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BK

Fifth edition

Oxford : Oxford University Press, [2011]

xiv, 537 stran : barevné ilustrace ; 27 cm

ISBN 978-0-19-954142-3 (brožováno)

Obsahuje bibliografii na stranách 513-515 a rejstřík

001636154

Brief contents : Introduction and orientation 1 // 1 The foundations of quantum mechanics 9 // Mathematical background 1 Complex numbers 35 // 2 Linear motion and the harmonic oscillator 37 // Mathematical background 2 Differential equations 66 // 3 Rotational motion and the hydrogen atom 69 // 4 Angular momentum 99 // Mathematical background 3 Vectors 121 // 5 Group theory 125 // Mathematical background 4 Matrices 166 // 6 Techniques of approximation 170 // 7 Atomic spectra and atomic structure 210 // 8 An introduction to molecular structure 258 // 9 Computational chemistry 295 // 10 Molecular rotations and vibrations 338 // Mathematical background 5 Fourier series and Fourier transforms 379 // 11 Molecular electronic transitions 382 // 12 The electric properties of molecules 407 // 13 The magnetic properties of molecules 437 // Mathematical background 6 Scalar and vector functions 474 // 14 Scattering theory 476 // Resource section 513 // Answers to selected exercises and problems 523 // Index 529 // Detailed contents // Introduction and orientation // o.l Black-body radiation 1 // 0.2 Heat capacities 2 // 0.3 The photoelectric and Compton effects 3 // 0.4 Atomic spectra 4 // 0.5 The duality of matter 5 // Operators in quantum mechanics 9 // 1.1 Linear operators 10 // 1.2 Eigenfunctions and eigenvalues 10 // 1.3 Representations 12 // 1.4 Commutation and non-commutation 13 // 1.5 The construction of operators 14 // 1.6 Integrals over operators 15 // 1.7 Dirac bracket and

Detailed contents : Introduction and orientation // 0.1 Black-body radiation 1 // 0.2 Heat capacities 2 // 0.3 The photoelectric and Compton effects 3 // 0.4 Atomic spectra 4 // 0.5 The duality of matter 5 // Operators in quantum mechanics 9 // 1.1 Linear operators 10 // 1.2 Eigenfunctions and eigenvalues 10 // 1.3 Representations 12 // 1.4 Commutation and non-commutation 13 // 1.5 The construction of operators 14 // 1.6 Integrals over operators 15 // 1.7 Dirac bracket and matrix notation 16 // (a) Dirac brackets 16 // (b) Matrix notation 17 // 1.8 Hermitian operators 17 // (a) The definition of hermiticity 18 // (b) The consequences of hermiticity 19 // The postulates of quantum mechanics 20 // 1.9 States and wavefunctions 20 // 1.10 The fundamental prescription 21 // 1.11 The outcome of measurements 2 2 // 1.12 The interpretation of the wavef unction 24 // 1.13 The equation for the wavef unction 24 // 1.14 The separation of the Schrödinger equation 25 // The specification and evolution of states 26 // 1.15 Simultaneous observables 27 // 1.16 The uncertainty principle 28 // 1.17 Consequences of the uncertainty principle 30 // 1.18 The uncertainty in energy and time 31 // 1.19 Time-evolution and conservation laws 31 // Mathematical background 1 Complex numbers 35 // MBl.l Definitions 35 // MB1.2 Polar representation 35 // MB1.3 Operations 36 // 2 Linear motion and the harmonic oscillator // // The characteristics of wavefunctions 37 // 2.1 Constraints on the wavefunction 37 // 2.2 Some general remarks on the Schrödinger equation 38 // (a) The curvature of the wavefunction 38 // (b) Qualitative solutions 39 // (c) The emergence of quantization 40 // (d) Penetration into non-classical regions 40 // Translational motion 41 // 2.3 Energy and momentum 41 // 2.4 The significance of the coefficients 42 // 2.5 The flux density 43 // 2.6 Wavepackets 44 //

Penetration into and through barriers 44 // 2.7 An infinitely thick potential wall 45 // 2.8 A barrier of finite width 46 // (a) The case E< V 46 // (b) The case E> V 48 // 2.9 The Eckart potential barrier 48 // Particle in a box 49 // 2.10 The solutions 50 // 2.11 Features of the solutions 51 // 2.12 The two-dimensional square well 52 // 2.13 Degeneracy 53 // The harmonic oscillator 54 // 2.14 The solutions 55 // 2.15 Properties of the solutions 57 // 2.16 The classical limit 58 // Further information 60 // 2.1 The motion of wavepackets 60 // 2.2 The harmonic oscillator: solution by factorization 61 // 2.3 The harmonic oscillator: the standard solution 62 // 2.4 The virial theorem 62 // Mathematical background 2 Differential equations 66 // MB2.1 The structure of differential equations 66 // MB2.2 The solution of ordinary differential equations 66 // MB2.3 The solution of partial differential equations 67 // 3 Rotational motion and the hydrogen atom // Particle on a ring 69 // 3.1 The hamiltonian and the Schrödinger equation 69 // 3.2 The angular momentum 70 // 3.3 The shapes of the wavefunctions 71 // 3.4 The classical limit 72 // 3.5 The circular square well 73 // (a) The separation of variables 73 // (b) The radial solutions 73 // věii I DETAILED CONTENTS // Particle on a sphere // 3.6 The Schrödinger equation and its solution // (a) The wavefunctions // (b) The allowed energies // 3.7 The angular momentum of the particle // 3.8 Properties of the solutions // 3.9 The rigid rotor // 3.10 Particle in a spherical well // 75 Mathematical background 3 Vectors 75 MB3.1 Definitions // 77 MB3.2 Operations // MB3.3 The graphical representation of vector operations /? // MB3.4 Vector differentiation // 80 81 // 83 5 Group theory // Motion in a Coulombic field // 3.11 The Schrödinger equation for hydrogenic atoms // 3.12 The separation of the relative coordinates //

3.13 The radial Schrödinger equation // (a) The solutions close to the nucleus for / = 0 // (b) The solutions close to the nucleus for / * 0 // (c) The complete solutions // (d) The allowed energies // 3.14 Probabilities and the radial distribution function // 3.15 Atomic orbitals // (a) s-orbitals // (b) p-orbitals // (c) d-and f-orbitals // (d) The radial extent of orbitals // 3.16 The degeneracy of hydrogenic atoms // Further information // 3.1 The angular wavefunctions // 3.2 Reduced mass // 3.3 The radial wave equation // 4 Angular momentum // The angular momentum operators // 4.1 The operators and their commutation relations // (a) The angular momentum operators // (b) The commutation relations // 4.2 Angular momentum observables // 4.3 The shift operators // The definition of the states // 4.4 The effect of the shift operators // 4.5 The eigenvalues of the angular momentum // 4.6 The matrix elements of the angular momentum // 4.7 The orbital angular momentum eigenfunctions // 4.8 Spin // (a) The properties of spin // (b) The matrix elements of spin operators // The angular momenta of composite systems // 4.9 The specification of coupled states // 4.10 The permitted values of the total angular momentum // 4.11 The vector model of coupled angular momenta // 4.12 The relation between schemes // (a) Singlet and triplet coupled states // (b) The construction of coupled states // (c) States of the configuration d2 // 4.13 The coupling of several angular momenta // The symmetries of objects // 5.1 Symmetry operations and elements // 5.2 The classification of molecules // The calculus of symmetry // 5.3 The definition of a group // 5.4 Group multiplication tables // 5.5 Matrix representations // 5.6 The properties of matrix representations // 5.7 The characters of representations // 5.8 Characters and classes // 5.9 Irreducible representations //

5.10 The great and little orthogonality theorems // Reduced representations // 5.11 The reduction of representations // 5.12 Symmetry-adapted bases // (a) Projection operators // (b) The generation of symmetry-adapted bases // The symmetry properties of functions // 5.13 The transformation of p-orbitals // 5.14 The decomposition of direct-product bases // 5.15 Direct-product groups // 5.16 Vanishing integrals // 5.17 Symmetry and degeneracy // The full rotation group // 5.18 The generators of rotations // 5.19 The representation of the full rotation group // 5.20 Coupled angular momenta // Applications // Mathematical background 4 Matrices // MB4.1 Definitions // MB4.2 Matrix addition and multiplication MB4.3 Eigenvalue equations // 6 Techniques of approximation // The semiclassical approximation Time-independent perturbation theory // 6.1 Perturbation of a two-level system // 6.2 Many-level systems // (a) Formulation of the problem // (b) The first-order correction to the energy // (c) The first-order correction to the wavefunction // (d) The second-order correction to the energy // 6.3 Comments on the perturbation expressions // (a) The role of symmetry // (b) The closure approximation // 6.4 Perturbation theory for degenerate states // Variation theory // 6.5 The Rayleigh ratio // 6.6 The Rayleigh-Ritz method // The Hellmann-Feynman theorem Time-dependent perturbation theory // 6.7 The time-dependent behaviour of a two-level system // (a) The solutions // (b) The Rabi formula // Many-level systems: the variation of constants // (a) The general formulation // (b) The effect of a slowly switched constant perturbation 198 // (c) The effect of an oscillating perturbation 199 // 6.9 Transition rates to continuum states // 6.10 The Einstein transition probabilities // 6.11 Lifetime and energy uncertainty // Further information // 6.1 Electric dipole transitions //

7 Atomic spectra and atomic structure // The spectrum of atomic hydrogen 210 // 7.1 The energies of the transitions 210 // 7.2 Selection rules 211 // (a) The Laporte selection rule 211 // (b) Constraints on ?I 212 // (c) Constraints on Amf 212 // (d) Higher-order transitions 213 // 7.3 Orbital and spin magnetic moments 214 // (a) The orbital magnetic moment 214 // (b) The spin magnetic moment 215 // 7.4 Spin-orbit coupling 215 // 7.5 The fine-structure of spectra 217 // 7.6 Term symbols and spectral details 218 // 7.7 The detailed spectrum of hydrogen 219 // The structure of helium 221 // 7.8 The helium atom 221 // (a) Atomic units 221 // (b) The orbital approximation 222 // 7.9 Excited states of helium 224 // 7.10 The spectrum of helium / 225 // 7.11 The Pauli principle 227 // Many-electron atoms 229 // 7.12 Penetration and shielding 230 // 7.13 Periodicity 232 // 7.14 Slater atomic orbitals 233 // 7.15 Slater determinants and the Condon-Slater rules 234 // 7.16 Self-consistent fields 235 // (a) The Hartree-Fock equations 235 // (b) One-electron energies 237 // 7.17 Restricted and unrestricted Hartree-Fock calculations 238 // 7.18 Density functional procedures 239 // {a) The Thomas-Fermi method 239 // (b) The Thomas-Fermi-Dirac method 242 // 7.19 Term symbols and transitions of many-electron atoms 243 // (a) Russell-Saunders coupling 243 // (b) Excluded terms 244 // (c) Selection rules 245 // 7.20 Hund’s rules and Racah parameters 245 // 7.21 Alternative coupling schemes 247 // Atoms in external fields 248 // 7.22 The normal Zeeman effect 248 // 7.23 The anomalous Zeeman effect 249 // 7.24 The Stark effect 251 // Further information 253 // 7.1 The Hartree-Fock equations 253 // 7.2 Vector coupling schemes 253 // 7.3 Functionals and functional derivatives 254 // 7.4 Solution of the Thomas-Fermi equation 255 // 8 An introduction to molecular structure //

The Born-Oppenheimer approximation // 8.1 The formulation of the approximation // 8.2 An application: the hydrogen molecule-ion // (a) The molecular potential energy curves // (b) The molecular orbitals // Molecular orbital theory // 8.3 Linear combinations of atomic orbitals // (a) The secular determinant // (b) The Coulomb integral // (c) The resonance integral // (d) The LCAO-MO energy levels for the hydrogen molecule-ion // (e) The LCAO-MOs for the hydrogen molecule-ion // 8.4 The hydrogen molecule // Configuration interaction // Diatomic molecules // (a) Criteria for atomic orbital overlap and bond formation 269 // (b) Homonuclear diatomic molecules 270 // (c) Heteronuclear diatomic molecules 272 // Molecular orbital theory of polyatomic molecules 274 // 8.7 Symmetry-adapted linear combinations 274 // (a) The H2O molecule 274 // (b) The NH3 molecule 276 // 8.8 Conjugated ji-systems and the Hückel approximation 276 // 8.9 Ligand field theory 282 // (a) The SALCs of the octahedral complex 282 // (b) The molecular orbitals of the octahedral complex 282 // (c) The ground-state configuration: low- and high-spin // complexes 283 // (d) Tanabe-Sugano diagrams 284 // (e) Jahn-Teller distortion 284 // (f) Metal-ligand ? bonding 285 // The band theory of solids // 8.10 The tight-binding approximation // 8.11 The Kronig-Penney model // 8.12 Brillouin zones // Further information // 8.1 Molecular integrals // 9 Computational chemistry // The Hartree-Fock self-consistent field method // 9.1 The formulation of the approach // 9.2 The Hartree-Fock approach // 9.3 The Roothaan equations // 9.4 The selection of basis sets // (a) Gaussian-type orbitals // (b) The construction of contracted Gaussians // (c) Calculational accuracy and the basis set // Electron correlation // 9.5 Configuration state functions // 9.6 Configuration interaction // 9.7 Cl calculations //

9.8 Multiconfiguration methods // 9.9 Moller-Plesset many-body perturbation theory // 9.10 The coupled-cluster method // (a) Formulation of the method // (b) The coupled-cluster equations // Density functional theory // 9.11 The Hohenberg-Kohn existence theorem // 9.12 The Hohenberg-Kohn variational theorem // 9.13 The Kohn-Sham equations // 9.14 The exchange-correlation challenge // (a) Local density approximations // (b) More elaborate functionals // Gradient methods and molecular properties // 9.15 Energy derivatives and the Hessian matrix // 9.16 Analytical procedures // Semiempirical methods // 9.17 Conjugated n-electron systems // (a) The Hückel approximation // (b) The Pariser-Parr-Pople method // 9.18 General procedures // Molecular mechanics // 9.19 Force fields // 9.20 Quantum mechanics-molecular mechanics // 10 Molecular rotations and vibrations // Spectroscopic transitions // 10.1 Absorption and emission // 10.2 Raman processes // Molecular rotation 340 // 10.3 Rotational energy levels 342 // (a) Symmetric rotors 342 // (b) Spherical rotors 344 // (c) Linear rotors 344 // (d) Centrifugal distortion 344 // 10.4 Pure rotational selection rules 345 // (a) The gross selection rule 345 // (b) The specific selection rules 345 // (c) Wavenumbers of allowed transitions 346 // 10.5 Rotational Raman selection rules 347 // 10.6 Nuclear statistics 349 // (a) The case of CO2 349 // (b) The case of H2 350 // (c) A more general case 352 // The vibrations of diatomic molecules 353 // 10.7 The vibrational energy levels of diatomic molecules 353 // (a) Harmonic oscillation 353 // (b) Anharmonic oscillation 354 // 10.8 Vibrational selection rules 356 // (a) The gross selection rule 356 // (b) The specific selection rule 357 // (c) The effect of anharmonicities on allowed transitions 358 // 10.9 Vibration-rotation spectra of diatomic molecules 358 //

10.10 Vibrational Raman transitions of diatomic molecules 360 // The vibrations of polyatomic molecules 361 // 10.11 Normal modes 362 // (a) Potential energy 362 // (b) Normal coordinates 363 // (c) Vibrational wavefunctions and energies 364 // 10.12 Vibrational and Raman selection rules for // polyatomic molecules 365 // (a) Infrared activity 365 // (b) Raman activity 366 // (c) Group theory and molecular vibrations 366 // 10.13 Further effects on vibrational and rotational // spectra 369 // (a) The effects of anharmonicity 369 // (b) Coriolis forces 372 // (c) Inversion doubling 373 // Further information 374 // 10.1 Centrifugal distortion 374 // 10.2 Normal modes: an example 375 // Mathematical background 5 Fourier series and // Fourier transforms 379 // MB5.1 Fourier series 379 // MB5.2 Fourier transforms 380 // MB5.3 The convolution theorem 381 // 11 Molecular electronic transitions // The states of diatomic molecules 382 // 11.1 The Hund coupling cases 382 // 11.2 Decoupling and ?-doubling 384 // 11.3 Selection and correlation rules 386 // Vibronic transitions 387 // 11.4 The Franck-Condon principle 388 // 11.5 The rotational structure of vibronic transitions 390 // The electronic spectra of polyatomic molecules 391 // 11.6 Symmetry considerations 391 // 11.7 Chromophores 392 // 11.8 Vibronically allowed transitions 393 // 11.9 Singlet-triplet transitions 395 // The fates of excited states 396 // 11.10 Non-radiative decay 396 // 11.11 Radiative decay 398 // (a) Fluorescence 398 // (b) Phosphorescence 398 // Excited states and chemical reactions 399 // 11.12 The conservation of orbital symmetry 399 // 11.13 Electrocyclic reactions 399 // 11.14 Cycloaddition reactions 401 // 11.15 Photochemically induced electrocyclic reactions 402 // 11.16 Photochemically induced cycloaddition reactions 404 // 12 The electric properties of molecules //

The response to electric fields 407 // 12.1 Molecular response parameters 407 // 12.2 The static electric polarizability 409 // (a) The mean polarizability and polarizability volume 409 // (b) The polarizability and molecular properties 411 // (c) Polarizabilities and molecular spectroscopy 412 // (d) Polarizabilities and dispersion interaction 413 // (e) Retardation effects 416 // Bulk electrical properties 417 // 12.3 The relative permittivity and the electric susceptibility 417 // (a) Non-polar molecules 418 // (b) Polar molecules 419 // 12.4 Refractive index 421 // (a) The dynamic polarizability 422 // (b) The molar refractivity 424 // (c) The refractive index and dispersion 424 // Optical activity 425 // 12.5 Circular birefringence and optical rotation 425 // 12.6 Magnetically induced polarization 427 // 12.7 Rotational strength 429 // (a) Symmetry properties 429 // (b) Optical rotatory dispersion 429 // (c) Estimation of rotational strengths 430 // Further information 432 // 12.1 Oscillator strength 432 // 12.2 Sum rules 432 // 12.3 The Maxwell equations 433 // (a) The general form of the equations 433 // (b) The equations for fields in a vacuum 433 // (c) The propagation of fields in a polarizable medium 434 // (d) Propagation in chiral media 434 // 13 The magnetic properties of molecules // The description of magnetic fields // 13.1 Basic concepts // 13.2 Paramagnetism // 13.3 The vector potential // (a) The formulation of the vector potential // (b) Gauge invariance // Magnetic perturbations // 13.4 The perturbation hamiltonian // 13.5 The magnetic susceptibility // (a) Expressions for the susceptibility // (b) Contributions to the susceptibility // (c) The role of the gauge // 13.6 The current density // (a) Real wavef unctions // (b) Orbitally degenerate states, zero field // (c) Orbitally non-degenerate states, non-zero field //

13.7 The diamagnetic current density // 13.8 The paramagnetic current density // Magnetic resonance parameters // 13.9 Shielding constants // (a) The nuclear field // (b) The hamiltonian // (c) The first-order correction to the energy // (d) Contributions to the shielding constant // 13.10 The diamagnetic contribution to shielding // 13.11 The paramagnetic contribution to shielding // 13.12 Theg-value // (a) The spin hamiltonian // (b) Formulating the g-value // 13.13 Spin-spin coupling // 13.14 Hyperfine interactions // (a) Dipolar coupling // (b) The Fermi contact interaction // (c) The total interaction // 13.15 Nuclear spin-spin coupling // (a) The formulation of the problem // (b) Coupling through a chemical bond // Further information // 13.1 The hamiltonian in the presence of a magnetic field // 13.2 The dipolar vector potential // Mathematical background 6 // MB6.1 Definitions // MB6.2 Differentiation // 14 Scattering theory // The fundamental concepts // 14.1 The scattering matrix // 14.2 The scattering cross-section // Scalar and vector functions // Elastic scattering // 14.3 Stationary scattering states // (a) The scattering amplitude // (b) The differential cross-section // 14.4 Scattering by a central potential // (a) The partial-wave stationary scattering state // (b) The partial-wave equation // (c) The scattering phase shift // (d) The scattering matrix element // (e) The scattering cross-section // 14.5 Scattering by a spherical square well // (a) The S-wave radial wavefunction and phase shift // (b) Background and resonance phase shifts // (c) The Breit-Wigner formula // (d) The resonance contribution to the scattering matrix element // 14.6 Methods of approximation // (a) The WKB approximation // (b) The Bom approximation // Multichannel scattering // 14.7 The scattering matrix for multichannel processes // 14.8 Inelastic scattering 504 //

(a) The form of the multichannel stationary scattering state 505 // (b) Scattering amplitude and cross-sections 505 // (c) The close-coupling approximation 506 // 14.9 Reactive scattering 507 // 14.10 The S matrix and multichannel resonances 508 // Further information 509 // 14.1 Green’s functions 509 // Resource section 513 // Further reading 513 // 1 Character tables and direct products 516 // 2 Vector coupling coefficients 520 // 3 Wigner-Witmer rules 521 // Answers to selected exercises and problems 523 // Index 529