Keywords:
Molecular spectroscopy.
;
Electronic books.
Type of Medium:
Online Resource
Pages:
1 online resource (162 pages)
Edition:
1st ed.
ISBN:
9783319159584
Series Statement:
Lecture Notes in Physics Series ; v.900
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=6284385
DDC:
539.6
Language:
English
Note:
Intro -- Preface -- References -- Contents -- List of Figures -- 1 Introduction -- 1.1 Rotation: The Rigid Rotor -- 1.2 Vibration: The Harmonic Oscillator -- 1.3 Electronic Structure: The Particle in a Box and the Hydrogen Atom -- 1.4 Transition Selection and Propensity Rules: J, Franck-Condon, and S -- 1.5 Rotational Branches, Vibrational Bands, and ElectronicTransitions -- 1.6 Some Sum Rules -- 1.7 Eigenstates are Stationary -- References -- 2 Hierarchy of Terms in the Effective Hamiltonian -- 2.1 Adiabatic and Diabatic Representations -- 2.1.1 Introduction -- 2.1.2 Adiabatic vs. Diabatic Representations -- 2.2 Hspin-orbit -- 2.3 HROT, the Rotational Operator -- 2.4 Hund's Cases -- 2.4.1 H(0) vs. H(1) -- 2.5 Two Basis Sets for the 22 ``Two-Level'' Problem -- 2.6 Some Reasons for Patterns -- 2.7 Straight Line Plots -- 2.8 Stacked Plots -- 2.9 Angular Momenta: A Brief Summary -- 2.10 Where Have We Been and Where are We Going? -- References -- 3 Spectroscopic Perturbations: Homogeneous and Heterogeneous -- 3.1 What Is a Perturbation? -- 3.2 Level Shifts and Intensity Borrowing -- 3.3 Two Qualitatively Distinct Classes of Perturbation: Homogeneous and Heterogeneous -- 3.4 Franck-Condon Factors -- 3.5 Which Franck-Condon Factors Should I Use? -- 3.6 Intensity Borrowed from a Nearby Bright State -- 3.7 Intensity Borrowed from an Energetically Remote Bright State -- 3.8 Intensity Interference Effects -- References -- 4 The Effective Hamiltonian for Diatomic Molecules -- 4.1 Introduction -- 4.2 Main Topics of This Lecture -- 4.2.1 R-Dependence -- 4.2.2 How Do We Account for Interactions with Energetically Remote States? -- 4.2.3 Van Vleck Transformation -- 4.3 R-Dependence Is Encoded in v,J Dependence -- 4.3.1 Transition Moments: μ (R) →Mv,v -- 4.3.2 Centrifugal Distortion, De -- 4.3.3 Vibration-Rotation Interaction, αe: A Small Surprise.
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4.4 Van Vleck Transformation for Non-1+ States -- 4.4.1 Centrifugal Distortion -- 4.4.2 The Van Vleck Transformation -- 4.4.2.1 List of Initial and Final States -- 4.4.2.2 List of Relevant Intermediate States -- 4.4.2.3 Railroad Diagrams -- 4.4.2.4 Harvest the Information in Each Railroad Diagram -- 4.4.3 Example of Centrifugal Distortion in a 3 State -- 4.4.4 -Doubling -- 4.4.4.1 Elimination of Nonsense -- 4.4.4.2 Relationship Between Parity and e/f-Symmetry -- 4.4.4.3 The Central Role of -States -- 4.4.4.4 General -Doubling Hamiltonian, HLD -- 4.4.4.5 Worked Examples -- < -- 31 ef|H|31 ef> -- , a Diagonal Contribution -- < -- 31 ef|H|30 ef> -- , an Off-Diagonal Contribution -- -Doubling in a 1 State Due to an Energetically Remote 3+ State -- 4.5 Summary -- References -- 5 Rotation of Polyatomic Molecules -- 5.1 Introduction -- 5.2 Rotational Energy Levels of Rigid Polyatomic Rotors -- 5.2.1 Symmetric Top -- 5.2.2 Asymmetric Top -- 5.3 Correlation Diagrams: WHY? -- 5.3.1 Prolate-Oblate Top Correlation Diagram -- 5.3.2 Assignments of Rotational Transitions -- 5.4 Vibrational Dependence of Rotational Constants -- References -- 6 Quantum Beats -- 6.1 Introduction -- 6.2 Time-Dependent Schrödinger Equation (TDSE) -- 6.3 ``Bright'' and ``Dark'' States -- 6.4 Dynamics -- 6.5 Quantum Beats -- 6.5.1 Simple Two-Level Quantum Beats -- 6.5.2 Two-Level Treatment of QB with Complex Energies -- 6.5.3 What Does a Quantum Beat Signal Look Like? -- 6.5.4 Population Quantum Beats -- 6.5.4.1 Polarization Quantum Beats -- 6.5.4.2 Direction Cosine Matrix Element Based Picture of Polarization Quantum Beats -- 6.5.4.3 Zeeman vs. Stark Polarization Quantum Beats -- 6.5.5 Level-Crossing vs. Anticrossing -- References -- 7 The Effective Hamiltonian for Polyatomic Molecule Vibration -- 7.1 The Effective Vibrational Hamiltonian for PolyatomicMolecules.
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7.2 Harmonic Oscillator -- 7.2.1 Matrix Elements of P and Q -- 7.2.2 Dimensionless Forms: , , -- 7.2.2.1 Matrix Elements and Selection Rules -- 7.2.2.2 Use of Commutation Rules -- 7.2.2.3 We Use this Result to Evaluate Matrix Elements of (0) -- 7.2.2.4 Matrix Elements of Anharmonic V(Q) -- 7.3 Polyatomic Molecules -- 7.3.1 Basis Set as Product of 3N-6 Harmonic Oscillator Eigenstates -- 7.3.2 Matrix Elements of V(1,2,…3N-6) in the ψ(0)v1,v2,…,3N-6 Basis Set -- 7.3.3 Breakdown of Non-Degenerate Perturbation Theory -- 7.3.4 Polyads -- 7.3.5 Patterns for Spectral Assignment and Mechanisms of Intramolecular Vibrational Redistribution (IVR) and Unimolecular Isomerization -- 7.4 Polyads in the Acetylene Electronic Ground State (S0) -- References -- 8 Intramolecular Dynamics: Representations, Visualizations, and Mechanisms -- 8.1 From the ``Pluck'' at t=0 to the Time-Evolving State -- 8.2 Perturbation Theory -- 8.3 Toluene: A Hindered Rotor. A Fully Worked Out Example -- 8.4 The Pluck: (Q,t=0) -- 8.5 (Q,t) Contains too Much Information -- 8.5.1 Motion in Real Space -- 8.5.2 Motion in State Space -- 8.6 Mechanism -- References.
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