000 07494nam a22004458i 4500
001 CR9781139236294
003 UkCbUP
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006 m|||||o||d||||||||
007 cr||||||||||||
008 120126s2014||||enk o ||1 0|eng|d
020 _a9781139236294 (ebook)
020 _z9781107028524 (hardback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQC176
_b.W65 2014
082 0 0 _a530.4/1015122
_223
100 1 _aWolfram, Thomas,
_d1936-
_eauthor.
_968356
245 1 0 _aApplications of group theory to atoms, molecules, and solids /
_cThomas Wolfram, Şinasi Ellialtioğlu.
246 3 _aApplications of Group Theory to Atoms, Molecules, & Solids
264 1 _aCambridge :
_bCambridge University Press,
_c2014.
300 _a1 online resource (xii, 471 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 _aMachine 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.
505 0 _aContents 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.
505 0 _aContents 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.
505 0 _aContents 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.
505 0 _aContents 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.
505 0 _aContents note continued: 14.4. Metallic and semiconducting nanotubes -- 14.5. The nanotube density of states -- 14.6. Curvature and energy gaps -- References -- Exercises.
520 _aThe 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. Using a clearly defined, eight-step program, this book helps readers to understand the power of group theory, what information can be obtained from it, and how to obtain it. The book takes in modern topics, such as graphene, carbon nanotubes and isotopic frequencies of molecules, as well as more traditional subjects: the vibrational and electronic states of molecules and solids, crystal field and ligand field theory, transition metal complexes, space groups, time reversal symmetry, and magnetic groups. With over 100 end-of-chapter exercises, this book is invaluable for graduate students and researchers in physics, chemistry, electrical engineering and materials science.
650 0 _aSolids
_xMathematical models.
_93269
650 0 _aMolecular structure.
_92334
650 0 _aAtomic structure.
_915485
650 0 _aGroup theory.
_914163
776 0 8 _iPrint version:
_z9781107028524
856 4 0 _uhttps://doi.org/10.1017/CBO9781139236294
942 _cEBK
999 _c82352
_d82352