new and fresh. It is designed to inform, educate and make the reader think. It strongly emphasizes understanding.The book can be used at many levels, by many different classes of readers ? from those who merely want brief explanations (perhaps just of terminology), who just want to skim, to those who wish the most thorough understanding.

Author: R. Daudel
Publisher: Springer Science & Business Media
ISBN: 9789027722461
Category : Science
Languages : en
Pages : 326

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Book Description
This volume is the second of a set of two which contain 28 selected from the l. j. O invited lectures given at the internatim;al seminar of the same title held at the Centre de Mecanique Ondulatoire Appliquee du Centre National de la Recherche Scientifique in Paris (France) from October 1983 to May 1985. They are intended to provide a survey of topics of current interest relative to the structure and the dynamics of molecular systems. The papers have been selected on the basis of their relevance to the following four topics: i) molecular conformations and transformations; H) molecular relaxation and motion; iii) charge, spin and momentum distributions and intermolecular interactions; iv) collective phenomena in condensed matter. The first volume deals mostly with the first two topics, the second volume mostly with the last two. The two volumes consist of an approximately equal number of self-con tained, reference contributions covering recent achievements in active branches of molecular physics and physical chemistry. The first two papers of the present volume deal with theoretical aspects of intermolecular interactions: the first paper with the physical origin of the so-called non-exchange molecular terms, a complete deriva tion of which is given using Rayleigh-Schrodinger second-order perturba tion theory; the second paper with the symmetry analysis of the effects of interactions between rigid molecules and crystal environments, using the isodynamic-group theoretical approach devised by Altmann for non rigid systems.

Author: Robert A. Evarestov
Publisher: Springer Science & Business Media
ISBN: 3540487484
Category : Science
Languages : en
Pages : 559

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Book Description
This book delivers a comprehensive account of the main features and possibilities of LCAO methods for the first principles calculations of electronic structure of periodic systems. The first part describes the basic theory underlying the LCAO methods applied to periodic systems and the use of wave-function-based, density-based (DFT) and hybrid hamiltonians. The second part deals with the applications of LCAO methods for calculations of bulk crystal properties.

Author: R. G. Woolley
Publisher: Springer Science & Business Media
ISBN: 1468437372
Category : Science
Languages : en
Pages : 560

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Book Description
The Advanced Study Institute on "Quantum Dynamics of Molecules: The New Experimental Challenge to Theorists," which was sponsored by the Scientific Affairs Division of NATO, was held at Trinity Hall, Ca~bridge, England from September 15th till September 29th, 1979. In all, a total of 79 lecturers and students attended the meeting: they had diverse backgrounds in chemistry, physics and mathematics. In my proposal to NATO requesting financial support for an Advanced Study Institute, I suggested that molecular physics was facing a qualitatively new experimental situation in which the exploration of previously inaccessible dynamical phenomena would become of increasing importance. At the same time I was aware that in recent years powerful theoretical techniques, that might prove crucial tools for the interpretation of the new experiments, have been developed in mathematics and theoretical physics. The aim of the ASI was to review at an advanced level these recent developments, juxtaposing new theory with new experimental pos sibilities in the hope that the participants in the-Institute would through their subsequent work increase the awareness of the whole molecular theory community of the changing nature of chemical physics. The recent developments in laser spectroscopy, particle scatter ing experiments and molecular beam technology imply that an entirely new class of phenomena involving molecules in gasses and liquids can now be investigated.

Author: Simon L. Altmann
Publisher: Courier Corporation
ISBN: 0486445186
Category : Mathematics
Languages : en
Pages : 356

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Book Description
This text presents a consistent description of the geometric and quaternionic treatment of rotation operators. Covers the fundamentals of symmetries, matrices, and groups and presents a primer on rotations and rotation matrices. Also explores rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, more. Includes problems with solutions.

Author: Shoon K. Kim
Publisher: Cambridge University Press
ISBN: 0521640628
Category : Mathematics
Languages : en
Pages : 512

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Book Description
From the pioneering author in the field, this book is ideal for condensed matter physicists and physical chemists.

Author: Patrick W. M. Jacobs
Publisher: Cambridge University Press
ISBN: 9780521642507
Category : Mathematics
Languages : en
Pages : 520

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Book Description
This book provides a rigorous account on the fundamentals and applications of Group Theory to chemical physics.

Author: Paul G. Mezey
Publisher: Springer Science & Business Media
ISBN: 940113698X
Category : Science
Languages : en
Pages : 296

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Book Description
Molecular chirality is one of the fundamental aspects of chemistry. Chirality properties of molecules have implications in a wide variety of subjects, ranging from the basic quantum mechanical properties of simple of a few atoms to molecular optical activity, asymmetric synthesis, systems and the folding pattern of proteins. Chirality, in both the geometrical and the topological sense, has also been the subject of investigations in various branches of mathematics. In particular, new developments in a branch of topology, called knot theory, as well as in various branches of discrete mathematics, have led to a novel perspective on the topological aspects of molecular chirality. Some of the mathematical advances have already found applications to the interpretation of new concepts in theoretical chemistry and mathematical chemistry, as well as to novel synthetic approaches leading to new molecules of exceptional structural properties. Some of the new developments in molecular chirality have been truly fundamental to the theoretical understanding and to the actual practice of many aspects of chemistry. The progress in this field has been very rapid, even accelerating in recent years, and a review appears more than justified. This book offers a selection of subjects covering some of the latest developments. Our primary aim is to clarify some of the basic concepts that are the most prone to misinterpretation and to provide brief introductions to some of those subjects that are expected to have further, important contributions to our understanding of molecular properties and chemical reactivity.

Author: Gregory S. Chirikjian
Publisher: CRC Press
ISBN: 1000697339
Category : Mathematics
Languages : en
Pages : 555

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Book Description
First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.