Applications of group theory to atoms, molecules, and solids /Thomas Wolfram, Şinasi Ellialtioğlu.
- Cambridge : Cambridge University Press, (c)2014.
- 1 online resource (xii, 471 pages) : illustrations
Includes bibliographies and index.
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.
"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"--
9781107472068 9781139236294
Solids--Mathematical models. Molecular structure. Atomic structure. Group theory.