Calculation of OH-stretching band intensities of the water dimer and trimer

Vibrational Spectra of Highly Anharmonic Water Clusters: Molecular Dynamics and Harmonic Analysis Revisited with Constrained Nuclear-Electronic Orbital Methods

Vibrational spectroscopy is widely used to gain insights into structural and dynamic properties of chemical, biological, and materials systems. Thus, an efficient and accurate method to simulate vibrational spectra is desired. In this paper, we justify and employ a microcanonical molecular simulation scheme to calculate the vibrational spectra of three challenging water clusters: the neutral water dimer (H4O2), the protonated water trimer (H7O3+), and the protonated water tetramer (H9O4+). We find that with the accurate description of quantum nuclear delocalization effects through the constrained nuclear-electronic orbital framework, including vibrational mode coupling effects through molecular dynamics simulations can additionally improve the vibrational spectrum calculations. In contrast, without the quantum nuclear delocalization picture, conventional ab initio molecular dynamics may even lead to less accurate results than harmonic analysis.

Reduced-dimensional vibrational models of the water dimer

A model based on the finite-basis representation of a vibrational Hamiltonian expressed in internal coordinates is developed. The model relies on a many-mode, low-order expansion of both the kinetic energy operator and the potential energy surface (PES). Polyad truncations and energy ceilings are used to control the size of the vibrational basis to facilitate accurate computations of the OH stretch and HOH bend intramolecular transitions of the water dimer (H₂ ¹⁶O)₂. Advantages and potential pitfalls of the applied approximations are highlighted. The importance of choices related to the treatment of the kinetic energy operator in reduced-dimensional calculations and the accuracy of different water dimer PESs are discussed. A range of different reduced-dimensional computations are performed to investigate the wavenumber shifts in the intramolecular transitions caused by the coupling between the intra- and intermolecular modes. With the use of symmetry, full 12-dimensional vibrational energy levels of the water dimer are calculated, predicting accurately the experimentally observed intramolecular fundamentals. It is found that one can also predict accurate intramolecular transition wavenumbers for the water dimer by combining a set of computationally inexpensive reduced-dimensional calculations, thereby guiding future effective-Hamiltonian treatments.

Vibrational Spectroscopy of the Water Dimer at Jet-Cooled and Atmospheric Temperatures

The vibrational spectroscopy of the water dimer provides an understanding of basic hydrogen bonding in water clusters, and with about one water dimer for every 1,000 water molecules, it plays a critical role in atmospheric science. Here, we review how the experimental and theoretical progress of the past decades has improved our understanding of water dimer vibrational spectroscopy under both cold and warm conditions. We focus on the intramolecular OH-stretching transitions of the donor unit, because these are the ones mostly affected by dimer formation and because their assignment has proven a challenge. We review cold experimental results from early matrix isolation to recent mass-selected jet expansion techniques and, in parallel, the improvements in the theoretical anharmonic models. We discuss and illustrate changes in the vibrational spectra of complexes upon increasing temperature, and the difficulties in recording and calculating these spectra. In the atmosphere, water dimer spectra at ambient temperature are crucial. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Exploring the anharmonic vibrational structure of carbon dioxide trimers

Our previously developed mbCO2 potential [O. Sode and J. N. Cherry, J. Comput. Chem. 38, 2763 (2017)] is used to describe the vibrational structure of the intermolecular motions of the CO₂ trimers: barrel-shaped and cyclic trimers. Anharmonic corrections are accounted for using the vibrational self-consistent field theory, vibrational second-order Møller-Plesset perturbation (VMP2) theory, and vibrational configuration interaction (VCI) methods and compared with experimental observations. For the cyclic structure, we revise the assignments of two previously observed experimental peaks based on our VCI and VMP2 results. We note that the experimental band observed near 13 cm^-1 is the out-of-phase out-of-plane degenerate motion with E″ symmetry, while the peak observed at 18 cm^-1 likely corresponds to the symmetric out-of-plane torsion A″ vibration. Since the VCI treatment of the vibrational motions accounts for vibrational mixing and delocalization, overtones and combination bands were also observed and quantified in the intermolecular regions of the two trimer isomers.

Graphical Transition Moment Decomposition and Conceptual Density Functional Theory Approaches to Study the Fundamental and Lower-Level Overtone Absorption Intensities of Some OH Stretching Vibrations

The investigation of electron density migrations caused by molecular structure changes is of central importance in various fields of chemistry. To address this topic in general and to study absorption intensities of vibrations, we analyze sensitive dipole moment functions (DMFs) of a molecule by combining the linear response function of conceptual DFT and bond dipoles separated by the quantum theory of atoms in molecules with a graphical transition moment decomposition scheme. The fundamental intensities of OH stretching vibrations depend strongly on the substituents but only weakly on the molecular conformations. Interestingly, in some alcohols, completely opposite trends have been observed for the lower-level overtone intensities: a weak substituent dependence but a stronger conformation dependence. It is well known that the formation of a hydrogen-bonded complex increases the OH stretching fundamental intensity, but less well known is the decrease in their overtone intensities. To investigate these characteristics comprehensively, we calculated their intensities (Δv = 1, 2, and 3) for conformers of ethanol and trifluoroethanol (TFE) and hydrogen-bonded phenol (PhOH) systems via the DFT method in the local mode model for the OH stretching coordinate ΔR. Their first and second derivatives of the electron density with respect to ΔR were calculated and interpreted using their bond moments. For ethanol and TFE, the OH, CC, and CH bond moments were found to make an important contribution to the molecular DMF derivatives parallel to the OH bond. The OH bond contributes only to the first derivative of DMF, and its conformational dependence is determined by the magnitude of the charge polarization of each structure. The electron density derivatives in the CC bond region were largely maintained during the internal rotation; thus, their conformation-dependent contributions were expressed by a geometrical factor of the CC bond direction. The CH bond at the antiperiplanar position of the OH bond was found to make a remarkably large contribution to the second derivative of DMF in the gauche conformer. The importance of electron density migration on substituents was also identified in the hydrogen-bonded phenol, in which the π-electron density change on the aromatic ring was clearly shown. This migration creates the DMF derivatives both perpendicular and parallel to the OH bond and strongly affects the absorption intensities. In all the cases, some bond moments on the substituents contribute to the first and second DMF derivatives in a structure-dependent manner, thus explaining their stereoelectronic effects.

Understanding the anharmonic vibrational structure of the carbon dioxide dimer

Understanding the vibrational structure of the CO₂ system is important to confirm the potential energy surface and interactions in such van der Waals complexes. In this work, we use our previously developed mbCO2 potential function to explore the vibrational structure of the CO₂ monomer and dimer. The potential function has been trained to reproduce the potential energies at the CCSD(T)-F12b/aug-cc-pVTZ level of electronic structure theory. The harmonic approximation, as well as anharmonic corrections using vibrational structure theories such as vibrational self-consistent field, vibrational second-order Møller-Plesset perturbation, and vibrational configuration interaction (VCI), is applied to address the vibrational motions. We compare the vibrational results using the mbCO2 potential function with traditional electronic structure theory results and to experimental frequencies. The anharmonic results for the monomer most closely match the experimental data to within 3 cm^-1, including the Fermi dyad frequencies. The intermolecular and intramolecular dimer frequencies were treated separately and show good agreement with the most recent theoretical and experimental results from the literature. The VCI treatment of the dimer vibrational motions accounts for vibrational mixing and delocalization, such that we observe the dimer Fermi resonance phenomena, both in the intramolecular and intermolecular regions.

The water dimer reaction OH + (H2O)2 → (H2O)-OH + H2O

The stationary points, including the entrance complex, transition states, and the exit complex, for the reaction OH + (H₂O)₂ → (H₂O)OH + H₂O have been carefully examined using the "gold standard" CCSD(T) method with the correlation-consistent basis sets up to cc-pVQZ. The complex (H₂O)₂OH is found to lie 10.8 kcal mol^-1 below the separated reactants. This complex should be observable in the gas phase via vibrational or microwave spectroscopy. Seven unique transition states were found. One pathway for the title reaction has no barrier, in which the OH radical captures a whole water molecule from the water dimer. For the hydrogen abstraction pathways the lowest classical barrier height is predicted to be 5.9 kcal mol^-1 (TS1) relative to separated reactants, and the other pathways are of higher barriers, i.e., 17.8 (TS2) and 18.4 (TS3) kcal mol^-1. The harmonic vibrational frequencies and the zero-point vibrational energies of the stationary points for the reaction are also reported.

On the benefits of localized modes in anharmonic vibrational calculations for small molecules

Anharmonic vibrational calculations can already be computationally demanding for relatively small molecules. The main bottlenecks lie in the construction of the potential energy surface and in the size of the excitation space in the vibrational configuration interaction (VCI) calculations. To address these challenges, we use localized-mode coordinates to construct potential energy surfaces and perform vibrational self-consistent field and L-VCI calculations [P. T. Panek and C. R. Jacob, ChemPhysChem 15, 3365 (2014)] for all vibrational modes of two prototypical test cases, the ethene and furan molecules. We find that the mutual coupling between modes is reduced when switching from normal-mode coordinates to localized-mode coordinates. When using such localized-mode coordinates, we observe a faster convergence of the n-mode expansion of the potential energy surface. This makes it possible to neglect higher-order contributions in the n-mode expansion of the potential energy surface or to approximate higher-order contributions in hybrid potential energy surfaces, which reduced the computational effort for the construction of the anharmonic potential energy surface significantly. Moreover, we find that when using localized-mode coordinates, the convergence with respect to the VCI excitation space proceeds more smoothly and that the error at low orders is reduced significantly. This makes it possible to devise low-cost models for obtaining a first approximation of anharmonic corrections. This demonstrates that the use of localized-mode coordinates can be beneficial already in anharmonic vibrational calculations of small molecules and provides a possible avenue for enabling such accurate calculations also for larger molecules.

Molecular orbital analysis of the hydrogen bonded water dimer

As an essential interaction in nature, hydrogen bonding plays a crucial role in many material formations and biological processes, requiring deeper understanding. Here, using density functional theory and post-Hartree-Fock methods, we reveal two hydrogen bonding molecular orbitals crossing the hydrogen-bond’s O and H atoms in the water dimer. Energy decomposition analysis also shows a non-negligible contribution of the induction term. Our finding sheds light on the essential understanding of hydrogen bonding in ice, liquid water, functional materials and biological systems.

Infrared spectroscopic probing of dimethylamine clusters in an Ar matrix

Amines have many atmospheric sources and their clusters play an important role in aerosol nucleation processes. Clusters of a typical amine, dimethylamine (DMA), of different sizes were measured with matrix isolation IR (infrared) and NIR (near infrared) spectroscopy. The NIR vibrations are more separated and therefore it is easier to distinguish different sizes of clusters in this region. The DMA clusters, up to DMA tetramer, have been optimized using density functional methods, and the geometries, binding energies and thermodynamic properties of DMA clusters were obtained. The computed frequencies and intensities of NH-stretching vibrations in the DMA clusters were used to interpret the experimental spectra. We have identified the fundamental transitions of the bonded NH-stretching vibration and the first overtone transitions of the bonded and free NH-stretching vibration in the DMA clusters. Based on the changes in vibrational intensities during the annealing processes, the growth of clusters was clearly observed. The results of annealing processes indicate that DMA molecules tend to form larger clusters with lower energies under matrix temperatures, which is also supported by the calculated reaction energies of cluster formation.

Absorption intensity changes and frequency shifts of fundamental and first overtone bands for OH stretching vibration of methanol upon methanol–pyridine complex formation in CCl4: analysis by NIR/IR spectroscopy and DFT calculations

The first overtone of the OH stretching mode of the OH–N hydrogen bond of the methanol–pyridine complex was observed.

Combined IR/NIR and density functional theory calculations analysis of the solvent effects on frequencies and intensities of the fundamental and overtones of the C ═ O stretching vibrations of acetone and 2-hexanone

Vibrational overtone studies primarily focus on X-H stretching overtone transitions, where X is an atom like C, O, N, or S. In contrast, the studies on the C ═ O stretching overtones are very scattered. To advance the research in this field, we measured the fundamental, first, and second overtones of the C ═ O stretching vibration of acetone and 2-hexanone in n-hexane, CCl4, and CHCl3, as well as in the vapor phase using FT-IR/FT-NIR spectroscopy. Density functional theory (DFT) calculations have also been performed to help the assignment of the C ═ O stretching bands and to guide interpretation of the experimental results. It was found that the wavenumbers, absorption intensities, and oscillator strengths of the C ═ O stretching bands show marked solvent dependence. In the fundamental and the first overtone regions, the intensities of the C ═ O stretching vibration were found to be pronouncedly more intense than those of the C-H stretching vibration. In the second overtone region, the intensities of the C-H stretching vibration are comparable to those of the C ═ O stretching vibration. The theoretical and observed decrease in integrated intensity upon going from the fundamental to the first overtone of the C ═ O stretching vibration is around 50, which is significantly larger than those of the O-H, C-H, and S-H stretching vibration. Both the calculated and experimental results suggest that excessive weakness in the C ═ O stretching overtone was shown to be a result of both a low anharmonicity and a substantial reduction in the oscillator strength. These results provide new insight into our understanding of the C ═ O stretching vibration.

Fundamental and overtone vibrational spectroscopy, enthalpy of hydrogen bond formation and equilibrium constant determination of the methanol-dimethylamine complex

We have measured gas phase vibrational spectra of the bimolecular complex formed between methanol (MeOH) and dimethylamine (DMA) up to about 9800 cm(-1). In addition to the strong fundamental OH-stretching transition we have also detected the weak second overtone NH-stretching transition. The spectra of the complex are obtained by spectral subtraction of the monomer spectra from spectra recorded for the mixture. For comparison, we also measured the fundamental OH-stretching transition in the bimolecular complex between MeOH and trimethylamine (TMA). The enthalpies of hydrogen bond formation (ΔH) for the MeOH-DMA and MeOH-TMA complexes have been determined by measurements of the fundamental OH-stretching transition in the temperature range from 298 to 358 K. The enthalpy of formation is found to be -35.8 ± 3.9 and -38.2 ± 3.3 kJ mol(-1) for MeOH-DMA and MeOH-TMA, respectively, in the 298 to 358 K region. The equilibrium constant (Kp) for the formation of the MeOH-DMA complex has been determined from the measured and calculated transition intensities of the OH-stretching fundamental transition and the NH-stretching second overtone transition. The transition intensities were calculated using an anharmonic oscillator local mode model with dipole moment and potential energy curves calculated using explicitly correlated coupled cluster methods. The equilibrium constant for formation of the MeOH-DMA complex was determined to be 0.2 ± 0.1 atm(-1), corresponding to a ΔG value of about 4.0 kJ mol(-1).

Identification of the dimethylamine-trimethylamine complex in the gas phase

We have identified the dimethylamine-trimethylamine complex (DMA-TMA) at room temperature in the gas phase. The Fourier transform infrared (FTIR) spectrum of DMA-TMA in the NH-stretching fundamental region was obtained by spectral subtraction of spectra of each monomer. Explicitly correlated coupled cluster calculations were used to determine the minimum energy structure and interaction energy of DMA-TMA. Frequencies and intensities of NH-stretching transitions were also calculated at this level of theory with an anharmonic oscillator local mode model. The fundamental NH-stretching intensity in DMA-TMA is calculated to be approximately 700 times larger than that of the DMA monomer. The measured and calculated intensity is used to determine a room temperature equilibrium constant of DMA-TMA of 1.7 × 10(-3) atm(-1) at 298 K.

An adiabatic model for calculating overtone spectra of dimers such as (H(2)O)(2)

The near-infrared and visible wavelength spectrum of the water dimer is considered to be the major contributor to the so-called water continuum at these wavelengths. However, theoretical models of this spectrum require the simultaneous treatment of both monomer and dimer excitations. A model for treating this problem is proposed which is based upon a Franck-Condon-like separation between the monomer and dimer vibrational motions. In this model, one of the monomers is treated as the chromophore and its absorption is assumed to be given by its, possibly perturbed, vibrational band intensity. The main computational issue is the treatment of separate monomer and dimer motions. Various approaches for obtaining dimer vibration-rotation tunnelling spectra that allow for monomer motion are explored. These approaches include ways of treating the adiabatic separation of dimer vibrational modes from monomer vibrational modes. We classify the adiabatic separation methods under four main approaches: namely fixed-geometry, free-monomer, perturbed-monomer and coupled-monomer methods. The latter being the most computationally expensive as the monomer wave functions are dependent on the dimer coordinates. For each of these approaches, expectation values over the full potential are calculated for the given monomer vibrational wave functions. Various full (named VAP 2pD in the text) and partial (VAP (+p)D) averaging techniques are outlined to calculate the vibrationally averaged, monomer state-dependent, dimer interaction potentials. The computational costs associated with application of these techniques to the water dimer are estimated and the prospects for full calculations based on this approach are assessed.

Computational high-frequency overtone spectra of the water-ammonia complex

We have computed vibrational high-frequency overtone spectra of the water-ammonia complex, H(2)O-NH(3), and its isotopomers. The complex has been modeled as two independently vibrating monomer units. The internal coordinate Hamiltonians for each monomer unit have been constructed using exact gas phase kinetic energy operators. The potential energy and dipole moment surfaces have been calculated with the explicitly correlated coupled cluster method CCSD(T)-F12A and the valence triple-ζ VTZ-F12 basis around the equilibrium geometry of the complex. The vibrational eigenvalues have been calculated variationally and the eigenfunctions obtained have been used to compute the intensities of the absorption transitions. In H(2)O-NH(3), the water molecule acts as the proton donor and its symmetry is broken. The hydrogen-bonded OH bond oscillator undergoes a large redshift and intensity enhancement compared to the free hydrogen bond. Broken degeneracy of the asymmetric vibrations, quenched inversion splittings, and blueshift of the symmetric bending mode are the most visible changes in the ammonia unit.

On the cluster composition of supercritical water combining molecular modeling and vibrational spectroscopic data

The present study is aimed at a detailed analysis of supercritical water structure based on the combination of experimental vibrational spectra as well as molecular modeling calculations of isolated water clusters. We propose an equilibrium cluster composition model where supercritical water is considered as an ideal mixture of small water clusters (n=1-3) at the chemical equilibrium and the vibrational spectra are expected to result from the superposition of the spectra of the individual clusters, Thus, it was possible to extract from the decomposition of the midinfrared spectra the evolution of the partition of clusters in supercritical water as a function of density. The cluster composition predicted by this model was found to be quantitatively consistent with the near infrared and Raman spectra of supercritical water analyzed using the same procedure. We emphasize that such methodology could be applied to determine the portion of cluster in water in a wider thermodynamic range as well as in more complex aqueous supercritical solutions.