High-Level Quantum Calculations of the IR Spectra of the Eigen, Zundel, and Ring Isomers of H+(H2O)4 Find a Single Match to Experiment

Fully Quantum Simulation of Polaritonic Vibrational Spectra of Large Cavity-Molecule System

The formation of molecular vibrational polaritons, arising from the interplay between molecular vibrations and infrared cavity modes, is a quantum phenomenon necessitating accurate quantum dynamical simulations. Here, we introduce the cavity vibrational self-consistent field/virtual state configuration interaction method, enabling quantum simulation of the vibrational spectra of many-molecule systems within the optical cavity. Focusing on the representative (H2O)21 system, we showcase this parameter-free quantum approach's ability to capture both linear and nonlinear vibrational spectral features. Our findings highlight the growing prominence of molecular couplings among OH stretches and bending excited bands with increased light-matter interaction, revealing distinctive nonlinear spectral features induced by vibrational strong coupling.

Encoding a Many-Body Potential Energy Surface into a Grid-Based Matrix Product Operator

An efficient algorithm for compressing a given many-body potential energy surface (PES) of molecular systems into a grid-based matrix product operator (MPO) is proposed. The PES is once represented by a full-dimensional or truncated many-body expansion form, which is obtained by ab initio calculations at each grid mesh point, and then all terms in the expansion are compressed and merged into a single MPO while maintaining the bond dimension of the MPO as small as possible. It was shown that the ab initio PES of the H2CO was compressed by more than 2 orders of magnitude in the size of the site operators without loss of accuracy. By the use of grid basis, the tensor rank of the site operators of the MPO is reduced from four to three due to the diagonal nature of the position-dependent operators on grid basis, which significantly reduces the computational cost of the tensor contractions required in the real and imaginary time evolution of the matrix product state (MPS) wave functions with the grid-based MPO (Grid-MPO) Hamiltonian. Similar to other grid-based methods, Grid-MPO is easily applicable to any kinds of potentials of molecular systems, such as analytical empirical model potentials expressed by position operators and ab initio potentials, if the values at the grid points are available. Using the Grid-MPO combined with the MPS, we calculated the time correlation function of the Eigen cation H 3 O + ( H 2 O ) 3 to predict the infrared spectrum and compared with the experimental and the previous theoretical studies. The actual scaling with the size of systems was examined for the multidimensional Henon-Heiles Hamiltonian. It was shown that the method is considerably accelerated by the graphic processing unit (GPU) because the sizes of site operators were kept small and all tensors were able to be stored on the VRAM of a GPU.

Near-infrared spectroscopy of H3O+⋯Xn (X = Ar, N2, and CO, n = 1-3)

Near-infrared (NIR) spectra of H3O+⋯Xn (X = Ar, N2, and CO, n = 1-3) in the first overtone region of OH-stretching vibrations (4800-7000 cm-1) were measured. Not only OH-stretching overtones but also several combination bands are major features in this region, and assignments of these observed bands are not obvious at a glance. High-precision anharmonic vibrational simulations based on the discrete variable representation approach were performed. The simulated spectra show good agreement with the observed ones and provide firm assignments of the observed bands, except in the case of X = CO, in which higher order vibrational mode couplings seem significant. This agreement demonstrates that the present system can be a benchmark for high precision anharmonic vibrational computations of NIR spectra. Band broadening in the observed spectra becomes remarkable with an increase of the interaction with the solvent molecule (X). The origin of the band broadening is explored by rare gas tagging experiments and anharmonic vibrational simulations of hot bands.

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.

Investigating Intramolecular H Atom Transfer Dynamics in β-Diketones with Ultrafast Infrared Spectroscopies and Theoretical Modeling

The vibrational signatures and ultrafast dynamics of the intramolecular H-bond in a series of β-diketones are investigated with 2D IR spectroscopy and computational modeling. The chosen β-diketones exhibit a range of H atom donor-acceptor distances and asymmetry along the H atom transfer coordinate that tunes the intramolecular H-bond strength. The species with the strongest H-bonds are calculated to have very soft H atom potentials, resulting in highly red-shifted OH stretch fundamental frequencies and dislocation of the H atom upon vibrational excitation. These soft potentials lead to significant coupling to the other normal mode coordinates and give rise to the very broad vibrational signatures observed experimentally. The 2D IR spectra in both the OH and OD stretch regions of the light and deuterated isotopologues reveal broadened and long-lived ground-state bleach signatures of the vibrationally hot molecules. Polarization-sensitive transient absorption measurements in the OH and OD stretch regions reveal notable isotopic differences in orientational dynamics. Orientational relaxation was measured to occur on ∼600 fs and ∼2 ps time scales for the light and deuterated isotopologues, respectively. The orientational dynamics are interpreted in terms of activated H/D atom transfer events driven by collective intramolecular structural rearrangements.

The coupling of the hydrated proton to its first solvation shell

The Zundel (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H}_{5}{O}_{2}^{+}$$\end{document}H5O2+) and Eigen (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H}_{9}{O}_{4}^{+}$$\end{document}H9O4+) cations play an important role as intermediate structures for proton transfer processes in liquid water. In the gas phase they exhibit radically different infrared (IR) spectra. The question arises: is there a least common denominator structure that explains the IR spectra of both, the Zundel and Eigen cations, and hence of the solvated proton? Full dimensional quantum simulations of these protonated cations demonstrate that two dynamical water molecules and an excess proton constitute this fundamental subunit. Embedded in the static environment of the parent Eigen cation, this subunit reproduces the positions and broadenings of its main excess-proton bands. In isolation, its spectrum reverts to the well-known Zundel ion. Hence, the dynamics of this subunit polarized by an environment suffice to explain the spectral signatures and anharmonic couplings of the solvated proton in its first solvation shell.

The Zundel [H(H₂O)₂]⁺ and Eigen [H(H₂O)₄]⁺ cations exhibit radicallly different infrared spectra and are the limiting dynamical structures involved in proton mobility in liquid water. Here, the authors find through quantum dynamics simulations that two polarized water molecules and a proton suffice to explain the key spectroscopic features connected to proton mobility for both species.

Accurate diffusion coefficients of the excess proton and hydroxide in water via extensive ab initio simulations with different schemes

Despite its simple molecular formula, obtaining an accurate in silico description of water is far from straightforward. Many of its very peculiar properties are quite elusive, and in particular, obtaining good estimations of the diffusion coefficients of the solvated proton and hydroxide at a reasonable computational cost has been an unsolved challenge until now. Here, I present extensive results of several unusually long ab initio molecular dynamics (MD) simulations employing different combinations of the Born-Oppenheimer and second-generation Car-Parrinello MD propagation methods with different ensembles (NVE and NVT) and thermostats, which show that these methods together with the RPBE-D3 functional provide a very accurate estimation of the diffusion coefficients of the solvated H₃O⁺ and OH^- ions, together with an extremely accurate description of several properties of neutral water (such as the structure of the liquid and its diffusion and shear viscosity coefficients). In addition, I show that the estimations of D_H3O⁺ and D_OH^- depend dramatically on the simulation length, being necessary to reach timescales in the order of hundreds of picoseconds to obtain reliable results.

Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning─Quo Vadis?

Atomistic simulations using accurate energy functions can provide molecular-level insight into functional motions of molecules in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the infrared spectroscopy of molecules in solution. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose molecular simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.

Towards complete assignment of the infrared spectrum of the protonated water cluster H+(H2O)21

The spectroscopic features of protonated water species in dilute acid solutions have been long sought after for understanding the microscopic behavior of the proton in water with gas-phase water clusters H⁺(H₂O)_n extensively studied as bottom-up model systems. We present a new protocol for the calculation of the infrared (IR) spectra of complex systems, which combines the fragment-based Coupled Cluster method and anharmonic vibrational quasi-degenerate perturbation theory, and demonstrate its accuracy towards the complete and accurate assignment of the IR spectrum of the H⁺(H₂O)₂₁ cluster. The site-specific IR spectral signatures reveal two distinct structures for the internal and surface four-coordinated water molecules, which are ice-like and liquid-like, respectively. The effect of inter-molecular interaction between water molecules is addressed, and the vibrational resonance is found between the O-H stretching fundamental and the bending overtone of the nearest neighboring water molecule. The revelation of the spectral signature of the excess proton offers deeper insight into the nature of charge accommodation in the extended hydrogen-bonding network underpinning this aqueous cluster.

Protonated water species have been the subject of numerous experimental and computational studies. Here the authors provide a nearly complete assignment of the experimental IR spectrum of the H⁺(H₂O)₂₁ water cluster based on high-level wavefunction theory and anharmonic vibrational quasi-degenerate perturbation theory.

Coupled Local-Mode Approach for the Calculation of Vibrational Spectra: Application to Protonated Water Clusters

Spectroscopic studies of protonated water clusters (PWCs) have yielded enormous insights into the fundamental nature of the hydrated proton. Here, we introduce a new coupled local-mode (CLM) approach to calculate PWC OH stretch vibrational spectra. The CLM method combines a sampling of representative configurations from density functional theory (DFT)-based ab initio molecular dynamics (AIMD) simulations with DFT calculations of local-mode vibrational frequencies and couplings. Calculations of inhomogeneous OH stretch vibrational spectra for H⁺(H₂O)₄ and H⁺(H₂O)₂₁ agree well with experiment and higher-level calculations, and decompositions of the calculated spectra in terms of the coupled modes aids in the interpretation of the spectra. This observation is consistent with the idea that capturing anharmonicity and coupling is as important to accuracy as the underlying level of electronic structure theory. The CLM calculations can easily discern the configuration that dominates the experimental measurement for H⁺(H₂O)₅, which can adopt several low-energy conformations.

Comparative studies of IR spectra of deprotonated serine with classical and thermostated ring polymer molecular dynamics simulations

Here we report the vibrational spectra of deprotonated serine calculated from the classical molecular dynamics (MD) simulations and thermostated ring-polymer molecular dynamics (TRPMD) simulation with third-order density-functional tight-binding. In our earlier study [Inakollu and Yu, "A systematic benchmarking of computational vibrational spectroscopy with DFTB3: Normal mode analysis and fast Fourier transform dipole autocorrelation function," J. Comput. Chem. 39, 2067 (2018)] of deprotonated serine, we observed a significant difference in the vibrational spectra with the classical MD simulations compared to the infrared multiple photon dissociation spectra. It was postulated that this is due to neglecting the nuclear quantum effects (NQEs). In this work, NQEs are considered in spectral calculation using the TRPMD simulations. With the help of potential of mean force calculations, the conformational space of deprotonated serine is analyzed and used to understand the difference in the spectra of classical MD and TRPMD simulations at 298.15 and 100 K. The high-frequency vibrational bands in the spectra are characterized using Fourier transform localized vibrational mode (FT-ν_N AC) and interatomic distance histograms. At room temperature, the quantum effects are less significant, and the free energy profiles in the classical MD and the TRPMD simulations are very similar. However, the hydrogen bond between the hydroxyl-carboxyl bond is slightly stronger in TRPMD simulations. At 100 K, the quantum effects are more prominent, especially in the 2600-3600 cm^-1, and the free energy profile slightly differs between the classical MD and TRPMD simulations. Using the FT-ν_N AC and the interatomic distance histograms, the high-frequency vibrational bands are discussed in detail.

Using Diffusion Monte Carlo Wave Functions to Analyze the Vibrational Spectra of H7O3+ and H9O4. J Phys Chem A 2021;125:7185-7197. [PMID: 34433268 DOI: 10.1021/acs.jpca.1c05025]

An approach for evaluating spectra from ground state probability amplitudes (GSPA) obtained from diffusion Monte Carlo (DMC) simulations is extended to improve the description of excited state energies and allow for coupling among vibrational excited states. This approach is applied to studies of the protonated water trimer and tetramer, and their deuterated analogs. These ions provide models for solvated hydronium, and analysis of these spectra provides insights into spectral signatures of proton transfer in aqueous environments. In this approach, we obtain a separable set of internal coordinates from the DMC ground state probability amplitude. A basis is then developed from products of the DMC ground state wave function and low-order polynomials in these internal coordinates. This approach provides a compact basis in which the Hamiltonian and dipole moment matrix are evaluated and used to obtain the spectrum. The resulting spectra are in good agreement with experiment and in many cases provide comparable agreement to the results obtained using much larger basis sets. In addition, the compact basis allows for interpretation of the spectral features and how they evolve with cluster size and deuteration.

Electron binding energies and Dyson orbitals of OnH2n+1 +,0,- clusters: Double Rydberg anions, Rydberg radicals, and micro-solvated hydronium cations

Ab initio electron propagator methods are employed to predict the vertical electron attachment energies (VEAEs) of OH₃ ⁺(H₂O)_n clusters. The VEAEs decrease with increasing n, and the corresponding Dyson orbitals are diffused over exterior, non-hydrogen bonded protons. Clusters formed from OH₃ ^- double Rydberg anions (DRAs) and stabilized by hydrogen bonding or electrostatic interactions between ions and polar molecules are studied through calculations on OH₃ ^-(H₂O)_n complexes and are compared with more stable H^-(H₂O)_n+1 isomers. Remarkable changes in the geometry of the anionic hydronium-water clusters with respect to their cationic counterparts occur. Rydberg electrons in the uncharged and anionic clusters are held near the exterior protons of the water network. For all values of n, the anion-water complex H^-(H₂O)_n+1 is always the most stable, with large vertical electron detachment energies (VEDEs). OH₃ ^-(H₂O)_n DRA isomers have well separated VEDEs and may be visible in anion photoelectron spectra. Corresponding Dyson orbitals occupy regions beyond the peripheral O-H bonds and differ significantly from those obtained for the VEAEs of the cations.

Multicomponent Coupled Cluster Singles and Doubles with Density Fitting: Protonated Water Tetramers with Quantized Protons

Nuclear quantum effects such as zero-point energy are important for describing a wide range of chemical properties. The nuclear-electronic orbital (NEO) approach incorporates such effects into quantum chemistry calculations by treating specified nuclei, typically protons, quantum mechanically on the same level as electrons. Herein, both the traditional and t₁-transformed NEO coupled cluster with singles and doubles (NEO-CCSD) methods are implemented with a density fitting (DF) scheme for approximating the four-center two-particle integrals. The enhanced computational efficiency enables calculations on larger molecules with multiple quantum protons. The NEO-DF-CCSD method predicts proton affinities within chemical accuracy. Its application to protonated water tetramers with all nine protons treated quantum mechanically produces the qualitatively correct ordering of the isomer energies, which are strongly influenced by the zero-point energy contributions inherently included in NEO energy calculations. This work showcases the capabilities of the NEO-DF-CCSD method and provides the foundation for future developments and applications.

Molecular Characterization of the Surface Excess Charge Layer in Droplets

The surface excess charge layer (SECL) in droplets has often been associated with distinct chemistry. We examine the effect of the nature of ions in the composition and structure of SECL by using molecular dynamics. We find that in the presence of simple ions the thickness of SECL is invariant not only with respect to droplet size but also with respect to the nature of the ions. In the presence of simple ions, this layer has a thickness of ∼1.5-1.7 nm but in the presence of macroions it may extend to ∼2.0 nm. The proportion of ions contained in SECL depends on the nature of the ions and the droplet size. For the same droplet size, I^- and model H₃O⁺ ions show considerably higher concentration than Na⁺ and Cl^- ions. We identify the maximum ion concentration region, which, in nanodrops, may partially overlap with SECL. As the relative shape fluctuations decrease when microdrop size is approached, the overlap between SECL and maximum ion concentration region increases. We suggest the extension of the bilayer droplet structure assumed in the equilibrium partitioning model of Enke to include the maximum ion concentration region that may not coincide with SECL in nanodrops. We compute the ion concentrations in SECL, which are those that should enter the kinetic equation in the ion-evaporation mechanism, instead of the overall drop ion concentration that has been used.

Vibrational Coupling in Solvated H3O+: Interplay between Fermi Resonance and Combination Band

Complex vibrational features of solvated hydronium ion, H₃O⁺, in 3 μm enable us to look into the vibrational coupling among O-H stretching modes and other degrees of freedom. Two anharmonic coupling schemes have often been engaged to explain observed spectra: coupling with the OH bending overtone, known as Fermi resonance (FR), has been proposed to account for the splitting of the OH stretch band at ∼3300 cm^-1 in H₃O⁺···Ar₃, but an additional peak in H₃O⁺···(N₂)₃ at the similar frequency region has been assigned to a combination band (CB) with the low-frequency intermolecular stretches. While even stronger vibrational coupling is expected in H₃O⁺···(H₂O)₃, such pronounced peaks are absent. In the present study, vibrational spectra of H₃O⁺···Kr₃ and H₃O⁺···(CO)₃ are measured to complement the existing spectra. Using ab initio anharmonic algorithms, we are able to assign the observed complex spectral features, to resolve seemingly contradictory notions in the interpretations, and to reveal simple pictures of the interplay between FR and CB.

Decoding the 2D IR spectrum of the aqueous proton with high-level VSCF/VCI calculations

The aqueous proton is a common and long-studied species in chemistry, yet there is currently intense interest devoted to understanding its hydration structure and transport dynamics. Typically described in terms of two limiting structures observed in gas-phase clusters, the Zundel H₅O₂ ⁺ and Eigen H₉O₄ ⁺ ions, the aqueous structure is less clear due to the heterogeneity of hydrogen bonding environments and room-temperature structural fluctuations in water. The linear infrared (IR) spectrum, which reports on structural configurations, is challenging to interpret because it appears as a continuum of absorption, and the underlying vibrational modes are strongly anharmonically coupled to each other. Recent two-dimensional IR (2D IR) experiments presented strong evidence for asymmetric Zundel-like motifs in solution, but true structure-spectrum correlations are missing and complicated by the anharmonicity of the system. In this study, we employ high-level vibrational self-consistent field/virtual state configuration interaction calculations to demonstrate that the 2D IR spectrum reports on a broad distribution of geometric configurations of the aqueous proton. We find that the diagonal 2D IR spectrum around 1200 cm^-1 is dominated by the proton stretch vibrations of Zundel-like and intermediate geometries, broadened by the heterogeneity of aqueous configurations. There is a wide distribution of multidimensional potential shapes for the proton stretching vibration with varying degrees of potential asymmetry and confinement. Finally, we find specific cross peak patterns due to aqueous Zundel-like species. These studies provide clarity on highly debated spectral assignments and stringent spectroscopic benchmarks for future simulations.

Identifying Eigen-like hydrated protons at negatively charged interfaces

Despite the importance of the hydrogen ion in a wide range of biological, chemical, and physical processes, its molecular structure in solution remains lively debated. Progress has been primarily hampered by the extreme diffuse nature of the vibrational signatures of hydrated protons in bulk solution. Using the inherently surface-specific vibrational sum frequency spectroscopy technique, we show that at selected negatively charged interfaces, a resolved spectral feature directly linked to the H₃O⁺ core in an Eigen-like species can be readily identified in a biologically compatible pH range. Centered at ~2540 cm⁻¹, the band is seen to shift to ~1875 cm⁻¹ when forming D₃O⁺ upon isotopic substitution. The results offer the possibility of tracking and understanding from a molecular perspective the behavior of hydrated protons at charged interfaces.

Hydrated protons are always present in aqueous solution, but their molecular structure remains under debate. Here the authors use vibrational sum frequency spectroscopy to show that at negatively charged liquid–vapor interfaces, protons adopt a specific configuration characteristic of Eigen-like species.

Reduced rovibrational coupling Cartesian dynamics for semiclassical calculations: Application to the spectrum of the Zundel cation

We study the vibrational spectrum of the protonated water dimer, by means of a divide-and-conquer semiclassical initial value representation of the quantum propagator, as a first step in the study of larger protonated water clusters. We use the potential energy surface from the work of Huang et al. [J. Chem. Phys. 122, 044308 (2005)]. To tackle such an anharmonic and floppy molecule, we employ fully Cartesian dynamics and carefully reduce the coupling to global rotations in the definition of normal modes. We apply the time-averaging filter and obtain clean power spectra relative to suitable reference states that highlight the spectral peaks corresponding to the fundamental excitations of the system. Our trajectory-based approach allows for the physical interpretation of the very challenging proton transfer modes. We find that it is important, for such a floppy molecule, to selectively avoid initially exciting lower energy modes, in order to obtain cleaner spectra. The estimated vibrational energies display a mean absolute error (MAE) of ∼29 cm^-1 with respect to available multiconfiguration time-dependent Hartree calculations and MAE ∼ 14 cm^-1 when compared to the optically active experimental excitations of the Ne-tagged Zundel cation. The reasonable scaling in the number of trajectories for Monte Carlo convergence is promising for applications to higher dimensional protonated cluster systems.

High-Level VSCF/VCI Calculations Decode the Vibrational Spectrum of the Aqueous Proton

The hydrated excess proton is a common species in aqueous chemistry, which complexes with water in a variety of structures. The infrared spectrum of the aqueous proton is particularly sensitive to this array of structures, which manifests as continuous IR absorption from 1000 to 3000 cm^-1 known as the "proton continuum". Because of the extreme breadth of the continuum and strong anharmonicity of the involved vibrational modes, this spectrum has eluded straightforward interpretation and simulation. Using protonated water hexamer clusters from reactive molecular dynamics trajectories, and focusing on their central H⁺(H₂O)₂ structures' spectral contribution, we reproduce the linear IR spectrum of the aqueous proton with a high-level local monomer quantum method and highly accurate many-body potential energy surface. The accuracy of this approach is first verified in the vibrational spectra of the two isomers of the protonated water hexamer in the gas phase. We then apply this approach to 800 H⁺(H₂O)₆ clusters, also written as [H⁺(H₂O)₂](H₂O)₄, drawn from multistate empirical valence bond simulations of the bulk liquid to calculate the infrared spectrum of the aqueous proton complex. Incorporation of anharmonic effects to the vibrational potential and quantum mechanical treatment of the proton produces a better agreement to the infrared spectrum compared to that of the double-harmonic approximation. We assess the correlation of the proton stretching mode with different atomistic coordinates, finding the best correlation with ⟨R_OH⟩, the expectation value of the proton-oxygen distance R_OH. We also decompose the IR spectrum based on normal mode vibrations and ⟨R_OH⟩ to provide insight on how different frequency regions in the continuum report on different configurations, vibrational modes, and mode couplings.

Quantum approaches to vibrational dynamics and spectroscopy: is ease of interpretation sacrificed as rigor increases?

The subject of this Perspective is quantum approaches, beyond the harmonic approximation, to vibrational dynamics and IR spectroscopy.

Ultrafast dynamics of hydrated excess protons in CH3CN:H2O mixtures

In a combined experimental and theoretical 2D-IR and pump-probe study we determine how ultrafast solvent motions govern the vibrational dynamics of the hydrated proton and the key role played by the underlying proton potential.

Revisit the landscape of protonated water clusters H+(H2O)n with n = 10-17: An ab initio global search

Using a genetic algorithm incorporated with density functional theory, we explore the ground state structures of protonated water clusters H⁺(H₂O)_n with n = 10-17. Then we re-optimize the isomers at B97-D/aug-cc-pVDZ level of theory. The extra proton connects with a H₂O molecule to form a H₃O⁺ ion in all H⁺(H₂O)_10-17 clusters. The lowest-energy structures adopt a monocage form at n = 10-16 and core-shell structure at n = 17 based on the MP2/aug-cc-pVTZ//B97-D/aug-cc-pVDZ+ZPE single-point-energy calculation. Using second-order vibrational perturbation theory, we further calculate the infrared spectra with anharmonic correction for the ground state structures of H⁺(H₂O)_10-17 clusters at the PBE0/aug-cc-pVDZ level. The anharmonic correction to the spectra is crucial since it reproduces the experimental results quite well. The extra proton weakens the O-H bond strength in the H₃O⁺ ion since the Wiberg bond order of the O-H bond in the H₃O⁺ ion is smaller than that in H₂O molecules, which causes a red shift of the O-H stretching mode in the H₃O⁺ ion.

Deconstructing Prominent Bands in the Terahertz Spectra of H7O3+ and H9O4+: Intermolecular Modes in Eigen Clusters

We report experimental vibrational action spectra (210-2200 cm^-1) and calculated IR spectra, using recent ab initio potential energy and dipole moment surfaces, of H₇O₃⁺ and H₉O₄⁺. We focus on prominent far-IR bands, which postharmonic analyses show, arise from two types of intermolecular motions, i.e., hydrogen bond stretching and terminal water wagging modes, that are similar in both clusters. The good agreement between experiment and theory further validates the accuracy of the potential and dipole moment surfaces, which was used in a recent theoretical study that concluded that infrared photodissociation spectra of the cold clusters correspond to the Eigen isomer. The comparison between theory and experiment adds further confirmation of the need of postharmonic analysis for these clusters.

Anharmonic vibrational spectra from double incremental potential energy and dipole surfaces

Using incremental approaches, size limitations for property surface generations are pushed significantly, enabling accurate large molecule anharmonic vibrational spectra calculations.