Molecular quantum mechanics

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Título:
Molecular quantum mechanics
Autor: P. W. Atkins (Peter William) 1940-
Ronald Friedman 1962-
Assuntos: Quantum chemistry; MECÂNICA CLÁSSICA; MECÂNICA QUÂNTICA
Notas: Includes bibliographical references (p. [513]-515) and index
Descrição: Black-body radiation -- Heat capacities -- The photoelectric and Compton effects -- Atomic spectra -- The duality of matter -- The foundations of quantum mechanics -- Operators in quantum mechanics -- Linear operators -- Eigenfunctions and eigenvalues -- Representations -- Commutation and non-commutation -- The construction of operators -- Integrals over operators -- Dirac bracket and matrix notation -- Dirac brackets -- Matrix notation -- Hermitian operators -- The definition of hermiticity -- The consequences of hermiticity -- The postulates of quantum mechanics -- States and wavefunctions -- The fundamental prescription -- The outcome of measurements -- The interpretation of the wavefunction -- The equation for the wavefunction -- The separation of the Schrodinger equation -- The specification and evolution of states
Simultaneous observables -- The uncertainty principle -- Consequences of the uncertainty principle -- The uncertainty in energy and time -- Time-evolution and conservation laws -- Mathematical background I Complex numbers -- Definitions -- Polar representation -- Operations -- Linear motion and the harmonic oscillator -- The characteristics of wavefunctions -- Constraints on the Wavefunction -- Some general remarks on the Schrodinger equation -- The curvature of the wavefuntion -- Qualitative solutions -- The emergence of quantization -- Penetration into non-classical regions -- Translational motion -- Energy and momentum -- The significance of the coefficients -- The flux density -- Wavepackets -- Penetration into and through barriers -- An infinitely thick potential wall -- A barrier of finite width -- The case E < V -- The case E > V -- The Eckart potential barrier -- Particle in a box -- The solutions
Features of the solutions -- The two-dimensional square well -- Degeneracy -- The harmonic oscillator -- The solutions -- Properties of the solutions -- The classical limit -- Further information -- The motion of wavepackets -- The harmonic oscillator: solutin by factorization -- The harmonic oscillator: the standard solution -- The virial theorem -- Mathematical background 2 Differential equations -- The structure of differential equations -- The solution of ordinary differential equations -- The solution of partial differential equations -- Rotational motion and the hydrogen atom -- Particle on a ring -- The hamiltonian and the Schrodinger equation -- The angular momentum -- The shapes of the wavefunctions -- The classical limit -- The circular square well -- The separation of variables -- The radial solutions -- Particle on a sphere -- The Schrodinger equation and its solution -- The wavefunctions -- The allowed energies
The angular momentum of the particle -- Properties of the solutions -- The rigid rotor -- Particle in a spherical well -- Motion in a Coulombic field -- The Schrodinger equation for hydrogenic atoms -- The separation of the relative coordinates -- The radial Schrodinger equation -- The solutions close to the nucleus for l=0 -- The solutions close to the nucleus for l≠0 -- The complete solutions -- The allowed energies -- Probabilities and the radial distribution function -- Atomic orbitals -- s-orbitals -- p-orbitals -- d-and f-orbitals -- The radial extent of orbitals -- The degeneracy of hydrogenic atoms -- Further information -- The angular wavefunctions -- Reduced mass -- The radial wave equation -- Angular momentum -- The angular momentum operators -- The operators and their commutation relations -- The angular momentum operators -- The commutation relations -- Angular momentum observables -- The shift operators -- The definition of the states
The effect of the shift operators -- The eigenvalues of the angular momentum -- The matrix elements of the angular momentum -- The orbital angular momentum eigenfunctions -- Spin -- The properties of spin -- The matrix elements of spin operators -- The angular momenta of composite systems -- The specification of coupled states -- The permitted values of the total angular momentum -- The vector model of coupled angular momenta -- The relation between schemes -- Singlet and triplet coupled states -- The construction of coupled states -- States of the configuration d2 -- The coupling of several angular momenta -- Mathematical background 3 Vectors -- Definitions -- Operations -- The graphical representation of vector operations -- Vector differentiation -- Group theory -- The symmetries of objects -- Symmetry operations and elements -- The classification of molecules -- The calculus of symmetry -- The definition of a group -- Group multiplication tables
Matrix representations -- The properties of matrix representations -- The characters of representations -- Characters and classes -- Irreducible representations -- The great and little orthogonality theorems -- Reduced representations -- The reduction of representations -- Symmetry-adapted bases -- Projection operators -- The generation of symmetry-adapted bases -- The symmetry properties of functions -- The transformation of p-orbitals -- The decomposition of direct-product bases -- Direct-product groups -- Vanishing integrals -- Symmetry and degeneracy -- The full rotation group -- The generators of rotations -- The representation of the full rotation group -- Coupled angular momenta -- Applications -- Mathematical background 4 Matrices -- Definitions -- Matrix addition and multiplication -- Eigenvalue equations -- Techniques of approximation -- The semiclassical approximation -- Time-independent perturbation theory
Perturbation of a two-level system -- Many-level systems -- Formulation of the problem -- The first-order correction to the energy -- The first-order correction to the wavefunction -- The second-order correction to the energy -- Comments on the perturbation expressions -- The role of symmetry -- The closure approximation -- Perturbation theory for degenerate states -- Variation theory -- The Rayleigh ratio -- The Rayleigh-Ritz method -- The Hellmann-Feynman theorem -- Time-dependent perturbation theory -- The time-dependent behaviour of a two-level system -- The solutions -- The Rabi formula -- Many-level systems: the variation of constants -- The general formulation -- The effect of a slowly switched constant perturbation -- The effect of an oscillating perturbation -- Transition rates to continuum states -- The Einstein transition probabilities -- Lifetime and energy uncertainty -- Further information -- Electric dipole transitions -- Atomic spectra and atomic structure -- The spectrum of atomic hydrogen
The energies of the transitions -- Selection rules -- The Laporte selection rule -- Constraints on δl -- Constraints on δm1 -- Higher-order transitions -- Orbital and spin magnetic moments -- The orbital magnetic moment -- The spin magnetic moment -- Spin-orbit coupling -- The fine-structure of spectra -- Term symbols and spectral details -- The detailed spectrum of hydrogen -- The structure of helium -- The helium atom -- Atomic units -- The orbital approximation -- Excited states of helium -- The spectrum of helium -- The Pauli principle -- Many-electron atoms -- Penetration and shielding -- Periodicity -- Slater atomic orbitals -- Slater determinants and the Condon-Slater rules -- Self-consistent fields -- The Hartree-Fock equations -- One-electron energies -- Restricted and unrestricted Hartree-Fock calculations -- Density functional procedures -- The Thomas-Fermi method -- The Thomas-Fermi-Dirac method -- Term symbols and transitions of many-electron atoms
Russell-Saunders coupling -- Excluded terms -- Selection rules -- Hund's rules and Racah parameters -- Alternative coupling schemes -- Atoms in external fields -- The normal Zeeman effect -- The anomalous Zeeman effect -- The Stark effect -- Further information -- The Hartree-Fock equations -- Vector coupling schemes -- Functionals and functional derivatives -- Solution of the Thomas-Fermi equation -- An introduction to molecular structure -- The Born-Oppenheimer approximation -- The formulation of the approximation -- An application: the hydrogen molecule-ion
Note continued: The molecular potential energy curves -- The molecular orbitals -- Molecular orbital theory -- Linear combinations of atomic orbitals -- The secular determinant -- The Coulomb integral -- The resonance integral -- The LCAO-MO energy levels for the hydrogen molecule-ion -- The LCAO-MOs for the hydrogen molecule-ion -- The hydrogen molecule -- Configuration interaction -- Diatomic molecules -- Criteria for atomic orbital overlap and bond formation -- Homonuclear diatomic molecules -- Heteronuclear diatomic molecules -- Molecular orbital theory of polyatomic molecules -- Symmetry-adapted linear combinations -- The H2O molecule -- The NH3 molecule -- Conjugated π-systems and the Huckel approximation -- Ligand field theory -- The SALCs of the octahedral complex -- The molecular orbitals of the octahedral complex -- The ground-state configuration: low-and high-spin complexes
Tanabe-Sugano diagrams -- Jahn-Teller distortion -- Metal-ligand π bonding -- The band theory of solids -- The tight-binding approximation -- The Kronig-Penney model -- Brillouin zones -- Further information -- Molecular integrals -- Computational chemistry -- The Hartree-Fock self-consistent field method -- The formulation of the approach -- The Hartree-Fock approach -- The Roothaan equations -- The selection of basis sets -- Gaussian-type orbitals -- The construction of contracted Gaussians -- Calculational accuracy and the basis set -- Electron Correlation -- Configuration state functions -- Configuration interaction -- Cl Calculations -- Multiconfiguration methods -- M ller-Plesset many-body perturbation theory -- The coupled-cluster method -- Formulation of the method -- The coupled-cluster equations -- Density functional theory -- The Hohenberg-Kohn existence theorem -- The Hohenberg-Kohn variational theorem
The Kohn-Sham equations -- The exchange-correlation challenge -- Local density approximations -- More elaborate functionals -- Gradient methods and molecular properties -- Energy derivatives and the Hessian matrix -- Analytical procedures -- Semiempirical methods -- Conjugated π-electron systems -- The Huckel approximation -- The Pariser-Parr-Pople method -- General procedures -- Molecular mechanics -- Force fields -- Quantum mechanics-molecular mechanics -- Molecular rotations and vibrations -- Spectroscopic transitions -- Absorption and emission -- Raman processes -- Molecular rotation -- Rotational energy levels -- Symmetric rotors -- Spherical rotors -- Linear rotors -- Centrifugal distortion -- Pure rotational selection rules -- The gross selection rule -- The specific selection rules -- Wavenumbers of allowed transitions -- Rotational Raman selection rules -- Nuclear statistics
The case of CO2 -- The case of H2 -- A more general case -- The vibrations of diatomic molecules -- The vibrational energy levels of diatomic molecules -- Harmonic oscillation -- Anharmonic oscillation -- Vibrational selection rules -- The gross selection rule -- The specific selection rule -- The effect of anharmonicities on allowed transitions -- Vibration-rotation spectra of diatomic molecules -- Vibrational Raman transitions of diatomic molecules -- The vibrations of polyatomic molecules -- Normal modes -- Potential energy -- Normal coordinates -- Vibrational wavefunctions and energies -- Vibrational and Raman selection rules for polyatomic molecules -- Infrared activity -- Raman activity -- Group theory and molecular vibrations -- Further effects on vibrational and rotational spectra -- The effects of anharmonicity -- Coriolis forces -- Inversion doubling -- Further information -- Centrifugal distortion -- Normal modes: an example -- Mathematical background 5 Fourier series and Fourier transforms
Fourier series -- Fourier transforms -- The convolution theorem -- Molecular electronic transitions -- The states of diatomic molecules -- The Hund coupling cases -- Decoupling and Λ-doubling -- Selection and correlation rules -- Vibronic transitions -- The Franck-Condon principle -- The rotational structure of vibronic transitions -- The electronic spectra of polyatomic molecules -- Symmetry considerations -- Chromophores -- Vibronically allowed transitions -- Singlet-triplet transitions -- The fates of excited states -- Non-radiative decay -- Radiative decay -- Fluorescence -- Phosphorescence -- Excited states and chemical reactions -- The conservation of orbital symmetry -- Electrocyclic reactions -- Cycloaddition reactions -- Photochemically induced electrocyclic reactions -- Photochemically induced cycloaddition reactions -- The electric properties of molecules -- The response to electric fields -- Molecular response parameters -- The static electric polarizability
The mean polarizability and polarizability volume -- The polarizability and molecular properties -- Polarizabilities and molecular spectroscopy -- Polarizabilities and dispersion interaction -- Retardation effects -- Bulk electrical properties -- The relative permittivity and the electric susceptibility -- Non-polar molecules -- Polar molecules -- Refractive index -- The dynamic polarizability -- The molar refractivity -- The refractive index and dispersion -- Optical activity -- Circular birefringence and optical rotation -- Magnetically induced polarization -- Rotational strength -- Symmetry properties -- Optical rotatory dispersion -- Estimation of rotational strengths -- Further information -- Oscillator strength -- Sum rules -- The Maxwell equations -- The general form of the equations -- The equations for fields in a vacuum -- The propagation of fields in a polarizable medium -- Propagation in chiral media -- The magnetic properties of molecules -- The description of magnetic fields
Basic concepts -- Paramagnetism -- The vector potential -- The formulation of the vector potential -- Gauge invariance -- Magnetic perturbations -- The perturbation hamiltonian -- The magnetic susceptibility -- Expressions for the susceptibility -- Contributions to the susceptibility -- The role of the gauge -- The current density -- Real wavefunctions -- Orbitally degenerate states, zero field -- Orbitally non-degenerate states, non-zero field -- The diamagnetic current density -- The paramagnetic current density -- Magnetic resonance parameters -- Shielding constants -- The nuclear field -- The hamiltonian -- The first-order correction to the energy -- Contributions to the shielding constant -- The diamagnetic contribution to shielding -- The paramagnetic contribution to shielding -- The g-value -- The spin hamiltonian -- Formulating the g-value -- Spin-spin coupling -- Hyperfine interactions -- Dipolar coupling -- The Fermi contact interaction
The total interaction -- Nuclear spin-spin coupling -- The formulation of the problem -- Coupling through a chemical bond -- Further information -- The hamiltonian in the presence of a magnetic field -- The dipolar vector potential -- Mathematical background 6 Scalar and vector functions -- Definitions -- Differentiation -- Scattering theory -- The fundamental concepts -- The scattering matrix -- The scattering cross-section -- Elastic scattering -- Stationary scattering states -- The scattering amplitude -- The differential cross-section -- Scattering by a central potential -- The partial-wave stationary scattering state -- The partial-wave equation -- The scattering phase shift -- The scattering matrix element -- The scattering cross-section -- Scattering by a spherical square well -- The S-wave radial wavefunction and phase shift -- Background and resonance phase shifts -- The Breit-Wigner formula -- The resonance contribution to the scattering matrix element
Methods of approximation -- The WKB approximation -- The Born approximation -- Multichannel scattering -- The scattering matrix for multichannel processes -- Inelastic scattering -- The form of the multichannel stationary scattering state -- Scattering amplitude and cross-sections -- The close-coupling approximation -- Reactive scattering -- The Smatrix and multichannel resonances -- Further information -- Green's functions -- Resource section -- Further reading
Note continued: Character tables and direct products -- Vector coupling coefficients -- Wigner-Witmer rules.
Editor: Oxford Oxford University Press New York
Data de criação/publicação: 2011
Formato: xiv, 537 p ill 25 cm.
Idioma: Inglês

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Molecular quantum mechanics

P. W. Atkins (Peter William) 1940- Ronald Friedman 1962-

Oxford Oxford University Press New York 2011

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