Muutke küpsiste eelistusi

E-raamat: Electron Dynamics in Molecular Interactions: Principles and Applications [World Scientific e-raamat]

(East Tennessee State Univ, Usa)
  • Formaat: 968 pages, Illustrations (black and white)
  • Ilmumisaeg: 24-Feb-2014
  • Kirjastus: Imperial College Press
  • ISBN-13: 9781848164888
Teised raamatud teemal:
  • World Scientific e-raamat
  • Hind: 222,68 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
  • Formaat: 968 pages, Illustrations (black and white)
  • Ilmumisaeg: 24-Feb-2014
  • Kirjastus: Imperial College Press
  • ISBN-13: 9781848164888
Teised raamatud teemal:
Hagelberg offers a synopsis of partially complementary and partially competing theories that address the problem of electronically non-adiabatic interactions in molecular dynamics. In particular, he introduces novel computational approaches and contrasts then with more traditional schemes of electron dynamics in molecules. He derives the models from their quantum theory roots, discusses their inter-relations, and outlines their characteristic applications to concrete chemical systems. Covering in turn preparations, methods, and special topics, he considers such topics as the ab initio theory of electronic structure, the time-independent theory of molecular collisions, quantum hydrodynamics, the optical control of electron multistate molecular dynamics, and electronic friction in interactions between molecules and surfaces. Distributed in the US by World Scientific. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

This volume aims at a comprehensive introduction into the theory of nonadiabatic molecular processes — an increasingly relevant and rapidly expanding segment of molecular quantum dynamics. This very active and current field of research deals with molecular interactions involving transitions between electronic states, which occur typically in cases of reactive scattering between molecules, photoexcitation or strong vibronic and rotational coupling between electronic and nuclear degrees of freedom.The main objective of Electron Dynamics in Molecular Interactions is to provide a synoptic presentation of some very recent theoretical efforts and to contrast them with the more traditional models of nonadiabatic molecular processes. In these presented models derived from their quantum dynamical fundaments, their interrelations are discussed, and their characteristic applications to concrete chemical systems are also outlined. This volume also includes an assessment of the present status of electron dynamics and a report on novel developments to meet the current challenges in the field.There is a need for a systematic comparative treatise as nonadiabatic theories, which are of considerably higher complexity than the more traditional adiabatic approaches, are steadily gaining in importance. This volume addresses a broad readership ranging from physics or chemistry graduate students to specialists in the field of theoretical quantum dynamics.
About This Book xix
Introduction: Electron Multistate Molecular Dynamics xxv
Part I Preparations
1(198)
1 Ab Initio Theory of Electronic Structure
3(42)
1.1 Molecular Orbitals
4(8)
1.1.1 Molecular and atomic orbitals
9(2)
1.1.2 Expectation values from molecular orbitals: The example of spin--orbit coupling
11(1)
1.2 The Minimal LCAO Model
12(4)
1.3 Hartree--Fock Theory
16(7)
1.3.1 The Hartree--Fock equations
17(4)
1.3.2 Koopmans' theorem
21(1)
1.3.3 The Hartree--Fock Hamiltonian
22(1)
1.4 The Restricted and the Unrestricted Hartree--Fock Formalism
23(7)
1.4.1 The restricted Hartree--Fock method
24(1)
1.4.2 The unrestricted Hartree--Fock method
25(2)
1.4.3 The Roothaan formalism
27(3)
1.5 Post-Hartree--Fock Methods
30(6)
1.5.1 Configuration interaction
31(3)
1.5.2 Many-body perturbation theory
34(2)
1.6 Excited Electronic States
36(5)
1.7 Appendix: The Functional Derivative
41(4)
2 The Adiabatic and the Diabatic Representation
45(42)
2.1 The Born--Oppenheimer Approximation
46(4)
2.2 Harmonic Vibrational Modes
50(4)
2.3 Adiabatic and Diabatic Frames
54(5)
2.3.1 The diabatic approximation
58(1)
2.4 Gauge Theoretical Form of the Nuclear Equation
59(4)
2.5 Avoided Crossings, Degeneracies, Conical Intersections
63(15)
2.5.1 Avoided crossings
63(2)
2.5.2 Conical intersections and the Jahn--Teller effect
65(3)
2.5.3 Jahn---Teller distortion
68(3)
2.5.4 The molecular Aharonov--Bohm effect
71(4)
2.5.5 The geometric phase in molecular pseudorotation
75(3)
2.6 Locating the Seam
78(9)
2.6.1 Intersection-adapted coordinates
79(3)
2.6.2 Determination of the seam space
82(2)
2.6.3 Seam subspaces by Lagrangian minimization
84(3)
3 Basic Concepts of Scattering Theory
87(34)
3.1 The Time-Dependent and the Time-Independent View of Scattering Processes
88(1)
3.2 Quantum Mechanical Equations of Motion
89(5)
3.3 The Scattering Matrix
94(10)
3.3.1 The Møller operators
96(2)
3.3.2 The Lippmann--Schwinger equations
98(2)
3.3.3 Unitarity of the S-matrix
100(4)
3.4 Elastic Scattering by a Spherical Potential
104(9)
3.4.1 The asymptotic scattering solution
104(3)
3.4.2 T-, S-, and K-matrix boundary conditions
107(4)
3.4.3 The elastic cross section
111(2)
3.5 Resonances
113(8)
4 Semiclassical Notions
121(40)
4.1 Path Integrals and the Quantum Propagator
122(14)
4.1.1 The quantum and the semiclassical propagator
123(5)
4.1.2 The Van Vleck propagator
128(5)
4.1.3 The monodromy matrix
133(3)
4.2 The WKB Approximation
136(10)
4.2.1 The WKB wave function
136(8)
4.2.2 The Bohr--Sommerfeld quantization rules for bound WKB states
144(2)
4.3 The Wigner Function: A Quantum Mechanical Phase Space Distribution
146(8)
4.3.1 Defining properties of the Wigner function
146(3)
4.3.2 Time dependence of the Wigner function
149(4)
4.3.3 The Moyal formalism
153(1)
4.4 Coherent States
154(7)
4.4.1 Coherent and particle number states
155(3)
4.4.2 Coherent states as minimal uncertainty solutions
158(1)
4.4.3 The nuclear coherent state
159(2)
5 Open Systems: Elements of Rate Theory
161(38)
5.1 Classical Rate Theory
163(6)
5.2 Quantum Transition State Theory
169(5)
5.2.1 The quantum transition state approximation
171(3)
5.3 The Euclidean Path Integral
174(7)
5.3.1 Classical polymer isomorphism
178(3)
5.4 Centroid Dynamics
181(6)
5.5 The Path Integral Form of the Golden Rule Rate Constant
187(3)
5.6 Beyond the Golden Rule: Reduced Density Matrix Theory
190(9)
5.6.1 A two-state problem
195(4)
Part II Methods
199(462)
6 Time-Independent Theory of Molecular Collisions I: Multichannel Scattering
201(44)
6.1 The Multichannel Problem
201(5)
6.2 The Lippmann---Schwinger Equation for Inelastic Scattering
206(4)
6.3 The Born Approximation
210(3)
6.3.1 The distorted-wave Born approximation (DWBA)
212(1)
6.4 Microreversibility
213(4)
6.5 R-matrix and Log Derivative Propagation
217(6)
6.5.1 The log derivative method
220(3)
6.6 Reactive Scattering I: The Differential Equation Approach
223(6)
6.6.1 Jacobi coordinates
224(3)
6.6.2 Hyperspherical coordinates
227(2)
6.7 Space-Fixed and Body-Fixed Frames of Reference
229(9)
6.7.1 Space-fixed representation
230(2)
6.7.2 Body-fixed representation
232(6)
6.8 Reactive Scattering II: The Integral Equation Approach
238(7)
7 Time-Independent Theory of Molecular Collisions II: The Electronic Problem
245(46)
7.1 Inclusion of the Electronic System
246(9)
7.1.1 The triatomic case
247(4)
7.1.2 The adiabatic case
251(2)
7.1.3 The diabatic case
253(2)
7.2 Case Study: The F + H2 Reaction
255(8)
7.3 Variational Procedures
263(8)
7.3.1 The Kohn variational principle
267(2)
7.3.2 Kohn anomalies
269(2)
7.4 Case Study: Quenching of the Sodium Atom 3p State by Interaction with Hydrogen Molecules
271(11)
7.4.1 Basis sets
277(2)
7.4.2 Algebraic realization of the outgoing wave variational principle
279(1)
7.4.3 Exciplex funnel dynamics
280(2)
7.5 The Landau--Zener--Stuckelberg Model of Nonadiabatic Transitions
282(9)
8 The Time-Dependent Self-Consistent Field Theory
291(50)
8.1 Time-Dependent Variational Principles
292(8)
8.1.1 Time-dependent perturbations
295(4)
8.1.2 Free and forced oscillations
299(1)
8.2 The Time-Dependent Hartree--Fock Theory: Application to Molecules
300(5)
8.3 Wave-Function-Based Ab Initio Molecular Dynamics
305(17)
8.3.1 Direct molecular dynamics in the time-dependent Hartree--Fock framework
305(2)
8.3.2 Classical trajectories within TDHF dynamics
307(5)
8.3.3 The Hellmann--Feynman theorem
312(3)
8.3.4 Ehrenfest dynamics
315(3)
8.3.5 Car--Parrinello dynamics
318(4)
8.4 Time-Dependent Hartree--Fock Dynamics in the Eikonal Approximation
322(11)
8.4.1 The eikonal approximation
324(3)
8.4.2 TDHF approach to the electronic problem within the eikonal approximation
327(2)
8.4.3 The Liouville--von Neumann equation in a traveling orbital basis
329(4)
8.5 Case Study: Light Emission in Slow Proton--Hydrogen Collisions
333(8)
9 Evolution of Coherent Molecular States: Electron Nuclear Dynamics Theory
341(42)
9.1 The Thouless Representation
343(5)
9.2 The END Equations
348(9)
9.2.1 Derivation of the END equations
349(5)
9.2.2 Interpretation of the END equations
354(3)
9.3 Two Special Cases: The Boosted Self-Consistent Field and the Linearized END Equations
357(4)
9.3.1 The boosted electronic system
357(3)
9.3.2 The linear version of the electronic END equations
360(1)
9.4 Inclusion of Nuclear Quantum Effects
361(15)
9.4.1 Trajectory interference
362(4)
9.4.2 Case study: H impact on molecular and atomic targets by END theory
366(6)
9.4.3 Rovibrational analysis of the nuclear system
372(4)
9.5 Nonadiabatic Effects in Bound Systems by END Theory: The Pseudorotation of H+3
376(7)
10 The Classical Electron Analog
383(20)
10.1 Critique of the Ehrenfest Representation
384(2)
10.2 The Classical Electron Analog
386(9)
10.2.1 The CEA equations of motion
388(1)
10.2.2 Adiabatic representation of the Hamilton function
389(2)
10.2.3 The classical analog of the electronic two-state problem
391(4)
10.3 CEA Theory Applied to a Conical Intersection Problem
395(8)
11 Hopping and Spawning
403(34)
11.1 The Trajectory Surface Hopping Method
404(4)
11.2 The Fewest Switches Algorithm
408(11)
11.2.1 Three test cases
413(5)
11.2.2 Complex-valued trajectories
418(1)
11.3 Spawning
419(10)
11.3.1 Applications to model problems
425(4)
11.4 Case Study: The Dynamics of Na*-Quenching by Collision with Hydrogen Molecules
429(4)
11.5 Comparison with Other Methods
433(4)
12 Semiclassical Propagator Techniques
437(54)
12.1 The Path Integral Approach to Molecular Dynamics
438(4)
12.2 Semiclassical Propagation and Surface Hopping
442(5)
12.3 The Initial Value Representation
447(4)
12.4 The Mapping Approach to Electronic Degrees of Freedom
451(6)
12.4.1 The Schwinger mapping formalism
452(2)
12.4.2 Extension to general N-level systems
454(3)
12.5 The Mapping Technique Applied to Nonadiabatic Dynamics
457(9)
12.5.1 The SC-IVR approach applied to nonadiabatic model cases
460(4)
12.5.2 Comparison with the Ehrenfest model
464(2)
12.6 Case Study: The S1--S2 Transition in Pyrazine: SC-IVR Treatment of a Conical Intersection Problem
466(5)
12.7 Numerical Procedures for Semiclassical Propagation Methods
471(11)
12.7.1 Monte Carlo integration
473(3)
12.7.2 Filinov filtering
476(3)
12.7.3 The forward-backward initial value representation
479(3)
12.8 Cellular Dynamics
482(9)
13 Quantum Hydrodynamics I: Coupled Trajectories in Bohmian Mechanics
491(26)
13.1 Elements of the Quantum Theory of Motion
492(7)
13.1.1 Quantum trajectories
495(3)
13.1.2 The pilot wave and the guided particle
498(1)
13.2 Lagrangian Quantum Hydrodynamics
499(6)
13.2.1 Assembling the wave function
502(1)
13.2.2 Technical challenges for quantum trajectory propagation
503(2)
13.3 Nonadiabatic Lagrangian Quantum Hydrodynamics
505(7)
13.4 The Classical Limit of the Quantum Theory of Motion
512(5)
14 Quantum Hydrodynamics II: The Semiclassical Liouville--Von Neumann Equation
517(30)
14.1 The Semiclassical Liouville Formalism for Multistate Problems
518(10)
14.1.1 Two coupled states: A model problem
524(4)
14.2 Phase Space Trajectory Implementation
528(6)
14.3 Generalized Quantum Hydrodynamics: Mixed States
534(8)
14.3.1 Pure states
538(2)
14.3.2 Mixed states
540(2)
14.4 Coupled Electronic States
542(5)
15 Wave Packet Propagation Methods
547(40)
15.1 The Grid Representation
548(9)
15.1.1 The discrete variable representation (DVR)
553(2)
15.1.2 The fast Fourier transform (FFT)
555(2)
15.2 Numerical Wave Packet Propagation Techniques
557(7)
15.2.1 The Crank--Nicolson scheme
557(2)
15.2.2 Split operator propagation
559(1)
15.2.3 Propagator expansion techniques
560(4)
15.3 The Multiconfiguration Time-Dependent Hartree (MCTDH) Method
564(10)
15.3.1 The time-dependent Hartree (TDH) approach
565(2)
15.3.2 The multiconfiguration time-dependent Hartree (MCTDH) approach
567(2)
15.3.3 The MCTDH equations
569(5)
15.4 Case Study: Photostability of Biologically Relevant Molecules
574(13)
15.4.1 Ultrafast deexcitation by passage through conical intersections in nucleic acid bases and base pairs
575(4)
15.4.2 Dynamics at the 1πσ*-S0 conical intersection of pyrrole
579(8)
16 Density Functional Dynamics
587(26)
16.1 Fundamentals of Density Functional Theory
588(7)
16.1.1 Exchange-correlation potentials
593(2)
16.2 Excited Electronic States in DFT
595(3)
16.3 Time-Dependent Density Functional Theory
598(7)
16.3.1 TDDFT in the linear response domain
601(2)
16.3.2 Time-dependent current density functional theory
603(2)
16.4 Direct Molecular Dynamics Based on DFT
605(8)
16.4.1 Calculating molecular photoabsorption spectra
606(2)
16.4.2 Molecular bonding properties analyzed by the electron localization function
608(1)
16.4.3 Combining TDDFT with standard methods of nonadiabatic dynamics
609(4)
17 Decoherence
613(48)
17.1 The Dissipative Liouville--von Neumann Equation
615(11)
17.2 Evaluating Decoherence Times in a Semiclassical Framework
626(10)
17.2.1 Ensemble average of the decoherence function
632(4)
17.3 Case Study: The Dynamics of Electron Hydration
636(8)
17.3.1 Isotope effects in hydrated electron relaxation
638(6)
17.4 Continuous Surface Switching: A Compromise between Mean-Field and Individual Surface Propagation
644(4)
17.5 Decay of Mixing
648(13)
17.5.1 Decoherence time
657(1)
17.5.2 Determining the decoherent state
658(3)
Part III Special Topics
661(180)
18 Ultrafast Optical Spectroscopy
663(52)
18.1 Linear and Nonlinear Polarization
664(5)
18.1.1 Deriving the pump--probe signal
666(3)
18.2 Theory of Nonlinear Polarization in Femtosecond Molecular Spectroscopy
669(13)
18.2.1 The perturbative approach
672(9)
18.2.2 The non-perturbative approach
681(1)
18.3 Polarization Studies of cis-trans Isomerization
682(8)
18.3.1 Adiabatic formulation
688(2)
18.4 The Density Matrix Approach to Simulating Pump---Probe Signals
690(10)
18.4.1 The pump--probe signal
698(2)
18.5 Case Study: Ultrafast Spectroscopy on Non-Stoichiometric Alkali-Halide Clusters
700(11)
18.5.1 Effective single-electron systems of the form NanFn-1
701(5)
18.5.2 Extension to nonadiabatic dynamics
706(5)
18.6 Appendix: Derivation of the Pump--Probe Signal S(td)
711(4)
19 Optical Control of Electron Multistate Molecular Dynamics
715(34)
19.1 Interaction of a Molecule with a Pulse of Light
716(3)
19.2 The Tannor--Rice Scheme: Optimal Control
719(6)
19.3 The Brumer--Shapiro Scheme: Coherent Control
725(5)
19.4 Case Study: Coherent Control of ICN Photodissociation
730(6)
19.5 Optimal Control in Pump--Probe Spectroscopy
736(13)
19.5.1 Case study: Application to Na3F2
743(6)
20 Electron Transfer in Condensed Media
749(68)
20.1 The Electronic Hamiltonian
753(3)
20.2 Electronic--Vibronic Coupling: The Spin-Boson Hamiltonian
756(4)
20.3 Adiabatic versus Nonadiabatic Electron Transfer
760(3)
20.4 Thermally Activated Transfer
763(4)
20.5 Inclusion of Nuclear Tunneling
767(7)
20.5.1 The continuous limit of nuclear frequencies
771(3)
20.6 Effects of Polar Solvents on Electron Transfer
774(16)
20.6.1 The dielectric displacement field
776(2)
20.6.2 Polarization and polarizability
778(5)
20.6.3 The free energy functional
783(3)
20.6.4 The electron transfer rate in a polar environment
786(4)
20.7 Ultrafast Electron Transfer
790(3)
20.8 Case Study: Aqueous Ferrous--Ferric Exchange
793(12)
20.8.1 Monte Carlo modeling
793(5)
20.8.2 Euclidean path integral simulations
798(6)
20.8.3 Recent quantum dynamical extensions
804(1)
20.9 Appendix: Formulae Relevant for Electron Transfer Theory within the Marcus Model
805(12)
20.9.1 Electron transfer in a vibrational bath: Formal procedures used in the derivation of the rate constant
806(4)
20.9.2 Derivation of the effective free energy functional Eq. (20.109)
810(3)
20.9.3 The density of states for electron transfer in a solvent: Calculating the trace Eq. (20.118)
813(4)
21 Electronic Friction in Molecule--Surface Interactions
817(24)
21.1 Langevin Formulation of Ehrenfest Dynamics
820(4)
21.2 An Ab Initio Model for Electronic Friction
824(4)
21.3 Case Study: Nonadiabatic Effects in the Interaction between the Cu(100) Surface and a CO Molecule
828(10)
21.3.1 Vibrational relaxation of CO on the Cu(100) surface: The impact of electronic friction
828(7)
21.3.2 Vibrational excitation and hot diffusion
835(3)
21.4 Beyond Langevin Theory
838(3)
Epilogue 841(6)
Bibliography 847(28)
Index 875