RIGHTS REVERTED - Molecular Rotation Spectra

by Kroto, H. W.

• ISBN13: 9780486495408
• ISBN10: 048649540X
• Format: Hardcover
• Copyright: 2003-02-20
• Publisher: Dover Publications

Summary

This rigorous mathematical treatment offers a blend of the physical understanding necessary to formulate problems related to molecular rotation spectra and the abstract quantum mechanical expertise needed to solve them. 95 illustrations. 1975 edition.

Table of Contents

Quantum Mechanical Methods	1	(11)
The Description of Molecular Rotation	1	(1)
Molecular Energy and the Quantum Mechanical Hamiltonian	1	(1)
The Harmonic Oscillator	2	(5)
Non-diagonal Matrices	7	(5)
The Perturbed Harmonic Oscillator Hamiltonian	7	(1)
Matrix Diagonalization	8	(2)
Perturbation Theory	10	(2)
The Hamiltonian for a Rotating Molecule	12	(10)
The Born--Oppenheimer Separation of Electronic and Nuclear Motion	12	(2)
The Partition of the Nuclear Kinetic Energy	14	(6)
Angular Momenta	20	(2)
Angular Momentum and the Energy Levels of a Rigid Rotor	22	(39)
Angular Momentum and Axes of Reference	22	(1)
Space-fixed Angular Momentum	22	(1)
The Eigenvalues of Angular-momentum Operators	23	(3)
Molecule-fixed Angular Momentum	26	(2)
The Eigenfunctions of the Angular Momentum Operators	28	(2)
General Approach to Solving the Rigid-rotor Hamiltonian	30	(1)
The Energy Levels of Spherical Top Molecules	31	(1)
The Energy Levels of Linear Molecules	31	(2)
The Energy Levels of Symmetric Top Molecules	33	(1)
The General Asymmetric Rotor Problem	34	(11)
Algebraic Solution for Low J Values	35	(6)
Numerical Procedures	41	(1)
Perturbation Solutions	42	(2)
Expectation Values <J2α>	44	(1)
The Rotational Eigenfunctions	45	(16)
Symmetry and the Complete Hamiltonian	45	(3)
Geometric Symmetry Operations	48	(2)
The Symmetry of the Rotational Eigenfunctions	50	(3)
Nuclear Spin and Statistical Weights	53	(8)
Interaction of Radiation with a Rotating Molecule	61	(34)
The Energy of a Molecule in an External Field	61	(1)
Field Time Dependence	62	(3)
Static Field Interactions, ω = 0	63	(1)
Resonant Interactions with Oscillating Fields, ω = ωnm	63	(1)
Non-resonant Interactions with Oscillating Fields, ω ≠ ωnm	64	(1)
Absorption and Emission Induced by Electric Dipole Interactions	65	(4)
The Absorption Coefficient	68	(1)
Dipole Moment Matrix Elements and Selection Rules	69	(12)
The General Selection Rules on j, k and m	71	(1)
The Matrix Elements of S	72	(3)
The Matrix Elements of μ and Molecular Selection Rules	75	(6)
Population Factors	81	(4)
Thermal Distribution over Vibrational States	82	(1)
Thermal Distribution over Rotational States	83	(2)
Line Shapes and Line Widths	85	(2)
Spectral Intensity	87	(3)
Raman Scattering	90	(5)
Basic Rotational Spectra and Analysis	95	(17)
The Absorption Spectra of Linear Molecules	95	(3)
The Absorption Spectra of Symmetric Tops	98	(1)
The Absorption Spectra of Asymmetric Rotors	99	(11)
Raman Spectra	110	(2)
Vibration--Rotation Interactions	112	(52)
The Vibration--Rotation Hamiltonian for Semi-rigid Molecules	112	(3)
The Semi-rigid Diatomic Molecule	115	(7)
Perturbation Theory Approach to Vibration--Rotation Interactions in Diatomic Molecules	117	(2)
High-resolution Rotational Spectra of Diatomic Molecules	119	(3)
Expansion of the Vibration-Rotation Hamiltonian	122	(3)
General Vibration--Rotation Theory Procedure	125	(7)
Vibrational Hamiltonian, Hoν	127	(3)
Vibrational Angular Momentum	130	(1)
Energy-level Expressions	130	(2)
Centrifugal Distortion in Polyatomic Molecules	132	(8)
Centrifugal Distortion in Symmetric Top Molecules	134	(4)
Centrifugal Distortion in Asymmetric Rotors	138	(2)
The Interpretation of Vibration-Rotation α Constants	140	(2)
The Inertial Defect	142	(3)
l-type Doubling	145	(3)
Fermi and Coriolis Resonances	148	(1)
Spectra of Semi-rigid Molecules	149	(7)
Centrifugal Distortion Effects in Symmetric Top Molecules	149	(2)
Vibrational Satellites, l-doubling	151	(5)
Structure Determination	156	(8)
The Equilibrium Structure	156	(2)
The rs Substitution, and rm Methods	158	(3)
General Problems in Structure Determinations	161	(3)
The Stark Effect	164	(15)
The Interaction between an Electric Charge Distribution and an Electric Potential	164	(1)
The Stark Interaction	165	(1)
First-order Stark Effect	166	(2)
Second-order Stark Effect	168	(5)
Stark Effect Patterns and Line Assignments	173	(3)
Dipole Moment Determination	176	(3)
Nuclear Quadrupole Hyperfine Interactions	179	(17)
Electric Interactions Involving the Nucleus	179	(1)
Spherical Tensors	180	(2)
The Quadrupole Hamiltonian and Energy-level Expressions	182	(6)
Spectra with Quadrupole Hyperfine Structure	188	(8)
Flexible Molecules	196	(28)
Definition of a Flexible Molecule	196	(1)
Internal Rotation	197	(19)
The Hamiltonian for Internal Rotation	198	(3)
The Solution of the Torsional Hamiltonian, Hτ	201	(6)
The Coupling of Internal Rotation with Overall Rotation	207	(1)
Barrier Height Determination from Internal Rotation Splittings	208	(6)
General Survey of Systems with Internal Rotation	214	(2)
Inversion of Ammonia	216	(4)
Spectra of Ammonia	218	(2)
Ring Puckering	220	(2)
Quasi-linear Molecules and Quasi-symmetric Tops	222	(2)
Rotational Spectra of Linear Molecules with Electronic Angular Momentum	224	(26)
Electronic Angular Momentum	224	(1)
Classification of Electronic States of Linear Molecules	224	(2)
Interactions Involving Electronic Angular Momentum	226	(2)
Spin--Orbit Coupling	227	(1)
Spin--Rotation Interactions	227	(1)
Spin--Spin Interactions	228	(1)
Λ-doubling	228	(1)
Hund's Coupling Cases	228	(2)
Energy Levels and Spectra; Hund's Cases a, b, and a--b	230	(9)
Hund's Case a Limit	232	(1)
Hund's Case b Limit	233	(2)
Λ-doubling Energy	235	(4)
Electron Resonance Spectra of Diatomic Molecules	239	(11)
The Hamiltonian for Electron Resonance	240	(2)
The Energy of a Free Radical in a Magnetic Field	242	(2)
Electron Resonance Spectra	244	(4)
Analysis	248	(2)
Experimental Techniques	250	(14)
Microwave Spectrometers	251	(4)
Microwave Sources	251	(2)
Microwave Cells	253	(2)
Detection and Amplification	255	(1)
Frequency Multiplier Millimetre Wave Techniques	255	(1)
Far Infra-red Fourier Transform Interferometers	256	(2)
Lamb Dip Techniques	258	(1)
Molecular Beam Techniques, Maser Spectrometers	259	(2)
Acoustic Detection Spectrometers	261	(1)
Multiple Resonance Experiments	261	(1)
Magnetic Resonance Spectroscopy	262	(1)
Raman Spectra	262	(1)
Other Experimental Techniques	263	(1)
Appendixes	264	(14)
A1 Notation	264	(5)
A1.1 Units of Angular Momentum Operators and Parameters	264	(1)
A1.2 Angular Momentum Quantum Numbers	264	(1)
A1.3 Zero Point and Equilibrium Quantities	265	(1)
A1.4 Cartesian Indices	265	(1)
A1.5 Summation Convention	266	(1)
A1.6 Permutation Symbol eijk	266	(3)
A2 Angular Velocities, ωα	269	(1)
A3 Reduction of the Double Commutator [J2, [J2, T]]	269	(1)
A4 Second-order Perturbation Contributions	270	(1)
A5 The Two-dimensional Harmonic Oscillator	271	(1)
A6 Kraitchman's Equations	272	(1)
A7 Diatomic Molecular Potential Constants	273	(1)
A8 The Van Vleck Transformation	274	(4)
References	278	(15)
Author Index	293	(6)
Subject Index	299