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Molecular Quantum Mechanics (Fourth Edition) by Peter Atkins and Ronald Friedman

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' Molecular Quantum Mechanics (Fourth Edition) written by Peter Atkins , University of Oxford and Ronald Friedman , Indiana Purdue Fort Wayne. One major change since the third edition has been our response to concerns about the mathematical complexity of the material. We have not sacrificed the mathematical rigour of the previous edition but we have tried in numerous ways to make the mathematics more accessible. We have introduced short commentaries into the text to remind the reader of the mathematical fundamentals useful in derivations. We have included more worked examples to provide the reader with further opportunities to see formulae in action. We have added new problems for each chapter. We have expanded the discussion on numerous occasions within the body of the text to provide further clarification for or insight into mathematical results. We have set aside Proofs and Illustrations (brief examples) from the main body of the text so that readers may find key results more readily. Where the depth of presentation started to seem too great in our judgement, we have sent material to the back of the chapter in the form of an Appendix or to the back of the book as a Further information section. Numerous equations are tabbed with www to signify that on the Website to accompany the text [www.oup.com/uk/ booksites/chemistry/] there are opportunities to explore the equations by substituting numerical values for variables.

Molecular Quantum Mechanics (Fourth Edition) written by Peter Atkins and Ronald Friedman cover the following topics.

• Introduction and orientation
0.2 Heat capacities
0.3 The photoelectric and Compton effects
0.4 Atomic spectra
0.5 The duality of matter
P R O B L E M S

• 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 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 Schro¨ 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

• Matrices in quantum mechanics
1.20 Matrix elements
1.21 The diagonalization of the hamiltonian

• The plausibility of the Schro¨ dinger equation
1.22 The propagation of light
1.23 The propagation of particles
1.24 The transition to quantum mechanics
P R O B L E M S

• 2. Linear motion and the harmonic oscillator

• The characteristics of acceptable wavefunctions

• Some general remarks on the Schro¨ dinger equation
2.1 The curvature of the wavefunction
2.2 Qualitative solutions
2.3 The emergence of quantization
2.4 Penetration into non-classical regions

• Translational motion
2.5 Energy and momentum
2.6 The significance of the coefficients
2.7 The flux density
2.8 Wavepackets

• Penetration into and through barriers
2.9 An infinitely thick potential wall
2.10 A barrier of finite width
2.11 The Eckart potential barrier

• Particle in a box
2.12 The solutions
2.13 Features of the solutions
2.14 The two-dimensional square well
2.15 Degeneracy

• The harmonic oscillator
2.16 The solutions
2.17 Properties of the solutions
2.18 The classical limit

• Translation revisited: The scattering matrix P R O B L E M S

• 3. Rotational motion and the hydrogen atom

• Particle on a ring
3.1 The hamiltonian and the Schro¨ dinger equation
3.2 The angular momentum
3.3 The shapes of the wavefunctions
3.4 The classical limit

• Particle on a sphere
3.5 The Schro¨ dinger equation and its solution
3.6 The angular momentum of the particle
3.7 Properties of the solutions
3.8 The rigid rotor

• Motion in a Coulombic field
3.9 The Schro¨ dinger equation for hydrogenic atoms
3.10 The separation of the relative coordinates
3.11 The radial Schro¨ dinger equation
3.12 Probabilities and the radial distribution function
3.13 Atomic orbitals
3.14 The degeneracy of hydrogenic atoms
P R O B L E M S

• 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 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
P R O B L E M S

• 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

• 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
P R O B L E M S

• 6. Techniques of approximation

• Time-independent perturbation theory
6.1 Perturbation of a two-level system
6.2 Many-level systems
6.3 The first-order correction to the energy
6.4 The first-order correction to the wavefunction
6.5 The second-order correction to the energy
6.6 Comments on the perturbation expressions
6.7 The closure approximation
6.8 Perturbation theory for degenerate states

• Variation theory
6.9 The Rayleigh ratio
6.10 The Rayleigh–Ritz method The Hellmann–Feynman theorem

• Time-dependent perturbation theory
6.11 The time-dependent behaviour of a two-level system
6.12 The Rabi formula
6.13 Many-level systems: the variation of constants
6.14 The effect of a slowly switched constant perturbation
6.15 The effect of an oscillating perturbation
6.16 Transition rates to continuum states
6.17 The Einstein transition probabilities
P R O B L E M S

• 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 Self-consistent fields
7.16 Term symbols and transitions of many-electron atoms
7.17 Hund’s rules and the relative energies of terms
7.18 Alternative coupling schemes

• Atoms in external fields
7.19 The normal Zeeman effect
7.20 The anomalous Zeeman effect
7.21 The Stark effect
P R O B L E M S

• 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
8.7 Heteronuclear diatomic molecules

• Molecular orbital theory of polyatomic molecules
8.9 Conjugated p-systems
8.10 Ligand field theory
8.11 Further aspects of ligand field theory

• The band theory of solids
8.12 The tight-binding approximation
8.13 The Kronig–Penney model
8.14 Brillouin zones
P R O B L E M S

• 9. The calculation of electronic structure

• The Hartree–Fock self-consistent field method
9.1 The formulation of the approach
9.2 The Hartree–Fock approach
9.3 Restricted and unrestricted Hartree–Fock

• calculations
9.4 The Roothaan equations
9.5 The selection of basis sets
9.6 Calculational accuracy and the basis set

• Electron correlation
9.7 Configuration state functions
9.8 Configuration interaction
9.9 CI calculations
9.10 Multiconfiguration and multireference methods
9.11 Møller–Plesset many-body perturbation theory
9.12 The coupled-cluster method

• Density functional theory
9.13 Kohn–Sham orbitals and equations
9.14 Exchange–correlation functionals

• Gradient methods and molecular properties
9.15 Energy derivatives and the Hessian matrix
9.16 Analytical derivatives and the coupled perturbed equations

• Semiempirical methods
9.17 Conjugated p-electron systems
9.18 Neglect of differential overlap

• Molecular mechanics
9.19 Force fields 333
9.20 Quantum mechanics–molecular mechanics
Software packages for electronic structure calculations
P R O B L E M S

• 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 Centrifugal distortion
10.5 Pure rotational selection rules
10.6 Rotational Raman selection rules
10.7 Nuclear statistics

• The vibrations of diatomic molecules
10.8 The vibrational energy levels of diatomic molecules
10.9 Anharmonic oscillation
10.10 Vibrational selection rules
10.11 Vibration–rotation spectra of diatomic molecules
10.12 Vibrational Raman transitions of diatomic molecules

• The vibrations of polyatomic molecules
10.13 Normal modes
10.14 Vibrational selection rules for polyatomic molecules
10.15 Group theory and molecular vibrations
10.16 The effects of anharmonicity
10.17 Coriolis forces
10.18 Inversion doubling
Appendix 10.1 Centrifugal distortion
P R O B L E M S

• 11. Molecular electronic transitions

• The states of diatomic molecules
11.1 The Hund coupling cases
11.2 Decoupling and L-doubling
11.3 Selection 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 fate of excited species
11.12 The conservation of orbital symmetry
11.13 Electrocyclic reactions
11.15 Photochemically induced electrocyclic reactions
P R O B L E M S

• 12. The electric properties of molecules

• The response to electric fields
12.1 Molecular response parameters
12.2 The static electric polarizability
12.3 Polarizability and molecular properties
12.4 Polarizabilities and molecular spectroscopy
12.5 Polarizabilities and dispersion forces
12.6 Retardation effects

• Bulk electrical properties
12.7 The relative permittivity and the electric susceptibility
12.8 Polar molecules
12.9 Refractive index

• Optical activity
12.10 Circular birefringence and optical rotation
12.11 Magnetically induced polarization
12.12 Rotational strength
P R O B L E M S

• 13. The magnetic properties of molecules

• The descriptions of magnetic fields
13.1 The magnetic susceptibility
13.2 Paramagnetism
13.3 Vector functions
13.4 Derivatives of vector functions
13.5 The vector potential

• Magnetic perturbations
13.6 The perturbation hamiltonian
13.7 The magnetic susceptibility
13.8 The current density
13.9 The diamagnetic current density
13.10 The paramagnetic current density

• Magnetic resonance parameters
13.11 Shielding constants
13.12 The diamagnetic contribution to shielding
13.13 The paramagnetic contribution to shielding
13.14 The g-value
13.15 Spin–spin coupling
13.16 Hyperfine interactions
13.17 Nuclear spin–spin coupling
P R O B L E M S

• 14. Scattering theory

• The formulation of scattering events
14.1 The scattering cross-section
14.2 Stationary scattering states

• Partial-wave stationary scattering states
14.3 Partial waves
14.4 The partial-wave equation
14.5 Free-particle radial wavefunctions and the scattering phase shift
14.6 The JWKB approximation and phase shifts
14.7 Phase shifts and the scattering matrix element
14.8 Phase shifts and scattering cross-sections
14.9 Scattering by a spherical square well
14.10 Background and resonance phase shifts
14.11 The Breit–Wigner formula
14.12 Resonance contributions to the scattering matrix element

• Multichannel scattering
14.13 Channels for scattering
14.14 Multichannel stationary scattering states
14.15 Inelastic collisions
14.16 The S matrix and multichannel resonances

• The Green’s function
14.17 The integral scattering equation and Green’s functions
14.18 The Born approximation
Appendix 14.1 The derivation of the Breit–Wigner formula
Appendix 14.2 The rate constant for reactive scattering

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