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Preface | |

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Errata | |

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Additional Notes | |

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Symmetry Transformations and Groups | |

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Symmetry transformations | |

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Definition of a symmetry operation | |

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Rotation operation. Symmetry axes | |

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Reflection operation. Symmetry planes | |

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Improper rotation. Rotoreflection axes | |

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Inversion | |

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Summary | |

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Multiplication of symmetry operations. Commutativity | |

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Interrelation between symmetry elements | |

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Symmetry axes | |

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Axes and planes | |

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Definition of a group | |

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Problems | |

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Point Groups and Their Classes | |

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Equivalent symmetry elements and atoms | |

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Classes of conjugated symmetry operations | |

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Rules for establishing classes | |

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Point groups | |

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The rotation groups C[subscript n] | |

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Groups of rotoreflection transformations S[subscript 2n] | |

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The groups C[subscript ch] | |

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The groups C[subscript nv] | |

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The dihedral groups D[subscript n] | |

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The groups D[subscript nh] | |

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The groups D[subscript nd] | |

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The cubic groups (T, T[subscript d], T[subscript h], O, O[subscript h]) | |

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Continuous groups | |

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Crystallographic point groups | |

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Rules for the determination of molecular symmetry | |

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Problems | |

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Representations of Point Groups | |

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Matrices and vectors | |

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Definition of a matrix | |

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Matrix multiplication | |

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Multiplication of block-diagonal matrices | |

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Matrix characters | |

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Matrix form of geometrical transformations | |

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Group Representations | |

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Reducible and irreducible representations | |

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Irreducible representations of the cubic group | |

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Atomic orbitals and the effect of symmetry operations | |

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Transformation of p orbitals under the cubic group | |

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Transformation of d wavefunctions under the group O | |

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Basis functions and irreducible representations | |

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Properties of irreducible representations | |

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Character tables | |

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Structure of tables | |

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Polar and axial vectors | |

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Complex-conjugate representations | |

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Groups with an inversion centre | |

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Systems of notation | |

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Problems | |

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Crystal Field Theory for One-Electron Ions | |

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Qualitative discussion | |

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Schrodinger equation and irreducible representations | |

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Splitting of one-electron levels in crystal fields | |

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Formula for reduction of representations | |

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Splitting of the p level in tetragonal, trigonal and rhombic fields | |

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Characters of rotation groups | |

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Classification of one-electron states in crystal fields | |

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Splitting of the d level in cubic fields | |

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Splitting of the d level in low-symmetry fields | |

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Representation-reduction tables. External fields | |

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Problems | |

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Many-Electron Ions in Crystal Fields | |

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Quantum states of a free atom | |

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Classification of levels in crystal fields | |

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Classification method for the LS scheme | |

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Parity rule | |

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Reduction tables for representations of the full rotation group | |

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Strong-crystal-field scheme | |

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The direct product of representations | |

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Definition of the direct product | |

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Characters of the direct product | |

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Decomposition of a direct product into irreducible parts | |

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Clebsch-Gordan coefficients | |

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Wigner coefficients | |

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Two-electron terms in a strong cubic field | |

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Energy levels of a two-electron d ion | |

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Nonrepeating representations | |

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Configuration mixing | |

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Many-electron terms in a strong cubic field | |

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Classification of three-electron terms | |

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Wavefunctions of three electrons | |

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Many-electron wavefunctions | |

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Energy levels | |

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Correlation diagrams | |

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Tanabe-Sugano diagrams | |

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Problems | |

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Semiempirical Crystal Field Theory | |

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Crystal field Hamiltonian | |

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Wigner-Eckart theorem for spherical tensors | |

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Spherical tensors | |

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Matrix elements of tensor operators | |

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Projection operators | |

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Spherical tensors in point groups | |

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Projection operator method | |

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Euler angles, and irreducible representations of the rotation groups | |

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Matrices of irreducible representations of point groups | |

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Basis functions of irreducible representations of point groups | |

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Crystal field effective Hamiltonian | |

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Rules for construction of invariants | |

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Energy levels and wavefunctions | |

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Low-symmetry and conformations of octahedral complexes | |

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Problems | |

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Theory of Directed Valence | |

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Directed valence | |

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Classification of directed [sigma] bonds | |

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Hybrid tetrahedral bonds | |

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Inequivalent hybrid bonds | |

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Site-symmetry method | |

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Classification of hybrid [pi] bonds | |

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Construction of hybrid orbitals | |

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Problems | |

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Molecular Orbital Method | |

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General background | |

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Group-theoretical classification of molecular orbitals | |

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Illustrative example | |

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Ammonia molecule | |

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Tetrahedral molecules: formulation of method | |

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Cyclic [pi] systems | |

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Transition metal complexes | |

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Sandwich-type compounds | |

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Superexchange in clusters | |

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Many-electron states in the molecular orbital method | |

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Molecular terms | |

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Cyclic [pi]-system terms | |

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Terms of transition metal complexes | |

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Magnetic states of dimeric clusters | |

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Problems | |

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Intensities of Optical Lines | |

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Selection rules for optical transitions | |

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Interaction with an electromagnetic field | |

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Selection rules | |

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Optical line polarization for allowed transitions | |

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Polarization dichroism in low-symmetry fields | |

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Wigner-Eckart theorem for point groups | |

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Polarization dependence of spectra for allowed transitions | |

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Approximate selection rules | |

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Two-photon spectra | |

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Selection rules for two-photon transitions | |

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Polarization dependence of two-photon spectra | |

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Effective dipole moment method | |

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Effective dipole moment | |

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Intensities of spectral lines | |

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Problems | |

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Double Groups | |

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Spin-orbit interaction | |

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Double-valued representations | |

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The concept of a double group | |

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Classes of double groups | |

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Character tables of the double groups | |

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Reduction of double-valued representations | |

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Problems | |

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Spin-Orbit Interaction in Crystal Fields | |

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Classification of fine-structure levels | |

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One-electron terms in a cubic field | |

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One-electron terms in low-symmetry fields | |

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Many-electron terms | |

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Spin-orbit splitting in one-electron ions | |

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Wavefunctions of fine-structure levels | |

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Spin-orbit splitting of p and d levels in a cubic field | |

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Selection rules for mixing of S[Gamma] terms | |

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Shifts in the fine-structure levels | |

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Fine structure of many-electron terms | |

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Effective spin-orbit interaction | |

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Symmetric and antisymmetric parts of the direct product | |

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Selection rules for real and imaginary operators | |

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Fine structure of optical lines | |

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Intensities and selection rules | |

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Deformation splitting, two-photon transitions | |

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Problems | |

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Electron Paramagnetic Resonance | |

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Magnetic resonance phenomena | |

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The spin Hamiltonian | |

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Zero-field splittings | |

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Zeeman interaction | |

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Hyperfine interaction for spin multiplets | |

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Electric field effects | |

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Linear electric field effect | |

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Quadratic electric field effect | |

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Combined influence of electric and magnetic fields | |

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Effective Hamiltonian for non-Kramers doublets | |

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Effective Hamiltonian for the spin-orbit multiplet | |

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Problems | |

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Exchange Interaction in Polynuclear Coordination Compounds | |

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The Heisenberg-Dirac-Van Vleck model | |

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Spin levels of symmetric trimeric and tetrameric clusters | |

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Trimeric clusters | |

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Tetrameric clusters | |

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Calculation of spin levels in the Heisenberg model | |

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Structure of the exchange Hamiltonian matrix | |

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Example of calculation of spin levels | |

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The 6j- and 9j-symbols | |

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Application of irreducible tensor method, recoupling | |

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Group-theoretical classification of exchange multiplets | |

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"Accidental" degeneracy | |

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Spin-orbit multiplets | |

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Conclusions from the group-theoretical classification | |

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Non-Heisenberg exchange interactions | |

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Paramagnetic resonance and hyperfine interactions | |

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Classification of multiplets of mixed-valence clusters | |

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Problems | |

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Vibrational Spectra and Electron-Vibrational Interactions | |

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Normal vibrations | |

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Degrees of freedom. Normal coordinates | |

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Classification of normal vibrations | |

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Construction of normal coordinates | |

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Selection rules for IR absorption and combination light scattering | |

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Electron-vibrational interactions | |

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Jahn-Teller effect | |

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Jahn-Teller theorem | |

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Adiabatic potentials | |

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Optical-band splitting in the static Jahn-Teller effect | |

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Vibronic satellites of electronic lines | |

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Polarization dependence of the vibronic satellite intensity | |

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Electron-vibrational interaction in mixed-valence clusters | |

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Problems | |

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Characters of Point Groups | |

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Matrices of Irreducible Representations of Selected Point Groups | |

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Basic Functions of Irreducible Representations of Selected Point Groups | |

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Decomposition of Products of Representations | |

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Effective Hamiltonians for Non-Kramers Doublets | |

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References | |

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Additional References | |

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Index | |