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El. knyga: Vibrational Dynamics Of Molecules

Edited by (Emory Univ, Usa)
  • Formatas: 604 pages
  • Išleidimo metai: 14-Jun-2022
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • Kalba: eng
  • ISBN-13: 9789811237928
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  • Formatas: 604 pages
  • Išleidimo metai: 14-Jun-2022
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • Kalba: eng
  • ISBN-13: 9789811237928
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"Vibrational Dynamics of Molecules represents the definitive concise text on the cutting-edge field of vibrational molecular chemistry. The included topics span the field, from fundamental theory such as collocation methods and vibrational CI methods, tointeresting applications such as astrochemistry, supramolecular systems and virtual computational spectroscopy. This is a useful reference for theoretical chemists, spectroscopists, physicists, undergraduate and graduate students, lecturers and software developers"--

Vibrational Dynamics of Molecules represents the definitive concise text on the cutting-edge field of vibrational molecular chemistry. The chapter contributors are a Who's Who of world leaders in the field. The editor, Joel Bowman, is widely considered as one of the founding fathers of theoretical reaction dynamics. The included topics span the field, from fundamental theory such as collocation methods and vibrational CI methods, to interesting applications such as astrochemistry, supramolecular systems and virtual computational spectroscopy. This is a useful reference for theoretical chemists, spectroscopists, physicists, undergraduate and graduate students, lecturers and software developers.
Preface v
About the Editor ix
1 Vibrational Configuration Interaction Theory
1(40)
Benjamin Schroder
Guntram Rauhut
1.1 Introduction
1(1)
1.2 General Aspects
2(3)
1.3 Basis Functions
5(3)
1.4 Completeness Issues
8(5)
1.4.1 Completeness of the Watson Hamiltonian
8(4)
1.4.2 Completeness of the correlation space
12(1)
1.5 Configuration Selection
13(4)
1.6 Eigenpair Determination and the Assignment of States
17(2)
1.7 Unitarily Transformed Normal Coordinates
19(3)
1.8 Incremental VCI Approaches, iVCI
22(5)
1.9 Infrared Intensities
27(2)
1.10 Rovibrational CI Theory, RVCI
29(3)
1.11 Summary
32(9)
Acknowledgments
33(1)
References
33(8)
2 Vibrational Coupled Cluster Theory
41(39)
Ove Christiansen
2.1 Introduction
41(1)
2.2 Second Quantization for Many-Mode Systems
41(5)
2.3 The Hamiltonian
46(2)
2.4 Vibrational Self-consistent Field Theory
48(2)
2.5 Vibrational Coupled Cluster Theory
50(11)
2.5.1 Iterative solution of the VCC equations
53(1)
2.5.2 Implementation and computational scaling
54(2)
2.5.3 Approximate VCC models from perturbational arguments
56(1)
2.5.4 Tensors, tensor decomposition and VCC and VCI compared
57(4)
2.5.5 Coordinates and kinetic energy operators
61(1)
2.6 Response Theory
61(8)
2.6.1 General aspects of response theory
61(3)
2.6.2 Excitation energies from VCC response theory
64(2)
2.6.3 Spectra from damped VCC response functions
66(1)
2.6.4 Excited states by VCC or VCC response theory: Discussion
67(2)
2.7 Time-Dependent Wave Functions
69(11)
2.7.1 Time-dependent dynamics with time-independent modals
69(3)
2.7.2 Time-dependent dynamics with time-dependent modals
72(2)
Acknowledgements
74(1)
References
74(6)
3 Tensor Network States for Vibrational Spectroscopy
80(65)
Nina Glaser
Alberto Baiardi
Markus Reiher
3.1 Introduction
80(3)
3.2 Tensor Decompositions and Tensor Network States
83(6)
3.2.1 Diagrammatic notation of tensor networks
83(1)
3.2.2 Tensor networks for quantum states
84(5)
3.3 MPS/MPO Formulation of the Density Matrix Renormalization Group
89(11)
3.3.1 Variational optimization in the MPS/MPO framework
89(2)
3.3.2 Canonical form
91(2)
3.3.3 Expectation values
93(2)
3.3.4 MPS optimization
95(3)
3.3.5 Site selection and ordering with quantum information measures
98(2)
3.4 DMRG for Vibrational Problems
100(7)
3.4.1 Vibrational Hamiltonians
100(5)
3.4.2 Initial guess and bond dimension
105(1)
3.4.3 Example -- Anharmonic ZPVE of ethylene
105(2)
3.5 Excited state DMRG
107(11)
3.5.1 Excited state targeting by constrained optimization with vDMRG[ ortho]
107(1)
3.5.2 Enhancing convergence by root homing: vDMRG[ maxO]
108(2)
3.5.3 Auxiliary operator-based algorithms: vDMRG[ SM] and vDMRG[ f]
110(2)
3.5.4 Inverse power iteration with MPS: The vDMRG[ IPI] algorithm
112(2)
3.5.5 Towards large-scale excited state DMRG: vDMRG[ FEAST]
114(2)
3.5.6 Example -- Vibrational transition energies of ethlyene
116(2)
3.6 Nuclear Dynamics with Matrix Product States
118(14)
3.6.1 Entanglement barrier effect in TD-DMRG
119(1)
3.6.2 State-of-the-Art TD-DMRG approaches
120(2)
3.6.3 Tangent-space TD-DMRG
122(4)
3.6.4 Quantum chemical applications of real-time TD-DMRG
126(1)
3.6.5 Example -- Absorption spectrum of pyrazine
127(2)
3.6.6 Imaginary-time TD-DMRG: Ground state optimization and thermal ensembles
129(1)
3.6.7 Enhancing the TD-DMRG efficiency
130(2)
3.7 Conclusion and Outlook
132(13)
References
134(11)
4 Diffusion Monte Carlo Approaches for Studying Large Amplitude Vibrational Motions in Molecules and Clusters
145(29)
Jacob M. Finney
Ryan J. DiRisio
Anne B. McCoy
4.1 Introduction
145(3)
4.2 Diffusion Monte Carlo
148(2)
4.3 Introducing Guiding Functions
150(6)
4.4 Evaluation of Excited States and Molecular Properties
156(6)
4.4.1 Obtaining excited state wave functions
156(2)
4.4.2 Obtaining molecular properties
158(4)
4.5 Applications
162(5)
4.5.1 Sensitivity of the ground state energy of water on the size of the time step
162(2)
4.5.2 Convergence of the zero-point energy of water hexamer with ensemble size
164(1)
4.5.3 Flexible trial wave functions
165(2)
4.6 Outlook
167(7)
Acknowledgements
169(1)
References
169(5)
5 Collocation Methods for Computing Vibrational Spectra
174(20)
Tucker Carrington
5.1 Introduction
174(1)
5.2 The Variational Method
175(1)
5.3 Sum of Product Potential Energy Surfaces
176(2)
5.4 Using Quadrature with a General PES
178(1)
5.5 The Collocation Method
179(9)
5.5.1 Collocation with a direct product basis and a direct product grid
181(3)
5.5.2 Using collocation with a pruned product basis
184(4)
5.6 Conclusion
188(6)
Acknowledgments
189(1)
References
189(5)
6 Vibration-Rotation-Tunneling Levels and Spectra of Van der Waals Molecules
194(41)
Ad van der Avoird
6.1 Introduction
194(3)
6.2 Theory
197(16)
6.2.1 Coordinates and Hamiltonian
197(3)
6.2.2 Basis set
200(2)
6.2.3 Methods to compute eigenstates
202(2)
6.2.4 Symmetry aspects
204(4)
6.2.5 Line intensities and spectra
208(3)
6.2.6 Open-shell systems
211(2)
6.2.7 Additional comments
213(1)
6.3 Illustrative Results
213(22)
6.3.1 H2O-H2
213(6)
6.3.2 O3-N2
219(3)
6.3.3 OH-HCl
222(8)
Acknowledgment
230(1)
References
230(5)
7 Vibrational and Rovibrational Spectroscopy Applied to Astrochemistry
235(61)
Ryan C. Fortenberry
Timothy J. Lee
7.1 Introduction
235(2)
7.2 Computational Aspects
237(6)
7.2.1 Theoretical framework
237(4)
7.2.2 QFFs in practice
241(2)
7.3 Predicting Vibrational and Rovibrational Spectra and Rovibrational Spectroscopic Constants to Identify Molecules in Astronomical Observations
243(15)
7.3.1 Small molecules in their ground electronic states
244(6)
7.3.2 Small molecules in excited vibrational states
250(1)
7.3.3 Small molecules in excited electronic states
251(4)
7.3.4 Large molecules in their ground electronic states
255(3)
7.4 Computing Rovibrational Line Lists for Eliminating "Weeds" and Providing Data for Modeling the Opacity of Exoplanet Atmospheres (Absorption and Emission)
258(7)
7.4.1 Small, stable, abundant molecules: Co2
260(2)
7.4.2 Small, stable molecules with large amplitude motions: NH3
262(1)
7.4.3 Small, stable molecules containing a heavy atom: SO2
263(2)
7.5 Simulating Cascade Emission Spectra of Large PAH Molecules (Emission)
265(8)
7.5.1 Cascade emission spectra from scaled harmonic frequencies
267(2)
7.5.2 Fully anharmonic cascade emission IR spectra
269(4)
7.6 Conclusions
273(23)
Acknowledgments
274(1)
References
275(21)
8 MULTIMODE, The n-Mode Representation of the Potential and Illustrations to IR Spectra of Glycine and Two Protonated Water Clusters
296(44)
Qi Yu
Chen Qu
Paul L. Houston
Riccardo Conte
Apurba Nandi
Joel M. Bowman
8.1 Introduction
296(3)
8.2 Normal Modes and Zero-Order Hamiltonians
299(3)
8.2.1 Brief digression on adiabatic switching and the Eckart conditions
301(1)
8.3 Fundamentals of Vibrational Configuration Interaction
302(18)
8.3.1 Second-order perturbation theory
303(3)
8.3.2 VSCF and VSCF+VCI
306(1)
8.3.3 The Watson Hamiltonian, the n-mode representation of potential and the excitation space
307(5)
8.3.4 IR spectra of glycine
312(2)
8.3.5 Potential energy surface
314(1)
8.3.6 Aspects of the glycine calculations
314(3)
8.3.7 MULTIMODE spectra
317(3)
8.4 IR Spectra of of H703+ and H904+
320(4)
8.4.1 Summary of MULTIMODE VSCF/VCI calculations
321(2)
8.4.2 Summary of quasi-classical MD, classical MD and TRPMD simulations
323(1)
8.5 Results and Discussion
324(6)
8.5.1 H703+
325(3)
8.5.2 H904+ (Eigen)
328(2)
8.6 Conclusions
330(10)
Acknowledgments
331(1)
References
331(9)
9 Vibrational Spectra of Flexible Systems using the MCTDH Approach
340(38)
H.-D. Meyer
M. Schroder
O. Vendrell
9.1 Introduction
340(1)
9.2 Multi-Configuration Time-Dependent Hartree
341(7)
9.2.1 Standard method
341(1)
9.2.2 MCTDH
342(1)
9.2.3 ML-MCTDH
343(3)
9.2.4 The constant mean-field integrator and the improved relaxation algorithm
346(1)
9.2.5 (ML-)MCTDH viewed as tensor contraction method
347(1)
9.3 Sum-of-Products Form of High-Dimensional Potential Energy Surfaces
348(4)
9.3.1 Evaluation of high-dimensional integrals
348(2)
9.3.2 PES re-fitting
350(2)
9.4 Malonaldehyde
352(11)
9.4.1 Coordinates and system Hamiltonian
353(3)
9.4.2 Ground state energy and tunneling splitting
356(4)
9.4.3 Excited states
360(3)
9.5 Zundel Cation: Transient Infrared Absorption Spectroscopy
363(15)
9.5.1 Calculation of infrared transient absorption spectra within the MCTDH framework
364(2)
9.5.2 Infrared transient absorption of the Zudel cation
366(5)
References
371(7)
10 Semiclassical Vibrational Dynamics for Molecular and Supra-Molecular Systems
378(38)
Riccardo Conte
Michele Ceotto
10.1 Introduction
378(6)
10.1.1 The semiclassical way to quantum spectroscopy
379(3)
10.1.2 Theoretical and practical challenges for the quantum spectroscopy of high dimensional molecular and supra-molecular systems
382(2)
10.2 Recent Methodological Advances
384(11)
10.2.1 The divide-and-conquer semiclassical initial value representation
384(2)
10.2.2 Choosing the subspaces for DC-SCIVR calculations
386(2)
10.2.3 Non-separability of the potential energy and ease of CPU times in DC-SCIVR simulations
388(3)
10.2.4 A practical workflow for DC-SCIVR implementation
391(1)
10.2.5 Semiclassical wavefunctions and IR spectra
391(4)
10.3 Some Remarkable Applications
395(11)
10.3.1 A small but challenging molecule: The Zundel cation
395(4)
10.3.2 Beyond experimental controversy: The case of the protonated glycine dimer
399(2)
10.3.3 Going big: Quantum spectroscopy of biological species
401(3)
10.3.4 How many water molecules are (spectroscopically) needed to solvate one?
404(2)
10.4 A Quick Look at Some Perspectives
406(10)
References
407(9)
11 Direct Dynamics for Vibrational Spectroscopy: From Large Molecules in the Gas Phase to the Condensed Phase
416(101)
Sana Bougueroua
Vladimir Chantitch
Wanlin Chen
Simone Pezzotti
Marie-Pierre Gaigeot
11.1 Introduction
416(2)
11.2 Basic Background on Molecular Dynamics
418(6)
11.3 Review of the Formalism for MD-based Dynamical Anharmonic Vibrational Spectroscopy
424(6)
11.4 A Hybrid Formalism for Dynamical Spectroscopy
430(10)
11.4.1 Demonstration for the IR spectroscopic signal
430(6)
11.4.2 Advantages of this hybrid formalism
436(2)
11.4.3 Extension to SFG spectroscopy
438(2)
11.5 Discussions on Some Possible Issues with MD-based Vibrational Spectroscopy
440(11)
11.5.1 Length of MD trajectories for spectroscopic signals
440(2)
11.5.2 Equipartition of energy
442(5)
11.5.3 Choice of temperature in the MD
447(2)
11.5.4 Zero point energy and quantum nuclei
449(2)
11.6 Forces in MD Simulations: What Level to Choose for Vibrational Spectroscopy?
451(4)
11.7 From the Peaks to Their Molecular Assignments: Revealing Vibrational Modes and Their Couplings
455(9)
11.7.1 Assignments of modes by VDOS or ICDOS
456(1)
11.7.2 Graph theory for modes assignments (Vib-Graph)
457(7)
11.8 Illustration 1: IR-MPD Spectroscopy and Conformational Dynamics of Floppy AlanH+ Protonated Peptides
464(16)
11.9 Illustration 2: THz-IR Spectroscopy of Peptides and Mapping their Vibrational Motions
480(9)
11.10 Illustration 3: THz-IR Spectroscopy and Conformational Assignment of the (Ac-Phe-OMe)2 0-Sheet Model -- How Vib-Graphs Provide a Quantitative View of Collective Anharmonic Modes
489(5)
11.11 Illustration 4: Versatility of DFT-MD for Vibrational Spectroscopy, Some Illustrations on Aqueous Interfaces and SFG Spectroscopy
494(4)
11.12 Where the Field of MD-based Vibrational Spectroscopy is Going To: Some Perspectives That We Want to Highlight
498(19)
11.12.1 Machine learning
498(3)
11.12.2 Hybrid formalism for dynamical MD-based spectroscopy based on pre-computed APT and Raman tensors
501(1)
11.12.3 Algorithmic graph theory
502(1)
Acknowledgments
502(1)
References
503(14)
12 Introduction to Vibropolaritons: Spectroscopy, Relaxation and Chemical Reactions
517(58)
Raphael F. Ribeiro
Joel Yuen-Zhou
12.1 Introduction
517(2)
12.2 Fundamentals of Strong Light-Matter Interactions and Polariton Chemistry
519(15)
12.2.1 Review and phenomenology of weak light-matter interactions
519(2)
12.2.2 Light-matter interactions in optical cavities
521(3)
12.2.3 Strong light-matter interactions and hybrid modes in optical cavities
524(10)
12.3 Vibropolariton Dynamics and Spectroscopy
534(18)
12.3.1 Infrared strong coupling and the formation of vibropolaritons
534(2)
12.3.2 Vibropolariton pump-probe spectroscopy: Experiments
536(3)
12.3.3 Vibropolariton dynamics
539(5)
12.3.4 Vibropolariton pump-probe spectroscopy: Theory
544(5)
12.3.5 Cavity-assisted vibrational energy transfer
549(3)
12.4 Vibropolariton Chemistry: Reaction Effects
552(16)
12.4.1 Experimental observations
553(3)
12.4.2 General theoretical considerations
556(2)
12.4.3 Adiabatic reactions: Cavity transition state theory
558(4)
12.4.4 Non-adiabatic reactions: Cavity Marcus-Levich-Jortner theory
562(6)
12.5 Conclusions
568(7)
Acknowledgments
569(1)
References
569(6)
Index 575
Dr Joel M Bowman is the Samuel Candler Dobbs Professor of Theoretical Chemistry at Emory University, USA, where he held the Department Chair position twice (1990-1993, 2003-2006). He is an elected Fellow of the American Physical Society (since 1990), American Association for the Advancement of Science (since 2005), and International Academy of Quantum Molecular Science (since 2013). He is a recipient of the Alexander von Humboldt Research Award in 2018 and the Dudley Herschbach Prize for Theoretical Chemistry in 2013. He is the author of more than 500 publications, and has a h-index of 83 as of 2021. He is Editor of Spectrochimica Acta A and a member of the Editorial Boards of Chemical Physics, Advances in Physical Chemistry and the International Journal of Quantum Chemistry. He holds a PhD in Chemistry from the California Institute of Technology, USA.

Dr Bowman is widely considered as one of the founding fathers of theoretical reaction dynamics. He has made significant contributions in the theory and computation of many aspects of chemical reaction dynamics and molecular vibrations. Notable among these were the development of ab initio potential energy surfaces in high dimensionality using permutationally invariant fitting bases. Examples include the reactions X + CH4 HX + CH3, X = H, O((3)P), F, Cl and intersystem crossing in O + C2H4. Potentials for H5+, CH5+, H5O2+, etc., have led to the most rigorous analyses of this complex cations. The approach has also resulted in the most accurate ab initio potential and dipole moment for water, built from 1, 2, 3-body high-level electronic energies and precisely fit. In addition, he developed the vibrational self-consistent field and virtual state CI approaches to coupled molecular vibrations. Subsequently the efficient and accurate n-mode representation of the potential was developed and incorporated into the code MULTIMODE. This code has been used in many applications ranging from the rovibrational spectroscopy of polyatomic molecules to the vibrational dynamics of molecular clusters, including water clusters and hydrated ions. He also discovered roaming dynamics, and developed powerful methods to combine aspects of transition state theory with reduced dimensionality quantum scattering treatment of reaction dynamics, among which J-shifting has been widely used.