Vibrational Dynamics of Molecules

Contents
Preface
About the Editor
1. Vibrational Configuration Interaction Theory
1.1. Introduction
1.2. General Aspects
1.3. Basis Functions
1.4. Completeness Issues
1.4.1. Completeness of the Watson Hamiltonian
1.4.2. Completeness of the correlation space
1.5. Configuration Selection
1.6. Eigenpair Determination and the Assignment of States
1.7. Unitarily Transformed Normal Coordinates
1.8. Incremental VCI Approaches, iVCI
1.9. Infrared Intensities
1.10. Rovibrational CI Theory, RVCI
1.11. Summary
Acknowledgments
References
2. Vibrational Coupled Cluster Theory
2.1. Introduction
2.2. Second Quantization for Many-Mode Systems
2.3. The Hamiltonian
2.4. Vibrational Self-consistent Field Theory
2.5. Vibrational Coupled Cluster Theory
2.5.1. Iterative solution of the VCC equations
2.5.2. Implementation and computational scaling
2.5.3. Approximate VCC models from perturbational arguments
2.5.4. Tensors, tensor decomposition and VCC and VCI compared
2.5.5. Coordinates and kinetic energy operators
2.6. Response Theory
2.6.1. General aspects of response theory
2.6.2. Excitation energies from VCC response theory
2.6.3. Spectra from damped VCC response functions
2.6.4. Excited states by VCC or VCC response theory: Discussion
2.7. Time-Dependent Wave Functions
2.7.1. Time-dependent dynamics with time-independent modals
2.7.2. Time-dependent dynamics with time-dependent modals
Acknowledgements
References
3. Tensor Network States for Vibrational Spectroscopy
3.1. Introduction
3.2. Tensor Decompositions and Tensor Network States
3.2.1. Diagrammatic notation of tensor networks
3.2.2. Tensor networks for quantum states
3.3. MPS/MPO Formulation of the Density Matrix Renormalization Group
3.3.1. Variational optimization in the MPS/MPO framework
3.3.2. Canonical form
3.3.3. Expectation values
3.3.4. MPS optimization
3.3.5. Site selection and ordering with quantum information measures
3.4. DMRG for Vibrational Problems
3.4.1. Vibrational Hamiltonians
3.4.1.1. Canonical quantization
3.4.1.2. n-Mode quantization
3.4.2. Initial guess and bond dimension
3.4.3. Example — Anharmonic ZPVE of ethylene
3.5. Excited State DMRG
3.5.1. Excited state targeting by constrained optimization with vDMRG[ortho]
3.5.2. Enhancing convergence by root homing: vDMRG[maxO]
3.5.3. Auxiliary operator-based algorithms: vDMRG[S&I] and vDMRG[f]
3.5.4. Inverse power iteration with MPS: The vDMRG[IPI] algorithm
3.5.5. Towards large-scale excited state DMRG: vDMRG[FEAST]
3.5.6. Example — Vibrational transition energies of ethlyene
3.6. Nuclear Dynamics with Matrix Product States
3.6.1. Entanglement barrier effect in TD-DMRG
3.6.2. State-of-the-Art TD-DMRG approaches
3.6.3. Tangent-space TD-DMRG
3.6.4. Quantum chemical applications of real-time TD-DMRG
3.6.5. Example — Absorption spectrum of pyrazine
3.6.6. Imaginary-time TD-DMRG: Ground state optimization and thermal ensembles
3.6.7. Enhancing the TD-DMRG efficiency
3.7. Conclusion and Outlook
References
4. Diffusion Monte Carlo Approaches for Studying Large Amplitude Vibrational Motions in Molecules and Clusters
4.1. Introduction
4.2. Diffusion Monte Carlo
4.3. Introducing Guiding Functions
4.4. Evaluation of Excited States and Molecular Properties
4.4.1. Obtaining excited state wave functions
4.4.2. Obtaining molecular properties
4.5. Applications
4.5.1. Sensitivity of the ground state energy of water on the size of the time step
4.5.2. Convergence of the zero-point energy of water hexamer with ensemble size
4.5.3. Flexible trial wave functions
4.6. Outlook
Acknowledgements
References
5. Collocation Methods for Computing Vibrational Spectra
5.1. Introduction
5.2. The Variational Method
5.3. Sum of Product Potential Energy Surfaces
5.4. Using Quadrature with a General PES
5.5. The Collocation Method
5.5.1. Collocation with a direct product basis and a direct product grid
5.5.1.1. Using collocation with the MCTDH method
5.5.2. Using collocation with a pruned product basis
5.6. Conclusion
Acknowledgments
References
6. Vibration-Rotation-Tunneling Levels and Spectra of Van der Waals Molecules
6.1. Introduction
6.2. Theory
6.2.1. Coordinates and Hamiltonian
6.2.2. Basis set
6.2.3. Methods to compute eigenstates
6.2.4. Symmetry aspects
6.2.5. Line intensities and spectra
6.2.6. Open-shell systems
6.2.7. Additional comments
6.3. Illustrative Results
6.3.1. H2O–H2
6.3.2. O3–N2
6.3.3. OH–HCl
Acknowledgment
References
7. Vibrational and Rovibrational Spectroscopy Applied to Astrochemistry
7.1. Introduction
7.2. Computational Aspects
7.2.1. Theoretical framework
7.2.2. QFFs in practice
7.3. Predicting Vibrational and Rovibrational Spectra and Rovibrational Spectroscopic Constants to Identify Molecules in Astronomical Observations
7.3.1. Small molecules in their ground electronic states
7.3.1.1. CCSD(T)-based methods
7.3.1.2. Explicitly correlated QFFs
7.3.2. Small molecules in excited vibrational states
7.3.3. Small molecules in excited electronic states
7.3.4. Large molecules in their ground electronic states
7.4. Computing Rovibrational Line Lists for Eliminating “Weeds” and Providing Data for Modeling the Opacity of Exoplanet Atmospheres (Absorption and Emission)
7.4.1. Small, stable, abundant molecules: CO2
7.4.2. Small, stable molecules with large amplitude motions: NH3
7.4.3. Small, stable molecules containing a heavy atom: SO2
7.5. Simulating Cascade Emission Spectra of Large PAH Molecules (Emission)
7.5.1. Cascade emission spectra from scaled harmonic frequencies
7.5.2. Fully anharmonic cascade emission IR spectra
7.6. Conclusions
Acknowledgments
References
8. MULTIMODE, The n-Mode Representation of the Potential and Illustrations to IR Spectra of Glycine and Two Protonated Water Clusters
8.1. Introduction
8.2. Normal Modes and Zero-Order Hamiltonians
8.2.1. Brief digression on adiabatic switching and the Eckart conditions
8.3. Fundamentals of Vibrational Configuration Interaction
8.3.1. Second-order perturbation theory
8.3.2. VSCF and VSCF+VCI
8.3.3. The Watson Hamiltonian, the n-mode representation of potential and the excitation space
8.3.4. IR spectra of glycine
8.3.5. Potential energy surface
8.3.6. Aspects of the glycine calculations
8.3.7. MULTIMODE spectra
8.4. IR Spectra of of H7O3+ and H9O4+
8.4.1. Summary of MULTIMODE VSCF/VCI calculations
8.4.2. Summary of quasi-classical MD, classical MD and TRPMD simulations
8.5. Results and Discussion
8.5.1. H7O3+
8.5.2. H9O4+ (Eigen)
8.6. Conclusions
Acknowledgments
References
9. Vibrational Spectra of Flexible Systems using the MCTDH Approach
9.1. Introduction
9.2. Multi-Configuration Time-Dependent Hartree
9.2.1. Standard method
9.2.2. MCTDH
9.2.3. ML-MCTDH
9.2.4. The constant mean-field integrator and the improved relaxation algorithm
9.2.5. (ML-)MCTDH viewed as tensor contraction method
9.3. Sum-of-Products Form of High-Dimensional Potential Energy Surfaces
9.3.1. Evaluation of high-dimensional integrals
9.3.2. PES re-fitting
9.4. Malonaldehyde
9.4.1. Coordinates and system Hamiltonian
9.4.1.1. Normal mode coordinates
9.4.1.2. Effective Hamiltonian
9.4.1.3. Mode combinations
9.4.1.4. PES fit
9.4.2. Ground state energy and tunneling splitting
9.4.3. Excited states
9.5. Zundel Cation: Transient Infrared Absorption Spectroscopy
9.5.1. Calculation of infrared transient absorption spectra within the MCTDH framework
9.5.2. Infrared transient absorption of the Zudel cation
References
10. Semiclassical Vibrational Dynamics for Molecular and Supra-Molecular Systems
10.1. Introduction
10.1.1. The semiclassical way to quantum spectroscopy
10.1.2. Theoretical and practical challenges for the quantum spectroscopy of high dimensional molecular and supra-molecular systems
10.2. Recent Methodological Advances
10.2.1. The divide-and-conquer semiclassical initial value representation
10.2.2. Choosing the subspaces for DC-SCIVR calculations
10.2.3. Non-separability of the potential energy and ease of CPU times in DC-SCIVR simulations
10.2.4. A practical workflow for DC-SCIVR implementation
10.2.5. Semiclassical wavefunctions and IR spectra
10.3. Some Remarkable Applications
10.3.1. A small but challenging molecule: The Zundel cation
10.3.2. Beyond experimental controversy: The case of the protonated glycine dimer
10.3.3. Going big: Quantum spectroscopy of biological species
10.3.4. How many water molecules are (spectroscopically) needed to solvate one?
10.4. A Quick Look at Some Perspectives
References
11. Direct Dynamics for Vibrational Spectroscopy: From Large Molecules in the Gas Phase to the Condensed Phase
11.1. Introduction
11.2. Basic Background on Molecular Dynamics
11.3. Review of the Formalism for MD-based Dynamical Anharmonic Vibrational Spectroscopy
11.4. A Hybrid Formalism for Dynamical Spectroscopy
11.4.1. Demonstration for the IR spectroscopic signal
11.4.2. Advantages of this hybrid formalism
11.4.3. Extension to SFG spectroscopy
11.5. Discussions on Some Possible Issues with MD-based Vibrational Spectroscopy
11.5.1. Length of MD trajectories for spectroscopic signals
11.5.2. Equipartition of energy
11.5.3. Choice of temperature in the MD
11.5.4. Zero point energy and quantum nuclei
11.6. Forces in MD Simulations: What Level to Choose for Vibrational Spectroscopy?
11.7. From the Peaks to Their Molecular Assignments: Revealing Vibrational Modes and Their Couplings
11.7.1. Assignments of modes by VDOS or ICDOS
11.7.2. Graph theory for modes assignments (Vib-Graph)
11.8. Illustration 1: IR-MPD Spectroscopy and Conformational Dynamics of Floppy AlanH+ Protonated Peptides
11.9. Illustration 2: THz-IR Spectroscopy of Peptides and Mapping their Vibrational Motions
11.10. Illustration 3: THz-IR Spectroscopy and Conformational Assignment of the (Ac-Phe-OMe)2 β-Sheet Model — How Vib-Graphs Provide a Quantitative View of Collective Anharmonic Modes
11.11. Illustration 4: Versatility of DFT-MD for Vibrational Spectroscopy, Some Illustrations on Aqueous Interfaces and SFG Spectroscopy
11.12. Where the Field of MD-based Vibrational Spectroscopy is Going To: Some Perspectives That We Want to Highlight
11.12.1. Machine learning
11.12.2. Hybrid formalism for dynamical MD-based spectroscopy based on pre-computed APT and Raman tensors
11.12.3. Algorithmic graph theory
Acknowledgments
References
12. Introduction to Vibropolaritons: Spectroscopy, Relaxation and Chemical Reactions
12.1. Introduction
12.2. Fundamentals of Strong Light-Matter Interactions and Polariton Chemistry
12.2.1. Review and phenomenology of weak light–matter interactions
12.2.2. Light–matter interactions in optical cavities
12.2.3. Strong light–matter interactions and hybrid modes in optical cavities
12.3. Vibropolariton Dynamics and Spectroscopy
12.3.1. Infrared strong coupling and the formation of vibropolaritons
12.3.2. Vibropolariton pump–probe spectroscopy: Experiments
12.3.3. Vibropolariton dynamics
12.3.4. Vibropolariton pump–probe spectroscopy: Theory
12.3.5. Cavity-assisted vibrational energy transfer
12.4. Vibropolariton Chemistry: Reaction Effects
12.4.1. Experimental observations
12.4.2. General theoretical considerations
12.4.3. Adiabatic reactions: Cavity transition state theory
12.4.4. Non-adiabatic reactions: Cavity Marcus–Levich–Jortner theory
12.5. Conclusions
Acknowledgments
References
Index