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Abstract
Attosecond science is a new and rapidly developing research area in which molecular dynamics are studied at the timescale of a few attoseconds.
Within the past decade, attosecond pump–probe spectroscopy has emerged as a powerful experimental technique that permits electron dynamics to be followed on their natural timescales. With the development of this technology, physical chemists have been able to observe and control molecular dynamics on attosecond timescales. From these observations it has been suggested that attosecond to few-femtosecond timescale charge migration may induce what has been called “post-Born-Oppenheimer dynamics”, where the nuclei respond to rapidly time-dependent force fields resulting from transient localization of the electrons. These real-time observations have spurred exciting new advances in the theoretical work to both explain and predict these novel dynamics.
This book presents an overview of current theoretical work relevant to attosecond science written by theoreticians who are presently at the forefront of its development. It is a valuable reference work for anyone working in the field of attosecond science as well as those studying the subject.
Table of Contents
| Section Title | Page | Action | Price |
|---|---|---|---|
| Front Cover | Cover | ||
| Attosecond Molecular Dynamics | i | ||
| Contents | v | ||
| Chapter 1 Introduction | 1 | ||
| 1.1 Introduction | 1 | ||
| 1.2 State-of-the-art of Molecular Attosecond Experiments | 6 | ||
| 1.2.1 Electron Localization Following Attosecond Molecular Photoionization | 11 | ||
| 1.2.2 Increasing the Complexity of the Molecule: N2 | 14 | ||
| 1.2.3 The Next Level of Complexity: Polyatomic Molecules | 16 | ||
| 1.3 Contents of this Book | 25 | ||
| References | 34 | ||
| Chapter 2 Low-dimensional Models for Simulating Attosecond Processes in Atoms and Molecules | 38 | ||
| 2.1 Introduction | 38 | ||
| 2.2 Electron Dynamics in Strong Fields | 39 | ||
| 2.2.1 Single Active Electron 1d Models | 39 | ||
| 2.2.2 Emission Times in High Harmonic Generation | 42 | ||
| 2.2.3 Short and Long Trajectories in Harmonic Generation: Quantum Path Interferences | 45 | ||
| 2.2.4 Structural Minima in Harmonic Spectra from Molecules | 47 | ||
| 2.2.5 Pros and Cons of 1d Models | 51 | ||
| 2.3 Accounting for the Nuclear Motion | 51 | ||
| 2.3.1 1d 1d Vibronic Model | 51 | ||
| 2.3.2 Dynamics of Molecular Photoionisation | 54 | ||
| 2.3.3 Influence of Nuclear Motion on High Harmonic Generation in Molecules | 59 | ||
| 2.4 Conclusion | 63 | ||
| References | 63 | ||
| Chapter 3 First-principles Many-electron Dynamics Using the B-spline Algebraic Diagrammatic Construction Approach | 68 | ||
| 3.1 Theoretical Method: Time-dependent B-spline ADC | 68 | ||
| 3.1.1 Intermediate State Representation Approach to ADC Ab Initio Schemes | 70 | ||
| 3.1.2 B-spline Basis Set | 74 | ||
| 3.1.3 Computational Procedure | 76 | ||
| 3.1.4 Time Propagation | 83 | ||
| 3.2 Results and Discussion | 87 | ||
| 3.2.1 Atomic Photoionisation Cross Sections by Combination of B-spline-ADC and Stieltjes Methods | 87 | ||
| 3.2.2 ADC(1) High Harmonic Generation Spectra of Ar Atom and Aligned CO2 Molecules | 89 | ||
| 3.2.3 Attosecond Transient Absorption Spectroscopy Calculation in a He Atom | 95 | ||
| 3.3 Conclusions | 97 | ||
| References | 99 | ||
| Chapter 4 Ultrafast Electron Dynamics as a Route to Explore Chemical Processes | 103 | ||
| 4.1 Problem Overview | 103 | ||
| 4.1.1 Chemistry as Dynamics of Quantum Particles | 103 | ||
| 4.1.2 Molecular States and Born–Oppenheimer Approximation | 105 | ||
| 4.1.3 Describing Correlated Electrons | 108 | ||
| 4.2 Correlated Electron Dynamics Following Ionization | 111 | ||
| 4.2.1 The Hole Density | 112 | ||
| 4.2.2 Choice of Cationic Basis and Initial State | 115 | ||
| 4.2.3 Basic Mechanisms | 117 | ||
| 4.3 Attochemistry | 123 | ||
| 1 Dyson ADC | 130 | ||
| 2 Non-Dyson ADC | 133 | ||
| References | 134 | ||
| Chapter 5 Time-dependent Multiconfigurational Theories of Electronic and Nuclear Dynamics of Molecules in Intense Laser Fields | 139 | ||
| 5.1 Introduction | 139 | ||
| 5.2 Multiconfiguration Time-dependent Hartree–Fock Theory | 142 | ||
| 5.2.1 EOMs for the Spin-orbitals | 145 | ||
| 5.2.2 The EOMs for CI Coefficients | 148 | ||
| 5.2.3 Time-dependent Natural Orbitals | 149 | ||
| 5.2.3.1 Definition of Instantaneous Natural Spin-orbitals | 149 | ||
| 5.2.3.2 EOMs for Time-dependent Natural Spin-orbitals | 150 | ||
| 5.3 Nuclear Dynamics of Molecules in Intense Near-infrared Fields: Time-Dependent Adiabatic State Approach | 151 | ||
| 5.4 Extension of MCTDHF to Treat Molecular Dynamics | 153 | ||
| 5.5 Results and Discussion | 156 | ||
| 5.5.1 Application of MCTDHF to Anisotropic Ionization of CO | 156 | ||
| 5.5.1.1 Ionization | 157 | ||
| 5.5.1.2 Effective Potential | 157 | ||
| 5.5.2 Application of the Basic Concept of the Time-dependent Adiabatic state Approach to H2 | 160 | ||
| 5.5.3 Application to an Ethanol Molecule in an Intense Laser Field | 164 | ||
| 5.5.4 Protonic Structure in CH3OH | 170 | ||
| 5.5.5 Comparison With Born–Huang Expansion for the Ground-state Wave Function of a One-dimensional H2 Model | 173 | ||
| 5.6 Conclusions | 176 | ||
| References | 178 | ||
| Chapter 6 Light-induced Conical Intersections | 183 | ||
| 6.1 Introduction | 183 | ||
| 6.2 Theory | 186 | ||
| 6.2.1 The Hamiltonian | 186 | ||
| 6.2.2 Nuclear Wave Packet Propagation and Dynamical Properties | 188 | ||
| 6.3 Results and Discussions | 190 | ||
| 6.3.1 Nuclear Wave Packet Quantum Interference | 190 | ||
| 6.3.2 Direct Signature of the Light-induced Conical Intersection | 197 | ||
| 6.3.3 A Quantum Control Strategy Using Light-induced Conical Intersections | 200 | ||
| 6.3.4 Competition of Intrinsic and Light-induced Nonadiabatic Phenomena | 205 | ||
| 6.4 Conclusions | 211 | ||
| References | 212 | ||
| Chapter 7 Theoretical Methodsfor Attosecond Coupled Electron-nuclear DynamicsIn Molecular Photoionization | 218 | ||
| 7.1 Introduction | 218 | ||
| 7.2 General Theoretical Background to Describe Ultrafast Dynamics in Molecular Photoionization | 221 | ||
| 7.2.1 Time-dependent Schrödinger Equation | 221 | ||
| 7.2.2 Electronic Continuum States | 224 | ||
| 7.2.2.1 The Single Channel Approximation | 225 | ||
| 7.2.2.2 Beyond the Single-channel Approximation | 225 | ||
| 7.2.2.3 Evaluation of Continuum Orbitals | 226 | ||
| 7.3 Theory for the Simplest One- and Two-electron Molecules H2+ and H2 | 228 | ||
| 7.3.1 One-electron Diatomic Molecule: H2 | 228 | ||
| 7.3.2 Two-electron Diatomic Molecule: H2 | 230 | ||
| 7.3.3 The Time Dependent Feshbach Close-coupling Method for H2 | 231 | ||
| 7.3.3.1 Bound States and Resonance States in QQQQ Subspace. | 234 | ||
| 7.3.3.2 Continuum States in PPPP Subspace. | 235 | ||
| 7.3.4 Nuclear Motion | 239 | ||
| 7.3.5 Relation with H2 Experiments | 240 | ||
| 7.4 Results from Full Dimensional Ab Initio Approaches (Hydrogenic Molecules) | 242 | ||
| 7.4.1 One-electron Diatomic Molecules | 243 | ||
| 7.4.2 Hydrogen Molecule | 249 | ||
| 7.4.2.1 Rabi Oscillations | 251 | ||
| 7.5 Beyond H2: Electron Dynamics in More Complex Diatomic Molecules | 254 | ||
| 7.6 Ultrafast Dynamics in Larger Molecules | 257 | ||
| 7.7 Conclusions | 263 | ||
| References | 264 | ||
| Chapter 8 How Nuclear Motion Affects Coherent Electron Dynamics in Molecules | 275 | ||
| 8.1 Introduction | 275 | ||
| 8.2 Theoretical Methods | 279 | ||
| 8.2.1 Ehrenfest Method | 281 | ||
| 8.2.2 DD-vMCG Method | 283 | ||
| 8.3 Implementation Details | 285 | ||
| 8.3.1 Implementation of the Ehrenfest Method | 285 | ||
| 8.3.2 Implementation of the DD-vMCG Method | 287 | ||
| 8.4 Applications | 291 | ||
| 8.4.1 Effect of (Mean-field) Nuclear Motion | 292 | ||
| 8.4.2 Effect of Nuclear Spatial Delocalization | 295 | ||
| 8.4.3 Effect of Quantum Nuclear Motion | 297 | ||
| 8.4.4 Design of Molecular Targets for Longer-lived Coherence | 299 | ||
| 8.5 Conclusion | 303 | ||
| References | 305 | ||
| Chapter 9 Attophotochemistry: Coherent Electronic Dynamics and Nuclear Motion | 308 | ||
| 9.1 The Basics | 308 | ||
| 9.2 The Grid | 313 | ||
| 9.3 Mass Effects | 320 | ||
| 9.4 Short Time Nuclear Dynamics | 321 | ||
| 9.5 Computing on the Fly | 322 | ||
| 9.6 Illustrative Examples | 323 | ||
| 9.6.1 Steering of Selective Dissociation in LiH | 324 | ||
| 9.6.2 LiH Computed on the Fly | 328 | ||
| 9.7 Excitation of N2 in the Far UV | 332 | ||
| 9.8 Dissociation Dynamics in HCN and DCN | 334 | ||
| 9.9 Concluding Remarks | 343 | ||
| References | 343 | ||
| Chapter 10 General Trajectory Surface Hopping Method for Ultrafast Nonadiabatic Dynamics | 348 | ||
| 10.1 Introduction | 348 | ||
| 10.2 Electronic State Representations | 349 | ||
| 10.3 Nonadiabatic Dynamics: SHARC | 353 | ||
| 10.3.1 From Quantum Dynamics to Molecular Dynamics | 353 | ||
| 10.3.2 From Born–Oppenheimer Molecular Dynamicsto Surface Hopping | 354 | ||
| 10.3.3 From Surface Hopping to SHARC | 358 | ||
| 10.3.4 Practical Aspects of SHARC Simulations | 360 | ||
| 10.4 Electronic Structure Methods | 362 | ||
| 10.4.1 Excited-state Energies and Gradients | 362 | ||
| 10.4.2 Nonadiabatic Couplings | 365 | ||
| 10.4.3 Spin–orbit Coupling and Scalar Relativistic Effects | 366 | ||
| 10.4.4 Dipole Moments and Dyson Norms | 367 | ||
| 10.5 Analysis | 368 | ||
| 10.5.1 Simulation of Observables | 368 | ||
| 10.5.2 Analysis of Electronic Evolution | 371 | ||
| 10.5.3 Analysis of Nuclear Evolution | 372 | ||
| 10.6 Example Application | 373 | ||
| 10.7 Summary | 377 | ||
| References | 378 | ||
| Chapter 11 Time-dependent Restricted-active-space Self-consistent-field Theory for Electron Dynamics on the Attosecond Timescale | 386 | ||
| 11.1 Introduction | 386 | ||
| 11.2 Brief Overview of Wavefunction-based Many-electron Theories | 387 | ||
| 11.3 Philosophy of the TD-RASSCF Theory | 390 | ||
| 11.4 Formulation of the TD-RASSCF Theory | 392 | ||
| 11.4.1 Equations of Motion for the Amplitudes | 395 | ||
| 11.4.2 Equations of Motion for the Orbitals | 396 | ||
| 11.4.2.1 Equations of Motion for the Q-space Orbitals | 396 | ||
| 11.4.2.2 Equations of Motion for the P-space Orbitals | 398 | ||
| 11.4.2.3 Even Excitation RAS Scheme | 400 | ||
| 11.4.2.4 General RAS Scheme | 401 | ||
| 11.5 Extraction of Observables from the TD-RASSCF Wavefunction | 403 | ||
| 11.5.1 Photoelectrons and High-order Harmonic Generation | 404 | ||
| 11.5.1.1 Photoelectrons | 404 | ||
| 11.5.1.2 High-order Harmonic Generation | 406 | ||
| 11.6 Properties of the TD-RASSCF Theory | 407 | ||
| 11.6.1 Gauge Invariance | 407 | ||
| 11.6.2 Numerical Performance | 408 | ||
| 11.7 Illustrative Applications of the TD-RASSCF Theory | 410 | ||
| 11.7.1 High-order Harmonic Generation | 411 | ||
| 11.7.2 Photoionization of Be | 413 | ||
| 11.7.2.1 Correlation Effects in Time-delays in Photoionization | 415 | ||
| 11.8 Summary and Conclusion | 418 | ||
| References | 419 | ||
| Chapter 12 Real-time and Real-space Time-dependent Density-functional Theory Approach to Attosecond Dynamics | 424 | ||
| 12.1 Introduction | 424 | ||
| 12.2 TDDFT in Real Time | 426 | ||
| 12.2.1 Perturbation Theory Approaches | 431 | ||
| 12.2.2 Electron–ion Dynamics | 434 | ||
| 12.2.3 Computational Issues | 436 | ||
| 12.3 Photon Absorption | 438 | ||
| 12.3.1 Equilibrium Linear Response | 438 | ||
| 12.3.2 Non-equilibrium Linear Response | 441 | ||
| 12.4 Photoelectron Spectroscopy | 445 | ||
| 12.4.1 Formalism | 445 | ||
| 12.4.2 Example | 450 | ||
| 12.5 Control of Electron Dynamics | 452 | ||
| 12.6 Conclusions and Remarks | 454 | ||
| References | 456 | ||
| Chapter 13 Elements of Structure Retrieval in Ultrafast Electron and Laser-induced Electron Diffraction from Aligned Polyatomic Molecules | 462 | ||
| 13.1 Introduction | 462 | ||
| 13.2 Conventional Gas-phase Electron Diffraction and the Independent Atom Model | 464 | ||
| 13.3 Structure Retrieval from Electron Diffractionof Aligned Molecules | 465 | ||
| 13.3.1 Genetic Algorithm for Reconstructing the Diffraction Pattern Corresponding to Perfectly 1-DAligned Molecules | 467 | ||
| 13.3.2 Calculating a Diffraction Pattern after Rotationand Averaging of the Angular Distribution | 468 | ||
| 13.3.3 Application of the Genetic Algorithm to Symmetric Top Molecules | 469 | ||
| 13.3.4 Application of the Genetic Algorithm to Asymmetric Top Molecules | 471 | ||
| 13.3.4.1 Expressing the Diffraction PatternsUsing Cylindrical Harmonics | 472 | ||
| 13.3.4.2 Applying the Genetic Algorithm | 474 | ||
| 13.3.4.3 Iterative Phase Retrieval Algorithm | 474 | ||
| 13.4 Laser-induced Electron Diffraction | 477 | ||
| 13.4.1 Historic Background and the Basic Ingredientsof the LIED | 477 | ||
| 13.4.2 Quantitative Rescattering Theory | 479 | ||
| 13.4.2.1 Atomic Targets | 479 | ||
| 13.4.2.2 Molecular Targets | 480 | ||
| 13.4.3 Application of the IAM to the LIED | 482 | ||
| 13.4.4 Recent LIED Experiments with Polyatomic Molecules | 485 | ||
| 13.4.5 Retrieval of the 2D Molecular Structure from the LIED Experiment with Aligned Molecules | 486 | ||
| 13.5 Summary and Conclusions | 490 | ||
| References | 492 | ||
| Subject Index | 494 |