Multidimensional quantum dynamics : MCTDH theory and applications
 Language
 English.
 Imprint
 Weinheim [Germany] : WileyVCH, c2009.
 Physical description
 xxiii, 419 p. : ill. ; 25 cm.
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QC174.12 .M847 2009

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QC174.12 .M847 2009
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Contributors
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 389406) and index.
 Contents

 Preface. List of Contributors. List of Symbols. Introduction (HansDieter Meyer, Fabien Gatti and Graham A. Worth). Part 1 Theory. 2 The Road to MCTDH (HansDieter Meyer, Fabien Gatti and Graham A. Worth). 2.1 The Standard Method. 2.2 TimeDependent Hartree. 3 Basic MCTDH Theory (HansDieter Meyer, Fabien Gatti and Graham A. Worth). 3.1 Wavefunction Ansatz and Equations of Motion. 3.2 The Constraint Operator. 3.3 Efficiency and Memory Requirements. 3.4 Multistate Calculations. 3.5 Parametrized Basis Functions:GMCTDH. 4 Integration Schemes (HansDieter Meyer, Fabien Gatti and Graham A. Worth). 4.1 The Variable MeanField (VMF) Integration Scheme. 4.2 A Simple Constant MeanField (CMF) Integration Scheme. 4.3 Why CMF Works. 4.4 SecondOrder CMF Scheme. 5 Preparation of the Initial Wavepacket (HansDieter Meyer, Fabien Gatti and Graham A. Worth). 5.1 Initial Wavepacket as Hartree Product. 5.2 Eigenstates and Operated Wavefunctions. 6 Analysis of the Propagated Wavepacket (HansDieter Meyer, Fabien Gatti and Graham A. Worth). 6.1 Runtime Analysis of Accuracy. 6.2 Spectra. 6.3 Optimal Control. 6.4 State Populations. 6.5 Reaction Probabilities. 7 MCTDH for Density Operators (HansDieter Meyer, Fabien Gatti and Graham A. Worth). 7.1 Wavefunctions and Density Operators. 7.2 Type I Density Operators. 7.3 Type II Density Operators. 7.4 Properties of MCTDH Density Operator Propagation. 8 Computing Eigenstates by Relaxation and Improved Relaxation (HansDieter Meyer, Fabien Gatti and Graham A. Worth). 8.1 Relaxation. 8.2 Improved Relaxation. 8.3 Technical Details. 9 Iterative Diagonalzation of Operators (Fermin HuarteLarranaga and Uwe Manthe). 9.1 Operators Defined by Propagation. 9.2 A Modified Lanczos Scheme. 9.3 The StateAveraged MCTDH Approach. 10 Correlation Discrete Variable Represenation (Fermin HuarteLarranaga and Uwe Manthe). 10.1 Introduction. 10.2 TimeDependent Discrete Variable Representation. 10.3 Correlation Discrete Variable Representation. 10.4 SymmetryAdapted Correlation Discrete Variable Representation. 10.5 Multidimensional Correlation Discrete Variable Representation. 11 Potential Representations (potfit) (HansDieter Meyer, Fabien Gatti and Graham A. Worth). 11.1 Expansion in Product Basis Sets. 11.2 Optimizing the Coefficients. 11.3 Optimizing the Basis. 11.4 The potfit Algorithm. 11.5 Contraction Over One Particle. 11.6 Separable Weights. 11.7 NonSeparable Weights. 11.8 Computational Effort and Memory Request. 12 Kinetic Energy Operators (HansDieter Meyer, Fabien Gatti and Graham A. Worth). 12.1 Introduction. 12.2 Vector Parametrization and Properties of Angular Momenta. 12.3 General Expression of KEO in Standard Polyspherical Coordinates. 12.4 Example. 12.5 Extensions. Part 2 Extension to New Areas. 13 Direct Dynamics With Quantum Nuclei (Benjamin Lasorne and Graham A. Worth). 13.1 Introduction. 13.2 Variational Multiconfiguration Gaussian Wavepackets. 13.3 Applications. 13.4 Conclusions. 14 Multilayer Formulation of the Multiconfiguration TimeDependent Hartree Theory (Haobin Wang and Michael Thoss). 14.1 Introduction. 14.2 From Conventional Wavepacket Propagation to MLMCTDH Theory: A Variational Perspective. 14.3 Concluding Remarks. 15 Shared Memory Parallelization of the Multiconfiguration TimeDependent Hartree Method (Michael Brill and HansDieter Meyer). 15.1 Motivation. 15.2 Shared Memory Parallelization of MCTDH. 15.3 Results and Conclusion. 16 Strongly Driven FewFermion Systems  MCTDHF (Gerald Jordan and Armin Scrinzi). 16.1 Equations of Motion for Indistinguishable Particles. 16.2 Computation of Operators. 16.3 Parallelization. 16.4 Observables and Transformations. 16.5 Applications. 17 The Multiconfigurational TimeDependent Hartree Method for Identical Particles and Mixtures Thereof (Ofir E. Alon, Alexej I. Streltsovo and Lorenz S. Cederbaum). 17.1 Preliminary Remarks. 17.2 Bosons or Fermions?  Unifying MCTDHB and MCTDHF. 17.3 BoseBose, FermiFermi and BoseFermi Mixtures. 17.4 MigherOrder Forces and Reduced Density Matrices. 17.5 Illustrative Numerical Examples for Bosons: MCTDHB. 17.6 Discussion and Perspectives. Part 3 Applications. 18 Multidimensional NonAdiabatic Dynamics (Graham A. Worth, Horst Koppel, Etienne Gindensperger and Lorenz S. Cederbaum). 18.1 Introduction. 18.2 The Vibronic Coupling Hamiltonian. 18.3 Combining the Vibronic Coupling Model with MCTDH. 18.4 Examples. 18.5 Effective Modes. 18.6 Summary. 19 MCTDH Calculation of Flux Correlation Functions: Rates and Reaction Probabilities for Polyatomic Chemical Reactions (Fermin HuarteLarranaga and Uwe Manthe). 19.1 Introduction. 19.2 Flux Correlation Functions and Quantum TransitionState Concept. 19.3 Rate Constant Calculations. 19.4 Application to Polyatomic Reactions. 19.5 The Effect of RotationVibration Coupling on Rater Constants. 19.6 Concluding Remarks and Outlook. 20 Reactive and NonReactive Scattering of Molecules From Surfaces (GeertJan Kroes, Rob van Harrevelt and Cedric Crespos). 20.1 Introduction. 20.2 Theory. 20.3 Applications of MCTDH Method to MoleculeSurface Scattering. 20.4 Summary and Outlook. 21 Intramolecular Vibrational Energy Redistribution and Infrared Spectroscopy (Fabien Gatti and Christophe Iung). 21.1 Introduction. 21.2 LocalMode Excitation of CH Stretch in Fluoroform and Toluene. 21.3 Study of Highly Excited States in HFCO and DFCO. 21.4 Selective Population of Vibrational Levels in H2CS in External Field. 21.5 CisTrans Isomerization of HONO. 21.6 Conclusion. 22 Open System Quantum Dynamics with Discretized Environments (Mathias Nest). 22.1 Introduction. 22.2 The SystemBase Ansatz. 22.3 Static and Dynamic Effects of the Bath. 22.4 Finite Temperatures. 22.5 Derivatives of MCTDH. 22.6 Summary and Outlook. 23 Proton Transfer and Hydrated Proton in Small Water Systems (Oriol Vendrell and HansDieter Meyer). 23.1 Introduction. 23.2 Photon Transfer Along Chain of HBonded Water Molecules. 23.3 Dynamics and Vibrational Spectroscopy of the Zundel Cation. 23.4 Conclusion. 24 LaserDriven Dynamics and Quantum Control of Molecular Wavepackets (Oliver Kuhn). 24.1 Introduction. 24.2 Theory. 24.3 Applications. 24.4 Summary. 25 Polyatomic Dynamics of Dissociative Electron Attachment to Water Using MCTDH (Daniel J. Haxton, Thomas N. Rescigno and C. William McCurdy). 25.1 Introduction. 25.2 Dissociative Electron Attachment to Water. 25.3 TimeDependent Treatment of DEA Within the LCP Model. 25.4 Coordinate Systems. 25.5 Hamiltonians. 25.6 Choice of Primitive Basis and Representation of Hamiltonians. 25.7 Representation of Potential Energy Functions Using potfit. 25.8 SingleParticle Function Expansion and Mode Combinations. 25.9 Propagation and Natural Orbitals. 25.10 Analysis of Flux to Calculate CrossSections. 25.11 Conclusion. 26 Ultracold FewBoson Systems in Traps (Sascha Zollner, HansDieter Meyer and Peter Schmelcher). 26.1 Introduction. 26.2 Model. 26.3 Ground State: Crossover From Weak to Strong Interactions. 26.4 Quantum Dynamics: Correlated Tunnelling in Double Wells. References. Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 This is the first book dedicated to this new and powerful computational method that 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.
(source: Nielsen Book Data)
Subjects
 Subject
 MCTDH.
 Quantum theory.
Bibliographic information
 Publication date
 2009
 Responsibility
 edited by HansDieter Meyer, Fabien Gatti, and Graham A. Worth.
 ISBN
 9783527320189
 3527320180