Wolfgang Demtroder. Molecular Physics. Theoretical Principles and Experimental Methods WILEY- VCH. WILEY-VCH Verlag GmbH & Co.

Transcription

1 Wolfgang Demtroder Molecular Physics Theoretical Principles and Experimental Methods WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA

2 v Preface xiii 1 Introduction Short Historical Overview Molecular Spectra Recent Developments The Concept of This Book 10 2 Molecular Electronic States Adiabatic Approximation and the Concept of Molecular Potentials Quantum-Mechanical Description of Free Molecules Separation of Electronic and Nuclear Wavefunctions Born-Oppenheimer Approximation Adiabatic Approximation Deviations From the Adiabatic Approximation Potentials, Curves and Surfaces, Molecular Term Diagrams and Spectra Electronic States of Diatomic Molecules Exact Treatment of the Rigid H^ Molecule Classification of Electronic Molecular States Energetic Ordering of Electronic States Symmetries of Electronic Wavefunctions Electronic Angular Momenta 38 2A3 Electron Configurations and Electronic States The Approximation of Separated Atoms The "United Atom" Approximation Molecular Orbitals and the Aufbau Principle 45 Molecular Physics. Theoretical Principles and Experimental Methods. Wolfgang Demtroder. Copyright 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN:

3 vi Correlation Diagrams Approximation Methods for the Calculation of Electronic Wavefunctions The Variational Method The LCAO Approximation Application of Approximation Methods to One-electron Systems A Simple LCAO Approximation for the H^ Molecule Deficiencies of the Simple LCAO Method Improved LCAO Approximations Many-electron Molecules Molecular Orbitals and the Single-particle Approximation The H 2 Molecule The Molecular Orbital Approximation for H The Heitler-London Approximation A Improvements of Both Methods Equivalence of Heitler-London and MO Approximation Generalized MO Ansatz Modern Ab Initio Methods The Hartree-Fock Approximation Configuration Interaction Ab Initio Calculations and Quantum Chemistry 76 3 Rotation, Vibration, and Potential Curves of Diatomic Molecules Quantum-mechanical Treatment Rotation of Diatomic Molecules The Rigid Rotor Centrifugal Distortion The Influence of Electron Rotation Molecular Vibrations The Harmonic Oscillator The Anharmonic Oscillator Morse Potential Taylor Expansion of Potentials Quartic Potential Generalized Potential Vibration-Rotation Interaction Term Values of the Vibrating Rotor; Dunham Expansion Term Values for the Morse Potential Term Values for a Generalized Potential Dunham Expansion Isotopic Shifts 700

4 vii 3.6 Determination of Potential Curves from Measured Term Values The WKB Approximation WKB Approximation and Dunham Expansion Other Potential Expansions The RKR Method The Inverted Perturbation Approach Potential Curves at Large Internuclear Distances Multipole Expansion Induction Contributions to the Interaction Potential Point-charge-induced Dipole (Ion-Atom Interaction) Interaction Between Two Neutral Atoms Lennard-Jones Potential Spectra of Diatomic Molecules Transition Probabilities Einstein Coefficients Transition Probabilities and Matrix Elements Matrix Elements in the Born-Oppenheimer Approximation Structure of the Spectra of Diatomic Molecules Vibration-Rotation Spectra Pure Vibrational Transitions Within an Electronic State Pure Rotational Transitions Vibration-Rotation Transitions Electronic Transitions R Centroid Approximation; the Franck-Condon Principle The Rotational Structure of Electronic Transitions Continuous Spectra Line Profiles of Spectral Lines Natural Linewidth Doppler Broadening Voigt Profiles Collisional Broadening of Spectral Lines Multi-photon Transitions Two-Photon Absorption Raman Transitions Raman Spectra Thermal Population of Molecular Levels Thermal Population of Rotational Levels Population of Vibration-Rotation Levels Nuclear Spin Statistics 171

5 viii 5 Molecular Symmetry and Group Theory Symmetry Operations and Symmetry Elements Foundations of Group Theory Molecular Point Groups 78/ 5.4 Classification of Molecular Point Groups The Point Groups C n, C nv, and C nh The Point Groups D n, D nd, and D nh , The groups S n The Point Groups T d and O h How to Find the Point Group of a Molecule Symmetry Types and Representations of Groups The Representation of the Group C2v The Representation of the Group C3 V Characters and Character Tables Sums, Products, and Reduction of Representations 79<S 6 Rotations and Vibrations of Polyatomic Molecules Transformation From the Laboratory System to the Molecule-fixed System Molecular Rotation The Rigid Rotor The Symmetric Top Quantum-mechanical Treatment of Rotation Centrifugal Distortion of the Symmetric Top The Asymmetric Top 2/5 6.3 Vibrations of Polyatomic Molecules Normal Modes Example: Calculation of the Stretching Vibrations of a Linear Molecule AB Degenerate Vibrations Quantum-mechanical Treatment Anharmonic Vibrations Vibration-Rotation Coupling Electronic States of Polyatomic Molecules Molecular Orbitals Hybridization Triatomic Molecules The BeH 2 Molecule The H 2 O Molecule 247

6 ix The CO 2 Molecule AB 2 Molecules and Walsh Diagrams Molecules With More Than Three Atoms The NH 3 Molecule Formaldehyde Electron Systems Butadiene Benzene Spectra of Polyatomic Molecules Pure Rotational Spectra Linear Molecules Symmetric Top Molecules Asymmetric Top Molecules Intensities of Rotational Transitions Symmetry Properties of Rotational Levels Statistical Weights and Nuclear Spin Statistics Line Profiles of Absorption Lines Vibration-Rotation Transitions Selection Rules and Intensities of Vibrational Transitions Fundamental Transitions Overtone and Combination Bands Rotational Structure of Vibrational Bands Electronic Transitions Fluorescence and Raman Spectra Breakdown of the Born-Oppenheimer Approximation, Perturbations in Molecular Spectra What is a Perturbation? Quantitative Treatment of Perturbations Adiabatic and Diabatic Basis Perturbations Between Two Levels Hund's Coupling Cases Discussion of Different Types of Perturbations Electrostatic Interaction Spin-Orbit Coupling Rotational Perturbations Vibronic Coupling Renner-Teller Coupling Jahn-Teller Effect 313

7 x Predissociation Autoionization Radiationless Transitions Molecules in External Fields Diamagnetic and Paramagnetic Molecules Zeeman Effect in Linear Molecules Spin-Orbit Coupling and External Magnetic Fields Molecules in Electric Fields: The Stark Effect Van der Waals Molecules and Clusters Van der Waals Molecules Clusters Alkali Metal Clusters Rare-gas Clusters Water Clusters Covalently Bonded Clusters Generation of Clusters Experimental Techniques in Molecular Physics Microwave Spectroscopy Infrared and Fourier Spectroscopy Classical Spectroscopy in the Visible and Ultraviolet Laser Spectroscopy Laser Absorption Spectroscopy Intracavity Laser Spectroscopy Absorption Measurements Using the Resonator Decay Time Photoacoustic Spectroscopy Laser-magnetic Resonance Spectroscopy Laser-induced Fluorescence Laser Spectroscopy in Molecular Beams Doppler-free Nonlinear Laser Spectroscopy Multi-photon Spectroscopy Double Resonance Techniques Coherent Anti-Stokes Raman Spectroscopy Time-resolved Laser Spectroscopy Femtochemistry Coherent Control 472

8 xi 12.5 Photoelectron Spectroscopy Experimental Setups Photoionization Processes ZEKE Spectroscopy Angular Distribution of Photoelectrons X-ray Photoelectron Spectroscopy (XPS) Mass Spectroscopy Magnetic Mass Spectrometers Quadrupole Mass Spectrometers Time-of-flight Mass Spectrometers Radiofrequency Spectroscopy Nuclear Magnetic Resonance Spectroscopy Electron Spin Resonance Conclusion 434 Appendix: Character Tables of Some Point Groups 437 Bibliography 441 Index 461