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Applications of group theory to atom...

Wolfram, Thomas, (1936-)

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Applications of group theory to atoms, molecules, and solids

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Applications of group theory to atoms, molecules, and solids/ by Thomas Wolfram, Sinasi Ellialtioglu.
作者:	Wolfram, Thomas,
其他作者:	Ellialtioglu, Sinasi.
出版者:	Cambridge :Cambridge University Press, : 2014.,
面頁冊數:	xii, 471 p. :ill., digital ;25 cm.
內容註:	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.
內容註:	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.
內容註:	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.
內容註:	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.
內容註:	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.
內容註:	Contents note continued: 14.4. Metallic and semiconducting nanotubes -- 14.5. The nanotube density of states -- 14.6. Curvature and energy gaps -- References -- Exercises.
標題:	Solids - Mathematical models. -
電子資源:	https://doi.org/10.1017/CBO9781139236294
ISBN:	9781139236294

Applications of group theory to atoms, molecules, and solids
Wolfram, Thomas,1936-

Applications of group theory to atoms, molecules, and solids[electronic resource] /by Thomas Wolfram, Sinasi Ellialtioglu. - Cambridge :Cambridge University Press,2014. - xii, 471 p. :ill., digital ;25 cm.

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.

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. 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.

ISBN: 9781139236294Subjects--Topical Terms:

1533194
Solids
--Mathematical models.

LC Class. No.: QC176 / .W65 2014

Dewey Class. No.: 530.41015122

Applications of group theory to atoms, molecules, and solids
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245 1 0 $a Applications of group theory to atoms, molecules, and solids $h [electronic resource] / $c by Thomas Wolfram, Sinasi Ellialtioglu.
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505 0 $a 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.
505 0 $a 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.
505 0 $a 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.
505 0 $a 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.
505 0 $a 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.
505 0 $a Contents note continued: 14.4. Metallic and semiconducting nanotubes -- 14.5. The nanotube density of states -- 14.6. Curvature and energy gaps -- References -- Exercises.
520 $a 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. 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 $a Solids $x Mathematical models. $3 1533194
650 0 $a Molecular structure. $3 592675
650 0 $a Atomic structure. $3 578760
650 0 $a Group theory. $3 523248
700 1 $a Ellialtioglu, Sinasi. $3 1898230
856 4 0 $u https://doi.org/10.1017/CBO9781139236294