| |
| |
| Preface | |
| |
| |
| Errata | |
| |
| |
| Additional Notes | |
| |
| |
| |
| Symmetry Transformations and Groups | |
| |
| |
| |
| Symmetry transformations | |
| |
| |
| |
| Definition of a symmetry operation | |
| |
| |
| |
| Rotation operation. Symmetry axes | |
| |
| |
| |
| Reflection operation. Symmetry planes | |
| |
| |
| |
| Improper rotation. Rotoreflection axes | |
| |
| |
| |
| Inversion | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Multiplication of symmetry operations. Commutativity | |
| |
| |
| |
| Interrelation between symmetry elements | |
| |
| |
| |
| Symmetry axes | |
| |
| |
| |
| Axes and planes | |
| |
| |
| |
| Definition of a group | |
| |
| |
| Problems | |
| |
| |
| |
| Point Groups and Their Classes | |
| |
| |
| |
| Equivalent symmetry elements and atoms | |
| |
| |
| |
| Classes of conjugated symmetry operations | |
| |
| |
| |
| Rules for establishing classes | |
| |
| |
| |
| Point groups | |
| |
| |
| |
| The rotation groups C[subscript n] | |
| |
| |
| |
| Groups of rotoreflection transformations S[subscript 2n] | |
| |
| |
| |
| The groups C[subscript ch] | |
| |
| |
| |
| The groups C[subscript nv] | |
| |
| |
| |
| The dihedral groups D[subscript n] | |
| |
| |
| |
| The groups D[subscript nh] | |
| |
| |
| |
| The groups D[subscript nd] | |
| |
| |
| |
| The cubic groups (T, T[subscript d], T[subscript h], O, O[subscript h]) | |
| |
| |
| |
| Continuous groups | |
| |
| |
| |
| Crystallographic point groups | |
| |
| |
| |
| Rules for the determination of molecular symmetry | |
| |
| |
| Problems | |
| |
| |
| |
| Representations of Point Groups | |
| |
| |
| |
| Matrices and vectors | |
| |
| |
| |
| Definition of a matrix | |
| |
| |
| |
| Matrix multiplication | |
| |
| |
| |
| Multiplication of block-diagonal matrices | |
| |
| |
| |
| Matrix characters | |
| |
| |
| |
| Matrix form of geometrical transformations | |
| |
| |
| |
| Group Representations | |
| |
| |
| |
| Reducible and irreducible representations | |
| |
| |
| |
| Irreducible representations of the cubic group | |
| |
| |
| |
| Atomic orbitals and the effect of symmetry operations | |
| |
| |
| |
| Transformation of p orbitals under the cubic group | |
| |
| |
| |
| Transformation of d wavefunctions under the group O | |
| |
| |
| |
| Basis functions and irreducible representations | |
| |
| |
| |
| Properties of irreducible representations | |
| |
| |
| |
| Character tables | |
| |
| |
| |
| Structure of tables | |
| |
| |
| |
| Polar and axial vectors | |
| |
| |
| |
| Complex-conjugate representations | |
| |
| |
| |
| Groups with an inversion centre | |
| |
| |
| |
| Systems of notation | |
| |
| |
| Problems | |
| |
| |
| |
| Crystal Field Theory for One-Electron Ions | |
| |
| |
| |
| Qualitative discussion | |
| |
| |
| |
| Schrodinger equation and irreducible representations | |
| |
| |
| |
| Splitting of one-electron levels in crystal fields | |
| |
| |
| |
| Formula for reduction of representations | |
| |
| |
| |
| Splitting of the p level in tetragonal, trigonal and rhombic fields | |
| |
| |
| |
| Characters of rotation groups | |
| |
| |
| |
| Classification of one-electron states in crystal fields | |
| |
| |
| |
| Splitting of the d level in cubic fields | |
| |
| |
| |
| Splitting of the d level in low-symmetry fields | |
| |
| |
| |
| Representation-reduction tables. External fields | |
| |
| |
| Problems | |
| |
| |
| |
| Many-Electron Ions in Crystal Fields | |
| |
| |
| |
| Quantum states of a free atom | |
| |
| |
| |
| Classification of levels in crystal fields | |
| |
| |
| |
| Classification method for the LS scheme | |
| |
| |
| |
| Parity rule | |
| |
| |
| |
| Reduction tables for representations of the full rotation group | |
| |
| |
| |
| Strong-crystal-field scheme | |
| |
| |
| |
| The direct product of representations | |
| |
| |
| |
| Definition of the direct product | |
| |
| |
| |
| Characters of the direct product | |
| |
| |
| |
| Decomposition of a direct product into irreducible parts | |
| |
| |
| |
| Clebsch-Gordan coefficients | |
| |
| |
| |
| Wigner coefficients | |
| |
| |
| |
| Two-electron terms in a strong cubic field | |
| |
| |
| |
| Energy levels of a two-electron d ion | |
| |
| |
| |
| Nonrepeating representations | |
| |
| |
| |
| Configuration mixing | |
| |
| |
| |
| Many-electron terms in a strong cubic field | |
| |
| |
| |
| Classification of three-electron terms | |
| |
| |
| |
| Wavefunctions of three electrons | |
| |
| |
| |
| Many-electron wavefunctions | |
| |
| |
| |
| Energy levels | |
| |
| |
| |
| Correlation diagrams | |
| |
| |
| |
| Tanabe-Sugano diagrams | |
| |
| |
| Problems | |
| |
| |
| |
| Semiempirical Crystal Field Theory | |
| |
| |
| |
| Crystal field Hamiltonian | |
| |
| |
| |
| Wigner-Eckart theorem for spherical tensors | |
| |
| |
| |
| Spherical tensors | |
| |
| |
| |
| Matrix elements of tensor operators | |
| |
| |
| |
| Projection operators | |
| |
| |
| |
| Spherical tensors in point groups | |
| |
| |
| |
| Projection operator method | |
| |
| |
| |
| Euler angles, and irreducible representations of the rotation groups | |
| |
| |
| |
| Matrices of irreducible representations of point groups | |
| |
| |
| |
| Basis functions of irreducible representations of point groups | |
| |
| |
| |
| Crystal field effective Hamiltonian | |
| |
| |
| |
| Rules for construction of invariants | |
| |
| |
| |
| Energy levels and wavefunctions | |
| |
| |
| |
| Low-symmetry and conformations of octahedral complexes | |
| |
| |
| Problems | |
| |
| |
| |
| Theory of Directed Valence | |
| |
| |
| |
| Directed valence | |
| |
| |
| |
| Classification of directed [sigma] bonds | |
| |
| |
| |
| Hybrid tetrahedral bonds | |
| |
| |
| |
| Inequivalent hybrid bonds | |
| |
| |
| |
| Site-symmetry method | |
| |
| |
| |
| Classification of hybrid [pi] bonds | |
| |
| |
| |
| Construction of hybrid orbitals | |
| |
| |
| Problems | |
| |
| |
| |
| Molecular Orbital Method | |
| |
| |
| |
| General background | |
| |
| |
| |
| Group-theoretical classification of molecular orbitals | |
| |
| |
| |
| Illustrative example | |
| |
| |
| |
| Ammonia molecule | |
| |
| |
| |
| Tetrahedral molecules: formulation of method | |
| |
| |
| |
| Cyclic [pi] systems | |
| |
| |
| |
| Transition metal complexes | |
| |
| |
| |
| Sandwich-type compounds | |
| |
| |
| |
| Superexchange in clusters | |
| |
| |
| |
| Many-electron states in the molecular orbital method | |
| |
| |
| |
| Molecular terms | |
| |
| |
| |
| Cyclic [pi]-system terms | |
| |
| |
| |
| Terms of transition metal complexes | |
| |
| |
| |
| Magnetic states of dimeric clusters | |
| |
| |
| Problems | |
| |
| |
| |
| Intensities of Optical Lines | |
| |
| |
| |
| Selection rules for optical transitions | |
| |
| |
| |
| Interaction with an electromagnetic field | |
| |
| |
| |
| Selection rules | |
| |
| |
| |
| Optical line polarization for allowed transitions | |
| |
| |
| |
| Polarization dichroism in low-symmetry fields | |
| |
| |
| |
| Wigner-Eckart theorem for point groups | |
| |
| |
| |
| Polarization dependence of spectra for allowed transitions | |
| |
| |
| |
| Approximate selection rules | |
| |
| |
| |
| Two-photon spectra | |
| |
| |
| |
| Selection rules for two-photon transitions | |
| |
| |
| |
| Polarization dependence of two-photon spectra | |
| |
| |
| |
| Effective dipole moment method | |
| |
| |
| |
| Effective dipole moment | |
| |
| |
| |
| Intensities of spectral lines | |
| |
| |
| Problems | |
| |
| |
| |
| Double Groups | |
| |
| |
| |
| Spin-orbit interaction | |
| |
| |
| |
| Double-valued representations | |
| |
| |
| |
| The concept of a double group | |
| |
| |
| |
| Classes of double groups | |
| |
| |
| |
| Character tables of the double groups | |
| |
| |
| |
| Reduction of double-valued representations | |
| |
| |
| Problems | |
| |
| |
| |
| Spin-Orbit Interaction in Crystal Fields | |
| |
| |
| |
| Classification of fine-structure levels | |
| |
| |
| |
| One-electron terms in a cubic field | |
| |
| |
| |
| One-electron terms in low-symmetry fields | |
| |
| |
| |
| Many-electron terms | |
| |
| |
| |
| Spin-orbit splitting in one-electron ions | |
| |
| |
| |
| Wavefunctions of fine-structure levels | |
| |
| |
| |
| Spin-orbit splitting of p and d levels in a cubic field | |
| |
| |
| |
| Selection rules for mixing of S[Gamma] terms | |
| |
| |
| |
| Shifts in the fine-structure levels | |
| |
| |
| |
| Fine structure of many-electron terms | |
| |
| |
| |
| Effective spin-orbit interaction | |
| |
| |
| |
| Symmetric and antisymmetric parts of the direct product | |
| |
| |
| |
| Selection rules for real and imaginary operators | |
| |
| |
| |
| Fine structure of optical lines | |
| |
| |
| |
| Intensities and selection rules | |
| |
| |
| |
| Deformation splitting, two-photon transitions | |
| |
| |
| Problems | |
| |
| |
| |
| Electron Paramagnetic Resonance | |
| |
| |
| |
| Magnetic resonance phenomena | |
| |
| |
| |
| The spin Hamiltonian | |
| |
| |
| |
| Zero-field splittings | |
| |
| |
| |
| Zeeman interaction | |
| |
| |
| |
| Hyperfine interaction for spin multiplets | |
| |
| |
| |
| Electric field effects | |
| |
| |
| |
| Linear electric field effect | |
| |
| |
| |
| Quadratic electric field effect | |
| |
| |
| |
| Combined influence of electric and magnetic fields | |
| |
| |
| |
| Effective Hamiltonian for non-Kramers doublets | |
| |
| |
| |
| Effective Hamiltonian for the spin-orbit multiplet | |
| |
| |
| Problems | |
| |
| |
| |
| Exchange Interaction in Polynuclear Coordination Compounds | |
| |
| |
| |
| The Heisenberg-Dirac-Van Vleck model | |
| |
| |
| |
| Spin levels of symmetric trimeric and tetrameric clusters | |
| |
| |
| |
| Trimeric clusters | |
| |
| |
| |
| Tetrameric clusters | |
| |
| |
| |
| Calculation of spin levels in the Heisenberg model | |
| |
| |
| |
| Structure of the exchange Hamiltonian matrix | |
| |
| |
| |
| Example of calculation of spin levels | |
| |
| |
| |
| The 6j- and 9j-symbols | |
| |
| |
| |
| Application of irreducible tensor method, recoupling | |
| |
| |
| |
| Group-theoretical classification of exchange multiplets | |
| |
| |
| |
| "Accidental" degeneracy | |
| |
| |
| |
| Spin-orbit multiplets | |
| |
| |
| |
| Conclusions from the group-theoretical classification | |
| |
| |
| |
| Non-Heisenberg exchange interactions | |
| |
| |
| |
| Paramagnetic resonance and hyperfine interactions | |
| |
| |
| |
| Classification of multiplets of mixed-valence clusters | |
| |
| |
| Problems | |
| |
| |
| |
| Vibrational Spectra and Electron-Vibrational Interactions | |
| |
| |
| |
| Normal vibrations | |
| |
| |
| |
| Degrees of freedom. Normal coordinates | |
| |
| |
| |
| Classification of normal vibrations | |
| |
| |
| |
| Construction of normal coordinates | |
| |
| |
| |
| Selection rules for IR absorption and combination light scattering | |
| |
| |
| |
| Electron-vibrational interactions | |
| |
| |
| |
| Jahn-Teller effect | |
| |
| |
| |
| Jahn-Teller theorem | |
| |
| |
| |
| Adiabatic potentials | |
| |
| |
| |
| Optical-band splitting in the static Jahn-Teller effect | |
| |
| |
| |
| Vibronic satellites of electronic lines | |
| |
| |
| |
| Polarization dependence of the vibronic satellite intensity | |
| |
| |
| |
| Electron-vibrational interaction in mixed-valence clusters | |
| |
| |
| Problems | |
| |
| |
| |
| Characters of Point Groups | |
| |
| |
| |
| Matrices of Irreducible Representations of Selected Point Groups | |
| |
| |
| |
| Basic Functions of Irreducible Representations of Selected Point Groups | |
| |
| |
| |
| Decomposition of Products of Representations | |
| |
| |
| |
| Effective Hamiltonians for Non-Kramers Doublets | |
| |
| |
| References | |
| |
| |
| Additional References | |
| |
| |
| Index | |