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1 | (12) |
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1.1 Rotation: The Rigid Rotor |
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1 | (1) |
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1.2 Vibration: The Harmonic Oscillator |
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2 | (1) |
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1.3 Electronic Structure: The Particle in a Box and the Hydrogen Atom |
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3 | (1) |
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1.4 Transition Selection and Propensity Rules: ΔJ, Franck--Condon, and ΔS |
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4 | (1) |
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1.5 Rotational Branches, Vibrational Bands, and Electronic Transitions |
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5 | (3) |
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8 | (2) |
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1.7 Eigenstates are Stationary |
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10 | (3) |
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11 | (2) |
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2 Hierarchy of Terms in the Effective Hamiltonian |
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13 | (20) |
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2.1 Adiabatic and Diabatic Representations |
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13 | (3) |
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13 | (1) |
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2.1.2 Adiabatic vs. Diabatic Representations |
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14 | (2) |
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16 | (1) |
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2.3 HROT, the Rotational Operator |
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17 | (1) |
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18 | (4) |
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22 | (1) |
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2.5 Two Basis Sets for the 2 × 2 "Two-Level" Problem |
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22 | (1) |
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2.6 Some Reasons for Patterns |
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23 | (1) |
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24 | (1) |
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25 | (4) |
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2.9 Angular Momenta: A Brief Summary |
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29 | (1) |
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2.10 Where Have We Been and Where are We Going? |
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30 | (3) |
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30 | (3) |
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3 Spectroscopic Perturbations: Homogeneous and Heterogeneous |
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33 | (14) |
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3.1 What Is a Perturbation? |
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33 | (8) |
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3.2 Level Shifts and Intensity Borrowing |
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41 | (1) |
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3.3 Two Qualitatively Distinct Classes of Perturbation: Homogeneous and Heterogeneous |
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42 | (1) |
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3.4 Franck--Condon Factors |
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42 | (1) |
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3.5 Which Franck--Condon Factors Should I Use? |
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43 | (1) |
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3.6 Intensity Borrowed from a Nearby Bright State |
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44 | (1) |
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3.7 Intensity Borrowed from an Energetically Remote Bright State |
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44 | (1) |
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3.8 Intensity Interference Effects |
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45 | (2) |
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46 | (1) |
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4 The Effective Hamiltonian for Diatomic Molecules |
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47 | (22) |
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47 | (2) |
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4.2 Main Topics of This Lecture |
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49 | (2) |
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49 | (1) |
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4.2.2 How Do We Account for Interactions with Energetically Remote States? |
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49 | (1) |
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4.2.3 Van Vleck Transformation |
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50 | (1) |
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4.3 R-Dependence Is Encoded in v, J Dependence |
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51 | (4) |
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4.3.1 Transition Moments: μ (R) → Mv',v" |
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51 | (1) |
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4.3.2 Centrifugal Distortion, De |
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52 | (2) |
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4.3.3 Vibration-Rotation Interaction, αe: A Small Surprise |
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54 | (1) |
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4.4 Van Vleck Transformation for Non-1 Σ+ States |
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55 | (12) |
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4.4.1 Centrifugal Distortion |
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56 | (1) |
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4.4.2 The Van Vleck Transformation |
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57 | (3) |
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4.4.3 Example of Centrifugal Distortion in a 3Π State |
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60 | (1) |
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61 | (6) |
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67 | (2) |
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68 | (1) |
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5 Rotation of Polyatomic Molecules |
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69 | (16) |
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69 | (5) |
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5.2 Rotational Energy Levels of Rigid Polyatomic Rotors |
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74 | (5) |
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74 | (1) |
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75 | (4) |
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5.3 Correlation Diagrams: WHY? |
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79 | (4) |
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5.3.1 Prolate--Oblate Top Correlation Diagram |
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79 | (2) |
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5.3.2 Assignments of Rotational Transitions |
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81 | (2) |
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5.4 Vibrational Dependence of Rotational Constants |
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83 | (2) |
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84 | (1) |
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85 | (28) |
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85 | (2) |
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6.2 Time-Dependent Schrodinger Equation (TDSE) |
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87 | (1) |
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6.3 "Bright" and "Dark" States |
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87 | (3) |
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90 | (8) |
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98 | (15) |
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6.5.1 Simple Two-Level Quantum Beats |
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98 | (2) |
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6.5.2 Two-Level Treatment of QB with Complex Energies |
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100 | (3) |
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6.5.3 What Does a Quantum Beat Signal Look Like? |
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103 | (1) |
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6.5.4 Population Quantum Beats |
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104 | (6) |
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6.5.5 Level-Crossing vs. Anticrossing |
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110 | (1) |
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110 | (3) |
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7 The Effective Hamiltonian for Polyatomic Molecule Vibration |
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113 | (16) |
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7.1 The Effective Vibrational Hamiltonian for Polyatomic Molecules |
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113 | (1) |
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114 | (4) |
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7.2.1 Matrix Elements of P and Q |
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114 | (1) |
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7.2.2 Dimensionless Forms: H, Q, P |
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114 | (4) |
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118 | (6) |
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7.3.1 Basis Set as Product of 3N -- 6 Harmonic Oscillator Eigenstates |
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118 | (1) |
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7.3.2 Matrix Elements of V(Q1, Q2, ... Q3N-6) in the ψ(0)v1,v2,...,3N-6 Basis Set |
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119 | (1) |
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7.3.3 Breakdown of Non-Degenerate Perturbation Theory |
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120 | (1) |
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121 | (2) |
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7.3.5 Patterns for Spectral Assignment and Mechanisms of Intramolecular Vibrational Redistribution (IVR) and Unimolecular Isomerization |
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123 | (1) |
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7.4 Polyads in the Acetylene Electronic Ground State (S0) |
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124 | (5) |
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127 | (2) |
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8 Intramolecular Dynamics: Representations, Visualizations, and Mechanisms |
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129 | |
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8.1 From the "Pluck" at t = 0 to the Time-Evolving State |
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130 | (1) |
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130 | (2) |
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8.3 Toluene: A Hindered Rotor. A Fully Worked Out Example |
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132 | (7) |
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8.4 The Pluck: Ψ(Q, t = 0) |
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139 | (1) |
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8.5 Ψ(Q, t) Contains too Much Information |
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140 | (5) |
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8.5.1 Motion in Real Space |
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141 | (2) |
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8.5.2 Motion in State Space |
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143 | (2) |
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145 | |
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153 | |