Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping

The following sections are included:

• INTRODUCTION

• PREFACE

• CONTENTS

The following sections are included:

• Introduction

• Methodology
  • Introduction
  • Degenerate Four-Wave Mixing
    • General description
    • Molecular holography
    • Resonant DFWM theory
    • Refinements for gas-phase spectroscopy
  • SEP-DFWM Spectroscopy

• Experimental Implementation

• Experimental Results and Discussion
  • Comparison to Fluorescence-Dip Detection
  • Dynamic Range and Sensitivity
  • Molecular Beam Studies

• Related Techniques

• Conclusions and Future Directions

• Acknowledgments

• References

The following sections are included:

• Introduction

• Theory
  • Relationship between the Nonlinear Polarization and the TSEP Signal
  • Correlation of the TSEP Nolinear Polarization to the Molecular Dynamics
  • Discussions

• Ozone Visible Photodissociation Dynamics
  • Experimental
  • Results and Discussion

• Summary

• Acknowledgments

• Appendix A. Third-Order Nonlinear Density Matrix for TSEP

• Appendix B. Tensorial Analysis of the TSEP Nonlinear Polarization

• References

The following sections are included:

• Introduction: Creating and Detecting Molecular Vibrational–Rotational Levels

• Laser Light for Fluorescence Dip SEP
  • Pulse Dye Laser Sources
  • Characteristics of Commercial Pulse Dye Lasers
  • PUMPing and DUMPing: Too much for Some and Not Enough for Others

• The Fluorescence Dip SEP Experimental Configuration
  • An Overview of the Null Experiment
  • The Laser Beams and SHG
  • The Optically Balanced Dual Beam
  • Sample Cell and Collection Optics
  • Balanced Detection and Electronics

• Some Experimental Considerations
  • Sensitivity Considerations for Fluorescence Dip SEP
  • Dump Laser Delay
  • Variations: Single PUMP Beam, Jet-Cooled Samples, ps Pumping
  • SEP Using Intermediate Predissociating States

• Future Directions
  • Rydberg Intermediate States
  • Laser Mode Cleanup
  • Temporal Tailoring

• Summary

• Acknowledgments

• References

The following sections are included:

• Introduction

• LIDFS of Polyatomic Molecules
  • The Vibrational Propensity Rules Related to Potential Energy Surfaces
  • LIDFS: Towards High Resolution and High Sensitivity

• LIDFS of CS₂
  • Introduction
  • The Cu Laser System and the LN–CCD Camera
  • LIF Excitation Spectrum of CS₂ Close to the Barrier to Linearity in the V¹B₂ State
  • LIDFS of CS₂ below 12 000 cm⁻¹: Fermi Resonances
  • LIDFS of CS₂ up to 19 200 cm⁻¹: Transition to Chaos

• LIDFS of NO₂
  • Vibronic Coupling in NO₂
  • LIF Excitation Spectrum of Jet Cooled NO₂
  • Experimental Considerations
  • LIDFS from Ten Rovibronic Levels Located Around 23 000 cm⁻¹
  • LIDFS from Levels Located Around 17000 cm⁻¹

• Conclusion

• Acknowledgments

• References

The following sections are included:

• Introduction — Challenges for Vibration–Rotational Studies of Transient Molecules

• Vibrational Spectroscopy Through Examining the Downward Transitions From an Excited Electronic State
  • Flash Photolysis Stimulated Emission Pumping (SEP)
  • Time-Resolved Fourier Transform Emission Spectroscopy (TR–FTES)

• The Excited Vibrational Levels of ã¹A₁ CH₂
  • Rovibrational Analysis of CH₂ Spectra
    • Spectroscopy and molecular constants
    • Perturbations in the ã¹A₁ rovibrational levels
  • Barrier Height to Linearity in the ã¹ A₁ State
  • The Renner–Teller Effect
  • Strong ΔK_a = 3 Transitions in the CH₂ Spectrum

• Reaction and Rotational Energy Transfer of Vibrationally Excited CH₂

• Concluding Remarks: A Comparison of the SEP and TR–FTES Techniques

• Acknowledgements

• References

The following sections are included:

• Introduction

• Experimental Details

• Results
  • Renner–Teller Effect in ²Π Triatomics
  • SEP Spectroscopy of NCO

• Future Work

• Acknowledgments

• References

The following sections are included:

• Introduction

• Experimental Details

• Fine and Hyperfine Structure of Triplet Rydberg States

• PFOODR Dispersed Fluorescence Spectroscopy: Bound → Bound, Bound → Quasibound, and Bound → Free Transitions

• Collisional Energy Transfer between the Na₂ and b₃Π_u States: The Gateway Effect

• Pulsed PFOODR Spectroscopy of Na₂ and Li₂

• Acknowledgments

• References

The following sections are included:

• Introduction

• Fundamentals of Mass-Selective ILSRS
  • The Method
  • Implementation
  • Depletion Mechanisms
    • Desirable Raman-induced Depletions
    • Other Spectral Features
  • Desirable Features of Mass-Selective ILSRS
  • Comparison with Other Methods

• Selected Results
  • Benzene Dimer
  • Benzene–(Ar)_n Clusters
  • Benzene–(N₂)_n Clusters

• Future Prospects
  • Neutrals
  • Ions
  • Conclusion

• Acknowledgments

• References

The following sections are included:

• Introduction

• Rate Equations
  • Solutions for Two-Level Systems
  • Sequences of Transitions: Stimulated Emission Pumping

• Coherent Excitation
  • Coherent Excitation Equations
  • The Density Matrix

• The Two-Level System
  • The Rotating Wave Approximation (RWA)
  • Resonant Pulses
  • Dressed States and Dressed Eigenvalues
  • Special Cases

• Adiabatic Passage
  • The Adiabatic Condition
  • The Bloch Vector and Adiabatic Passage
  • The Landau–Zener–Stueckelberg Model
  • Experimental Demonstration, Two-Level System
  • Multilevel Adiabatic Passage: Generalized LZS
  • Experimental Demonstration, Multilevel LZS

• Pulsed Three-State Excitation
  • Two-Photon Excitation
  • Three-Stete Chirps
  • Experimental Demonstration, Three-Level Chirp
  • Delayed Pulses: STIRAP
  • Experimental STIRAP with cw Lasers
  • Effect of Phase Fluctuations on STIRAP
  • STIRAP and the Density Matrix
  • STIRAP with Multilevel Systems
  • Other Applications of STIRAP

• Summary and Conclusions

• Acknowledgments

• Appendix: Numerical Estimates of the Rabi Frequencies
  • Plane Waves
  • Focused Beams
  • Pulsed Beams
  • Relative Line Strengths
  • The Geometric Factor
  • The Molecular Line Strengths
  • Spontaneous Emission

• References

The following sections are included:

• Introduction

• Experimental
  • Discharge Flow Apparatus
  • Pulsed Supersonic Free Jet Apparatus

• High Resolution Spectroscopy of Low-Lying Vibrational States of
  • Normal Mode Vibrations and Survey SEP Spectra
  • Spectra Involving Symmetric (a₁) Vibrational Modes: ν₁ through ν₃
    • Rotational line structure and selection rules
    • Observed SEP spectra
  • Spectra Involving Degenerate (e) Vibrational Modes: =₄ through =₆
    • Jahn–Teller effect, vibronic states, and vibronic selection rules
    • Observed SEP and LIF excitation spectra
  • Conclusions on the Jahn–Teller Mechanism

• Intramolecular Vibrational Energy Redistribution in Highly Excited
  • Rotation–Vibration Level Mixing and IVR
  • “Franck–Condon Windows”
  • Rotationally “Assigned” Zero Order States and Spectra
  • IVR Time Scales, Coupling Matrix Elements, and Rovibronic State Densities

• Unimolecular Dissociation of

• Discussion and Conclusions
  • Spectroscopy of Low-Lying Vibrational States of
  • Intramolecular Vibrational and Rovibrational Energy Redistribution (IVR)
  • Unimolecular Dissociation Rate Constants
    • RRKM model
    • Discussion and further developments
  • Conclusion

• Acknowledgments

• References

The following sections are included:

• Introduction

• Mode-Specific IVR

• State-Specific Unimolecular Dissociation Dynamics
  • Dissociation Rates
  • Rotational Distribution and Doppler Widths of CO Fragments

• Summary

• Acknowledgments

• References

The following sections are included:

• Introduction
  • Selection Rule Constraints
  • All-Optical Triple Resonance

• Experimental
  • Fluorescence Detection
  • Ionization Detection

• All-Optical Triple Resonance Spectroscopy of the Mutually Perturbed and b³Π_u States of Na₂ and K₂
  • Observations of the State and Perturbations
  • Observations of Unperturbed Levels of the b³Π_u State

• State-Selected Photodissociation by All-Optical Triple Resonance
  • Photodissociation as a “Half Collision”
  • State-Selected Photodissociation of K₂

• Acknowledgments

• References

The following sections are included:

• Introduction

• Vibrationally Highly Excited SO₂
  • Classical Dynamics of SO₂ and Vibrational Chaos
  • SEP and DF Spectroscopy of SO₂

• Vibrationally Highly Excited States of Acetylene
  • SEP Spectrum of Acetylene and Statistical Analysis
  • DF Spectroscopy of Acetylene and Darling–Dennison Resonance Tier
  • Feature State
  • Hierarchical Level Structure and IVR
  • SEP Clarification of Anharmonic Resonances

• SEP and DF Spectroscopy for Dynamical Processes

• Acknowledgments

• References

The simple and well understood models of rotational and vibrational motion which include “the rigid rotor”, “the simple harmonic oscillator” and “normal coordinates”, are fully applicable to the analysis of the spectra of highly vibrationally excited HCN, even when the molecule contains enough vibrational energy to isomerize to HNC. Further consideration of more sophisticated but fully understood concepts such as axis-switching, rotational-ℓ-doubling and local anharmonic perturbations allows the assignment of every vibrational level observed in stimulated emission pumping experiments. This allows the reduction of the experimentally derived spectra to a set of well defined molecular constants that can be directly compared to theoretical calculations on HCN. This paper reports on the present status of an on-going effort to determine the potential energy surface for the isomerization reaction, “Nature's own Hamiltonian” for a chemical reaction.

The following sections are included:

• Introduction

• Experimental: Method of SEID Spectroscopy

• Results and Discussion
  • Vibrational Frequencies of Hydrogen Bonded Complex of Phenol
  • Intramolecular Vibrational Redistribution (IVR) in the Ground-State Vibrational Levels of Isolated Molecules
    • IVR of hydrogen bonded complex of phenol
    • IVR of p-alkyl phenols and p-alkyl anilines
    • Large amplitude motion and IVR of trans-stilbene

• Stimulated Raman Spectroscopy

• References

The following sections are included:

• Introduction

• Experimental Methods and Data Analysis
  • Stimulated Emission Pumping of Ground State Vibrational Levels in Polyatomics
  • Probing Population of SEP-Prepared Levels with Laser Induced Fluorescence and Dispersed Fluorescence
  • Application of the SEP–SVLF Technique to Vibrational Relaxation Studies in Supersonic Free Jets
  • Verification of the Preparation and Probe Steps
  • Kinetics: Extraction of Rate Coefficients for Collision-Induced Vibrational Relaxation
    • Low energy collision experiments

• The Lennard–Jones Elastic Encounter Rate as a Means for Scaling Vibrational Relaxation Rates

• Experimental Results for S₀ p-Difluorobenzene
  • Extraction of Rate Coefficients
    • Bulb experiments
    • Free jet experiments
  • Dependence of Vibrational Relaxation Rates on the Nature of the Collision Partner
  • Dependence of Vibrational Relaxation Rates on Initial State
  • Vibrational Relaxation in S₀ p-Difluorobenzene Induced by Very Low Energy Collisions
  • The Role of Electronic Excitation in Determining Vibrutional Relaxation Rates in Polyatomics

• A Semiempirical Model for Estimating Vibrational Relaxation Rates in Polyatomics
  • Development of the Model
  • Predictions of the Model for p-Difluorobenzene Vibrational Relaxation

• Conclusion and Future Directions

• References

The stimulated emission pumping (SEP) technique has made the study of highly vibrationally excited molecules increasingly appealing, enabling sophisticated spectroscopic probes to be converted to preparation techniques. With such an approach even relatively improbable processes, such as vibrational energy transfer and chemical reactivity, may be studied. This article describes studies of the vibrational quantum number dependence of the vibrational relaxation of highly vibrationally excited Nitric Oxide and Oxygen. The NO experiments are one of the first data sets on bimolecular energy transfer for molecules with several hundreds of kJ/mol of internal energy. Information is obtained showing to what extent energy transfer theories designed for low vibrational energy can be applied in this case. Strong evidence is also obtained suggesting that qualitatively different mechanisms such as “transient chemical bond formation” can influence the rate of vibrational energy transfer at high vibrational energy. Vibrational energy transfer of highly vibrationally excited O₂ is of current interest to the full understanding of the stratospheric ozone problem. This problem and initial experimental results are also presented.

The following sections are included:

• Introduction

• Theoretical Background
  • Ab Initio Potential
  • Energy Level Pattern
  • Infrared Selection Rules
  • Intensities of Stimulated Emission Pumping Transitions

• Experimental

• Results
  • Bound States
  • Dissociation Limits
  • Metastable Levels

• Discussion
  • Intermolecular Vibrational Levels of OH–Ar (X²Π)
  • Refinement of the Average OH (X²Π) + Ar Interaction Potential
  • OH (X²Π) + Ar Difference Potential
    • Parity splitting of rotational levels
    • Spin-orbit predissociation

• Conclusions

• Acknowledgments

• References

The following sections are included:

• Molecular Clusters and Spectroscopy

• Ion-Dip Spectroscopy of Molecular Clusters

• Dynamics from Ion-Dip Spectroscopy

• IDS and Cluster Dissociation

• Limitations of Ion-Dip Spectroscopy

• IDS in the Weak Electronic Coupling Limit: Phenylacetylene–NH₃, Ar

• IDS in the Strong Electronic Coupling Limit: Phenol–H₂O
  • Phenol and PhOH(H₂O)_n, n = 1–4 Excitation Spectra
  • Ion-Dip Spectroscopy of Phenol: Pumping the Band
  • Ion-Dip Spectrum of PhOD: Pumping the Band
  • Cluster Ion-Dip Spectroscopy of PhOH(H₂O)₁
    • PhOH(H₂O)₁: Pumping the Band
  • Measurement of the Relaxation Rate Constant, δ, for the Dip
  • PhOH(H₂O)₁ IDS Line Assignments
  • PhOD(D₂O)₁ Ion-Dip Spectra: Pumping the Band
  • Intermolecular Intermediate States: the and Bands
  • IDS of PhOH(H₂O)₂: Pumping the Band
  • IDS of PhOH(H₂O)₃: Pumping the Band
  • IDS of PhOH(H₂O)₄: Two Isomers
    • Pumping the Band: ω_pump = 36172 cm⁻¹
    • Pumping the Band: ω_pump = 36302 cm⁻¹

• Summary

• Acknowledgments

• References

Assigning spectra and inferring dynamics from c.w. data can be difficult, and sometimes ambiguous and controversial. The ambiguity can be due to a poor understanding of the nature of the “feature” state whose Franck–Condon amplitudes determine the spectral intensities. Such difficulties can arise when the vibrational overlaps are small, corresponding to the wings of an absorption or emission band. This is the case in SEP at 28000 cm⁻¹ in acetylene or in typical radiationless processes.

The following sections are included:

• Introduction
  • Computing Spectra
  • A Case Study: HCN

• The Recursive Residue Generation Method
  • Overview
  • The Standard Approach: Matrix Diagonalization
  • General Aspects of the Recursion Method
  • What is a Residue?
  • Lanczos Recursion: How it Works
  • Residues from the Tridiagonal Matrix
  • Using the QL Algorithm
  • Concluding Remarks

• Application to HCN
  • Description of the Molecular System
  • Excited State Description, Dipole Function, and Selection Rules
  • Results
    • The ^rR₀(0) DUMP transition [(J′ = 1, K′ = 1, f) → (J″ = 0, K″ = 0, e)]
    • The ^PP₂(4) DUMP transition [(J′ = 3, K′ = 1, f) → (J″ = 4, K″ = 2, e)]

• Discussion

• Acknowledgments

• References

The following sections are included:

• Introduction
  • Symmetry Properties of the Molecule
  • Structures of Acetylene

• CNPI–MS Group Theory of Acetylene
  • Asymmetric Rotor Labels
  • CNPI–MS Operations
    • Parity and particle exchange
    • Trans-bent C_2h structure
    • Cis-bent C_2v structure
    • Vinylidene a-axis C_2v structure
    • Nonplanar C₂ acetylene
      • The c-axis C₂ structure
      • The b-axis C₂ structure
      • Isotopic substitution effects
    • The linear D_∞h structure

• Statistical Weights

• Vibrational and Electronic Symmetry
  • Symmetry of the Vibrational Wavefunction
    • The trans-bent normal modes
    • The cis-bent normal modes
    • The vinylidene normal modes
    • Vibrations in nonplanar C₂ acetylene
    • The linear normal modes
  • Symmetry of the Electronic Wavefunction

• Selection Rules

• Isomerization in Acetylene
  • State Specific Coupling and Isomerization
  • Identifying Vinylidene States
  • Isomerization and Isomer Specific Spin-Orbit Coupling
  • Torsional Tunneling in Nonplanar Acetylene

• Conclusions

• Acknowledgments

• References

The following sections are included:

• Introduction

• Spectral Trees

• Analysis of Trees

• A Comparison to an Experimental Spectrum

• Energy Transfer and Assignability

• Conclusion

• Acknowledgment

• References

Stimulated Emission Pumping (SEP) and other double resonance techniques provide very large quantities of high-resolution, wide-dynamic-range, quantum-number-sorted spectral data. Deriving information about intramolecular dynamics without detailed line-by-line assignment of fully-resolved transitions between individual eigenstates requires the development of new methods of recognizing patterns and of identifying hierarchical levels of coupling in the spectrum. Power spectrum analysis, and methods using level statistics have been the only alternative to traditional eigenstate assignment and modeling methods for extracting dynamical behavior. We illustrate the limitations of these methods and describe two promising new techniques for spectral pattern recognition. The first, the extended autocorrelation function (XAC), allows complex patterns parameterized in a multi-dimensional way to be located in a spectrum in the presence of interfering data. We describe the motivation for this method, and illustrate its application to synthetic systems, and to C₂H₂ dispersed fluorescence data. The second, parsimonious trees, allows direct model-free identification of multiple clusters of coupling matrix element values from a spectrum in which the underlying dynamics has a hierarchical or sequential structure. For this method, we also describe the motivation, apply it to synthetic systems, and to both band origin and rovibrational data in the optical spectrum of NO₂.

The following sections are included:

• Introduction

• Dynamics and Assignment of Coupled Vibrations from Experimental Spectra of Systems with a Single Strong Resonance
  • Polyad Phase Sphere Dynamics From Fits of Resonance Spectra
  • Bifurcation and Catastrophe Map Classification of Strongly Coupled Dynamics
  • New Assignments of Spectra of Strongly Coupled Vibrations
  • Nonlinear Dynamics and Semiclassical Quantization of Integrable Resonance Fitting Hamiltonians
    • Integrable single resonance fitting Hamiltonians and invariant tori and actions
    • EBK quantization of the tori and dynamically based quantum number assignments corresponding to the invariant actions

• Dynamical Analysis of Spectra of Classically Chaotic Systems
  • Introductory Remarks and Summary
  • Periodic Orbit Theory of Semiclassical Quantization
  • Relation of Chaotic Quantization Conditions to Molecular Spectral Classification and Assignment
  • Invariant Cantori as Phase Space Remnants of Invariant Tori
  • Quantization of Cantori and Spectral Classification and Assignment

• Systems with Many Degrees of Freedom
  • Approximate Dynamical Constants of Motion and Quantum Number Assignments of Polyatomics with Multiple Fermi Resonances
  • Bifurcation Structure of the Many Degree of Freedom Phase Space

• Bootstrap Fitting and Potential Surfaces of Highly Excited Polyatomics

• Summary and Conclusions

• Acknowledgment

• References

The following sections are included:

• Introduction

• Rotation–Vibration Hamiltonians

• Canonical Van Vleck Perturbation Theory

• Rotation–Vibration Mixing in H₂CO
  • K-Mixing
  • Spectral Congestion
  • Vibrationally Induced Rotation–Vibration Mixing

• Random Matrix Approach to State Mixing
  • Vibration–Vibration Mixing
  • Rotation–Vibration Mixing

• Summary and Future Directions

• Acknowledgments

• References

The following sections are included:

• Introduction

• Vibration–Rotation Separation and the Watson Hamiltonian

• Rotation-Induced Vibrational Energy Flow — An Elementary Example

• Nonlinear Resonances and the Classical Mechanics of the Pendulum

• Application of the Pendulum Picture to Rotation Mediated Vibrational Energy Flow

• Generalizing the Pendulum — The Asymmetric Top Mapping

• Dynamics and Quantization of the Asymmetric Top

• The Asymmetric Top Mapping (ATM) in Intramolecular Dynamics

• Application to Energy Flow in Formaldehyde

• New Decoupling Schemes for the Vibration–Rotation Hamiltonian — the BT Transformation

• Conclusion

• References

The following sections are included:

• Introduction

• Regular and Chaotic Spectra
  • Regular Spectroscopy, Regular States, and Regular Motions
  • Chaotic Spectra, Chaotic States, and Chaotic Motions

• Low Resolution Spectra of the Sodium Trimer

• Application to

• LiCN Spectra in the Isomerization Region

• SEP and DF Spectra in HCCH

• Acknowledgment

• References

The following sections are included:

• INDEX