Preface |
|
v | |
About the Editor |
|
ix | |
|
1 Vibrational Configuration Interaction Theory |
|
|
1 | (40) |
|
|
|
|
1 | (1) |
|
|
2 | (3) |
|
|
5 | (3) |
|
|
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) |
|
|
27 | (2) |
|
1.10 Rovibrational CI Theory, RVCI |
|
|
29 | (3) |
|
|
32 | (9) |
|
|
33 | (1) |
|
|
33 | (8) |
|
2 Vibrational Coupled Cluster Theory |
|
|
41 | (39) |
|
|
|
41 | (1) |
|
2.2 Second Quantization for Many-Mode Systems |
|
|
41 | (5) |
|
|
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) |
|
|
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) |
|
|
74 | (1) |
|
|
74 | (6) |
|
3 Tensor Network States for Vibrational Spectroscopy |
|
|
80 | (65) |
|
|
|
|
|
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) |
|
|
91 | (2) |
|
|
93 | (2) |
|
|
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) |
|
|
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) |
|
|
134 | (11) |
|
4 Diffusion Monte Carlo Approaches for Studying Large Amplitude Vibrational Motions in Molecules and Clusters |
|
|
145 | (29) |
|
|
|
|
|
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) |
|
|
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) |
|
|
167 | (7) |
|
|
169 | (1) |
|
|
169 | (5) |
|
5 Collocation Methods for Computing Vibrational Spectra |
|
|
174 | (20) |
|
|
|
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) |
|
|
188 | (6) |
|
|
189 | (1) |
|
|
189 | (5) |
|
6 Vibration-Rotation-Tunneling Levels and Spectra of Van der Waals Molecules |
|
|
194 | (41) |
|
|
|
194 | (3) |
|
|
197 | (16) |
|
6.2.1 Coordinates and Hamiltonian |
|
|
197 | (3) |
|
|
200 | (2) |
|
6.2.3 Methods to compute eigenstates |
|
|
202 | (2) |
|
|
204 | (4) |
|
6.2.5 Line intensities and spectra |
|
|
208 | (3) |
|
|
211 | (2) |
|
6.2.7 Additional comments |
|
|
213 | (1) |
|
|
213 | (22) |
|
|
213 | (6) |
|
|
219 | (3) |
|
|
222 | (8) |
|
|
230 | (1) |
|
|
230 | (5) |
|
7 Vibrational and Rovibrational Spectroscopy Applied to Astrochemistry |
|
|
235 | (61) |
|
|
|
|
235 | (2) |
|
7.2 Computational Aspects |
|
|
237 | (6) |
|
7.2.1 Theoretical framework |
|
|
237 | (4) |
|
|
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) |
|
|
273 | (23) |
|
|
274 | (1) |
|
|
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) |
|
|
|
|
|
|
|
|
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) |
|
|
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) |
|
|
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) |
|
|
325 | (3) |
|
|
328 | (2) |
|
|
330 | (10) |
|
|
331 | (1) |
|
|
331 | (9) |
|
9 Vibrational Spectra of Flexible Systems using the MCTDH Approach |
|
|
340 | (38) |
|
|
|
|
|
340 | (1) |
|
9.2 Multi-Configuration Time-Dependent Hartree |
|
|
341 | (7) |
|
|
341 | (1) |
|
|
342 | (1) |
|
|
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) |
|
|
350 | (2) |
|
|
352 | (11) |
|
9.4.1 Coordinates and system Hamiltonian |
|
|
353 | (3) |
|
9.4.2 Ground state energy and tunneling splitting |
|
|
356 | (4) |
|
|
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) |
|
|
371 | (7) |
|
10 Semiclassical Vibrational Dynamics for Molecular and Supra-Molecular Systems |
|
|
378 | (38) |
|
|
|
|
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) |
|
|
407 | (9) |
|
11 Direct Dynamics for Vibrational Spectroscopy: From Large Molecules in the Gas Phase to the Condensed Phase |
|
|
416 | (101) |
|
|
|
|
|
|
|
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) |
|
|
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) |
|
|
502 | (1) |
|
|
503 | (14) |
|
12 Introduction to Vibropolaritons: Spectroscopy, Relaxation and Chemical Reactions |
|
|
517 | (58) |
|
|
|
|
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) |
|
|
568 | (7) |
|
|
569 | (1) |
|
|
569 | (6) |
Index |
|
575 | |