Multidimensional Quantum Dynamics: MCTDH Theory and Applications

✍ Scribed by Hans-Dieter Meyer, Fabien Gatti, Graham A. Worth

• Publisher: Wiley-VCH
• Year: 2009
• Tongue: English
• Leaves: 446
• Category: Library

✦ Synopsis

The first book dedicated to this new and powerful computational method begins with a comprehensive description of MCTDH and its theoretical background. There then follows a discussion of recent extensions of MCTDH, such as the treatment of identical particles, leading to the MCTDHF and MCTDHB methods for fermions and bosons. The third section presents a wide spectrum of very different applications to reflect the large diversity of problems that can be tackled by MCTDH. The result is handbook and ready reference for theoretical chemists, physicists, chemists, graduate students, lecturers and software producers.

✦ Table of Contents

Multidimensional Quantum Dynamics......Page 4
Contents......Page 8
Preface......Page 18
List of Contributors......Page 20
List of Symbols......Page 24
1 Introduction......Page 28
Part 1 Theory......Page 36
2 The Road to MCTDH......Page 38
2.1 The Standard Method......Page 39
2.2 Time-Dependent Hartree......Page 40
3.1 Wavefunction Ansatz and Equations of Motion......Page 44
3.2 The Constraint Operator......Page 47
3.3 Efficiency and Memory Requirements......Page 49
3.4 Multistate Calculations......Page 54
3.5 Parametrized Basis Functions: G-MCTDH......Page 55
4.1 The Variable Mean-Field (VMF) Integration Scheme......Page 58
4.2 A Simple Constant Mean-Field (CMF) Integration Scheme......Page 59
4.3 Why CMF Works......Page 60
4.4 Second-Order CMF Scheme......Page 61
5.1 Initial Wavepacket as Hartree Product......Page 64
5.2 Eigenstates and Operated Wavefunctions......Page 65
6.1 Runtime Analysis of Accuracy......Page 68
6.2.1 Photoabsorption Spectra......Page 70
6.2.2 Eigenvalues and Filter Diagonalization......Page 73
6.2.3 Time-Resolved Spectra......Page 75
6.4 State Populations......Page 77
6.5 Reaction Probabilities......Page 79
7.1 Wavefunctions and Density Operators......Page 84
7.2 Type I Density Operators......Page 85
7.3 Type II Density Operators......Page 87
7.4 Properties of MCTDH Density Operator Propagation......Page 88
8.2 Improved Relaxation......Page 90
8.3 Technical Details......Page 93
9.1 Operators Defined by Propagation......Page 96
9.2 A Modified Lanczos Scheme......Page 97
9.3 The State-Averaged MCTDH Approach......Page 98
10.1 Introduction......Page 100
10.2 Time-Dependent Discrete Variable Representation......Page 101
10.3 Correlation Discrete Variable Representation......Page 103
10.5 Multidimensional Correlation Discrete Variable Representation......Page 105
11.1 Expansion in Product Basis Sets......Page 108
11.2 Optimizing the Coefficients......Page 109
11.3 Optimizing the Basis......Page 110
11.4 The potfit Algorithm......Page 111
11.6 Separable Weights......Page 113
11.7 Non-Separable Weights......Page 114
11.8 Computational Effort and Memory Request......Page 115
12.1 Introduction......Page 118
12.2 Vector Parametrization and Properties of Angular Momenta......Page 119
12.2.1 Examples......Page 120
12.2.2.1 Defining a Set of N – 1 Vectors and the Corresponding Classical Kinetic Energy......Page 122
12.2.2.2 Introduction of the Body-Fixed Frame and Quantization......Page 123
12.2.2.3 Introduction of the Body-Fixed Projections of the Angular Momenta Associated With the N – 1 Vectors......Page 124
12.3.1.1 Definition of the BF frame: Figure 12.3......Page 126
12.3.1.2 Polyspherical Parametrization......Page 127
12.3.1.3 Properties of the BF Projections of the Angular Momenta......Page 128
12.3.1.4 General Expression of the KEO in Polyspherical Coordinates......Page 131
12.3.1.5 Introduction of a Primitive Basis Set of Spherical Harmonics......Page 132
12.4 Examples......Page 133
12.4.1 Scattering Systems: H(2) + H(2)......Page 134
12.4.2 Semi-Rigid Molecules: HFCO......Page 135
12.5.1 Separation Into Subsystems......Page 136
12.5.2 Constrained Operators......Page 137
Part 2 Extension to New Areas......Page 138
13.1 Introduction......Page 140
13.2.1 Gaussian Wavepacket Ansatz......Page 142
13.2.2 Equations of Motion......Page 144
13.2.3 Integration Scheme......Page 147
13.2.4 Initial Wavepacket......Page 148
13.2.5 Direct Dynamics Implementation......Page 149
13.3 Applications......Page 151
13.4 Conclusions......Page 155
14.1 Introduction......Page 158
14.2.1 Conventional Approach Based on Time-Independent Configurations......Page 159
14.2.2 The Multiconfiguration Time-Dependent Hartree Method......Page 161
14.2.3 The Multilayer Formulation of the MCTDH Theory......Page 165
14.3 Concluding Remarks......Page 172
15.2 Shared Memory Parallelization of MCTDH......Page 176
15.2.1 Equations of Motion and Runtime Distribution......Page 177
15.2.2 Parallelization of the MCTDH Coefficients Propagation......Page 178
15.2.3 Parallelization of the Mean-Field Computation......Page 179
15.2.5 Parallelization Scheme......Page 180
15.2.6 Load Balancing and Memory Requirements......Page 181
15.3.1 Benchmark Systems......Page 183
15.3.3 Results......Page 184
15.3.4 Conclusion and Outlook......Page 186
16.1 Equations of Motion for Indistinguishable Particles......Page 188
16.1.1 Model System: Laser-Driven Few-Electron Systems......Page 189
16.1.2 Spin......Page 190
16.2.1 K and Mean-Field Operators......Page 191
16.2.2 Spatial Discretization......Page 192
16.2.3 One-Particle Operators......Page 195
16.2.4.1 Representation of H on a Coarse Grid......Page 196
16.2.4.2 H-Matrix Representation......Page 197
16.3 Parallelization......Page 198
16.3.1 Application of the Inverse Overlap Matrix S(–1)......Page 199
16.3.2 Parallel Computation of Mean Fields......Page 200
16.4.1 Orbital Transformations......Page 201
16.4.3 One- and Two-Particle Expectation Values......Page 202
16.4.4 All-Particle Observables......Page 203
16.4.5 Spectra......Page 204
16.5.1 Ionization of Linear Molecules......Page 205
16.5.1.1 High-Harmonic Spectra of Molecules......Page 206
16.5.2 Cold Fermionic Atoms......Page 209
17.1 Preliminary Remarks......Page 212
17.2.1 Basic Ingredients......Page 213
17.2.2 Equations of Motion with Reduced Density Matrices......Page 216
17.3.1 Ingredients for Mixtures......Page 219
17.3.2 Equations of Motion With Intra- and Inter-Species Reduced Density Matrices......Page 221
17.4 Higher-Order Forces and Reduced Density Matrices......Page 223
17.4.1 Ingredients for Three-Body Interactions......Page 224
17.4.2 Equations of Motion With Three-Body Reduced Density Matrix......Page 225
17.5 Illustrative Numerical Examples for Bosons: MCTDHB......Page 226
17.6 Discussion and Perspectives......Page 231
Part 3 Applications......Page 236
18.1 Introduction......Page 238
18.2 The Vibronic Coupling Hamiltonian......Page 239
18.3 Combining the Vibronic Coupling Model with MCTDH......Page 242
18.4.1 Allene Cation......Page 246
18.4.2 Cr(CO)(5)......Page 248
18.4.3 Benzene Cation......Page 251
18.5 Effective Modes......Page 254
18.6 Summary......Page 256
19.1 Introduction......Page 258
19.2.1 Thermal Rates From Flux Correlation Functions......Page 260
19.2.2 Thermal Flux Operator: Properties and Physical Interpretation......Page 262
19.2.3 Calculation of N(E) and k(T)......Page 264
19.3.2 Statistical Sampling......Page 266
19.4 Application to Polyatomic Reactions......Page 268
19.5 The Effect of Rotation–Vibration Coupling on Rate Constants......Page 272
19.6 Concluding Remarks and Outlook......Page 273
20.1 Introduction......Page 276
20.2 Theory......Page 278
20.3.1 Rotationally and Diffractionally Inelastic Scattering......Page 281
20.3.2.1 Dissociative Chemisorption of H(2) on Metal Surfaces......Page 282
20.3.2.2 Dissociative Chemisorption of N(2) on Metal Surfaces......Page 289
20.3.2.3 Dissociative Chemisorption of CH(4) on Ni(111)......Page 290
20.3.3 Photodissociation of Molecules on Insulator Surfaces......Page 291
20.3.4 Molecule–Surface Dynamics With Dissipation......Page 293
20.4 Summary and Outlook......Page 296
21.1 Introduction......Page 302
21.2 Local-Mode Excitation of CH Stretch in Fluoroform and Toluene......Page 304
21.3 Study of Highly Excited States in HFCO and DFCO......Page 306
21.4 Selective Population of Vibrational Levels in H(2)CS in External Field......Page 312
21.5 Cis–Trans Isomerization of HONO......Page 314
21.6 Conclusion......Page 317
22.1 Introduction......Page 320
22.2 The System–Bath Ansatz......Page 322
22.3.1 Static Effect: Lamb Shift......Page 324
22.3.2 Small-Amplitude Motion......Page 325
22.3.3 Inelastic Surface Scattering: Adsorption......Page 327
22.4.1 Random-Phase Wavefunctions......Page 329
22.4.2 Inelastic Surface Scattering: Adsorption......Page 330
22.4.3 Initial Slip and Coupling to Photons......Page 333
22.5 Derivatives of MCTDH......Page 334
22.6 Summary and Outlook......Page 335
23.1 Introduction......Page 338
23.2.1 Model for the Simulation of a Proton Wire......Page 340
23.2.2 Dynamics of a Proton Wire......Page 341
23.3 Dynamics and Vibrational Spectroscopy of the Zundel Cation......Page 343
23.3.1 Set-Up of the Hamiltonian Operator......Page 345
23.3.2 Representation of the Potential Energy Surface for H(5)O(2)(+)......Page 348
23.3.3 Ground Vibrational State and Eigenstates in the Low-Frequency Domain......Page 351
23.3.4 Infrared Absorption Spectrum......Page 354
23.3.5 Analysis of the Middle Spectral Region and Dynamics of the Cluster......Page 357
23.4 Conclusion......Page 359
24.1 Introduction......Page 362
24.2 Theory......Page 363
24.3.1 Vibrational Ladder Climbing in a Haem–CO Model......Page 366
24.3.2 Hydrogen-Bond Dynamics......Page 371
24.3.3 Predissociation Dynamics of Matrix-Isolated Diatomics......Page 374
24.4 Summary......Page 379
25.1 Introduction......Page 382
25.2 Dissociative Electron Attachment to Water......Page 384
25.3 Time-Dependent Treatment of DEA Within the LCP Model......Page 386
25.4 Coordinate Systems......Page 388
25.5 Hamiltonians......Page 389
25.6 Choice of Primitive Basis and Representation of Hamiltonians......Page 390
25.8 Single-Particle Function Expansion and Mode Combinations......Page 391
25.10.1 Two-Body Breakup......Page 394
25.10.2 Three-Body Breakup......Page 398
25.11 Conclusion......Page 400
26.1 Introduction......Page 402
26.2 Model......Page 403
26.2.2 Modelling the Interaction......Page 404
26.3.1 Density Profiles......Page 405
26.3.3 Fermionized Bosons Versus Fermions: Momentum Distribution......Page 407
26.4 Quantum Dynamics: Correlated Tunnelling in Double Wells......Page 409
26.4.1 From Uncorrelated to Pair Tunnelling......Page 410
26.4.2 Spectral Analysis......Page 412
26.4.3 Role of Correlations......Page 413
References......Page 416
Index......Page 434