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E-raamat: Spectra and Dynamics of Small Molecules: Alexander von Humboldt Lectures

  • Formaat: PDF+DRM
  • Sari: Lecture Notes in Physics 900
  • Ilmumisaeg: 14-Apr-2015
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319159584
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  • Formaat: PDF+DRM
  • Sari: Lecture Notes in Physics 900
  • Ilmumisaeg: 14-Apr-2015
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319159584

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These seven lectures are intended to serve as an introduction for beginning graduate students to the spectra of small molecules. The author succeeds in illustrating the concepts by using language and metaphors that capture and elegantly convey simple insights into dynamics that lie beyond archival molecular constants. The lectures can simultaneously be viewed as a collection of interlocking special topics that have fascinated the author and his students over the years. Though neither a textbook nor a scholarly monograph, the book provides an illuminating perspective that will benefit students and researchers alike.
1 Introduction
1(12)
1.1 Rotation: The Rigid Rotor
1(1)
1.2 Vibration: The Harmonic Oscillator
2(1)
1.3 Electronic Structure: The Particle in a Box and the Hydrogen Atom
3(1)
1.4 Transition Selection and Propensity Rules: ΔJ, Franck--Condon, and ΔS
4(1)
1.5 Rotational Branches, Vibrational Bands, and Electronic Transitions
5(3)
1.6 Some Sum Rules
8(2)
1.7 Eigenstates are Stationary
10(3)
References
11(2)
2 Hierarchy of Terms in the Effective Hamiltonian
13(20)
2.1 Adiabatic and Diabatic Representations
13(3)
2.1.1 Introduction
13(1)
2.1.2 Adiabatic vs. Diabatic Representations
14(2)
2.2 Hspin--orbit
16(1)
2.3 HROT, the Rotational Operator
17(1)
2.4 Hund's Cases
18(4)
2.4.1 H(0) vs. H(1)
22(1)
2.5 Two Basis Sets for the 2 × 2 "Two-Level" Problem
22(1)
2.6 Some Reasons for Patterns
23(1)
2.7 Straight Line Plots
24(1)
2.8 Stacked Plots
25(4)
2.9 Angular Momenta: A Brief Summary
29(1)
2.10 Where Have We Been and Where are We Going?
30(3)
References
30(3)
3 Spectroscopic Perturbations: Homogeneous and Heterogeneous
33(14)
3.1 What Is a Perturbation?
33(8)
3.2 Level Shifts and Intensity Borrowing
41(1)
3.3 Two Qualitatively Distinct Classes of Perturbation: Homogeneous and Heterogeneous
42(1)
3.4 Franck--Condon Factors
42(1)
3.5 Which Franck--Condon Factors Should I Use?
43(1)
3.6 Intensity Borrowed from a Nearby Bright State
44(1)
3.7 Intensity Borrowed from an Energetically Remote Bright State
44(1)
3.8 Intensity Interference Effects
45(2)
References
46(1)
4 The Effective Hamiltonian for Diatomic Molecules
47(22)
4.1 Introduction
47(2)
4.2 Main Topics of This Lecture
49(2)
4.2.1 R-Dependence
49(1)
4.2.2 How Do We Account for Interactions with Energetically Remote States?
49(1)
4.2.3 Van Vleck Transformation
50(1)
4.3 R-Dependence Is Encoded in v, J Dependence
51(4)
4.3.1 Transition Moments: μ (R) → Mv',v"
51(1)
4.3.2 Centrifugal Distortion, De
52(2)
4.3.3 Vibration-Rotation Interaction, αe: A Small Surprise
54(1)
4.4 Van Vleck Transformation for Non-1 Σ+ States
55(12)
4.4.1 Centrifugal Distortion
56(1)
4.4.2 The Van Vleck Transformation
57(3)
4.4.3 Example of Centrifugal Distortion in a 3Π State
60(1)
4.4.4 Λ-Doubling
61(6)
4.5 Summary
67(2)
References
68(1)
5 Rotation of Polyatomic Molecules
69(16)
5.1 Introduction
69(5)
5.2 Rotational Energy Levels of Rigid Polyatomic Rotors
74(5)
5.2.1 Symmetric Top
74(1)
5.2.2 Asymmetric Top
75(4)
5.3 Correlation Diagrams: WHY?
79(4)
5.3.1 Prolate--Oblate Top Correlation Diagram
79(2)
5.3.2 Assignments of Rotational Transitions
81(2)
5.4 Vibrational Dependence of Rotational Constants
83(2)
References
84(1)
6 Quantum Beats
85(28)
6.1 Introduction
85(2)
6.2 Time-Dependent Schrodinger Equation (TDSE)
87(1)
6.3 "Bright" and "Dark" States
87(3)
6.4 Dynamics
90(8)
6.5 Quantum Beats
98(15)
6.5.1 Simple Two-Level Quantum Beats
98(2)
6.5.2 Two-Level Treatment of QB with Complex Energies
100(3)
6.5.3 What Does a Quantum Beat Signal Look Like?
103(1)
6.5.4 Population Quantum Beats
104(6)
6.5.5 Level-Crossing vs. Anticrossing
110(1)
References
110(3)
7 The Effective Hamiltonian for Polyatomic Molecule Vibration
113(16)
7.1 The Effective Vibrational Hamiltonian for Polyatomic Molecules
113(1)
7.2 Harmonic Oscillator
114(4)
7.2.1 Matrix Elements of P and Q
114(1)
7.2.2 Dimensionless Forms: H, Q, P
114(4)
7.3 Polyatomic Molecules
118(6)
7.3.1 Basis Set as Product of 3N -- 6 Harmonic Oscillator Eigenstates
118(1)
7.3.2 Matrix Elements of V(Q1, Q2, ... Q3N-6) in the ψ(0)v1,v2,...,3N-6 Basis Set
119(1)
7.3.3 Breakdown of Non-Degenerate Perturbation Theory
120(1)
7.3.4 Polyads
121(2)
7.3.5 Patterns for Spectral Assignment and Mechanisms of Intramolecular Vibrational Redistribution (IVR) and Unimolecular Isomerization
123(1)
7.4 Polyads in the Acetylene Electronic Ground State (S0)
124(5)
References
127(2)
8 Intramolecular Dynamics: Representations, Visualizations, and Mechanisms
129
8.1 From the "Pluck" at t = 0 to the Time-Evolving State
130(1)
8.2 Perturbation Theory
130(2)
8.3 Toluene: A Hindered Rotor. A Fully Worked Out Example
132(7)
8.4 The Pluck: Ψ(Q, t = 0)
139(1)
8.5 Ψ(Q, t) Contains too Much Information
140(5)
8.5.1 Motion in Real Space
141(2)
8.5.2 Motion in State Space
143(2)
8.6 Mechanism
145
References
153
Robert Field is the Haslam and Dewey Professor of Chemistry at MIT. His research specialties include dynamics encoded in frequency domain spectra of small, gas phase molecules, at high excitation, where all standard energy level patterns are broken: spectroscopic perturbations, Rydberg states, and unimolecular isomerization. His favorite experimental techniques include Stimulated Emission Pumping and Chirped Pulse Millimeter Wave spectroscopy.