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E-grāmata: Quantum Chemistry and Dynamics of Excited States: Methods and Applications

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Quantum Chemistry and Dynamics of Excited States: Methods and ApplicationsPalielināt
  • Formāts: EPUB+DRM
  • Izdošanas datums: 26-Nov-2020
  • Izdevniecība: John Wiley & Sons Inc
  • Valoda: eng
  • ISBN-13: 9781119417743
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An introduction to the rapidly evolving methodology of electronic excited states

For academic researchers, postdocs, graduate and undergraduate students, Quantum Chemistry and Dynamics of Excited States: Methods and Applications reports the most updated and accurate theoretical techniques to treat electronic excited states. From methods to deal with stationary calculations through time-dependent simulations of molecular systems, this book serves as a guide for beginners in the field and knowledge seekers alike. Taking into account the most recent theory developments and representative applications, it also covers the often-overlooked gap between theoretical and computational chemistry.

An excellent reference for both researchers and students, Excited States provides essential knowledge on quantum chemistry, an in-depth overview of the latest developments, and theoretical techniques around the properties and nonadiabatic dynamics of chemical systems.

Readers will learn:

&;      Essential theoretical techniques to describe the properties and dynamics of chemical systems

&;      Electronic Structure methods for stationary calculations

&;      Methods for electronic excited states from both a quantum chemical and time-dependent point of view

&;      A breakdown of the most recent developments in the past 30 years

For those searching for a better understanding of excited states as they relate to chemistry, biochemistry, industrial chemistry, and beyond, Quantum Chemistry and Dynamics of Excited States provides a solid education in the necessary foundations and important theories of excited states in photochemistry and ultrafast phenomena.

List of Contributors
xix
Preface xxiii
1 Motivation and Basic Concepts
1(12)
Sandra Gomez
Ignacio Fdez Galvan
Roland Lindh
Leticia Gonzalez
1.1 Mission and Motivation
1(3)
1.2 Atomic Units
4(1)
1.3 The Molecular Hamiltonian
5(1)
1.4 Dirac or Bra-Ket Notation
6(1)
1.5 Index Definitions
7(1)
1.6 Second Quantization Formalism
7(2)
1.7 Born-Oppenheimer Approximation and Potential Energy Surfaces
9(1)
1.8 Adiabatic Versus Diabatic Representations
10(1)
1.9 Conical Intersections
11(1)
1.10 Further Reading
12(1)
1.11 Acknowledgments
12(1)
Part I Quantum Chemistry
13(342)
2 Time-Dependent Density Functional Theory
15(17)
Miquel Huix-Rotllant
Nicolas Ferre
Mario Barbatti
2.1 Introduction
15(1)
2.2 TDDFT Fundamentals
16(6)
2.2.1 The Runge-Gross Theorems
16(2)
2.2.2 The Time-Dependent Kohn-Sham Approach
18(1)
2.2.3 Solutions of Time-Dependent Kohn-Sham Equations
19(1)
2.2.3 Real-Time TDDFT
19(1)
2.2.3 Linear-Response TDDFT
20(2)
2.3 Linear-Response TDDFT in Action
22(10)
2.3.1 Vertical Excitations and Energy Surfaces
22(1)
2.3.1 Vertical Excitations: How Good are They?
23(2)
2.3.1 Reconstructed Energy Surfaces: How Good are They?
25(3)
2.3.2 Conical Intersections
28(2)
2.3.3 Coupling Terms and Auxiliary Wave Functions
30(1)
2.3.3 The Casida Ansatz
30(1)
2.3.3 Time-Derivative Non-Adiabatic Couplings
31(1)
23 A Non-Adiabatic Dynamics
32(15)
2.4 Excited States and Dynamics with TDDFT Variants and Beyond
34(1)
2.5 Conclusions
35(12)
Acknowledgments
36(1)
References
36(11)
3 Multi-Configurational Density Functional Theory: Progress and Challenges
47(30)
Erik Donovan Hedegdrd
3.1 Introduction
47(3)
3.2 Wave Function Theory
50(1)
3.3 Kohn-Sham Density Functional Theory
50(7)
3.3.1 Density Functional Approximations
53(1)
3.3.2 Density Functional Theory for Excited States
54(1)
3.3.2 Issues Within the Time-Dependent Density Functional Theory Ansatz
55(1)
3.3.2 Self-Interaction Error
55(1)
3.3.2 Degeneracies, Near-Degeneracies and the Symmetry Dilemma
56(1)
3.4 Multi-Configurational Density Functional Theory
57(7)
3.4.1 Semi-Empirical Multi-Configurational Density Functional Theory
57(1)
3.4.2 Multi-Configurational Density Functional Theory Based the On-Top Pair Density
58(1)
3.4.2 Density Matrices and the On-Top Pair Density
59(1)
3.4.2 Energy Functional and Excited States with the On-Top Pair Density
60(1)
3.4.3 Multi-Configurational Density Functional Theory Based on Range-Separation
61(1)
3.4.3 Energy Functional and Excited States in Range-Separated Methods
62(1)
3.4.3 The Range-Separation Parameter in Excited State Calculations
62(2)
3.5 Illustrative Examples
64(2)
3.5.1 Excited States of Organic Molecules
64(1)
3.5.2 Excited States for a Transition Metal Complex
65(1)
3.6 Outlook
66(11)
Acknowledgments
67(1)
References
67(10)
4 Equation-of-Motion Coupled-Cluster Models
77(32)
Monika Musiat
4.1 Introduction
77(2)
4.2 Theoretical Background
79(5)
4.2.1 Coupled-Cluster Wave Function
79(1)
4.2.2 The Equation-of-Motion Approach
80(1)
4.2.3 Similarity-Transformed Hamiltonian
81(1)
4.2.4 Davidson Diagonalization Algorithm
82(2)
4.3 Excited States: EE-EOM-CC
84(5)
4.3.1 EE-EOM-CCSD Model
84(2)
4.3.2 EE-EOM-CCSDT Model
86(1)
4.3.3 EE-EOM-CC Results
87(2)
4.4 Ionized States: IP-EOM-CC
89(2)
4.4.1 IP-EOM-CCSD Model
89(1)
4.4.2 IP-EOM-CCSDT Model
89(1)
4.4.3 IP-EOM-CC Results
90(1)
4.5 Electron-Attached States: EA-EOM-CC
91(3)
4.5.1 EA-EOM-CCSD Model
92(1)
4.5.2 EA-EOM-CCSDT Model
92(1)
4.5.3 EA-EOM-CC Results
92(2)
4.6 Doubly-Ionized States: DIP-EOM-CC
94(3)
4.6.1 DIP-EOM-CCSD Model
95(1)
4.6.2 DIP-EOM-CCSDT Model
95(1)
4.6.3 DIP-EOM-CC Results
96(1)
4.7 Doubly Electron-Attached States: DEA-EOM-CC
97(3)
4.7.1 DEA-EOM-CCSD Model
98(1)
4.7.2 DEA-EOM-CCSDT Model
98(1)
4.7.3 DEA-EOM-CC Results
98(2)
4.8 Size-Extensivity Issue in the EOM-CC Theory
100(2)
4.9 Final Remarks
102(7)
References
103(6)
5 The Algebraic-Diagrammatic Construction Scheme for the Polarization Propagator
109(24)
Andreas Dreuw
5.1 Original Derivation via Green's Functions
110(2)
5.2 The Intermediate State Representation
112(2)
5.3 Calculation of Excited State Properties and Analysis
114(3)
5.3.1 Excited State Properties
114(2)
5.3.2 Excited-State Wave Function and Density Analyses
116(1)
5.4 Properties and Limitations of ADC
117(2)
5.5 Variants of EE-ADC
119(6)
5.5.1 Extended ADC(2)
119(1)
5.5.2 Unrestricted EE-ADC Schemes
120(1)
5.5.3 Spin-Flip EE-ADC Schemes
121(1)
5.5.4 Spin-Opposite-Scaled ADC Schemes
122(1)
5.5.5 Core-Valence Separated (CVS) EE-ADC
123(2)
5.6 Describing Molecular Photochemistry with ADC Methods
125(1)
5.6.1 Potential Energy Surfaces
125(1)
5.6.2 Environment Models within ADC
126(1)
5.7 Brief Summary and Perspective
126(7)
Bibliography
127(6)
6 Foundation of Multi-Configurational Quantum Chemistry
133(72)
Giovanni Li Manni
Kai Guther
Dongxia Ma
Werner Dobrautz
6.1 Scaling Problem in FCI, CAS and RAS Wave Functions
136(2)
6.2 Factorization and Coupling of Slater Determinants
138(3)
6.2.1 Slater Condon Rules
140(1)
6.3 Configuration State Functions
141(17)
6.3.1 The Unitary Group Approach (UGA)
142(1)
6.3.1 Analogy between CSFs and Spherical Harmonics
143(1)
6.3.1 Gel'fand-Tsetlin Basis
143(2)
6.3.1 Paldus and Weyl Tables
145(3)
6.3.1 The Step-Vector
148(1)
6.3.2 The Graphical Unitary Group Approach (GUGA)
148(5)
6.3.3 Evaluation of Non-Vanishing Hamiltonian Matrix Elements
153(1)
6.3.3 One-Body Coupling Coefficients
154(3)
6.3.3 Two-Body Matrix Elements
157(1)
6.4 Configuration Interaction Eigenvalue Problem
158(7)
6.4.1 Iterative Methods
159(1)
6.4.1 Lanczos Algorithm
159(1)
6.4.1 Davidson Algorithm
160(2)
6.4.2 Direct-CI Algorithm
162(3)
6.5 The CASSCF Method
165(17)
6.5.1 The MCSCF Parameterization
167(2)
6.5.2 The MCSCF Gradient and Hessian
169(1)
6.5.3 One-Step and Two-Step Procedures
170(1)
6.5.4 Augmented Hessian Method
171(1)
6.5.5 Matrix form of the First and Second Derivatives in MCSCF
171(4)
6.5.6 Quadratically Converging Method with Optimal Convergence
175(3)
6.5.7 Orbital-CI Coupling Terms
178(1)
6.5.8 Super-CI for the Orbital Optimization
179(2)
6.5.9 Redundancy of Active Orbital Rotations
181(1)
6.6 Restricted and Generalized Active Space Wave Functions
182(7)
6.6.1 GUGA Applied to CAS, RAS and GAS Wave Functions
184(2)
6.6.2 Redundancies in GASSCF Orbital Rotations
186(1)
6.6.3 MCSCF Molecular Orbitals
187(1)
6.6.4 GASSCF Applied to the Gd2 Molecule
188(1)
6.7 Excited States
189(2)
6.7.1 Multi-State CI Solver
190(1)
6.7.2 State-Specific and State-Averaged MCSCF
191(1)
6.8 Stochastic Multiconfigurational Approaches
191(14)
6.8.1 FCIQMC Working Equation
192(4)
6.8.2 Multi-Wave Function Approach for Excited States
196(1)
6.8.3 Sampling Reduced Density Matrices
196(2)
Bibliography
198(7)
7 The Density Matrix Renormalization Group for Strong Correlation in Ground and Excited States
205(42)
Leon Freitag
Markus Reiher
7.1 Introduction
205(2)
7.2 DMRG Theory
207(11)
7.2.1 Renormalization Group Formulation
207(3)
7.2.2 Matrix Product States and Matrix Product Operators
210(4)
7.2.3 MPS-MPO Formulation of DMRG
214(3)
7.2.4 Connection between the Renormalization Group and the MPS-MPO Formulation of DMRG
217(1)
7.2.5 Developments to Enhance DMRG Convergence and Performance
218(1)
7.3 DMRG and Orbital Entanglement
218(2)
7.4 DMRG in Practice
220(5)
7.4.1 Calculating Excited States with DMRG
220(1)
7.4.2 Factors Affecting the DMRG Convergence and Accuracy
220(1)
7.4.3 Post-DMRG Methods for Dynamic Correlation and Environment Effects
221(1)
7.4.4 Analytical Energy Gradients and Non-Adiabatic Coupling Matrix Elements
222(2)
7.4.5 Tensor Network States
224(1)
7.5 Applications in Quantum Chemistry
225(5)
7.6 Conclusions
230(17)
Acknowledgment
231(1)
References
231(16)
8 Excited-State Calculations with Quantum Monte Carlo
247(30)
Jonas Feldt
Claudia Filippi
8.1 Introduction
247(2)
8.2 Variational Monte Carlo
249(3)
8.3 Diffusion Monte Carlo
252(4)
8.4 Wave Functions and their Optimization
256(5)
8.4.1 Stochastic Reconfiguration Method
258(1)
8.4.2 Linear Method
259(2)
8.5 Excited States
261(4)
8.5.1 Energy-Based Methods
261(2)
8.5.2 Time-Dependent Linear-Response VMC
263(1)
8.5.3 Variance-Based Methods
264(1)
8.6 Applications to Excited States of Molecular Systems
265(4)
8.7 Alternatives to Diffusion Monte Carlo
269(8)
Bibliography
270(7)
9 Multi-Reference Configuration Interaction
277(22)
Felix Plasser
Hans Lischka
9.1 Introduction
277(1)
9.2 Basics
278(11)
9.2.1 Configuration Interaction and the Variational Principle
278(2)
9.2.2 The Size-Extensivity Problem of Truncated CI
280(2)
9.2.3 Multi-Reference Configuration Spaces
282(4)
9.2.4 Many-Electron Basis Functions: Determinants and CSFs
286(1)
9.2.5 Workflow
287(2)
9.3 Types of MRCI
289(5)
9.3.1 Uncontracted and Contracted MRCI
289(2)
9.3.2 MRCI with Extensivity Corrections
291(2)
9.3.3 Types of Selection Schemes
293(1)
9.3.4 Construction of Orbitals
293(1)
9.4 Popular Implementations
294(1)
9.5 Conclusions
295(4)
References
295(4)
10 Multi-Configurational Reference Perturbation Theory with a CASSCF Reference Function
299(56)
Roland Lindh
Ignacio Fdez Galvan
10.1 Rayleigh-Schrodinger Perturbation Theory
300(13)
10.1.1 The Single-State Theory
300(1)
10.1.1 The Conventional Projectional Derivation
300(4)
10.1.1 The Bi-Variational Approach
304(4)
10.1.2 Convergence Properties and Intruder States
308(2)
10.1.2 Real and Imaginary Shift Techniques
310(3)
10.2 Moller-Plesset Perturbation Theory
313(7)
10.2.1 The Reference Function
314(1)
10.2.2 The Partitioning of the Hamiltonian
315(1)
10.2.3 The First-Order Interacting Space and Second-Order Energy Correction
316(4)
10.3 State-Specific Multi-Configurational Reference Perturbation Methods
320(18)
10.3.1 The Generation of the Reference Hamiltonian
321(1)
10.3.2 CAS-MP2 Theory
322(1)
10.3.3 CASPT2 Theory
323(1)
10.3.3 The Partitioning of the Hamiltonian
324(1)
10.3.3 The First-Order Interacting Space
325(3)
10.3.3 Other Active Space References
328(1)
10.3.3 Benchmark Results
329(1)
10.3.3 IPEA Shift
330(1)
10.3.4 MRMP2 Theory
331(1)
10.3.4 The Partitioning of the Hamiltonian
331(1)
10.3.4 The First-Order Interacting Space
332(1)
10.3.5 NEVPT2 Theory
333(1)
10.3.5 The Partitioning of the Hamiltonian
333(2)
10.3.5 The First-Order Interacting Space
335(1)
10.3.6 Performance Improvements
336(2)
10.4 Quasi-Degenerate Perturbation Theory
338(3)
10.5 Multi-State Multi-Configurational Reference Perturbation Methods
341(2)
10.5.1 Multi-State CASPT2 Theory
341(1)
10.5.2 Extended MS-CASPT2 Theory
342(1)
10.6 Summary and Outlook
343(12)
Acknowledgments
345(1)
References
345(5)
Appendix
350(5)
Part II Nuclear Dynamics
355(300)
11 Exact Quantum Dynamics (Wave Packets) in Reduced Dimensionality
357(26)
Sebastian Reiter
Daniel Keefer
Regina de Vivie-Riedle
11.1 Introduction
357(1)
11.2 Fundamentals of Molecular Quantum Dynamics
358(6)
11.2.1 Wave Packet Dynamics
358(2)
11.2.2 Time-Propagator Schemes
360(2)
11.2.3 Excited State Wave Packet Dynamics
362(1)
11.2.4 Surfaces and Coupling Elements in Reactive Coordinates
362(2)
11.3 Choice of Dynamical Coordinates and Hamiltonian in Reduced Dimensionality
364(14)
11.3.1 Manual Selection by Chemical Intuition
364(1)
11.3.2 The G-Matrix Formalism
365(1)
11.3.2 General Setup
366(1)
11.3.2 Practical Computation of the G-Matrix Elements
367(1)
11.3.2 Photorelaxation of Uracil in Linear Reactive Coordinates
367(2)
11.3.3 Automatic Generation of Linear Coordinates
369(1)
11.3.3 IRC Based Approach
369(2)
11.3.3 Trajectory-Based Approach
371(1)
11.3.3 Comparison of Both Techniques for Linear Subspaces
372(2)
11.3.4 Automatic Generation of Non-Linear Coordinates
374(4)
11.4 Summary and Further Remarks
378(5)
References
379(4)
12 Multi-Configuration Time-Dependent Hartree Methods: From Quantum to Semiclassical and Quantum-Classical
383(30)
M. Bonfanti
G. A. Worth
I. Burghardt
12.1 Introduction
383(2)
12.2 Time-Dependent Variational Principle and MCTDH
385(5)
12.2.1 Variational Principle and Tangent Space Projections
385(1)
12.2.2 MCTDH: Variational Multi-Configurational Wave Functions
386(1)
12.2.2 MCTDH Wave Function Ansatz
386(2)
12.2.2 MCTDH Equations of Motion
388(1)
12.2.3 ML-MCTDH: Hierarchical Representations
389(1)
12.3 Gaussian-Based MCTDH
390(6)
12.3.1 G-MCTDH and vMCG
390(1)
12.3.1 G-MCTDH Wave Function Ansatz
391(1)
12.3.1 G-MCTDH Equations of Motion
392(1)
12.3.1 vMCG Equations of Motion
393(1)
12.3.2 2L-GMCTDH
394(1)
12.3.2 Wave Function Ansatz
394(1)
12.3.2 Equations of Motion
395(1)
12.4 Quantum-Classical Multi-Configurational Approaches
396(3)
12.4.1 Quantum-Classical Limit of G-MCTDH
396(2)
12.4.2 Quantum-Classical Scheme with Finite-Width Wave Packets
398(1)
12.4.3 Related Approaches
399(1)
12.5 How to use MCTDH & Co
399(1)
12.6 Synopsis and Application to Donor-Acceptor Complex
400(5)
12.6.1 Hamiltonian, Spectral Densities, and Potential Surfaces
400(2)
12.6.2 Ultrafast Coherent Charge Transfer Dynamics
402(1)
12.6.3 Comparison of Methods
403(2)
12.7 Conclusions and Outlook
405(8)
Acknowledgments
406(1)
References
406(7)
13 Gaussian Wave Packets and the DD-vMCG Approach
413(22)
Graham A. Worth
Benjamin Lasorne
13.1 Historical Background
413(2)
13.2 Basic Theory
415(9)
13.2.1 Gaussian Wave Packets
415(3)
13.2.2 General Equations of Motion
418(1)
13.2.2 Coefficients and Parameters
418(1)
13.2.2 CX-Formalism
419(1)
13.2.2 Nuclear and Electronic Degrees of Freedom
420(2)
13.2.3 Variational Multi-Configurational Gaussian Approach
422(2)
13.3 Example Calculations
424(1)
13.4 Tunneling Dynamics: Salicylaldimine
425(1)
13.5 Non-Adiabatic Dynamics: The Butatriene Cation
426(2)
13.6 Direct Non-Adiabatic Dynamics: Formamide
428(3)
13.7 Summary
431(1)
13.8 Practical Implementation
431(4)
Acknowledgments
431(1)
References
431(4)
14 Full and Ab Initio Multiple Spawning
435(34)
Basile F. E. Curchod
14.1 Introduction
435(1)
14.2 Time-Dependent Molecular Schrodinger Equation in a Gaussian Basis
436(4)
14.2.1 Central Equations of Motion
436(3)
14.2.2 Dynamics of the Trajectory Basis Functions
439(1)
14.3 Full Multiple Spawning
440(3)
14.3.1 Full Multiple Spawning Equations
440(2)
14.3.2 Spawning Algorithm
442(1)
14.4 Extending Full Multiple Spawning
443(4)
14.4.1 External Field in Full Multiple Spawning
444(1)
14.4.2 Spin-Orbit Coupling in Full Multiple Spawning
445(2)
14.5 Ab Initio Multiple Spawning
447(7)
14.5.1 From Full- to Ab Initio Multiple Spawning
447(2)
14.5.2 Testing the Approximations of Ab Initio Multiple Spawning
449(1)
14.5.3 On-the-Fly Ab/nifio Multiple Spawning
450(1)
14.5.4 Ab Initio Multiple Spawning versus Trajectory Surface Hopping
451(3)
14.6 Dissecting an Ab Initio Multiple Spawning Dynamics
454(5)
14.6.1 The Different Steps of an Ab Initio Multiple Spawning Dynamics
454(1)
14.6.2 Example of Ab Initio Multiple Spawning Dynamics - the Photo-Chemistry of Cyclohexadiene
455(4)
14.7 In Silico Photo-Chemistry with Ab Initio Multiple Spawning
459(3)
14.8 Summary
462(7)
References
463(6)
15 Ehrenfest Methods for Electron and Nuclear Dynamics
469(30)
Adam Kirrander
Morgane Vacher
15.1 Introduction
469(1)
15.2 Theory of the (Simple) Ehrenfest Method
470(4)
15.2.1 Wave Function Ansatz
471(1)
15.2.2 Equations of Motion
472(2)
15.3 Theory of the Multi-Configurational Ehrenfest Method
474(6)
15.3.1 Wave Function Ansatz
474(2)
15.3.2 Equations of Motion
476(3)
15.3.3 Computational Aspects
479(1)
15.4 Applications
480(10)
15.4.1 Coupled Electron and Nuclear Dynamics Upon Sudden Ionization
481(4)
15.4.2 Ultrafast Scattering as a Probe of Nuclear Dynamics
485(5)
15.5 Conclusion
490(9)
References
491(8)
16 Surface Hopping Molecular Dynamics
499(32)
Sebastian Mai
Philipp Marquetand
Leticia Gonzalez
16.1 Introduction
499(1)
16.2 Basics of Surface Hopping
500(3)
16.2.1 Advantages and Disadvantages
500(1)
16.2.2 General Algorithm
501(2)
16.3 Surface Hopping Ingredients
503(10)
16.3.1 Nuclear Motion
503(1)
16.3.2 Wave Function Propagation
504(1)
16.3.3 Decoherence
505(2)
16.3.4 Surface Hopping Algorithm
507(2)
16.3.5 Kinetic Energy Adjustment and Frustrated Hops
509(2)
16.3.6 Coupling Terms and Representations
511(2)
16.4 Practical Remarks
513(8)
16.4.1 Choice of the Electronic Structure Method
513(3)
16.4.2 Initial Conditions
516(2)
16.4.3 Example Application and Trajectory Analysis
518(3)
16.5 Popular Implementations
521(1)
16.6 Conclusion and Outlook
522(9)
Acknowledgments
522(1)
References
522(9)
17 Exact Factorization of the Electron-Nuclear Wave Function: Theory and Applications
531(32)
Federica Agostini
E. K. U. Gross
17.1 Introduction
531(2)
17.2 The Time-Dependent Molecular Problem in the Exact-Factorization Formulation
533(3)
17.2.1 Wave Function Ansatz
533(2)
17.2.2 Equations of Motion
535(1)
17.3 The Born-Oppenheimer Framework and the Exact Factorization
536(9)
17.3.1 One-Dimensional Case: Time-Dependent Potential Energy Surface
538(4)
17.3.2 Two-Dimensional Case: Time-Dependent Potential Energy Surface and Time-Dependent Vector Potential
542(3)
17.4 Trajectory-Based Solution of the Exact-Factorization Equations
545(8)
17.4.1 CT-MQC: The Approximations
546(3)
17.4.2 CT-MQC: Photo-Induced Ring Opening in Oxirane
549(2)
17.4.3 CT-MQC: The Algorithm
551(2)
17.5 The Molecular Berry Phase
553(3)
17.6 Conclusions
556(7)
Acknowledgments
556(1)
References
556(7)
18 Bohmian Approaches to Non-Adiabatic Molecular Dynamics
563(32)
Guillermo Albareda
Ivano Tavernelli
18.1 Introduction
563(2)
18.2 A Practical Overview of Bohmian Mechanics
565(4)
18.2.1 The Postulates
565(1)
18.2.2 Computation of Bohmian Trajectories
566(1)
18.2.2 Trajectories from the Schrodinger Equation
566(1)
18.2.2 Trajectories from the Hamilton-Jacobi Equation
567(1)
18.2.2 Trajectories from a Complex Action
568(1)
18.2.3 Computation of Expectation Values
569(1)
18.3 The Born-Huang Picture of Molecular Dynamics
569(4)
18.3.1 The Molecular Schrodinger Equation in Position Space
569(1)
18.3.2 Schrodinger Equation in the Born-Huang Basis
570(1)
18.3.2 The Born-Oppenheimer Approximation: The Adiabatic Case
571(1)
18.3.2 Non-Adiabatic Dynamics
572(1)
18.4 BH-Based Approaches
573(6)
18.4.1 The Non-Adiabatic Bohmian Dynamics Equations (NABDY)
573(2)
18.4.2 Implementation in Molecular Dynamics: The Adiabatic Case
575(2)
18.4.3 The Approximate Quantum Potential Approach
577(2)
18.5 Non-BH Approaches
579(9)
18.5.1 The Conditional Wave Function Approach
579(2)
18.5.1 Hermitian Conditional Wave Function Approach
581(1)
18.5.2 The Interacting Conditional Wave Function Approach
582(3)
18.5.3 Time-Dependent Quantum Monte Carlo
585(3)
18.6 Conclusions
588(7)
References
589(6)
19 Semiclassical Molecular Dynamics for Spectroscopic Calculations
595(34)
Riccardo Conte
Michele Ceotto
19.1 Introduction
595(3)
19.2 From Feynman's Path Integral to van Vleck's Semiclassical Propagator
598(3)
19.3 The Semiclassical Initial Value Representation and the Heller-Herman-Kluk-Kay Formulation
601(2)
19.4 A Derivation of the Heller-Herman-Kluk-Kay Propagator
603(1)
19.5 The Time-Averaging Filter
604(2)
19.6 The Multiple Coherent States SCIVR
606(4)
19.7 The "Divide-and-Conquer" SCIVR
610(5)
19.8 Mixed SCIVR Dynamics: Towards Semiclassical Spectroscopy in Condensed Phase
615(3)
19.9 Semiclassical Spectroscopy Workflow
618(1)
19.10 A Taste of Semiclassical Spectroscopy
619(3)
19.11 Summary and Conclusions
622(7)
Acknowledgments
624(1)
Bibliography
624(5)
20 Path-Integral Approaches to Non-Adiabatic Dynamics
629(26)
Maximilian A. C. Sailer
Johan E. Runeson
Jeremy O. Richardson
20.1 Introduction
629(2)
20.2 Semiclassical Theory
631(2)
20.2.1 Mapping Approach
631(1)
20.2.2 Linearized Semiclassical Dynamics
632(1)
20.3 Non-Equilibrium Dynamics
633(7)
20.3.1 Spin-Boson Systems
634(2)
20.3.2 Non-Equilibrium Correlation Functions
636(4)
20.4 Non-Adiabatic Path-Integral Theory
640(6)
20.4.1 Mean-Field Path-Integral Sampling
640(1)
20.4.2 Non-Adiabatic Ring-Polymer Molecular Dynamics
641(3)
20.4.3 Alleviation of the Negative Sign
644(1)
20.4.4 Practical Implementation of Monte Carlo Sampling
644(2)
20.5 Equilibrium Correlation Functions
646(2)
20.6 Conclusions
648(7)
Acknowledgments
649(1)
References
649(6)
Index 655
Professor Leticia Gonzįlez teaches at the Department of Chemistry at the University of Vienna, Austria. She is a theoretical chemist world-known for her work on molecular excited states and ultrafast dynamics simulations. Besides publishing over 250 papers and several reviews on excited states and dynamics, she has developed the SHARC program package to simulate non-adiabatic dynamics.

Professor Roland Lindh currently teaches at Uppsala University, Sweden. He is a member of the editorial board of International Journal of Quantum Chemistry and the MOLCAS quantum chemistry program project. He co-authored the book "Multiconfigurational Quantum Chemistry" and is an expert on method development for multiconfigurational wave function theory.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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