SUBJECT INDEX

Activated complex, 624Activated state, 624Activation by coordination, 639, 741, 742Activation energy, 624, 656Adiabatic approximation, 15, 175, 325, 730

criterion, 327full, 328simple (Born–Oppenheimer), 327

Adiabatic potential energy surface (APES), 7,327

in Jahn–Teller problems, see JT problemsAmplification rule, see Jahn–Teller distortionsAngular overlap model, 151Anharmonicity

corrections, 638, 742vibronic, 335

Antiferrodistortive interactions (ordering), 567Antiferromagnetic interaction (ordering), 444,

457Arrenius reaction rate, 624Atomic

charge effective, 23, 146, 437functions, 19

relativistic, 32Slater type, 22

orbital (AO), 19

Electronic Structure and Properties of Transition Metal Compounds: Introduction to the Theory,Second Edition By Isaac B. BersukerCopyright © 2010 John Wiley & Sons, Inc.

hybridized, 24state, 18

one-electron, 19multielectron, 36

term, 36Auger electron spectroscopy, 422

Basis set, 24, 157contracted, 159correlation consistent, 160double-zeta, 158extended, 158Gaussian, 158Huzinaga, 159minimal, 158Pople, 159superposition error, 161valence, 158

Berry pseudorotation, see PseudorotationBispinor, 31, 168, 185Bohr magneton, 29, 380Bond order, 145Bonding

coordination, 11, 241diorbital, 257, 261metal–metal, 279

745

746 SUBJECT INDEX

monoorbital, 257, 259, 728multicenter, 273multiorbital, 257, 741valence, 10σ , π , δ, . . ., 25σ + π , 27, 269

Bridging ligand, 279Broken symmetry effect, 568

Chargecapacitance, see Redox capacitancedistribution, 133effective, 22, 144, 434transfer, 144

intramolecular, 579mutual compensation, 213orbital, 144, 258, 640spectra, 416

Charge-controlled reactions, 571Chemical activation of

carbon monoxide, 642, 646cyan, 742, 743dinitrogen, 646, 729dioxygen, 650double bond, 663hydrogen, 649, 729JT induced, 652nitrogen monoxide, 648

Chemical bond. See also Bondingclassification, 11, 238

genealogical, 239conjugated (orbital), 11, 240coordination, 11, 241definition, 7, 15donor-acceptor, 11, 241in nontransition elements, 245valence, 10, 239

Chemical hardness (softness), 588Chemical potential, 588Chemical reaction

carbonyl insertion, 666charge-controlled, 629CO reductive hydrogenation, 666energy barrier, 656ligand coupling and cleavage, 662olefin insertion, 674orbital-controlled, 630photochemical, 682rate, 624stereoselective, 630substitution, 656symmetry rules, 630trans-effect, 657Ziegler–Natta polymerization, 677

Chemical reactivity, 623Chemical shift, see Photoelectron spectracis-effect, 544Clebsh–Gordan coefficients, 73, 93, 187Computer

experiment, 6programs, 165

Configuration interaction (CI), 44, 108, 162CI satellites, 434multireference (MRCI), 163s-configuration interaction, 455

Coordinatesnormal, 328symmetrized, 335, 731

Coordination bond. See also Chemical bonddefinition, 9, 241features, 243

Coordination compound (system)definition, 10, 241of posttransition elements, 245of pretransition elements, 245mixed-valence, 591

Coordination theory, 10Correlation effects, see Electron correlation

effectsCoulomb integral, 45, 134Coupled-cluster approximation, 163Covalence

electrons, 251in ESR, 452in JT distortions, 452weak, 149, 717

Creutz–Taube ion, see Mixed-valence compoundsCrossover phenomenon, see Spin-crossoverCrystal field

extrastabilization, 124, 712icosahedral, 696, 714parameter, 121theory, 84

Curie law, 448

d electron heterogeneity, 149, 175, 211Deformation density (DD), 143, 484, 737

DD modelling, 490fragment DD, 488

Density functional theory (DFT), 171, 718, 722time-domain DFT (TDDFT), 177

Density matrix, 145Diamagnetism, 445Dichroism (polychroism), 468

circular, 468magnetic circular, 468

Dipolar instability, 376Dirac equation, 28, 168

SUBJECT INDEX 747

Doppler effect, 474Double exchange, 597Dushinsky effect, see Optical spectraδ-function, δ-symbol, 47, 58

Effective charge, 22, 144, 434Electron affinity, 580Electron-conformational effects, 609Electron correlation effects, 115, 157, 161Electron potentials, see Standard electron

potentialsElectron transfer

intermolecular, 579outer-sphere, 583probability (in MV compounds), 600reactions, 580

Electron spin resonance (ESR) spectra, 449angular dependence, 453covalence reduction, 452fine structure, 455g-factor, 446, 450hyperfine structure, 455in the Jahn–Teller effect, 452super-hyperfine structure, 456

Electronegativity, 580Electroneutrality principle, 213, 640Electronic configuration, 36, 71, 247

complementary, 42, 46, 92high-spin, 100, 105, 251, 715low-spin, 107, 251, 715

Electronic density, 143reference, 488spherical model, 514

Electronic equation, 326Electronic transitions. See also Optical spectra

absorption coefficient, 397band shapes, 396charge transfer, 416d-d, 406

between degenerate states, 422, 735forbidden, 402Franck–Condon principle, 393

factor, 393, 401intervalence, 544

radiationless, 401vertical, 393

vibrational induced, 409zero-phonon line, 401

ENDOR, 457Epikernel principle, 522Exchange-correlation potential, 173Exchange interaction, 8, 45, 457

anisotropic, 465antiferromagnetic, 457

antisymmetric, 464biquadratic, 464double exchange, 536ferromagnetic, 457indirect, 457isotropic, 459

Excitation by coordination, 258Extinction coefficient, see Optical spectraExtrastabilization energy, 124EXAFS, see X-ray absorption spectroscopy

Fenske–Hall method, 169Fermi

contact interaction, 455, 475hole, 161

Ferrimagnetic ordering, 444Ferrodistortive

interactions, 567ordering, 567

Ferroelastic interactions, see Structural phasetransitions, ferroelastic

Ferroelectric interactions, see Structural phasetransitions, ferroelectric

Ferroelectricity, 568Ferromagnetic interaction (ordering), 444, 457Ferrimagnetism, 445Ferromagnetism, 445Fine-structure constant, 32Fockian (Fock effective Hamiltonian), 50, 134,

155Force constant, primary, 339Form-function, see Optical spectraFourier transform, 440Fragmentary calculations, 202Fragment deformation density, 488Franck–Condon principle, see Electronic

transitionsFrontier orbitals, 627

generalized, 628

γ -Resonance spectroscopy (GRS), 472, 737isomer shift, 475quadrupole splitting, 476hyperfine structure, 478

GAMESS (computer programs), 165GAUSSIAN (computer programs), 165Gaussian functions, 158Geometry optimization, 165Group orbital, 137Group representation, 64, 692

character, 65, 692irreducible (IrRep), 66two-valued (double group), 81, 187

748 SUBJECT INDEX

Hamiltonian, 12Dzyaloshinsky–Moriya, 464HDVV, 459Ising, 465relativistic, see Dirac equationspin-Hamiltonian, 448

Hard and soft acids and base, 587Harmonic

approximation, 329oscillator, 329

Hartree approximation, 47, 173Hartree–Fock, 47, 134

equation, 49limit solution, 158method, 47restricted, 156unrestricted, 156wavefunction, 23

Hartree–Fock–Roothane method, 154Heitler–London approximation, 8Helicoidal structure, 571High-spin complexes, 100, 105, 715Hindered rotations, see PseudorotationsHOMO (highest occupied MO), 149Huckel method

extended, 192iterative (SCCC), 193, 716

Hund rule, 38Hypsochromic series, 413Hybridization, 24, 51, 707Hysteresis, 467

Icosahedral field, 130, 696, 714Incommensurate phases, 571Inert gas rule, 516, 738

generalized, 517INDO, 175Infrared absorption, 417Intersection (nonintersection) rule, 113Intervalence transition, 596Intuition, 2Ionization energy (potential), 22Irreducible representation (IrRep), see Group

representationIsomer

distortion isomers, 559shift, 475

j-j coupling, 40, 52, 193, 311, 707Jahn–Teller

active modes, 347dynamics, 363distortions

amplification rule, 521

isomer, 559off-center, 528pulsating, 313static, 309

effect, 348cooperative, 567dynamic, 363hidden, 387static, 360

problemsmultimode, 352E ⊗ b1, 543E ⊗ (b1 + b2), 353E ⊗ e, 353(E + A) ⊗ e, 375T ⊗ (e + t2), 364T ⊗ e, 365T ⊗ t2, 366(A1g + T1u) ⊗ t1u, 372(A1g + T1u) ⊗ (t1u + eg + t2g), 536�8 × (e + t2), 369pseudo-effect, 349, 369, 738. See also

Pseudo JT effectstabilization energy, 354theorem, 344

Kohn–Sham equations, 172Koopmans theorem, 50, 254Kramers doublet, 294, 346, 449Kroneker index, see δ-function, δ-symbol

Landeg factor, 446, 450intervals, 39, 446

Langeven theory, 443LCAO, 133Ligand

activation, see Chemical activationcoordination

bridging, 279geometry, 530mutual influence, 544semibridging, 288

Ligand fieldarbitrary, 112intermediate, 116parameter, 121strong, 106, 117, 251theory, 123weak, 100, 103, 116, 251

Local density approximation (LDA), 175Localization–delocalization

alternative, 592coexistence, 604, 740

SUBJECT INDEX 749

Lone pairs, 509, 535, 738inert, 535

Low-spin complexes, see Electronicconfigurations

LUMO (lowest unoccupied MO), 149

Madelung potential, 193Magnetic

anisotropy, 443circular dichroism, 468exchange coupling, 457hyperfine structure, 479moment, 444, 735

reduction (quenching), 446orbitals, 460, 737susceptibility, 443, 447, 736

Magnetization, 443Marcus equation, 625Metal–metal bond, 236Mixed-valence

compounds, 591dimmers, 592

Creutz–Taube ion, 594intervalence transition, 596parameter, 593phase transitions, 605trimers, 601

Moleculardynamics, 206engineering, 1, 15magnets, 465mechanics, 206modeling, 206orbitals, 132

antibonding, 147bonding, 147nonbonding, 147symmetrized, 74, 137vibronic, 343

shapes, 506symmetry, 54vibrations, 325

Mossbauer effect, 472Moeller–Plesset (MP) approximation, 163Multielectron

states, 36terms, 37wavefunctions, 40

Multimode problem, see JT problem, multimodeMultiorbital bonding, see BondingMutual influence of ligands, 544, 739

cis-influence, 544trans-effect, 657

trans-influence, 544vibronic theory, 549

Nephelauxeticeffect, 414series, 414, 733

Neutron diffraction, 493Nonintersection rule, 113, 712Normal coordinates, 80Nuclear hyperfine splitting, see γ -Resonance

spectroscopyNuclear magnetic resonance (NMR), 540

Operator, 12, 56Optical activity, 468Optical spectra. See also Electronic transitions

absorption coefficient, 397band

form function, 398maximum, 399, 400shape, 396width, 400

d-d, 405, 422dichroism (polychroism), 403dipolar, 396Dushinski effect, 398extinction coefficient, 404oscillator strength, 404, 406parity forbidden, 405resonance fluorescence, 401selection rules, 402, 733spectral density, 397spin-forbidden (intersystem combinations),

405Stocks shift, 401vibrational broadening, 393vibrational induced, 409zero-phonon line, 401

Orbital. See also Molecular orbital (MO)chemical shift, 437contraction, 303frontier, see HOMO, LUMOGaussian, see Basis sethybridization, 24, 27, 52, 508overlap, 24Slater type, see Basis setsymmetry rules, 741vibronic constants, 340, 610, 636

Orbital-controlled reactions, 571Oscillator strength, see Optical spectraOverlap

density, 144differential, 25integral, 24, 140

750 SUBJECT INDEX

Overlap (Continued)model, see Angular overlap modelnegative, 151orbitals, 24population, 144zero differential, 188

Pairing energy, 109, 251, 465, 712Paradigm TEST (two electronic states in

transformations), 381, 732, 740Paramagnetic

relaxation, 457susceptibility, 443, 447, 736

Paramagnetism, 443temperature independent (Van Fleck), 448

Paulimatrices, 31principle, 8, 36, 40, 72

Phase transitions, see Structural phase transitionsPhotoelectron spectra, 427

angular dependence, 436Auger (APS), 422chemical shift, 436, 735moments of distribution, 433multiplet structure, 435projection formula, 76shake-up satellites, 431ultraviolet (UPS), 422X-ray (XPS), 422

Pseudo-degeneracy, see Pseudo JTEPseudo Jahn–Teller effect, 349, 369, 738

illustration, 374multilevel, 378strong, 370weak, 370

Pseudopotentials, 170Pseudorotation, 362, 539, 738

Berry, 509, 540Jahn–Teller, 541

Pulse motions (pulsating deformations), 362Plasticity effect, 554, 739

Quasirelativisticapproach, 167, 185parameterization, 198

Quadrupole splitting, 476Quantum-mechanical/molecular mechanics

(QM/MM) method, 211

Racah parameters, 36, 42, 46, 107Radiationless transition, 401Rayleigh scattering, 419Raman effect, 418

resonance spectra, 421spectra, 420, 734

Reactivity, see Chemical reactivityReagents

electrophilic, 628nucleophilic, 628radical, 628

Redox capacitance, 584Redox nobility, 304Relativistic. See also Quasirelativistic

approaches, 167, 184atomic states, 30, 32

functions, 34, 51contraction, 303effects , 13, 185, 303, 314

Renner–Teller effect, 347Resonance integral, 134, 140Roothaan method, 143Russell–Saunders coupling, 36, 52, 707

Schrodinger equation, 12, 325, etc.Secular equation, 11, 135, 141Selection rules, 70, 402, 709Self-consistent field (SCF) method, 48, 154Semiclassical approximation, 358, 398Semiempirical methods, 187Slater–Condon parameters, 36, 42, 46Slater orbitals, 22, 158Spectrochemical series, 412, 733Spin-crossover, 130, 465, 482, 715, 727Spin density, 493Spin-Hamiltonian, 448Spin-orbital

coupling constant, 30, 39interaction, 28, 186splitting, 311

reduction, 314Spin multiplicity, 36Spin-resonance, see Electron spin resonance

(ESR)ferroelastic, 570ferroelectric, 568helicoidal, 509incommensurate, 571in MV trimers, 605order-disorder, 566structural-magnetic, 572

Super-exchange (indirect exchange) interaction,459

Super-hyperfine interaction, see ESRSupramolecular chemistry, 663Symmetry

breaking, 568classification on, 65, 124

SUBJECT INDEX 751

double group, 81group, 60

representations, 64tables of, 692

molecular, 54transformation (operation), 54, 60transformation matrix, 56

character, 65, 692Symmetrized

orbitals, 74, 76, 78vibrations, 74

Tanabe–Sugano diagrams, 112, 130TEST, see Paradigm TESTTopological (Berry) phase, 363, 731trans effect, 657trans influence, 474Transition dipole moment, 341Tunnelling, 362

Unitary transformation, 49, 58Undistinguishability principle, 8, 40

Valenceactivity, 304basis set, 146bond, 10, 241directed, 27, 508, 737state, energy of ionization (EIVS), 192

Variational principle, 47, 134Vibrational

induced transitions, see Optical spectrarepresentation, 79

Vibrations, 325classification, 70fundamental frequency, 418harmonic, 328mechanical, 330normal, 70overtone (anharmonic), 418symmetrized, 74, 80, 734

Vibronicamplification, 521anharmonicity, 335constants, 338

dimensionless, 360linear, 338orbital, 340quadratic, 339

effect, cooperative, 566interaction (coupling), 326, 337molecular orbital, 343reduction, 363

factor, 364in ESR spectra, 452

stereochemistry, 519

Wave-particle duality, 3Wigner–Eckart theorem, 73

XANES, 440Xα method, 375X-ray absorption spectroscopy (EXAFS), 440

Zeeman effect, 450, 478Zeise salt, 233Zero-phonon line, 401, 473