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Molecular Quantum Mechanics

ISBN: 9780199274987 | 0199274983
Edition: 4th
Format: Paperback
Publisher: Oxford University Press, USA
Pub. Date: 2/17/2005

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SummaryTable of Contents
Ronald Friedman is Professor, Department of Chemistry, Indiana University Purdue University Fort Wayne, USA.
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, unravelling those fundamental physical principleswhich explain how all matter behaves.With the clarity of exposition and rich pedagogy which have established the book... MORE
Introduction and orientation1(1)
Black-body radiation
1(2)
Heat capacities
3(1)
... MORE
The photoelectric and Compton effects
4(1)
Atomic spectra
5(1)
The duality of matter
6(2)
Problems
8(1)
The foundations of quantum mechanics
9(34)
Operators in quantum mechanics
9(10)
Linear operators
10(1)
Eigenfunctions and eigenvalues
10(2)
Representations
12(1)
Commutation and non-commutation
13(1)
The construction of operators
14(1)
Integrals over operators
15(1)
Dirac bracket notation
16(1)
Hermitian operators
17(2)
The postulates of quantum mechanics
19(6)
States and wavefunctions
19(1)
The fundamental prescription
20(1)
The outcome of measurements
20(2)
The interpretation of the wavefunction
22(1)
The equation for the wavefunction
23(1)
The separation of the Schrodinger equation
23(2)
The specification and evolution of states
25(7)
Simultaneous observables
25(2)
The uncertainty principle
27(2)
Consequences of the uncertainty principle
29(1)
The uncertainty in energy and time
30(1)
Time-evolution and conservation laws
30(2)
Matrices in quantum mechanics
32(4)
Matrix elements
32(2)
The diagonalization of the hamiltonian
34(2)
The plausibility of the Schrodinger equation
36(7)
The propagation of light
36(2)
The propagation of particles
38(1)
The transition to quantum mechanics
39(1)
Problems
40(3)
Linear motion and the harmonic oscillator
43(28)
The characteristics of acceptable wavefunctions
43(1)
Some general remarks on the Schrodinger equation
44(3)
The curvature of the wavefunction
45(1)
Qualitative solutions
45(1)
The emergence of quantization
46(1)
Penetration into non-classical regions
46(1)
Translational motion
47(4)
Energy and momentum
48(1)
The significance of the coefficients
48(1)
The flux density
49(1)
Wavepackets
50(1)
Penetration into and through barriers
51(4)
An infinitely thick potential wall
51(1)
A barrier of finite width
52(2)
The Eckart potential barrier
54(1)
Particle in a box
55(5)
The solutions
56(1)
Features of the solutions
57(1)
The two-dimensional square well
58(1)
Degeneracy
59(1)
The harmonic oscillator
60(6)
The solutions
61(2)
Properties of the solutions
63(2)
The classical limit
65(1)
Translation revisited: The scattering matrix
66(5)
Problems
68(3)
Rotational motion and the hydrogen atom
71(27)
Particle on a ring
71(5)
The hamiltonian and the Schrodinger equation
71(2)
The angular momentum
73(1)
The shapes of the wavefunctions
74(2)
The classical limit
76(1)
Particle on a sphere
76(8)
The Schrodinger equation and its solution
76(3)
The angular momentum of the particle
79(2)
Properties of the solutions
81(1)
The rigid rotor
82(2)
Motion in a Coulombic field
84(14)
The Schrodinger equation for hydrogenic atoms
84(1)
The separation of the relative coordinates
85(1)
The radial Schrodinger equation
85(5)
Probabilities and the radial distribution function
90(1)
Atomic orbitals
91(3)
The degeneracy of hydrogenic atoms
94(2)
Problems
96(2)
Angular momentum
98(24)
The angular momentum operators
98(4)
The operators and their commutation relations
99(2)
Angular momentum observables
101(1)
The shift operators
101(1)
The definition of the states
102(10)
The effect of the shift operators
102(2)
The eigenvalues of the angular momentum
104(2)
The matrix elements of the angular momentum
106(2)
The angular momentum eigenfunctions
108(2)
Spin
110(2)
The angular momenta of composite systems
112(10)
The specification of coupled states
112(1)
The permitted values of the total angular momentum
113(2)
The vector model of coupled angular momenta
115(2)
The relation between schemes
117(2)
The coupling of several angular momenta
119(1)
Problems
120(2)
Group theory
122(46)
The symmetries of objects
122(7)
Symmetry operations and elements
123(1)
The classification of molecules
124(5)
The calculus of symmetry
129(16)
The definition of a group
129(1)
Group multiplication tables
130(1)
Matrix representations
131(4)
The properties of matrix representations
135(2)
The characters of representations
137(1)
Characters and classes
138(1)
Irreducible representations
139(3)
The great and little orthogonality theorems
142(3)
Reduced representations
145(6)
The reduction of representations
146(1)
Symmetry-adapted bases
147(4)
The symmetry properties of functions
151(10)
The transformation of p-orbitals
151(1)
The decomposition of direct-product bases
152(3)
Direct-product groups
155(2)
Vanishing integrals
157(2)
Symmetry and degeneracy
159(2)
The full rotation group
161(4)
The generators of rotations
161(1)
The representation of the full rotation group
162(2)
Coupled angular momenta
164(1)
Applications
165(3)
Problems
166(2)
Techniques of approximation
168(39)
Time-independent perturbation theory
168(15)
Perturbation of a two-level system
169(2)
Many-level systems
171(1)
The first-order correction to the energy
172(2)
The first-order correction to the wavefunction
174(1)
The second-order correction to the energy
175(1)
Comments on the perturbation expressions
176(2)
The closure approximation
178(2)
Perturbation theory for degenerate states
180(3)
Variation theory
183(4)
The Rayleigh ratio
183(2)
The Rayleigh-Ritz method
185(2)
The Hellmann-Feynman theorem
187(2)
Time-dependent perturbation theory
189(18)
The time-dependent behaviour of a two-level system
189(3)
The Rabi formula
192(1)
Many-level systems: the variation of constants
193(2)
The effect of a slowly switched constant perturbation
195(2)
The effect of an oscillating perturbation
197(2)
Transition rates to continuum states
199(1)
The Einstein transition probabilities
200(3)
Lifetime and energy uncertainty
203(1)
Problems
204(3)
Atomic spectra and atomic structure
207(42)
The spectrum of atomic hydrogen
207(12)
The energies of the transitions
208(1)
Selection rules
209(3)
Orbital and spin magnetic moments
212(2)
Spin-orbit coupling
214(2)
The fine-structure of spectra
216(1)
Term symbols and spectral details
217(1)
The detailed spectrum of hydrogen
218(1)
The structure of helium
219(10)
The helium atom
219(3)
Excited states of helium
222(2)
The spectrum of helium
224(1)
The Pauli principle
225(4)
Many-electron atoms
229(13)
Penetration and shielding
229(2)
Periodicity
231(2)
Slater atomic orbitals
233(1)
Self-consistent fields
234(2)
Term symbols and transitions of many-electron atoms
236(3)
Hund's rules and the relative energies of terms
239(1)
Alternative coupling schemes
240(2)
Atoms in external fields
242(7)
The normal Zeeman effect
242(1)
The anomalous Zeeman effect
243(2)
The Stark effect
245(1)
Problems
246(3)
An introduction to molecular structure
249(38)
The Born-Oppenheimer approximation
249(4)
The formulation of the approximation
250(1)
An application: the hydrogen molecule-ion
251(2)
Molecular orbital theory
253(13)
Linear combinations of atomic orbitals
253(5)
The hydrogen molecule
258(1)
Configuration interaction
259(2)
Diatomic molecules
261(4)
Heteronuclear diatomic molecules
265(1)
Molecular orbital theory of polyatomic molecules
266(12)
Symmetry-adapted linear combinations
266(3)
Conjugated π-systems
269(5)
Ligand field theory
274(2)
Further aspects of ligand field theory
276(2)
The band theory of solids
278(9)
The tight-binding approximation
279(2)
The Kronig-Penney model
281(3)
Brillouin zones
284(1)
Problems
285(2)
The calculation of electronic structure
287(55)
The Hartree-Fock self-consistent field method
288(14)
The formulation of the approach
288(1)
The Hartree-Fock approach
289(2)
Restricted and unrestricted Hartree-Fock calculations
291(2)
The Roothaan equations
293(3)
The selection of basis sets
296(5)
Calculational accuracy and the basis set
301(1)
Electron correlation
302(14)
Configuration state functions
303(1)
Configuration interaction
303(2)
Cl calculations
305(3)
Multiconfiguration and multireference methods
308(2)
Moller-Plesset many-body perturbation theory
310(3)
The coupled-cluster method
313(3)
Density functional theory
316(5)
Kohn-Sham orbitals and equations
317(2)
Exchange-correlation functionals
319(2)
Gradient methods and molecular properties
321(4)
Energy derivatives and the Hessian matrix
321(1)
Analytical derivatives and the coupled perturbed equations
322(3)
Semiempirical methods
325(7)
Conjugated π-electron systems
326(3)
Neglect of differential overlap
329(3)
Molecular mechanics
332(4)
Force fields
333(1)
Quantum mechanics-molecular mechanics
334(2)
Software packages for electronic structure calculations
336(6)
Problems
339(3)
Molecular rotations and vibrations
342(40)
Spectroscopic transitions
342(2)
Absorption and emission
342(2)
Raman processes
344(1)
Molecular rotation
344(13)
Rotational energy levels
345(4)
Centrifugal distortion
349(1)
Pure rotational selection rules
349(2)
Rotational Raman selection rules
351(2)
Nuclear statistics
353(4)
The vibrations of diatomic molecules
357(8)
The vibrational energy levels of diatomic molecules
357(2)
Anharmonic oscillation
359(1)
Vibrational selection rules
360(2)
Vibration-rotation spectra of diatomic molecules
362(2)
Vibrational Raman transitions of diatomic molecules
364(1)
The vibrations of polyatomic molecules
365(14)
Normal modes
365(3)
Vibrational selection rules for polyatomic molecules
368(1)
Group theory and molecular vibrations
369(4)
The effects of anharmonicity
373(3)
Coriolis forces
376(1)
Inversion doubling
377(2)
Appendix 10.1 Centrifugal distortion
379(3)
Problems
380(2)
Molecular electronic transitions
382(25)
The states of diatomic molecules
382(4)
The Hund coupling cases
382(2)
Decoupling and A-doubling
384(2)
Selection rules
386(1)
Vibronic transitions
386(4)
The Franck-Condon principle
386(3)
The rotational structure of vibronic transitions
389(1)
The electronic spectra of polyatomic molecules
390(6)
Symmetry considerations
391(1)
Chromophores
391(2)
Vibronically allowed transitions
393(2)
Singlet-triplet transitions
395(1)
The fate of excited species
396(11)
Non-radiative decay
396(1)
Radiative decay
397(2)
The conservation of orbital symmetry
399(1)
Electrocyclic reactions
399(2)
Cycloaddition reactions
401(2)
Photochemically induced electrocyclic reactions
403(1)
Photochemically induced cycloaddition reactions
404(2)
Problems
406(1)
The electric properties of molecules
407(29)
The response to electric fields
407(11)
Molecular response parameters
407(2)
The static electric polarizability
409(2)
Polarizability and molecular properties
411(2)
Polarizabilities and molecular spectroscopy
413(1)
Polarizabilities and dispersion forces
414(4)
Retardation effects
418(1)
Bulk electrical properties
418(9)
The relative permittivity and the electric susceptibility
418(2)
Polar molecules
420(2)
Refractive index
422(5)
Optical activity
427(9)
Circular birefringence and optical rotation
427(2)
Magnetically induced polarization
429(2)
Rotational strength
431(3)
Problems
434(2)
The magnetic properties of molecules
436(37)
The descriptions of magnetic fields
436(6)
The magnetic susceptibility
436(1)
Paramagnetism
437(2)
Vector functions
439(1)
Derivatives of vector functions
440(1)
The vector potential
441(1)
Magnetic perturbations
442(10)
The perturbation hamiltonian
442(2)
The magnetic susceptibility
444(3)
The current density
447(3)
The diamagnetic current density
450(1)
The paramagnetic current density
451(1)
Magnetic resonance parameters
452(21)
Shielding constants
452(4)
The diamagnetic contribution to shielding
456(2)
The paramagnetic contribution to shielding
458(1)
The g-value
459(3)
Spin-spin coupling
462(1)
Hyperfine interactions
463(4)
Nuclear spin-spin coupling
467(4)
Problems
471(2)
Scattering theory
473(40)
The formulation of scattering events
473(6)
The scattering cross-section
473(2)
Stationary scattering states
475(4)
Partial-wave stationary scattering states
479(18)
Partial waves
479(1)
The partial-wave equation
480(1)
Free-particle radial wavefunctions and the scattering phase shift
481(3)
The JWKB approximation and phase shifts
484(2)
Phase shifts and the scattering matrix element
486(2)
Phase shifts and scattering cross-sections
488(2)
Scattering by a spherical square well
490(2)
Background and resonance phase shifts
492(2)
The Breit-Wigner formula
494(1)
Resonance contributions to the scattering matrix element
495(2)
Multichannel scattering
497(5)
Channels for scattering
497(1)
Multichannel stationary scattering states
498(1)
Inelastic collisions
498(3)
The S matrix and multichannel resonances
501(1)
The Green's function
502(6)
The integral scattering equation and Green's functions
502(2)
The Born approximation
504(4)
Appendix 14.1 The derivation of the Breit-Wigner formula
508(1)
Appendix 14.2 The rate constant for reactive scattering
509(4)
Problems
510(3)
Further information
513(40)
Classical mechanics
513(6)
Action
513(2)
The canonical momentum
515(1)
The virial theorem
516(2)
Reduced mass
518(1)
Solutions of the Schrodinger equation
519(15)
The motion of wavepackets
519(2)
The harmonic oscillator: solution by factorization
521(2)
The harmonic oscillator: the standard solution
523(2)
The radial wave equation
525(1)
The angular wavefunction
526(1)
Molecular integrals
527(1)
The Hartree--Fock equations
528(4)
Green's functions
532(1)
The unitarity of the S matrix
533(1)
Group theory and angular momentum
534(3)
The orthogonality of basis functions
534(1)
Vector coupling coefficients
535(2)
Spectroscopic properties
537(6)
Electric dipole transitions
537(1)
Oscillator strength
538(2)
Sum rules
540(1)
Normal modes: an example
541(2)
The electromagnetic field
543(4)
The Maxwell equations
543(3)
The dipolar vector potential
546(1)
Mathematical relations
547(6)
Vector properties
547(2)
Matrices
549(4)
Further reading
553(4)
Appendix 1557(5)
Appendix 2562(1)
Answers to selected problems563(2)
Index565

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