Vibration

- [2023 - JPCL - Proton transfer in water complexs revealed by IRMPD and AIMD]
- Pure AIMD simulations in B3LYP and CP2K

- [2023 - JCTC - A Periodic VSCF study of OH stretching in ice XI]: CRYSTAL23 code
- [2023 - Nat comm. - Two-dimensional infrared-Raman spectroscopy as a probe of water’s tetrahedrality]
- Peer-review report, scripts and raw data are included
- MD vs TRPMD, nuclear quantum effects and temperature dependence, using qTIP4P/F
- The librations (400 ~ 1000 cm $^{-1}$) of water molecules, carries rich information about liquid water

- [2022 - JPCC - Ceotto Group - IR of water on TiO2]: there are some discussions on zero-point energy and one must provide kinetic energy higher than zero-point energy in a classical MD simulation.
- [2022 - J. Mol. Spectrosc. - Spectroscopy with Free Electron Lasers and Synchrotron Radiation]
- [2021 - JCC - Non long-range corrected density functionals incorrectly describe the intensity of the C-H stretching band in polycyclic aromatic hydrocarbons]
- [2021 - J. Phys. D: Appl. Phys. - Raman spectra of hydrocarbons under extreme conditions of pressure and temperature: a first-principles study]
- autocorrelation of C-H bonds and H-C-H angles

- [2021 - J. Chem. Inf. Model. - Predicting Infrared Spectra with Message Passing Neural Networks]
- [2021 - JCTC - Transfer Learning to CCSD(T): Accurate Anharmonic Frequencies from Machine Learning Models]
- [2021 - My Trajectory in Molecular Reaction Dynamics and Spectroscopy]
- [2021 - JCTC - Christian Ochsenfeld et.al.]: Quantitative Comparison of Experimental and Computed IR-Spectra Extracted from Ab Initio Molecular Dynamics
- [2020 - Faraday Discuss. - temperature dependence of the vibrational spectrum of porphycene]: MD vs TRPMD for NH streching mode
- Neural network PES and KRR dipole moment surface
- 1D double-well to explain the underlying physics

- [2020 - Faraday Discuss. - Which quantum statistics–classical dynamics method is best for water?]
- MD, TRPMD, CMD, QCMD, LSC-IVR
- Gas, liquid and ice, using the q-TIP4P/F model potential
- 150K and 300K

- [2020 - PCCP - Raman spectrum and polarizability of liquid water from deep neural networks]
- Deep-kit and DP-gen
- Reducing the statistical error in a spectrum calculation by ML-MD
- Temperature dependence of the OH/OD stretch

- [2020 - JCP - On-the-fly ab initio semiclassical evaluation of vibronic spectra at finite temperature]
- 1D model potential

- [2020 - JPCA - Snakes on the Rungs of Jacob’s Ladder: Anomalous Vibrational Spectra from Double-Hybrid DFT Methods]
- The double hybrid functional predicts very unphysical frequencies for some CHNO species

- [2020 - JPCA - Comprehensive Benchmark Results for the Accuracy of Basis Sets for Anharmonic Molecular Vibrations]
- The accuracy and convergence of Gaussin's split-valence basis sets (6-31G, 6-311+G(d, p), ...) are systemically investigated. def2-TZVPP is a large basis set and considered as one reference basis set.
- Benchmark on def2 basis sets and Jensen's basis sets are coming soon

- [2020 -JCTC - Dual Basis Approach for Ab Initio Anharmonic Calculations of Vibrational Spectroscopy: Application to Microsolvated Biomolecules]
- [2020 - JPCL - Glycolic Acid as a Vibrational Anharmonicity Benchmark]
- Harmonic and VPT2 studies of Glycolic Acid (C2H4O3) using B3LYP-D3, B2PLYP-D3, MP2, and CCSD(T)
- B3LYP-D3 has a good error cancellation and thus shows good harmonic frequencies.
- With the VPT2 approach, CCSD(T) achieves the lowest error compared with the experiment.

- [2020 - PCCP - On the separability of large-amplitude motions in anharmonic frequency calculations]
- [2019 - PNAS - Nanoscale infrared imaging analysis of carbonaceous chondrites to understand organic-mineral interactions during aqueous alteration]
- AFM-based IR measurements of minerals with a high spatial resolution. The cantilever of AFM has a characteristic thermal expansion when the sample absorbs light. The oscillation amplitude of the cantilever is directly proportional to the amount of light absorbed.
- Slices (70-100nm) Meteorites
- Why different substrates for different meteorites

- [2019 - Faraday Discussions]:Conformational assignment of gas phase peptides and their H-bonded complexes using far-IR/THz: IR-UV ion dip experiment, DFT-MD spectroscopy, and graph theory for mode assignment
- [2018 - ACS Omega - André F. Rodrigues-Oliveira et.al.]: Evaluation of Common Theoretical Methods for Predicting Infrared Multiphotonic Dissociation Vibrational Spectra of Intramolecular Hydrogen-Bonded Ions [IRMPD-vib-xc]
- [2018 - PCCP - Spin-state dependence of the structural and vibrational properties of solvated iron(ii) polypyridyl complexes from AIMD simulations: aqueous [Fe(bpy)3]Cl2, a case study]
- [2017 - JCTC - Simulation of Vibronic Spectra of Flexible Systems: Hybrid DVR-Harmonic Approaches]
- Treating large-amplitude motion (LAM) within the static anharmonic approach

- [2017 - JCTC - Christian Ochsenfeld et.al. Efficient and Accurate Born–Oppenheimer Molecular Dynamics for Large Molecular Systems]
- [2017 - JCTC - Daria R. Galimberti et.al.]: Combining Static and Dynamical Approaches for Infrared Spectra Calculations of Gas Phase Molecules and Clusters
- [2017 - PhD thesis - Martin Thomas]: Theoretical Modeling of Vibrational Spectra in the Liquid Phase
- As the intensity ratio of the two bands clearly depends on the energy, classical dynamics provides again not a quantitative estimation of the quantum spectrum, but a qualitative insight even into special effects like Fermi resonance is possible.
- In general, MD simulations with classical particles contain a description of anharmonicity effects in qualitative agreement with the corresponding quantum particles. This allows to observe overtones and combination bands in the power spectra.

- [2016 - JPCA - Huan Wang et.al. Complete Assignment of the Infrared Spectrum of the Gas-Phase Protonated Ammonia Dimer]
- AIMD vs VPT2
- Combination bands, overtone, resonances from AIMD

- [2015 - Chemistry - Interplay of Exciton Coupling and Large-Amplitude Motions in the Vibrational Circular Dichroism Spectrum of Dehydroquinidine]
- Boltzman weighting of different conformers
- Large-amplitude motions in dihedral angles

- [2014 - JPCA - Approximate First-Principles Anharmonic Calculations of Polyatomic Spectra Using MP2 and B3LYP Potentials: Comparisons with Experiment]
- [2014 - PCCP - Dispersion corrected DFT approaches for anharmonic vibrational frequency calculations: nucleobases and their dimers]
- The most promising method to get anharmonic IR of large systems is VPT2 with the hybrid functional (B3LYP) and medium size (SNSD) basis sets.
- Dispersion interactions should be properly treated in order to compute IR of weakly bound molecular complexes.
- Empirical scaling factors
- simple/universal scaling factors for all fundamental frequencies
- sophisticated scaling factors: different scaling factors are applied for different modes without the guarantee of transferability.
- Zero-point energies need different scaling factors than vibrational frequencies.
- vibrational frequencies can be scaled but not intensities.

- In order to assign vibrational modes, one has to visualize the atomic displacements along normal modes and compare with experiments.
- CC/DFT hybrid approaches for calculating anharmonic IR for medium-sized molecules: harmonic at couple cluster level and anharmonic corrections at B3LYP level
- CCSD(T)/CBS is limited to 10-15 atoms for harmonic calculations while B2PLYP can be used for larger systems.

- Uracil test case
- a good test system which does not have the problem in out-of-plane NH2 vibration, has highly accurate theoretical results (CCSD) available.
- VPT2 with B3LYP provides accurate frequencies because of the good quality of both harmonic and anharmonic contributions, not a lucky error cancellations.
`(more proofs?)`

- B3LYP-D3 provides almost identical results as B3LYP for both harmonic and anharmonic calculations.
- B3LYP-DCP, M06-2X and wB97XD yield less accurate harmonic frequencies.
- M06-2X and wB97XD are worsened for anharmonic corrections.

- B3LYP and B3LYP-D3 provide nearly equivalent harmonic and anharmonic frequencies for 6 different nucleobases.

- [2013 - JCTC - Anharmonic Vibrational Frequency Calculations Are Not Worthwhile for Small Basis Sets]
- [2013 - PCCP - Sergei D. Ivanov, Dominik Marx el.al.]:Theoretical spectroscopy using molecular dynamics: theory and application to CH5+ and its isotopologues
- Theory behind getting IR from MD
- CH$_5^+$ is chosen as it is a typical floppy system with an unusually flat PES and undergoes intricate large-amplitude motion "hydrogen scrambling"
- Mode assignment from AIMD trajectories (difficult for floppy molecules)
- Conformer-weighted AIMD spectra

- [2012 - JCTC - Gerald Mathias et.al. Infrared Spectroscopy of Fluxional Molecules from (ab Initio) Molecular Dynamics: Resolving Large-Amplitude Motion, Multiple Conformations, and Permutational Symmetries]
- Band assignments (large-amplitude motion) from MD trajectories, taking CH$_5^+$ as an example

- [2011 - JCTC - Gerald Mathias et.al. Generalized Normal Coordinates for the Vibrational Analysis of Molecular Dynamics Simulations]
- [2011 - JCTC - Direct Calculations of Mid- and Near-IR Absorption and Circular Dichroism Spectra of Chiral Molecules Using QM/MM Molecular Dynamics Simulation Method]
- first overtone and combination bands

- [2010 - JCTC - Harmonic and Anharmonic Vibrational Frequency Calculations with the Double-Hybrid B2PLYP Method: Analytic Second Derivatives and Benchmark Studies]
- [2009 - JCP - Dominik Marx et.al. On the applicability of centroid and ring polymer path integral molecular dynamics for vibrational spectroscopy]
- [2006 - JACS - Popular Theoretical Methods Predict Benzene and Arenes To Be Nonplanar]
- MP2 produces imaginary frequencies for planar benzene.
- MP2, MP3, and CISD levels favor non-planar benzene, while RHF, B3LYP, and BLYP methods do not have this problem.
- Atomic natural orbital (ANO) basis sets can minimize basis set superposition errors

- [2006 - PCCP - Dominik Marx et.al. Understanding hydrogen scrambling and infrared spectrum of bare CH5+ based on ab initio simulations]
- Massive Nose-Hoover chain thermostat guarantees that all modes are properly thermalized at the target temperature

- [2004 - JCP - Dominik Marx et.al. Quantum corrections to classical time-correlation functions: Hydrogen bonding and anharmonic floppy modes]
- [2004 - JCPA - Accurate Vibrational Spectra of Large Molecules by Density Functional Computations beyond the Harmonic Approximation: The Case of Azabenzenes]
- The inclusion of Hartree-Fock exchanges in exchange correlation in necessary for vibrational properties of organic molecules.
- For azabenzenes, anharmonic corrections do not have huge impacts on zero-point energies, but cannot be ignored in quantitative studies.

- [2003 - JPCB - Ab Initio Molecular Dynamics Computation of the Infrared Spectrum of Aqueous Uracil]
- Fermi resonances are not well described in our classical approach
- IR in solution, contribution from solvent and solute

- [2019 - JCP - Understanding the anharmonic vibrational structure of the carbon dioxide dimer]
- CCSD(T)-F12b/aug-cc-pVTZ

- [2007 - JCP - Fermi resonance in CO2 : A combined electronic coupled-cluster and vibrational configuration-interaction prediction]
- CCSD(T)/cc-pVTZ and VSCF

- [1993 - CPL - Accurate ab initio quartic force fields for the N2O and CO2 molecules]
- CCSD(T)/cc-pVTZ anharmonic VPT2 calculations of gas phase CO2

- [1995 - PRB - Ab initio molecular dynamics in adaptive coordinates]: AIMD simulations on single CO2 molecule reproduce Fermi resonance.

- Ceotto Michele: AIMD
- Dominik Marx: AIMD
- Vincenzo Barone : Anharmonic, VPT2, basis set

`fundamental band`

: the vibration from the vibrational ground state to the vibrational first excited state`overtone band`

: the vibration from the vibrational ground state to the high-order (> 1) excited vibrational states`combination band`

: the superposition of two fundamental bands. The combination band is forbidden by harmonic oscillator selection rules.`hot band`

: the transition between two excited vibrational states`resonance`

: a resonance occurs when the energy of the normal modes or the sum of modes are close to one another in energy.- Harmonic approximation will overestimate the energies of the fundamentals due to the neglect of anharmonicity.
`floppy molecule`

: the structure is not at all rigid, but rather constantly changing. It is also called`fluctuating`

and`fuxional`

. The bond connectivity has not been modified during the dynamical changes.- CH$_5^+$: 2005-Science-Dominik Marx
- Various cis/trans conformations by thermally driven isomerization transitions
- Methyl groups can easily undergo internal rotations

- VPT2 needs
`6N-11`

Hessian calculations for a nonlinear system where`2*(3N-6)+1 = 6N-12+1 = 6N-11`

. The`6N-11`

comes about due to the use of a two-sided finite difference approach to find the derivatives of the force constants with respect to displacements along each of the normal modes, plus one calculation for the unperturbed geometry. - IR of molecular systems with increasing size and in different environments.

Phonons are collective atomic motions in solids. Due to the periodic boundary conditions, the Hessian is in principle a matrix of infinite size. The finite-displacement supercell approach is a common method to calculate phonon related properties. If long-range vibrations are important, a large supercell is needed.

- For medium size PAHs, the addition of
`D3`

has minor effects on band positions and intensities. There might be divergences for some vibrational peaks. `SPECTRO program`

not available online: Gaw, J. F.; Willets, A.; Green, W. H.; Handy, N. C. in Advances in Molecular Vibrations and Collision Dynamics; Bowman, J. M.; Ratner, M. A., Eds.; JAI Press, Inc.: Greenwich, CT, 1991; pp 170– 185.- IR from AIMD intrinsically contains some anharmonic effects. However, other anharmonic effects like mode coupling leading to combination bands and Fermi resonances are still not included because the nuclear motion is treated classically.
- J. Horníček, P. Kaprálová, and P. Bouř, J. Chem. Phys. 127, 084502 (2007).
- J. Hudecová, K.H. Hopmann, and P. Bouř, J. Phys. Chem. B 116, 336 (2012).
- M. Thomas, M. Brehm, R. Fligg, P. Vöhringer, and B. Kirchner, Phys. Chem. Chem. Phys. 15, 6608 (2013).
- S.A. Fischer, T.W. Ueltschi, P.Z. El-Khoury, A.L. Mifflin, W.P. Hess, H.-F. Wang, C.J. Cramer, and N. Govind, J. Phys. Chem. B 120, 1429 (2016).