(Ebook) Molecular Quantum Mechanics 5th Edition by Peter W Atkins, Ronald S Friedman ISBN 0199541426 9780199541423

(Ebook) Molecular Quantum Mechanics 5th Edition by Peter W Atkins, Ronald S Friedman ISBN 0199541426 9780199541423

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ISBN 10: 0199541426 
ISBN 13: 9780199541423
Author: Peter W Atkins, Ronald S Friedman

Quantum mechanics embraces the behaviour of all known forms of matter, including the atoms and molecules from which we, and all living organisms, are composed. Molecular Quantum Mechanics leads us through this absorbing yet challenging subject, exploring the fundamental physical principles that explain how all matter behaves. With the clarity of exposition and extensive learning features that have established the book as a leading text in the field, Molecular Quantum Mechanics takes us from the foundations of quantum mechanics, through quantum models of atomic, molecular, and electronic structure, and on to discussions of spectroscopy, and the electronic and magnetic properties of molecules. Lucid explanations and illuminating artworks help to visualise the many abstract concepts upon which the subject is built. Fully updated to reflect the latest advances in computational techniques, and enhanced with more mathematical support and worked examples than ever before, Molecular Quantum Mechanics remains the ultimate resource for those wishing to master this important subject. Online Resource Centre For students: Interactive worksheets to help students master mathematical concepts through hands-on learning Solutions to selected exercises and problems For registered adopters of the book: Figures in electronic format Solutions to all exercises and problems

(Ebook) Molecular Quantum Mechanics 5th Table of contents:

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
1.8 Hermitian operators
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 Schr?dinger 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 1 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 Schr?dinger equation
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
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: solution 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 Schr?dinger equation
3.2 The angular momentum
3.3 The shapes of the wavefunctions
3.4 The classical limit
3.5 The circular square well
Particle on a sphere
3.6 The Schr?dinger equation and its solution
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 Schr?dinger equation for hydrogenic atoms
3.12 The separation of the relative coordinates
3.13 The radial Schr?dinger equation
3.14 Probabilities and the radial distribution function
3.15 Atomic 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
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
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
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
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
6.3 Comments on the perturbation expressions
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
6.8 Many-level systems: the variation of constants
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
7.3 Orbital and spin magnetic moments
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
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
7.17 Restricted and unrestricted Hartree?Fock calculations
7.18 Density functional procedures
7.19 Term symbols and transitions of many-electron atoms
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
Molecular orbital theory
8.3 Linear combinations of atomic orbitals
8.4 The hydrogen molecule
8.5 Configuration interaction
8.6 Diatomic molecules
Molecular orbital theory of polyatomic molecules
8.7 Symmetry-adapted linear combinations
8.8 Conjugated π-systems and the H?ckel approximation
8.9 Ligand field theory
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
Electron correlation
9.5 Configuration state functions
9.6 Configuration interaction
9.7 CI calculations
9.8 Multiconfiguration methods
9.9 M?ller?Plesset many-body perturbation theory
9.10 The coupled-cluster method
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
Gradient methods and molecular properties
9.15 Energy derivatives and the Hessian matrix
9.16 Analytical procedures
Semiempirical methods
9.17 Conjugated ?-electron systems
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
10.4 Pure rotational selection rules
10.5 Rotational Raman selection rules
10.6 Nuclear statistics
The vibrations of diatomic molecules
10.7 The vibrational energy levels of diatomic molecules
10.8 Vibrational selection rules
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
10.12 Vibrational and Raman selection rules for polyatomic molecules
10.13 Further effects on vibrational and rotational spectra
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 A-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
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
Bulk electrical properties
12.3 The relative permittivity and the electric susceptibility
12.4 Refractive index
Optical activity
12.5 Circular birefringence and optical rotation
12.6 Magnetically induced polarization
12.7 Rotational strength
Further information
12.1 Oscillator strength
12.2 Sum rules
12.3 The Maxwell equations
13 The magnetic properties of molecules
The description of magnetic fields
13.1 Basic concepts
13.2 Paramagnetism
13.3 The vector potential
Magnetic perturbations
13.4 The perturbation hamiltonian
13.5 The magnetic susceptibility
13.6 The current density
13.7 The diamagnetic current density
13.8 The paramagnetic current density
Magnetic resonance parameters
13.9 Shielding constants
13.10 The diamagnetic contribution to shielding
13.11 The paramagnetic contribution to shielding
13.12 The g-value
13.13 Spin?spin coupling
13.14 Hyperfine interactions
13.15 Nuclear spin?spin coupling
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
14.4 Scattering by a central potential
14.5 Scattering by a spherical square well
14.6 Methods of approximation
Multichannel scattering
14.7 The scattering matrix for multichannel processes
14.8 Inelastic scattering
14.9 Reactive scattering
14.10 The S matrix and multichannel resonances
Further information
14.1 Green?s functions

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