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BL
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| Record Number
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661174
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dltt
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| Main Entry
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Wolfram, Thomas,1936-
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| Title & Author
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Applications of group theory to atoms, molecules, and solids /\ Thomas Wolfram, Şinasi Ellialtıoğlu
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| Page. NO
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xii, 471 pages :: illustrations ;; 26 cm
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| ISBN
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9781107028524 (hardback)
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: 1107028523 (hardback)
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| Bibliographies/Indexes
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Includes bibliographical references and index
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| Contents
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Machine generated contents note: 1.Introductory example: Squarene -- 1.1.In-plane molecular vibrations of squarene -- 1.2.Reducible and irreducible representations of a group -- 1.3.Eigenvalues and eigenvectors -- 1.4.Construction of the force-constant matrix from the eigenvalues -- 1.5.Optical properties -- References -- Exercises -- 2.Molecular vibrations of isotopically substituted KB2 molecules -- 2.1.Step 1: Identify the point group and its symmetry operations -- 2.2.Step 2: Specify the coordinate system and the basis functions -- 2.3.Step 3: Determine the effects of the symmetry operations on the basis functions -- 2.4.Step 4: Construct the matrix representations for each element of the group using the basis functions -- 2.5.Step 5: Determine the number and types of irreducible representations -- 2.6.Step 6: Analyze the information contained in the decompositions -- 2.7.Step 7: Generate the symmetry functions -- 2.8.Step 8: Diagonalize the matrix eigenvalue equation --
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Contents note continued: 2.9.Constructing the force-constant matrix -- 2.10.Green's function theory of isotopic molecular vibrations -- 2.11.Results for isotopically substituted forms of H2O -- References -- Exercises -- 3.Spherical symmetry and the full rotation group -- 3.1.Hydrogen-like orbitals -- 3.2.Representations of the full rotation group -- 3.3.The character of a rotation -- 3.4.Decomposition of D(l) in a non-spherical environment -- 3.5.Direct-product groups and representations -- 3.6.General properties of direct-product groups and representations -- 3.7.Selection rules for matrix elements -- 3.8.General representations of the full rotation group -- References -- Exercises -- 4.Crystal-field theory -- 4.1.Splitting of d-orbital degeneracy by a crystal field -- 4.2.Multi-electron systems -- 4.3.Jahn---Teller effects -- References -- Exercises -- 5.Electron spin and angular momentum -- 5.1.Pauli spin matrices -- 5.2.Measurement of spin --
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Contents note continued: 5.3.Irreducible representations of half-integer angular momentum -- 5.4.Multi-electron spin-orbital states -- 5.5.The L---S-coupling scheme -- 5.6.Generating angular-momentum eigenstates -- 5.7.Spin---orbit interaction -- 5.8.Crystal double groups -- 5.9.The Zeeman effect (weak-magnetic-field case) -- References -- Exercises -- 6.Molecular electronic structure: The LCAO model -- 6.1.N-electron systems -- 6.2.Empirical LCAO models -- 6.3.Parameterized LCAO models -- 6.4.An example: The electronic structure of squarene -- 6.5.The electronic structure of H2O -- References -- Exercises -- 7.Electronic states of diatomic molecules -- 7.1.Bonding and antibonding states: Symmetry functions -- 7.2.The "building-up" of molecular orbitals for diatomic molecules -- 7.3.Heteronuclear diatomic molecules -- Exercises -- 8.Transition-metal complexes -- 8.1.An octahedral complex -- 8.2.A tetrahedral complex -- References -- Exercises --
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Contents note continued: 9.Space groups and crystalline solids -- 9.1.Definitions -- 9.2.Space groups -- 9.3.The reciprocal lattice -- 9.4.Brillouin zones -- 9.5.Bloch waves and symmorphic groups -- 9.6.Point-group symmetry of Bloch waves -- 9.7.The space group of the k-vector, gsk -- 9.8.Irreducible representations of gsk -- 9.9.Compatibility of the irreducible representations of gk -- 9.10.Energy bands in the plane-wave approximation -- References -- Exercises -- 10.Application of space-group theory: Energy bands for the perovskite structure -- 10.1.The structure of the ABO3 perovskites -- 10.2.Tight-binding wavefunctions -- 10.3.The group of the wawvector, gk -- 10.4.Irreducible representations for the perovskite energy bands -- 10.5.LCAO energies for arbitrary k -- 10.6.Characteristics of the perovskite bands -- References -- Exercises -- 11.Applications of space-group theory: Lattice vibrations -- 11.1.Eigenvalue equations for lattice vibrations --
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Contents note continued: 11.2.Acoustic-phonon branches -- 11.3.Optical branches: Two atoms per unit cell -- 11.4.Lattice vibrations for the perovskite structure -- 11.5.Localized vibrations -- References -- Exercises -- 12.Time reversal and magnetic groups -- 12.1.Time reversal in quantum mechanics -- 12.2.The effect of T on an electron wavefunction -- 12.3.Time reversal with an external field -- 12.4.Time-reversal degeneracy and energy bands -- 12.5.Magnetic crystal groups -- 12.6.Co-representations for groups with time-reversal operators -- 12.7.Degeneracies due to time-reversal symmetry -- References -- Exercises -- 13.Graphene -- 13.1.Graphene structure and energy bands -- 13.2.The analogy with the Dirac relativistic theory for massless particles -- 13.3.Graphene lattice vibrations -- References -- Exercises -- 14.Carbon nanotubes -- 14.1.A description of carbon nanotubes -- 14.2.Group theory of nanotubes -- 14.3.One-dimensional nanotube energy bands --
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Contents note continued: 14.4.Metallic and semiconducting nanotubes -- 14.5.The nanotube density of states -- 14.6.Curvature and energy gaps -- References -- Exercises
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| Abstract
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"The majority of all knowledge concerning atoms, molecules, and solids has been derived from applications of group theory. Taking a unique, applications-oriented approach, this book gives readers the tools needed to analyze any atomic, molecular, or crystalline solid system"--
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| Subject
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Solids-- Mathematical models
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| Subject
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Molecular structure
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| Subject
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Atomic structure
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| Subject
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Group theory
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| Dewey Classification
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530.4/1015122
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| LC Classification
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QC176.W65 2013
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| Added Entry
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Ellialtıoğlu, Şinasi
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