Conical Intersections

The following sections are included:

• Foreword

• Preface

• Contents

The following sections are included:

• Introduction

• Exploring the Intersection Space: The Extended Conical Intersection Seam
  • Theory

• Extended Seam Benchmarks
  • Fulvene
  • The 2A₁/1A₁ conical intersection seam in butadiene

• Applications of the Extended Seam of a Conical Intersection to Photochemical Mechanisms
  • The photoinduced isomerization of 1,3-cyclohexadiene (CHD) to cZc-hexatriene (HT)
  • Diarylethylenes
  • The keto-enol tautomerism of o-hydroxyphenyl-(1,3,5)-triazine

• Valence Bond Analysis of Conical Intersections
  • Twisted intermolecular charge transfer (T-(ICT)) in aminobenzonitrile (ABN) compounds
  • What happens when one does a conical intersection circuit in the branching plane?

• Exploring the Conical Intersection Seam using Dynamics
  • A model cyanine system: The extended seam for cis-trans double bond isomerization
  • Benzene
  • Biological chromophores: PYP

• Conclusions

• Acknowledgments

• References

The following sections are included:

• Introduction

• The πσ^*-driven Photochemistry of Acidic Aromatic Systems

• Excited-State Electron/Proton Transfer in Intra-Molecularly Hydrogen-Bonded Aromatic Systems

• Excited-State Electron/Proton Transfer in Inter-Molecularly Hydrogen-Bonded Aromatic Systems

• Chromophores with Flexible Side-Chains: Electron/Proton Transfer in Amino Acids and Peptides

• Conclusions

• Acknowledgments

• References

The following sections are included:

• Introduction

• Noncrossing Rule

• Branching and Seam Spaces

• Symmetry and Three-State Conical Intersections: The Jahn–Teller Effect

• First Accidental Three-State Conical Intersection:

• Locating Accidental Three-State Conical Intersections

• Consequences of Three-State Conical Intersections
  • Connectivity
  • Geometric phase
  • Nonadiabatic couplings

• Characterizing Three-State Conical Intersections

• Three-State Conical Intersections in Chemical Systems
  • Three-state conical intersections in radicals
  • Three-state conical intersections in closed-shell organic systems

• Dynamics

• Concluding Remarks

• Acknowledgments

• References

The following sections are included:

• Introduction

• Spin-Free and Relativistically Generalized Jahn–Teller Selection Rules

• JT and SO Coupling in Trigonal Systems

• Relativistic Jahn–Teller Coupling in Tetrahedral Systems

• Jahn–Teller and Spin-Orbit Coupling in High-Spin States of Trigonal Systems

• Examples: Transition-Metal Trifluorides and Group V Tetrahedral Cations

• Conclusions

• Acknowledgments

• References

The following sections are included:

• Introduction

• Time-Independent Description of Single-Surface Dynamics
  • Topology and encirclement
  • Symmetry approach
  • Path-integral approach
  • Relation between symmetry and path-integral approaches
  • Distinction between scattering and bound states

• Time-Dependent Description of Single-Surface Dynamics
  • Symmetry approach
  • Path-integral approach

• Time-Dependent Description of Dynamics on Two Coupled Surfaces
  • Symmetry approach
  • Time-ordered-product path-integral approach
  • Behaviour of Feynman paths at CI seam

• Numerical Applications
  • Cancellation of GP effects in the hydrogen-exchange reaction
    • Reaction paths and potential energy surface
    • Cancellation of GP effects in state-to-state cross sections
  • Geometric phase effects in two-surface population transfer
    • Wave packet calculations on E × e Jahn–Teller model
    • Effect of GP on population transfer

• Conclusions

• Acknowledgments

• References

The following sections are included:

• Introduction
  • Electron spectroscopies
  • Scope of this work

• Vibronic Coupling Model
  • Vibronic wave functions
    • The initial state
    • The final state: Nonadiabatic Ansatz
      • Time-independent nonrelativistic wave functions
      • Wave functions including the spin-orbit interaction
    • Determination of time-independent wave functions
      • Nonrelativistic Schrödinger equation
      • Schrödinger equation including the spin-orbit interaction
  • Spectral intensity distribution function
    • Nonrelativistic formulation
    • Inclusion of spin-orbit coupling
  • Hamiltonians
    • Coulomb or nonrelativistic diabatic Hamiltonian, H^d
    • Kinetic energy operator
  • Computational issues
    • Construction of diabatic Hamiltonians for bound states
    • Optimal bases and Franck–Condon overlaps
    • Lanczos procedure: Open-ended fine grained parallel approach

• Applications
  • Overview: Conical intersections not required by symmetry
  • Azolyls: Electronic structure
    • Imidazolyl
    • Pyrazolyl
    • Pyrrolyl
  • Pyrrolyl: Detailed computations
    • Electronic structure treatment
    • Construction and accuracy of H^d
      • Nascent H^d
      • Improving the accuracy and extending the domain of utility of H^d
      • Sensitivity of simulated photoelectron spectrum to H^{d, w}
    • Photoelectron spectrum of pyrrolyl
  • Isopropoxy
    • Electronic structure treatment
    • An unexpected conical topography
    • Photoelectron spectrum of isopropoxide
    • Implications

• Conclusions

• Acknowledgments

• Appendices

• References

The following sections are included:

• Introduction

• Methodological Framework
  • The multimode vibronic coupling approach
  • The concept of regularized diabatic states
  • Electronic structure calculations
  • Quantum dynamical calculations

• Illustrative Examples
  • Formaldehyde
    • General; electronic structure calculations
    • Potential energy surfaces and diabatic Hamiltonian
    • VUV absorption spectrum
    • Time-dependent electronic populations
  • Pyrrole
    • Vibronic coupling Hamiltonian for pyrrole
    • Electronic structure calculations and coupling constants
    • Potential energy surfaces and conical intersections
    • Time-dependent electronic populations
  • Fluorinated benzene cations
    • Vibronic coupling Hamiltonian for the fluorobenzene cations
    • Electronic structure calculations and coupling constants
    • Potential energy surfaces and conical intersections
    • Photoelectron spectra
    • Time-dependent electronic populations
    • Relation to the fluorescence yield

• Concluding Remarks

• Acknowledgments

• References

The following sections are included:

• Introduction

• Multimode System-Bath Hamiltonian
  • System-bath Hamiltonian
  • Spectral densities

• Effective Modes at a Conical Intersection
  • Definition of effective-mode subspace
  • Hierarchical structure of the bath
  • Alternative sets of effective modes
  • Generalization to more than two electronic states

• Effective-Plus-Residual Bath Models
  • Model 1: Secondary bath coupled to primary effective modes
  • Model 2: Mori-type chain
  • Model 3: Mori-type chain with Markovian closure
  • Dynamical evolution and moment conservation rules
  • Example: Ultrafast photophysics of semiconductor polymer junctions

• Hierarchical Approximations of the Spectral Density
  • Spectral densities in the transformed representation
  • Tuning mode bath
    • Spectral densities
    • Example: S₂-S₁ CoIn in pyrazine coupled to a tuning mode bath
  • General correlated bath

• Discussion and Conclusions

• Note Added in Proof

• Acknowledgments

• Appendices

• References

The following sections are included:

• Introduction

• Ab Initio Multiple Spawning
  • Overview
  • Full multiple spawning dynamics — wavefunction ansatz
  • Full multiple spawning dynamics — spawning
  • Full multiple spawning dynamics — initial conditions
  • Ab initio multiple spawning — electronic structure considerations

• Applications

• Conclusions

• Acknowledgments

• References

The following sections are included:

• Introduction

• Non-Born–Oppenheimer Molecular Dynamics
  • Coupled potential energy surfaces
  • Efficient integration of NBO trajectories
  • Initial conditions for photochemistry

• Fewest Switches with Time Uncertainty

• Coherent Switches with Decay of Mixing

• Summary of Recent Tests and Applications

• Concluding Remarks

• Acknowledgments

• References

The following sections are included:

• Introduction

• Nonadiabatic Dynamics Based on Classical Trajectories
  • The time-dependent equations
  • Implications of the local approximation
  • The surface hopping approach

• Initial Conditions
  • Wigner and quasi-Wigner distributions
  • Sampling with trajectory simulations
  • Sampling in special points
  • The excited-state distribution

• Electronic Structure Methods

• Analytical Gradient
  • MCSCF gradient
  • State-averaged MCSCF gradient
  • MRCI gradient

• Nonadiabatic Coupling Terms
  • NAC vectors in MCSCF and MRCI formalism
  • Time-derivative NAC terms

• Dynamics Close to Conical Intersections

• Conclusions and Outlook

• Acknowledgments

• References

The following sections are included:

• Introduction

• Theory
  • Propagation of quantum amplitudes
  • Fewest switches algorithm
  • Velocity adjustment
  • Adiabatic representation

• Implementation of Trajectory Surface Hopping
  • Algorithm
  • Initial sampling

• Electronic Structure Methods
  • Ab initio CASSCF and MRCI
  • Semiempirical methods
  • Hybrid QM/MM

• Applications
  • Methaniminium cation
  • 9H-adenine

• Summary and Outlook

• Note Added in Proof

• Acknowledgments

• References

The following sections are included:

• Introduction

• Nonadiabatic Dynamics “on the Fly” in the Framework of Time-Dependent Density Functional Theory (TDDFT)
  • Tully's surface hopping in the framework of TDDFT
    • Representation of the electronic wavefunction within the Kohn–Sham linear response method
    • Nonadiabatic coupling in the framework of TDDFT and TDDFTB with localized basis sets

• Simulation of Time-Resolved Photoelectron Spectra (TRPES)
  • Wigner distribution approach for the simulation of time-resolved photoelectron spectra
  • Stieltjes imaging approach for approximate description of photoionization continuum

• Field-Induced Surface-Hopping Method (FISH) for Simulation and Control of Ultrafast Photodynamics

• Applications of the Nonadiabatic Dynamics “on the Fly”
  • Ultrafast dynamics of photoswitching
    • Computational
    • Ultrafast photoswitching in benzylideneaniline (BAN)
  • Ultrafast internal conversion through conical intersection in pyrazine
    • Computational
    • Simulation of TRPES for pyrazine and comparison with experimental spectra
  • Ultrafast photodynamics of adenine in microsolvated environment
    • Computational
    • Influence of solvation on the nonradiative relaxation of adenine

• Applications of the Field-Induced Surface-Hopping Method (FISH) for the Control of Ultrafast Dynamics by Shaped Laser Fields
  • Optimal control of trans-cis isomerization in a molecular switch
    • Computational
    • Selective trans-cis isomerization of N-MEI
  • Optimal dynamic discrimination
    • Computational
    • Discrimination of RBF and FMN by shaped laser pulses

• Conclusions and Outlook

• Acknowledgments

• References

The following sections are included:

• Introduction

• Quantum Control Theory
  • Time-dependent Schrödinger equation
  • Minimal model analysis
    • First-order optical transitions
    • First-order nonadiabatic transitions
    • Pre-target state
  • Optimal control theory (OCT)
    • Optimal control simulation
    • Other (approximate) control methods

• Case Studies
  • Wave packet shaping utilizing CI-induced nonadiabatic transitions
  • Geometric phase effects on coherent control of CI-induced dynamics

• Conclusions

• Acknowledgments

• References

The following sections are included:

• Introduction

• Experimental Methods
  • Photofragment translational spectroscopy
  • Ion imaging methods
  • H Rydberg atom photofragment translational spectroscopy

• Results
  • Azoles
  • Phenols
  • Larger analogues

• Future Prospects

• References

The following sections are included:

• Introduction

• Wavepacket Dynamics
  • Born–Oppenheimer wavepacket dynamics
  • Nonadiabatic wave-packet dynamics
  • Selection of experimental observables

• Principles of Time-Resolved Photoelectron Spectroscopy
  • Photoelectron spectroscopy as a probe
    • Motivation
    • Description of photoionization
  • Description of electronic and nuclear degrees of freedom
    • Complementary Koopmans' correlations (Type I)
    • Corresponding Koopmans' correlations (Type II)
    • Franck–Condon Spectra

• Applications of Time-Resolved Photoelectron Spectroscopy
  • Experimental demonstration of TRPES
  • Interrogation of molecular dynamics employing TRPES
    • Excited state intramolecular proton transfer
    • Photostability of DNA bases

• Concluding Remarks

• Acknowledgments

• References

The following sections are included:

• Introduction

• Femtosecond Time-Resolved Pump-Probe Schemes for Organic Chromophores

• Radiationless Electronic Deactivation in Free DNA Bases

• Electronic Deactivation in H-Bridged Base Pairs, π-Stacked Dimers and Oligonucleotides

• Conformer-Specific Photochemistry of Furylfulgides

• Ultrafast Photoisomerization of Azobenzenes

• Conclusions

• Acknowledgments

• References

The following sections are included:

• Introduction
  • The polarization anisotropy
  • Tuning and coupling coordinates

• Theory
  • Model system and Hamilitonian
  • Reduced density matrix and Redfield equations
  • Effect of electronic relaxation on the anisotropy

• Experiment
  • A D_4h silicon naphthalocyanine (SiNc)
  • A D_2h free-base naphthalocyanine (H₂Nc)

• Discussion

• Conclusion

• References

The following sections are included:

• Index