Spectra and Dynamics of Small Molecules

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 1.1 Rotation: The Rigid Rotor............................................. 1 1.2 Vibration: The Harmonic Oscillator .................................. 2 1.3 Electronic Structure: The Particle in a Box and the Hydrogen Atom........................................................ 3 1.4 Transition Selection and Propensity Rules: ?J , Franck–Condon, and ?S .............................................. 4 1.5 Rotational Branches, Vibrational Bands, and Electronic Transitions ............................................................. 5 1.6 Some Sum Rules....................................................... 8 1.7 Eigenstates are Stationary ............................................. 10 References ..................................................................... 11 2 Hierarchy of Terms in the Effective Hamiltonian ........................ 13 2.1 Adiabatic and Diabatic Representations .............................. 13 2.1.1 Introduction.................................................... 13 2.1.2 Adiabatic vs. Diabatic Representations ...................... 14 spin–orbit 2.2 H ................................................................ 16 2.3 HROT, the Rotational Operator ........................................ 17 2.4 Hund’s Cases........................................................... 18 .0/ 3 Spectroscopic Perturbations: Homogeneous and Heterogeneous . . . . . . 33 3.1 What Is a Perturbation?................................................ 33 3.2 Level Shifts and Intensity Borrowing................................. 41 vs. H ................................................... 22 .1/ 2.4.1 H 2.5 Two Basis Sets for the 2 ? 2 “Two-Level” Problem ................. 22 2.6 Some Reasons for Patterns ............................................ 23 2.7 Straight Line Plots ..................................................... 24 2.8 Stacked Plots........................................................... 25 2.9 Angular Momenta: A Brief Summary ................................ 29 2.10 Where Have We Been and Where are We Going? ................... 30 References ..................................................................... 30 vii viii Contents 3.3 Two Qualitatively Distinct Classes of Perturbation: Homogeneous and Heterogeneous.................................... 42 3.4 Franck–Condon Factors ............................................... 42 3.5 Which Franck–Condon Factors Should I Use?....................... 43 3.6 Intensity Borrowed from a Nearby Bright State ..................... 44 3.7 Intensity Borrowed from an Energetically Remote Bright State . . . . 44 3.8 Intensity Interference Effects.......................................... 45 References ..................................................................... 46 4 The Effective Hamiltonian for Diatomic Molecules ...................... 47 4.1 Introduction ............................................................ 47 4.2 Main Topics of This Lecture .......................................... 49 4.2.1 R-Dependence ................................................. 49 4.2.2 How Do We Account for Interactions with Energetically Remote States? ................................. 49 4.2.3 VanVleckTransformation.................................... 50 4.3 R-DependenceIsEncodedinv;J Dependence..................... 51 4.3.1 Transition Moments: ?.R/ ! Mv0;v00 ........................ 51 4.3.2 Centrifugal Distortion, De .................................... 52 4.3.3 Vibration-Rotation Interaction, ̨e : A Small Surprise . . . . . . . 54 4.4 VanVleckTransformationforNon-1†C States...................... 55 4.4.1 Centrifugal Distortion ......................................... 56 4.4.2 The Van Vleck Transformation ............................... 57 4.4.3 Example of Centrifugal Distortion in a 3... State ............ 60 4.4.4 ƒ-Doubling .................................................... 61 4.5 Summary ............................................................... 67 References ..................................................................... 68 5 Rotation of Polyatomic Molecules.......................................... 69 5.1 Introduction ............................................................ 69 5.2 Rotational Energy Levels of Rigid Polyatomic Rotors .............. 74 5.2.1 Symmetric Top ................................................ 74 5.2.2 Asymmetric Top ............................................... 75 5.3 Correlation Diagrams: WHY? ........................................ 79 5.3.1 Prolate–Oblate Top Correlation Diagram .................... 79 5.3.2 Assignments of Rotational Transitions ....................... 81 5.4 Vibrational Dependence of Rotational Constants .................... 83 References ..................................................................... 84 6 Quantum Beats............................................................... 85 6.1 Introduction ............................................................ 85 6.2 Time-Dependent Schrödinger Equation (TDSE)..................... 87 6.3 “Bright” and “Dark” States............................................ 87 6.4 Dynamics............................................................... 90 6.5 Quantum Beats......................................................... 98 6.5.1 Simple Two-Level Quantum Beats ........................... 98 6.5.2 Two-Level Treatment of QB with Complex Energies . . . . . . . 100 6.5.3 What Does a Quantum Beat Signal Look Like? ............. 103 6.5.4 Population Quantum Beats.................................... 104 6.5.5 Level-Crossing vs. Anticrossing .............................. 110 References ..................................................................... 110 7 The Effective Hamiltonian for Polyatomic Molecule Vibration . . . . . . . . 113 7.1 The Effective Vibrational Hamiltonian for Polyatomic Molecules .............................................................. 113 7.2 Harmonic Oscillator ................................................... 114 7.2.1 Matrix Elements of P and Q .................................. 114 OOO 7.3.1 Basis Set as Product of 3N ? 6 Harmonic Oscillator Eigenstates ......................................... 118 OOO 7.2.2 Dimensionless Forms: H, Q, P ............................... 114 7.3 Polyatomic Molecules ................................................. 118 7.3.2 Matrix Elements of V.Q1 ; Q2 ; : : : Q3N-6 / in the .0/ Basis Set ................................ 119 v1 ;v2 ;:::;3N ?6 7.3.3 Breakdown of Non-Degenerate Perturbation Theory . . . . . . . . 120 7.3.4 Polyads......................................................... 121 7.3.5 Patterns for Spectral Assignment and Mechanisms of Intramolecular Vibrational Redistribution (IVR) and Unimolecular Isomerization . . . . . . 123 7.4 Polyads in the Acetylene Electronic Ground State (S0) ............. 124 References ..................................................................... 127 8 Intramolecular Dynamics: Representations, Visualizations, and Mechanisms ............................................................. 129 8.1 From the “Pluck” at t D 0 to the Time-Evolving State .............. 130 8.2 Perturbation Theory ................................................... 130 8.3 Toluene: A Hindered Rotor. A Fully Worked Out Example . . . . . . . . . 132 8.4 ThePluck:‰.Q;tD0/.............................................. 139 8.5 ‰.Q; t/ Contains too Much Information ............................. 140 8.5.1 Motion in Real Space ......................................... 141 8.5.2 Motion in State Space ......................................... 143 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.

暂无其它内容！

暂时还没有人为这本书评论！