The quantum classical theory /

This book describes mixed classical and quantum theories of dynamical processes with a particular emphasis on molecular collisions. Purely quantum or purely classical approaches are inadequate for many systems. The quantum classical theory is important to conduct practical calculations involving rea...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Billing, Gert D.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Oxford ; New York : Oxford University Press, 2003.
Temas:
Quantum chemistry.
Molecular dynamics.
Chimie quantique.
Dynamique moléculaire.
SCIENCE > Chemistry > Physical & Theoretical.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Abbreviations
  • 1 Introduction
  • 2 Rigorous theories
  • 2.1 Path-integral approach
  • 2.1.1 The short time propagator
  • 2.1.2 The classical limit
  • 2.1.3 The Van Vleck propagator
  • 2.2 Gaussians at work
  • 2.2.1 Cellular dynamics
  • 2.2.2 A semi-classical IVR propagator
  • 2.3 An orthorgonal basis set
  • 2.4 Bohmian mechanics
  • 2.5 Mixing of Gauss-Hermite and ordinary basis sets
  • 2.5.1 The classical path approximation
  • 2.5.2 The exact equations of motion in the TDGH basis
  • 2.6 Bound states and Gauss-Hermite functions.
  • 2.6.1 The Morse-oscillator in a Gauss-Hermite basis
  • 2.6.2 Treatment of 2D systems in the G-H basis
  • 2.6.3 The quantum-classical correlation
  • 2.6.4 Spherical harmonics in a Gauss-Hermite basis set
  • 2.7 Second quantization and Gauss-Hermite functions
  • 2.8 Quantum dressed classical mechanics
  • 2.8.1 The DVR scheme
  • 2.8.2 Arbitrarily sized systems
  • 2.9 The MCTDH approach
  • 2.10 Summary
  • 3 Approximate theories
  • 3.1 Time-dependent SCF
  • 3.2 The classical path theory
  • 3.2.1 Relation to other theories
  • 3.2.2 Energy transfer
  • 3.2.3 The V[sub(q)]R[sub(q)]T[sub(c)] method.
  • 3.2.4 The V[sub(q)]R[sub(c)]T[sub(c)] method
  • 3.2.5 The V[sub(q)]R[sub(c)]T[sub(c)] method for diatom-diatom collisions
  • 3.2.6 Reactive scattering
  • 3.2.7 Summary
  • 3.3 Non-adiabatic transitions
  • 3.3.1 Pechukas theory
  • 3.3.2 Tully's approach
  • 3.3.3 Spawning method
  • 3.3.4 The multi-trajectory and TDGH-DVR methods
  • 4 Second quantization
  • 4.1 Diatom-diatom collisions
  • 4.2 General hamiltonians
  • 5 More complex systems
  • 5.1 Potential energy surfaces
  • 5.1.1 The Born-Oppenheimer separation
  • 5.1.2 Approximate interaction potentials
  • 5.2 Polyatomic molecules.
  • 5.2.1 Second quantization solution for U
  • 5.2.2 The classical degrees of freedom
  • 5.2.3 Rate-constants
  • 5.2.4 Some case studies
  • 5.3 Chemical processes at surfaces
  • 5.4 Reaction path methods
  • 5.4.1 Surface characteristics
  • 5.4.2 The reaction path method
  • 5.4.3 Reaction path constraints
  • 5.4.4 Absolute rate-constants
  • 5.4.5 Second quantization approach
  • 5.4.6 Initialization of the reaction path dynamics
  • 5.4.7 Cross sections and rate-constants
  • 5.5 The reaction volume approach
  • 5.5.1 A simplified hamiltonian
  • 5.6 Summary.
  • 5.7 Chemical processes in clusters and solution
  • 5.7.1 Centroid molecular dynamics
  • 6 Conclusion
  • Appendices
  • Bibliography
  • Index
  • A
  • B
  • C
  • D
  • E
  • F
  • G
  • H
  • I
  • K
  • L
  • M
  • N
  • P
  • Q
  • R
  • S
  • T
  • V
  • W.

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