Applications of group theory to atoms, molecules, and solids / Thomas Wolfram, Şinasi Ellialtioğlu.

Format:

Book

Author/Creator:

Wolfram, Thomas, 1936- author.

Language:

English

Subjects (All):

Solids--Mathematical models.

Solids.

Molecular structure.

Atomic structure.

Group theory.

Physical Description:

1 online resource (xii, 471 pages) : digital, PDF file(s).

Other Title:

Applications of Group Theory to Atoms, Molecules, & Solids

Place of Publication:

Cambridge : Cambridge University Press, 2014.

Language Note:

English

Summary:

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.

Contents:

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

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

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

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)

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

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

8. Transition-metal complexes

8.1. An octahedral complex

8.2.A tetrahedral complex

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

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

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

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

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

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

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

ISBN:

1-107-45408-5

1-107-46117-0

1-107-45914-1

1-107-46843-4

1-107-47307-1

1-107-46494-3

1-107-47206-7

1-139-23629-6