TY  - BOOK
AU  - Wolfram,Thomas
TI  - Applications of group theory to atoms, molecules, and solids /Thomas Wolfram, Şinasi Ellialtioğlu
SN  - 9781107472068
AV  - QC176 .A675 2014
PY  - 2014///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Solids
KW  - Mathematical models
KW  - Molecular structure
KW  - Atomic structure
KW  - Group theory
KW  - Electronic Books
N1  - 2; 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; 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; 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; 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; 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; Contents note continued: 14.4. Metallic and semiconducting nanotubes --; 14.5. The nanotube density of states --; 14.6. Curvature and energy gaps --; References --; Exercises; 2; b
N2  - "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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