TY - BOOK AU - Atkins,P.W. AU - Friedman,Ronald TI - Molecular quantum mechanics SN - 9780199541423 (pbk) U1 - 530.12 PY - 2011/// CY - Oxford, New York PB - Oxford University Press KW - Quantum chemistry N1 - Machine generated contents note: 0.1. Black-body radiation -- 0.2. Heat capacities -- 0.3. The photoelectric and Compton effects -- 0.4. Atomic spectra -- 0.5. The duality of matter -- 1. The foundations of quantum mechanics -- Operators in quantum mechanics -- 1.1. Linear operators -- 1.2. Eigenfunctions and eigenvalues -- 1.3. Representations -- 1.4. Commutation and non-commutation -- 1.5. The construction of operators -- 1.6. Integrals over operators -- 1.7. Dirac bracket and matrix notation -- a. Dirac brackets -- b. Matrix notation -- 1.8. Hermitian operators -- a. The definition of hermiticity -- b. The consequences of hermiticity -- The postulates of quantum mechanics -- 1.9. States and wavefunctions -- 1.10. The fundamental prescription -- 1.11. The outcome of measurements -- 1.12. The interpretation of the wavefunction -- 1.13. The equation for the wavefunction -- 1.14. The separation of the Schrodinger equation -- The specification and evolution of states. 1.15. Simultaneous observables -- 1.16. The uncertainty principle -- 1.17. Consequences of the uncertainty principle -- 1.18. The uncertainty in energy and time -- 1.19. Time-evolution and conservation laws -- Mathematical background I Complex numbers -- MB1.1. Definitions -- MB1.2. Polar representation -- MB1.3. Operations -- 2. Linear motion and the harmonic oscillator -- The characteristics of wavefunctions -- 2.1. Constraints on the Wavefunction -- 2.2. Some general remarks on the Schrodinger equation -- a. The curvature of the wavefuntion -- b. Qualitative solutions -- c. The emergence of quantization -- d. Penetration into non-classical regions -- Translational motion -- 2.3. Energy and momentum -- 2.4. The significance of the coefficients -- 2.5. The flux density -- 2.6. Wavepackets -- Penetration into and through barriers -- 2.7. An infinitely thick potential wall -- 2.8. A barrier of finite width -- a. The case E V -- 2.9. The Eckart potential barrier -- Particle in a box -- 2.10. The solutions. 2.11. Features of the solutions -- 2.12. The two-dimensional square well -- 2.13. Degeneracy -- The harmonic oscillator -- 2.14. The solutions -- 2.15. Properties of the solutions -- 2.16. The classical limit -- Further information -- 2.1. The motion of wavepackets -- 2.2. The harmonic oscillator: solutin by factorization -- 2.3. The harmonic oscillator: the standard solution -- 2.4. The virial theorem -- Mathematical background 2 Differential equations -- MB2.1. The structure of differential equations -- MB2.2. The solution of ordinary differential equations -- MB2.3. The solution of partial differential equations -- 3. Rotational motion and the hydrogen atom -- Particle on a ring -- 3.1. The hamiltonian and the Schrodinger equation -- 3.2. The angular momentum -- 3.3. The shapes of the wavefunctions -- 3.4. The classical limit -- 3.5. The circular square well -- a. The separation of variables -- b. The radial solutions -- Particle on a sphere -- 3.6. The Schrodinger 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 -- Motion in a Coulombic field -- 3.11. The Schrodinger equation for hydrogenic atoms -- 3.12. The separation of the relative coordinates -- 3.13. The radial Schrodinger equation -- a. The solutions close to the nucleus for l=0 -- b. The solutions close to the nucleus for l & ne;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 -- Mathematical background 3 Vectors -- MB3.1. Definitions -- MB3.2. Operations -- MB3.3. The graphical representation of vector operations -- MB3.4. Vector differentiation -- 5. Group theory -- 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 -- 6.8. Many-level systems: the variation of constants -- a. The general formulation -- b. The effect of a slowly switched constant perturbation -- c. The effect of an oscillating perturbation -- 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. 7.1. The energies of the transitions -- 7.2. Selection rules -- a. The Laporte selection rule -- b. Constraints on & delta;l -- c. Constraints on & delta;m1 -- d. Higher-order transitions -- 7.3. Orbital and spin magnetic moments -- a. The orbital magnetic moment -- b. The spin magnetic moment -- 7.4. Spin-orbit coupling -- 7.5. The fine-structure of spectra -- 7.6. Term symbols and spectral details -- 7.7. The detailed spectrum of hydrogen -- The structure of helium -- 7.8. The helium atom -- a. Atomic units -- b. The orbital approximation -- 7.9. Excited states of helium -- 7.10. The spectrum of helium -- 7.11. The Pauli principle -- Many-electron atoms -- 7.12. Penetration and shielding -- 7.13. Periodicity -- 7.14. Slater atomic orbitals -- 7.15. Slater determinants and the Condon-Slater rules -- 7.16. Self-consistent fields -- a. The Hartree-Fock equations -- b. One-electron energies -- 7.17. Restricted and unrestricted Hartree-Fock calculations -- 7.18. Density functional procedures -- a. The Thomas-Fermi method -- (b). The Thomas-Fermi-Dirac method -- 7.19. Term symbols and transitions of many-electron atoms. (A). Russell-Saunders coupling -- (b). Excluded terms -- (c). Selection rules -- 7.20. Hund's rules and Racah parameters -- 7.21. Alternative coupling schemes -- Atoms in external fields -- 7.22. The normal Zeeman effect -- 7.23. The anomalous Zeeman effect -- 7.24. The Stark effect -- Further information -- 7.1. The Hartree-Fock equations -- 7.2. Vector coupling schemes -- 7.3. Functionals and functional derivatives -- 7.4. Solution of the Thomas-Fermi equation -- 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. Note continued: (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 -- 8.5. Configuration interaction -- 8.6. Diatomic molecules -- (a). Criteria for atomic orbital overlap and bond formation -- (b). Homonuclear diatomic molecules -- (c). Heteronuclear diatomic molecules -- Molecular orbital theory of polyatomic molecules -- 8.7. Symmetry-adapted linear combinations -- (a). The H2O molecule -- (b). The NH3 molecule -- 8.8. Conjugated & pi;-systems and the Huckel approximation -- 8.9. Ligand field theory -- (a). The SALCs of the octahedral complex -- (b). The molecular orbitals of the octahedral complex -- (c). The ground-state configuration: low-and high-spin complexes. (D). Tanabe-Sugano diagrams -- (e). Jahn-Teller distortion -- (f). Metal-ligand & pi; bonding -- 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. Møller-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 & pi;-electron systems -- (a). The Huckel 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 -- 10.3. Rotational energy levels -- (a). Symmetric rotors -- (b). Spherical rotors -- (c). Linear rotors -- (d). Centrifugal distortion -- 10.4. Pure rotational selection rules -- (a). The gross selection rule -- (b). The specific selection rules -- (c). Wavenumbers of allowed transitions -- 10.5. Rotational Raman selection rules -- 10.6. Nuclear statistics. A. The case of CO2 -- b. The case of H2 -- c. A more general case -- The vibrations of diatomic molecules -- 10.7. The vibrational energy levels of diatomic molecules -- a. Harmonic oscillation -- b. Anharmonic oscillation -- 10.8. Vibrational selection rules -- a. The gross selection rule -- b. The specific selection rule -- c. The effect of anharmonicities on allowed transitions -- 10.9. Vibration-rotation spectra of diatomic molecules -- 10.10. Vibrational Raman transitions of diatomic molecules -- The vibrations of polyatomic molecules -- 10.11. Normal modes -- a. Potential energy -- b. Normal coordinates -- c. Vibrational wavefunctions and energies -- 10.12. Vibrational and Raman selection rules for polyatomic molecules -- a. Infrared activity -- b. Raman activity -- c. Group theory and molecular vibrations -- 10.13. Further effects on vibrational and rotational spectra -- a. The effects of anharmonicity -- b. Coriolis forces -- c. Inversion doubling -- Further information -- 10.1. Centrifugal distortion -- 10.2. Normal modes: an example -- Mathematical background 5 Fourier series and Fourier transforms. MB5.1. Fourier series -- MB5.2. Fourier transforms -- MB5.3. The convolution theorem -- 11. Molecular electronic transitions -- The states of diatomic molecules -- 11.1. The Hund coupling cases -- 11.2. Decoupling and & Lambda;-doubling -- 11.3. Selection and correlation rules -- Vibronic transitions -- 11.4. The Franck-Condon principle -- 11.5. The rotational structure of vibronic transitions -- The electronic spectra of polyatomic molecules -- 11.6. Symmetry considerations -- 11.7. Chromophores -- 11.8. Vibronically allowed transitions -- 11.9. Singlet-triplet transitions -- The fates of excited states -- 11.10. Non-radiative decay -- 11.11. Radiative decay -- a. Fluorescence -- b. Phosphorescence -- Excited states and chemical reactions -- 11.12. The conservation of orbital symmetry -- 11.13. Electrocyclic reactions -- 11.14. Cycloaddition reactions -- 11.15. Photochemically induced electrocyclic reactions -- 11.16. Photochemically induced cycloaddition reactions -- 12. The electric properties of molecules -- The response to electric fields -- 12.1. Molecular response parameters -- 12.2. The static electric polarizability. A. The mean polarizability and polarizability volume -- b. The polarizability and molecular properties -- c. Polarizabilities and molecular spectroscopy -- d. Polarizabilities and dispersion interaction -- e. Retardation effects -- Bulk electrical properties -- 12.3. The relative permittivity and the electric susceptibility -- a. Non-polar molecules -- b. Polar molecules -- 12.4. Refractive index -- a. The dynamic polarizability -- b. The molar refractivity -- c. The refractive index and dispersion -- Optical activity -- 12.5. Circular birefringence and optical rotation -- 12.6. Magnetically induced polarization -- 12.7. Rotational strength -- a. Symmetry properties -- b. Optical rotatory dispersion -- c. Estimation of rotational strengths -- Further information -- 12.1. Oscillator strength -- 12.2. Sum rules -- 12.3. The Maxwell equations -- a. The general form of the equations -- b. The equations for fields in a vacuum -- c. The propagation of fields in a polarizable medium -- d. Propagation in chiral media -- 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 wavefunctions -- 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. The g-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 Scalar and vector functions -- MB6.1. Definitions -- MB6.2. Differentiation -- 14. Scattering theory -- The fundamental concepts -- 14.1. The scattering matrix -- 14.2. The scattering cross-section -- 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 Born approximation -- Multichannel scattering -- 14.7. The scattering matrix for multichannel processes -- 14.8. Inelastic scattering -- a. The form of the multichannel stationary scattering state -- b. Scattering amplitude and cross-sections -- c. The close-coupling approximation -- 14.9. Reactive scattering -- 14.10. The Smatrix and multichannel resonances -- Further information -- 14.11. Green's functions -- Resource section -- Further reading. Note continued: 1. Character tables and direct products -- 2. Vector coupling coefficients -- 3. Wigner-Witmer rules ER -