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| molecular symmetry: Molecular Symmetry David J. Willock, 2009-03-16 Symmetry and group theory provide us with a formal method for the description of the geometry of objects by describing the patterns in their structure. In chemistry it is a powerful method that underlies many apparently disparate phenomena. Symmetry allows us to accurately describe the types of bonding that can occur between atoms or groups of atoms in molecules. It also governs the transitions that may occur between energy levels in molecular systems, which in turn allows us to predict the absorption properties of molecules and hence their spectra. Molecular Symmetry lays out the formal language used in the area using illustrative examples of particular molecules throughout. It then applies the ideas of symmetry to describe molecular structure, bonding in molecules and consider the implications in spectroscopy. Topics covered include: Symmetry elements Symmetry operations and products of operations Point groups used with molecules Point group representations, matrices and basis sets Reducible and irreducible representations Applications in vibrational spectroscopy Symmetry in chemical bonding Molecular Symmetry is designed to introduce the subject by combining symmetry with spectroscopy in a clear and accessible manner. Each chapter ends with a summary of learning points, a selection of self-test questions, and suggestions for further reading. A set of appendices includes templates for paper models which will help students understand symmetry groups. Molecular Symmetry is a must-have introduction to this fundamental topic for students of chemistry, and will also find a place on the bookshelves of postgraduates and researchers looking for a broad and modern introduction to the subject. |
| molecular symmetry: Fundamentals of Molecular Symmetry P.R. Bunker, P. Jensen, 2018-10-03 Winner of a 2005 CHOICE Outstanding Academic Book Award Molecular symmetry is an easily applied tool for understanding and predicting many of the properties of molecules. Traditionally, students are taught this subject using point groups derived from the equilibrium geometry of the molecule. Fundamentals of Molecular Symmetry shows how to set up symmetry groups for molecules using the more general idea of energy invariance. It is no more difficult than using molecular geometry and one obtains molecular symmetry groups. The book provides an introductory description of molecular spectroscopy and quantum mechanics as the foundation for understanding how molecular symmetry is defined and used. The approach taken gives a balanced account of using both point groups and molecular symmetry groups. Usually the point group is only useful for isolated, nonrotating molecules, executing small amplitude vibrations, with no tunneling, in isolated electronic states. However, for the chemical physicist or physical chemist who wishes to go beyond these limitations, the molecular symmetry group is almost always required. |
| molecular symmetry: Molecular Symmetry and Spectroscopy Philip Bunker, 2012-12-02 Molecular Symmetry and Spectroscopy deals with the use of group theory in quantum mechanics in relation to problems in molecular spectroscopy. It discusses the use of the molecular symmetry group, whose elements consist of permutations of identical nuclei with or without inversion. After reviewing the permutation groups, inversion operation, point groups, and representation of groups, the book describes the use of representations for labeling molecular energy. The text explains an approximate time independent Schrödinger equation for a molecule, as well as the effect of a nuclear permutation or the inversion of E* on such equation. The book also examines the expression for the complete molecular Hamiltonian and the several groups of operations commuting with the Hamiltonian. The energy levels of the Hamiltonian can then be symmetrically labeled by the investigator using the irreducible representations of these groups. The text explains the two techniques to change coordinates in a Schrödinger equation, namely, (1) by using a diatomic molecule in the rovibronic Schrödinger equation, and (2) by a rigid nonlinear polyatomic molecule. The book also explains that using true symmetry, basis symmetry, near symmetry, and near quantum numbers, the investigator can label molecular energy levels. The text can benefit students of molecular spectroscopy, academicians, and investigators of molecular chemistry or quantum mechanics. |
| molecular symmetry: Molecular Symmetry And Group Theory Robert L. Carter, 2009-11-12 This comprehensive text provides readers with a thorough introduction to molecular symmetry and group theory as applied to chemical problems. Its friendly writing style invites the reader to discover by example the power of symmetry arguments for understanding otherwise intimidating theoretical problems in chemistry. A unique feature demonstrates the centrality of symmetry and group theory to a complete understanding of the theory of structure and bonding. Fundamental Concepts. Representations of Groups. Techniques and Relationships for Chemical Applications. Symmetry and Chemical Bonding. Equations for Wave Functions. Vibrational Spectroscopy. Transition Metal Complexes. |
| molecular symmetry: Symmetry Theory in Molecular Physics with Mathematica William McClain, 2010-03-12 Prof. McClain has, quite simply, produced a new kind of tutorial book. It is written using the logic engine Mathematica, which permits concrete exploration and development of every concept involved in Symmetry Theory. It is aimed at students of chemistry and molecular physics who need to know mathematical group theory and its applications, either for their own research or for understanding the language and concepts of their field. The book begins with the most elementary symmetry concepts, then presents mathematical group theory, and finally the projection operators that flow from the Great Orthogonality are automated and applied to chemical and spectroscopic problems. |
| molecular symmetry: The Irreducible Tensor Method for Molecular Symmetry Groups J. S. Griffith, 2006-03-10 Suitable for advanced undergraduates and graduate students, this text covers V coefficients for the octahedral group and other symmetry groups, W coefficients, irreducible products and their matrix elements, two-electron formulae for the octahedral group, fractional parentage, X coefficients, spin, and matrices of one-electron operators. 1962 edition. |
| molecular symmetry: Molecular Symmetry and Group Theory R. C. Maurya, J.M. Mir, 2019-09-02 The mathematical fundamentals of molecular symmetry and group theory are comprehensibly described in this book. Applications are given in context of electronic and vibrational spectroscopy as well as chemical reactions following orbital symmetry rules. Exercises and examples compile and deepen the content in a lucid manner. |
| molecular symmetry: Atomic & Molecular Symmetry Groups and Chemistry S.C. Rakshit, 2021-08-18 Atomic Symmetry Groups, being continuous groups, are just a fallout of the Lie Groups and Lie Algebras. Atoms are structurally simpler than molecules but atomic symmetry is more complex than molecular symmetry. In quantum mechanics we study atoms first and then the molecules. In symmetry studies, we do just the reverse. In this book, apart from theories, the description of both the symmetry groups – atomic and molecular, are attended with adequate applications. Please note: Taylor & Francis does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka. |
| molecular symmetry: Symmetry and Group theory in Chemistry M Ladd, 1998-09-01 A comprehensive discussion of group theory in the context of molecular and crystal symmetry, this book covers both point-group and space-group symmetries. - Provides a comprehensive discussion of group theory in the context of molecular and crystal symmetry - Covers both point-group and space-group symmetries - Includes tutorial solutions |
| molecular symmetry: Symmetry Principles in Solid State and Molecular Physics Melvin Lax, 2001-01-01 High-level text applies group theory to physics problems, develops methods for solving molecular vibration problems and for determining the form of crystal tensors, develops translational properties of crystals, more. 1974 edition. |
| molecular symmetry: Elements of Molecular Symmetry Yngve Öhrn, 2000-01-24 A unique, much-needed introduction to molecular symmetry and group theory Elements of Molecular Symmetry takes the topic of group theory a step further than most books, presenting a quantum chemistry treatment useful for computational, quantum, physical, and inorganic chemists alike. Clearly explaining how general groups and group algebra describe molecules, Yngve Öhrn first develops the theory, then provides coverage not only for point groups, but also permutation groups, space groups, and Lie groups. With over three decades of teaching experience, Dr. Öhrn brings to the discussion unprecedented depth and clarity, incorporating rigorous topics at a level accessible to anyone with basic knowledge of calculus and algebra. This unique and timely book: * Extends coverage to molecular orbital theory, * Utilizes powerful examples to illustrate basic concepts * Contains introductory material on space groups and continuous groups, including point-group character tables * Provides a solid background for exploring the theoretical literature |
| molecular symmetry: Symmetry And Spectroscopy Of Molecules K Veera Reddy, 1998 The Book Covers The Essential Basics Of The Group Theory That Are Required For All Sections Of Chemistry And Emphasizes The Necessity Of This Theory To Understand The Theoretical And Applied Aspects Of Molecular Spectroscopy. The Material In This Book Is Presented For A First And Final Year Postgraduate Level Students Of Indian Universities And The Subject Matter Covered In This Book Forms An Essential Part Of One Or Two Papers. This Text Is The Result Of A Long Felt Need For Developing Certain Novel Techniques For The Teaching Of This Course. No More Nightmares Of Group Theory And Spectroscopy! - Is The Ultimate Purpose Of This Book. A Window-Vision Has Been Provided In The Book While Presenting Most Of The Chapters And At Times A Pedagogical Approach Has Been Employed.Chapter 1 Is Presented As A Survey Into The World Of Symmetry Embodied In Nature And Man-Made Environment. Chapters 2 And 3 Journey Through The Basic Concepts Of Symmetry. A Chronology Of Concept-Learning Is Introduced In These Otherwise Highly Descriptive And Heavily Illustrative Chapters. A Number Of Exercises On Molecular Point Groups Is Presented In Chapter 3 With A Range Of Examples Drafted From Both Organic And Inorganic Molecules. The Structure And Symmetry Of Fullerene Molecules Are Presented In Some Detail For The First Time As A Class Room Example. The Background Provided For Non-Mathematical Chemistry Students In Chapters 4 And 5 Is Very Useful For The Advanced Aspects Of Group Theory. An Elaborate Treatment Given On Character Tables In Chapter 6 Serves As Thegate-Way For Many Applied Aspects Of Group Theory. Chapter 7 Contains Exclusive Details Onnormal Mode Analysis.The Information Presented In These Seven Chapters Will Be Vital To The Learning And Application Of All The Branches Of Spectroscopy. Chapter 8 Presents A Combined Treatment On Infrared And Raman Spectroscopies With Emphasis On Selection Rules And Application Of These Techniques To The Determination Of Molecular Structure Through The Use Of Group Theory. Group Theoretical Treatment Has Been Given While Discussing The Structure And Bonding Of Metal Complexes Presented In Chapters 9 And 11. The Formalisms Of Atomic Spectroscopy Are Presented In Chapter 10. Chapter 12 Deals With The Electronic Spectroscopy Of Metal Complexes That Enjoys The Fruits Of Group Theoretical Formulations. |
| molecular symmetry: Fundamentals of Molecular Symmetry P.R. Bunker, 2018-10-03 Winner of a 2005 CHOICE Outstanding Academic Book Award Molecular symmetry is an easily applied tool for understanding and predicting many of the properties of molecules. Traditionally, students are taught this subject using point groups derived from the equilibrium geometry of the molecule. Fundamentals of Molecular Symmetry shows how to set up symmetry groups for molecules using the more general idea of energy invariance. It is no more difficult than using molecular geometry and one obtains molecular symmetry groups. The book provides an introductory description of molecular spectroscopy and quantum mechanics as the foundation for understanding how molecular symmetry is defined and used. The approach taken gives a balanced account of using both point groups and molecular symmetry groups. Usually the point group is only useful for isolated, nonrotating molecules, executing small amplitude vibrations, with no tunneling, in isolated electronic states. However, for the chemical physicist or physical chemist who wishes to go beyond these limitations, the molecular symmetry group is almost always required. |
| molecular symmetry: Symmetry and Spectroscopy Daniel C. Harris, Michael D. Bertolucci, 1989-01-01 Informal, effective undergraduate-level text introduces vibrational and electronic spectroscopy, presenting applications of group theory to the interpretation of UV, visible, and infrared spectra without assuming a high level of background knowledge. 200 problems with solutions. Numerous illustrations. A uniform and consistent treatment of the subject matter. — Journal of Chemical Education. |
| molecular symmetry: Symmetry Roy McWeeny, 2012-05-23 Well-organized volume develops ideas of group and representation theory in progressive fashion. Emphasis on finite groups describing symmetry of regular polyhedra and of repeating patterns, plus geometric illustrations. |
| molecular symmetry: Symmetry through the Eyes of a Chemist Istvan Hargittai, Magdolna Hargittai, 2007-08-29 We have been gratified by the warm reception of our book, by reviewers, colleagues, and students alike. Our interest in the subject matter of this book has not decreased since its first appearance; on the contrary. The first and second editions envelop eight other symmetry-related books in the creation of which we have participated: I. Hargittai (ed.), Symmetry: Unifying Human Understanding, Pergamon Press, New York, 1986. I. Hargittai and B. K. Vainshtein (eds.), Crystal Symmetries. Shubnikov Centennial Papers, Pergamon Press, Oxford, 1988. M. Hargittai and I. Hargittai, Fedezziikf6l a szimmetri6t! (Discover Sym- try, in Hungarian), Tank6nyvkiad6, Budapest, 1989. I. Hargittai (ed.), Symmetry 2: Unifying Human Understanding, Pergamon Press, Oxford, 1989. I. Hargittai (ed.), Quasicrystals, Networks, and Molecules of Fivefold Sym- try, VCH, New York, 1990. I. Hargittai (ed.), Fivefold Symmetry, World Scientific, Singapore, 1992. I. Hargittai and C. A. Pickover (eds.), Spiral Symmetry, World Scientific, Singapore, 1992. I. Hargittai and M. Hargittai, Symmetry: A Unifying Concept, Shelter Publi- tions, Bolinas, California, 1994. We have also pursued our molecular structure research, and some books have appeared related to these activities: vi Preface to the Second Edition I. Hargittai and M. Hargittai (eds.), Stereochemical Applications of Gas-Phase Electron Diffraction, Parts A and B, VCH, New York, 1988. R. Gillespie and I. Hargittai, VSEPR Model of Molecular Geometry, Allyn and Bacon, Boston, 1991. A. Domenicano and I. Hargittai (eds.), Accurate Molecular Structures, Oxford University Press, Oxford, 1992. |
| molecular symmetry: Quantum Chemistry Ajit Thakkar, 2017-10-03 This book provides non-specialists with a basic understanding ofthe underlying concepts of quantum chemistry. It is both a text for second or third-year undergraduates and a reference for researchers who need a quick introduction or refresher. All chemists and many biochemists, materials scientists, engineers, and physicists routinely user spectroscopic measurements and electronic structure computations in their work. The emphasis of Quantum Chemistry on explaining ideas rather than enumerating facts or presenting procedural details makes this an excellent foundation text/reference. The keystone is laid in the first two chapters which deal with molecular symmetry and the postulates of quantum mechanics, respectively. Symmetry is woven through the narrative of the next three chapters dealing with simple models of translational, rotational, and vibrational motion that underlie molecular spectroscopy and statistical thermodynamics. The next two chapters deal with the electronic structure of the hydrogen atom and hydrogen molecule ion, respectively. Having been armed with a basic knowledge of these prototypical systems, the reader is ready to learn, in the next chapter, the fundamental ideas used to deal with the complexities of many-electron atoms and molecules. These somewhat abstract ideas are illustrated with the venerable Huckel model of planar hydrocarbons in the penultimate chapter. The book concludes with an explanation of the bare minimum of technical choices that must be made to do meaningful electronic structure computations using quantum chemistry software packages. |
| molecular symmetry: Chemical Applications of Symmetry and Group Theory Rakshit Ameta, Suresh C. Ameta, 2016-11-03 As the structure and behavior of molecules and crystals depend on their different symmetries, group theory becomes an essential tool in many important areas of chemistry. It is a quite powerful theoretical tool to predict many basic as well as some characteristic properties of molecules. Whereas quantum mechanics provide solutions of some chemical problems on the basis of complicated mathematics, group theory puts forward these solutions in a very simplified and fascinating manner. Group theory has been successfully applied to many chemical problems. Students and teachers of chemical sciences have an invisible fear from this subject due to the difficulty with the mathematical jugglery. An active sixth dimension is required to understand the concept as well as to apply it to solve the problems of chemistry. This book avoids mathematical complications and presents group theory so that it is accessible to students as well as faculty and researchers. Chemical Applications of Symmetry and Group Theory discusses different applications to chemical problems with suitable examples. The book develops the concept of symmetry and group theory, representation of group, its applications to I.R. and Raman spectroscopy, U.V spectroscopy, bonding theories like molecular orbital theory, ligand field theory, hybridization, and more. Figures are included so that reader can visualize the symmetry, symmetry elements, and operations. |
| molecular symmetry: Molecular Symmetry and Spectroscopy Philip R. Bunker, Per Jensen, 2006 The first edition, by P.R. Bunker, published in 1979, remains the sole textbook that explains the use of the molecular symmetry group in understanding high resolution molecular spectra. Since 1979 there has been considerable progress in the field and a second edition is required; the original author has been joined in its writing by Per Jensen. The Material of the first edition has been reorganized and much has been added. The molecular symmetry group is now introduced early on, and the explanation of how to determine nuclear spin statistical weights has been consolidated in one chapter, after groups, symmetry groups, character tables and the Hamiltonian have been introduced. A description of the symmetry in the three-dimensional rotation group K(spatial), irreducible spherical tensor operators, and vector coupling coefficients is now included. The chapters on energy levels and selection rules contain a great deal of material that was not in the first edition (much of it was undiscovered in 1979), concerning the Jahn-Teller effect, the Renner effect, Multichannel Quantum Defect Theory, the use of variational methods for calculating rotational-vibration energy levels, and the contact transformed rotation-vibration Hamiltonian. A new chapter is devoted entirely to weakly bound cluster molecules (often called Van der Waals molecules). A selection of experimental spectra is included in order to illustrate particular theoretical points. |
| molecular symmetry: Introduction to Symmetry and Group Theory for Chemists Arthur M. Lesk, 2004-07-14 This book is based on a one-semester course for advanced undergraduates specializing in physical chemistry. I am aware that the mathematical training of most science majors is more heavily weighted towards analysis – typ- ally calculus and differential equations – than towards algebra. But it remains my conviction that the basic ideas and applications of group theory are not only vital, but not dif?cult to learn, even though a formal mathematical setting with emphasis on rigor and completeness is not the place where most chemists would feel most comfortable in learning them. The presentation here is short, and limited to those aspects of symmetry and group theory that are directly useful in interpreting molecular structure and spectroscopy. Nevertheless I hope that the reader will begin to sense some of the beauty of the subject. Symmetry is at the heart of our understanding of the physical laws of nature. If a reader is happy with what appears in this book, I must count this a success. But if the book motivates a reader to move deeper into the subject, I shall be grati?ed. |
| molecular symmetry: Molecular Symmetry and Group Theory Alan Vincent, 2013-06-05 This substantially revised and expanded new edition of the bestselling textbook, addresses the difficulties that can arise with the mathematics that underpins the study of symmetry, and acknowledges that group theory can be a complex concept for students to grasp. Written in a clear, concise manner, the author introduces a series of programmes that help students learn at their own pace and enable to them understand the subject fully. Readers are taken through a series of carefully constructed exercises, designed to simplify the mathematics and give them a full understanding of how this relates to the chemistry. This second edition contains a new chapter on the projection operator method. This is used to calculate the form of the normal modes of vibration of a molecule and the normalised wave functions of hybrid orbitals or molecular orbitals. The features of this book include: * A concise, gentle introduction to symmetry and group theory * Takes a programmed learning approach * New material on projection operators, and the calcultaion of normal modes of vibration and normalised wave functions of orbitals This book is suitable for all students of chemistry taking a first course in symmetry and group theory. |
| molecular symmetry: Symmetry Breaking in Biology Rong Li, Bruce Bowerman, 2010 Experts examine the mechanisms by which cells polarize, divide asymmetrically, and produce asymmetric structures, providing examples from bacteria, yeast, plants, invertebrates, and mammals. Discussion include the molecular basis of polarization, mechanisms, and more. |
| molecular symmetry: Beautiful Symmetry Alex Berke, 2020-02-18 A coloring book that invites readers to explore symmetry and the beauty of math visually. Beautiful Symmetry is a coloring book about math, inviting us to engage with mathematical concepts visually through coloring challenges and visual puzzles. We can explore symmetry and the beauty of mathematics playfully, coloring through ideas usually reserved for advanced courses. The book is for children and adults, for math nerds and math avoiders, for educators, students, and coloring enthusiasts. Through illustration, language that is visual, and words that are jargon-free, the book introduces group theory as the mathematical foundation for discussions of symmetry, covering symmetry groups that include the cyclic groups, frieze groups, and wallpaper groups. The illustrations are drawn by algorithms, following the symmetry rules for each given group. The coloring challenges can be completed and fully realized only on the page; solutions are provided. Online, in a complementary digital edition, the illustrations come to life with animated interactions that show the symmetries that generated them. Traditional math curricula focus on arithmetic and the manipulation of numbers, and may make some learners feel that math is not for them. By offering a more visual and tactile approach, this book shows how math can be for everyone. Combining the playful and the pedagogical, Beautiful Symmetry offers both relaxing entertainment for recreational colorers and a resource for math-curious readers, students, and educators. |
| molecular symmetry: Orbital Symmetry Roland E. Lehr, Alan P. Marchand, 2013-09-03 Orbital Symmetry: A Problem-Solving Approach was born of the necessity to present to students Woodward and Hoffmann's approach to pericyclic reactions. Hence the tone is introductory, and the book is addressed primarily to an audience of advanced undergraduate and beginning graduate students. The text seeks to familiarize the readers with several of the more often encountered methods of analyzing pericyclic reactions, and these methods should enable the analysis of virtually all of them. Problem solving is the foundation of the approach. Both the introductory and theory sections include problems to prepare the reader for the more extensive chapters of problems that follow. All problems (except those in Chapter VII) are answered in the text and are fully referenced where appropriate. Many of the problems require the use of molecular models if they are to be appreciated. Prentice-Hall's Framework Molecular Models and Benjamin's Maruzen Models are best suited for the construction of the highly strained molecules often encountered in the problems, and their use is recommended. |
| molecular symmetry: Group theory and Symmetry in Chemistry Gurdeep Raj; Ajay Bhagi; Vinod Jain, |
| molecular symmetry: Group Theory for Chemists Kieran C. Molloy, 2004 This undergraduate text deals with basics of group theory and its application to the analysis of vibrational spectra, molecular orbital description of bonding, ligand field theory and other themes within inorganic chemistry. Concise and student- friendly, the book adopts a diagrammatic rather than a rigorous mathematic approach, providing support for lecture courses in chemical group theory offering students opportunities to test their understanding. Problem solving is stressed with numerous self-assessment questions and problem exercises, along with tutorial hints and solutions to selected problems. Part 1 covers the essentials of symmetry and group theory, including symmetry elements and operations, point groups and representations. Part 2 focuses on the application of group theory to vibrational spectroscop building step-wise to show how group theory guides the analysis of vibrational spectra. A brief overview of infrared and Raman spectroscopy techniques is followed by a complete worked example to reiterate key points from earlier sections. Part 3 describes the application of group theory to a molecular orbital approach to chemical bonding. After laying a foundation of the basic rules for forming molecular orbitals using H, and H as examples, the book addresses more complex problems by comparing angular and linear structures for water and planar and pyramidal structures for ammonia. A description of the application of group theory to the bonding in octahedral main group and transitional metal complexes then follows, including an analysis of the influencing crystal field splitting energies. The book concludes with a description of the bonding in ferrocene, bringing together all the ideas presented in earlier sections. |
| molecular symmetry: Properties of Materials Robert E. Newnham, 2005 Crystals are sometimes called 'Flowers of the Mineral Kingdom'. In addition to their great beauty, crystals and other textured materials are enormously useful in electronics, optics, acoustics and many other engineering applications. This richly illustrated text describes the underlying principles of crystal physics and chemistry, covering a wide range of topics and illustrating numerous applications in many fields of engineering using the most important materials today. Tensors, matrices, symmetry and structure-property relationships form the main subjects of the book. While tensors and matrices provide the mathematical framework for understanding anisotropy, on which the physical and chemical properties of crystals and textured materials often depend, atomistic arguments are also needed to quantify the property coefficients in various directions. The atomistic arguments are partly based on symmetry and partly on the basic physics and chemistry of materials. After introducing the point groups appropriate for single crystals, textured materials and ordered magnetic structures, the directional properties of many different materials are described: linear and nonlinear elasticity, piezoelectricity and electrostriction, magnetic phenomena, diffusion and other transport properties, and both primary and secondary ferroic behavior. With crystal optics (its roots in classical mineralogy) having become an important component of the information age, nonlinear optics is described along with the piexo-optics, magneto-optics, and analogous linear and nonlinear acoustic wave phenomena. Enantiomorphism, optical activity, and chemical anisotropy are discussed in the final chapters of the book. |
| molecular symmetry: Symmetry in Inorganic and Coordination Compounds Franca Morazzoni, 2021-04-28 This book addresses the nature of the chemical bond in inorganic and coordination compounds. In particular, it explains how general symmetry rules can describe chemical bond of simple inorganic molecules. Since the complexity of studying even simple molecules requires approximate methods, this book introduces a quantum mechanical treatment taking into account the geometric peculiarities of the chemical compound. In the case of inorganic molecules, a convenient approximation comes from symmetry, which constrains both the electronic energies and the chemical bonds. The book also gives special emphasis on symmetry rules and compares the use of symmetry operators with that of Hamiltonian operators. Where possible, the reactivity of molecules is also rationalized in terms of these symmetry properties. As practical examples, electronic spectroscopy and magnetism give experimental confirmation of the predicted electronic energy levels. Adapted from university lecture course notes, this book is the ideal companion for any inorganic chemistry course dealing with group theory. |
| molecular symmetry: Spectra of Atoms and Molecules Peter F. Bernath, 2005-04-21 1. Introduction. 1.1. Waves, Particles, and Units. 1.2. The Electromagnetic Spectrum. 1.3. Interaction of Radiation with Matter. 1.3a. Blackbody Radiation. 1.3b. Einstein A and B Coefficients. 1.3c. Absorption and Emission of Radiation. 1.3d. Beer's Law. 1.3e. Lineshape Functions. 1.3f. Natural Lifetime Broadening. 1.3g. Pressure Broadening. 1.3h. Doppler Broadening. 1.3i. Transit-Time Broadening. 1.3j. Power Broadening. 2. Molecular Symmetry. 2.1. Symmetry Operations. 2.1a. Operator Algebra. 2.1b. Symmetry Operator Algebra. 2.2. Groups. 2.2a. Point Groups. 2.2b. Classes. 2.2c. Subgroups. 2.3. |
| molecular symmetry: Symmetry, Group Theory, and the Physical Properties of Crystals Richard C Powell, 2010-12-01 Complete with reference tables and sample problems, this volume serves as a textbook or reference for solid-state physics and chemistry, materials science, and engineering. Chapters illustrate symmetry, and its role in determining solid properties, as well as a demonstration of group theory. |
| molecular symmetry: Group Theory Applied to Chemistry Arnout Jozef Ceulemans, 2013-09-03 Chemists are used to the operational definition of symmetry, which crystallographers introduced long before the advent of quantum mechanics. The ball-and-stick models of molecules naturally exhibit the symmetrical properties of macroscopic objects. However, the practitioner of quantum chemistry and molecular modeling is not concerned with balls and sticks, but with subatomic particles: nuclei and electrons. This textbook introduces the subtle metaphors which relate our macroscopic understanding of symmetry to the molecular world. It gradually explains how bodily rotations and reflections, which leave all inter-particle distances unaltered, affect the study of molecular phenomena that depend only on these internal distances. It helps readers to acquire the skills to make use of the mathematical tools of group theory for whatever chemical problems they are confronted with in the course of their own research. |
| molecular symmetry: Molecular Symmetry and Group Theory Robert L. Carter, 1997-12-16 A thorough introduction to molecular symmetry and group theory as applied to chemical problems. Readers will discover by example the power of symmetry arguments in understanding otherwise intimidating theoretical problems in chemistry. This book demonstrates the centrality of symmetry and group theory to a complete understanding of the theory of structure and bonding. |
| molecular symmetry: Molecular Physical Chemistry José J. C. Teixeira-Dias, 2017-01-16 This is the physical chemistry textbook for students with an affinity for computers! It offers basic and advanced knowledge for students in the second year of chemistry masters studies and beyond. In seven chapters, the book presents thermodynamics, chemical kinetics, quantum mechanics and molecular structure (including an introduction to quantum chemical calculations), molecular symmetry and crystals. The application of physical-chemical knowledge and problem solving is demonstrated in a chapter on water, treating both the water molecule as well as water in condensed phases. Instead of a traditional textbook top-down approach, this book presents the subjects on the basis of examples, exploring and running computer programs (Mathematica®), discussing the results of molecular orbital calculations (performed using Gaussian) on small molecules and turning to suitable reference works to obtain thermodynamic data. Selected Mathematica® codes are explained at the end of each chapter and cross-referenced with the text, enabling students to plot functions, solve equations, fit data, normalize probability functions, manipulate matrices and test physical models. In addition, the book presents clear and step-by-step explanations and provides detailed and complete answers to all exercises. In this way, it creates an active learning environment that can prepare students for pursuing their own research projects further down the road. Students who are not yet familiar with Mathematica® or Gaussian will find a valuable introduction to computer-based problem solving in the molecular sciences. Other computer applications can alternatively be used. For every chapter learning goals are clearly listed in the beginning, so that readers can easily spot the highlights, and a glossary in the end of the chapter offers a quick look-up of important terms. |
| molecular symmetry: Bonding through Code Daniel C. Fredrickson, 2020-09-16 This timely and unique publication is designed for graduate students and researchers in inorganic and materials chemistry and covers bonding models and applications of symmetry concepts to chemical systems. The book discusses the quantum mechanical basis for molecular orbital concepts, the connections between molecular orbitals and localized views of bonding, group theory, bonding models for a variety of compounds, and the extension of these ideas to solid state materials in band theory. Unlike other books, the concepts are made tangible to the readers by guiding them through their implementation in MATLAB functions. No background in MATLAB or computer programming is needed; the book will provide the necessary skills. Key Features Visualization of the Postulates of Quantum Mechanics to build conceptual understanding MATLAB functions for rendering molecular geometries and orbitals Do-it-yourself approach to building a molecular orbital and band theory program Introduction to Group Theory harnessing the 3D graphing capabilities of MATLAB Online access to a growing collection of applications of the core material and other appendices Bonding through Code is ideal for first-year graduate students and advanced undergraduates in chemistry, materials science, and physics. Researchers wishing to gain new tools for theoretical analysis or deepen their understanding of bonding phenomena can also benefit from this text. About the Author Daniel Fredrickson is a Professor in the Department of Chemistry at the University of Wisconsin–Madison, where his research group focuses on understanding and harnessing the structural chemistry of intermetallic phases using a combination of theory and experiment. His interests in crystals, structure, and bonding can be traced to his undergraduate research at the University of Washington (B.S. in Biochemistry, 2000) with Prof. Bart Kahr, his Ph.D. studies at Cornell University (2000–2005) with Profs. Stephen Lee and Roald Hoffmann, and his post-doctoral work with Prof. Sven Lidin at Stockholm University (2005–2008). As part of his teaching at UW–Madison since 2009, he has worked to enhance his department’s graduate course, Physical Inorganic Chemistry I: Symmetry and Bonding, through the incorporation of new material and the development of computer-based exercises. |
| molecular symmetry: An Introduction to Molecular Orbitals Yves Jean, François Volatron, 1993 This text for advanced undergraduate and graduate students guides the reader through a smooth progression from the most elementary ideas of molecular orbital theory to an understanding of the electronic structure, geometry, and reactivity of large molecules. It starts with simple molecules and proceeds to relatively large organometallic complexes. The slant is theoretical, but in the last chapter the authors strengthen the link between theory and experiment. Focusing on basic concepts, the authors take a qualitative approach, which enables this text to fill a void in the undergraduate curriculum. The book is intended as a core or supplementary text in an advanced chemistry course. |
| molecular symmetry: Reviews in Computational Chemistry Abby L. Parrill, Kenny B. Lipkowitz, 2017-03-16 The Reviews in Computational Chemistry series brings together leading authorities in the field to teach the newcomer and update the expert on topics centered on molecular modeling. • Provides background and theory, strategies for using the methods correctly, pitfalls to avoid, applications, and references • Contains updated and comprehensive compendiums of molecular modeling software that list hundreds of programs, services, suppliers and other information that every chemist will find useful • Includes detailed indices on each volume help the reader to quickly discover particular topics • Uses a tutorial manner and non-mathematical style, allowing students and researchers to access computational methods outside their immediate area of expertise |
| molecular symmetry: Molecular Physics Wolfgang Demtröder, 2008-09-26 The richly illustrated book comprehensively explains the important principles of diatomic and polyatomic molecules and their spectra in two separate, distinct parts. The first part concentrates on the theoretical aspects of molecular physics, such as the vibration, rotation, electronic states, potential curves, and spectra of molecules. The different methods of approximation for the calculation of electronic wave functions and their energy are also covered. The introduction of basics terms used in group theory and their meaning in molecular physics enables an elegant description of polyatomic molecules and their symmetries. Molecular spectra and the dynamic processes involved in their excited states are given its own chapter. The theoretical part then concludes with a discussion of the field of Van der Waals molecules and clusters. The second part is devoted entirely to experimental techniques, such as laser, Fourier, NMR, and ESR spectroscopies, used in the fields of physics, chemistry, biology, and material science. Time-resolved measurements and the influence of chemical reactions by coherent controls are also treated. A list of general textbooks and specialized literature is provided for further reading. With specific examples, definitions, and notes integrated within the text to aid understanding, this is suitable for undergraduates and graduates in physics and chemistry with a knowledge of atomic physics and familiar with the basics of quantum mechanics. |
| molecular symmetry: Group Theory Mildred S. Dresselhaus, Gene Dresselhaus, Ado Jorio, 2007-12-13 This concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters. |
Molecule - Wikipedia
In molecular sciences, a molecule consists of a stable system (bound state) composed of two or more atoms. Polyatomic ions may sometimes be usefully thought of as electrically charged …
MOLECULAR Definition & Meaning - Merriam-Webster
The meaning of MOLECULAR is of, relating to, consisting of, or produced by molecules. How to use molecular in a sentence.
Molecules | An Open Access Journal from MDPI
Jun 5, 2012 · Molecules is the leading international, peer-reviewed, open access journal of chemistry. Molecules is published semimonthly online by MDPI.
MOLECULAR Definition & Meaning - Dictionary.com
Molecular definition: of or relating to or caused by molecules.. See examples of MOLECULAR used in a sentence.
MOLECULAR | English meaning - Cambridge Dictionary
MOLECULAR definition: 1. relating to molecules (= the simplest units of a chemical substance): 2. relating to molecules…. Learn more.
Molecule | Definition, Examples, Structures, & Facts | Britannica
Apr 21, 2025 · What is a molecule in chemistry? How are atoms related to molecules? What are the different types of molecules based on their composition? How do molecules form chemical …
MOLECULAR definition and meaning | Collins English Dictionary
2 meanings: 1. of or relating to molecules 2. logic (of a sentence, formula, etc) capable of analysis into atomic formulae of.... Click for more definitions.
Molecular | definition of molecular by Medical dictionary
of, pertaining to, or composed of molecules. molecular disease any disease in which the pathogenesis can be traced to a single chemical substance, usually a protein, which is either …
molecular adjective - Definition, pictures, pronunciation and …
Definition of molecular adjective in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
Molecular Compounds - Definition, Examples, Properties, How to …
Jul 25, 2024 · Molecular compounds are substances formed when two or more atoms join together through chemical bonds. These atoms can be from the same element, like oxygen …
Molecule - Wikipedia
In molecular sciences, a molecule consists of a stable system (bound state) composed of two or more …
MOLECULAR Definition & Meaning - Merriam-Webster
The meaning of MOLECULAR is of, relating to, consisting of, or produced by molecules. How to use molecular …
Molecules | An Open Access Journal from MDPI
Jun 5, 2012 · Molecules is the leading international, peer-reviewed, open access journal of chemistry. …
MOLECULAR Definition & Meaning - Dictionary.com
Molecular definition: of or relating to or caused by molecules.. See examples of MOLECULAR used in a sentence.
MOLECULAR | English meaning - Cambridge Dictionary
MOLECULAR definition: 1. relating to molecules (= the simplest units of a chemical substance): 2. relating to …
