Full Dimensional Quantum Calculations of Vibrational Energies of H5O2+

Single-crystal superprotonic conductivity in an interpenetrated hydrogen-bonded quadruplex framework

A proton-transporting pathway is crucial to the conduction mechanism in fuel cells and biological systems. Here, we report a novel 5-fold interpenetrated three-dimensional (3D) hydrogen-bonded quadruplex framework, which exhibits an ultrahigh single-crystal proton conductivity of 1.2(1) × 10^-2 S cm^-1 at 95 °C and 98% relative humidity, benefitting from the spiral H₃O⁺/H₂O chains in 1D pore channels studded with COOH/COO^- groups.

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.

Analysis of the Proton Transfer Bands in the Infrared Spectra of Linear N2H+···OC and N2D+···OC Complexes Using Electric Field-Driven Classical Trajectories

In this work, we describe ab initio calculations and assignment of infrared (IR) spectra of hydrogen-bonded ion-molecular complexes that involve a fluxional proton: the linear N₂H⁺···OC and N₂D⁺···OC complexes. Given the challenges of describing fluxional proton dynamics and especially its IR activity, we use electric field-driven classical trajectories, i.e., the driven molecular dynamics (DMD) method that was developed by us in recent years and for similar applications, in conjunction with high-level electronic structure theory. Namely, we present a modified and a numerically efficient implementation of DMD specifically for direct (or "on the fly") calculations, which we carry out at the MP2-F12/AVDZ level of theory for the potential energy surface (PES) and MP2/AVDZ for the dipole moment surfaces (DMSs). Detailed analysis of the PES, DMS, and the time-dependence of the first derivative of the DMS, referred to as the driving force, for the highly fluxional vibrations involving H⁺/D⁺ revealed that the strongly non-harmonic PES and non-linear DMS yield remarkably complex vibrational spectra. Interestingly, the classical trajectories reveal a doublet in the proton transfer part of the spectrum with the two peaks at 1800 and 1980 cm^-1. We find that their shared intensity is due to a Fermi-like resonance interaction, within the classical limit, of the H⁺ parallel stretch fundamental and an H⁺ perpendicular bending overtone. This doublet is also observed in the deuterated species at 1360 and 1460 cm^-1.

Communication: Trapping a proton in argon: Spectroscopy and theory of the proton-bound argon dimer and its solvation

Ion-molecule complexes of the form H⁺Ar_n are produced in pulsed-discharge supersonic expansions containing hydrogen and argon. These ions are analyzed and mass-selected in a reflectron spectrometer and studied with infrared laser photodissociation spectroscopy. Infrared spectra for the n = 3-7 complexes are characterized by a series of strong bands in the 900-2200 cm^-1 region. Computational studies at the MP2/aug-cc-pVTZ level examine the structures, binding energies, and infrared spectra for these systems. The core ion responsible for the infrared bands is the proton-bound argon dimer, Ar-H⁺-Ar, which is progressively solvated by the excess argon. Anharmonic vibrational theory is able to reproduce the vibrational structure, identifying it as arising from the asymmetric proton stretch in combination with multiple quanta of the symmetric argon stretch. Successive addition of argon shifts the proton vibration to lower frequencies, as the charge is delocalized over more ligands. The Ar-H⁺-Ar core ion has a first solvation sphere of five argons.

MP4 Study of the Anharmonic Coupling of the Shared Proton Stretching Vibration of the Protonated Water Dimer in Equilibrium and Transition States

The structure and harmonic and anharmonic IR spectra of the protonated water dimer (PWD) were calculated in C₁, C₂, and C_s symmetry at the MP4/acc-pVTZ level of theory. We found that structure and IR spectra are practically identical in C₂ and C₁ symmetry, demonstrating that an equilibrium C₁ configuration of the PWD is not realized. Anharmonic coupling of the shared proton stretching vibration with all other modes in the PWD in C₂ and C_s symmetry was the focus of this investigation. For this purpose, 28 two-dimensional potential energy surfaces (2D PES) were built at the MP4/acc-pVTZ level of theory and the corresponding vibrational Schrödinger equations were solved using the DVR method. Differences in the coupling of the investigated mode with other modes in the C₂ and C_s configurations, along with some factors that determine the red- or blue-shift of the stretching vibration frequency, were analyzed. We obtained a rather reasonable value of the stretching frequency of the bridging proton (1058.4 cm^-1) unperturbed by Fermi resonance. The Fermi resonance between the fundamental vibration ν₇ and the combined vibration ν₂ + ν₆ of the same symmetry was analyzed through anharmonic second-order perturbation theory calculations, as well as by 3D PES constructed using Q₂, Q₆, and Q₇ as normal coordinates. A significant (up to 50%) transfer of intensity from the fundamental vibration to the combined one was found. We have estimated the frequency of the bridging proton stretching vibration in the C_s configuration of the PWD based on calculations of the intrinsic anharmonicity and anharmonic double modes interactions at the MP4/acc-pVTZ level of theory (1261 cm^-1).

Driven molecular dynamics studies of the shared proton motion in the H5O2+·Ar cluster: the effect of argon tagging and deuteration on vibrational spectra

We report IR spectra of H5O2(+) and H5O2(+)·Ar and their deuterium isotopologues using ab initio molecular dynamics. The trajectories were propagated as microcanonical (NVE) ensembles at energies corresponding to temperatures 50 and 100 K. The potential energy surface is calculated on-the-fly at the MP2/aug-cc-pVDZ level of theory. The calculations show that adding an argon atom to H5O2(+) introduces symmetry breaking in the Zundel core ion, causes blueshift in the shared proton vibration by about 200 cm(-1), and leads to the splitting of the OH stretch vibrations into four bands. Driven molecular dynamics (DMD) method is used to assign the spectrum by coupling the dipole moment to an external electric field oscillating at frequency ω. The broad feature at 1100 cm(-1) in the H5O2(+)·Ar spectrum is ascribed to the large amplitude shared proton vibration coupled with torsion and wag modes. MD MP2 simulations predict the H/D redshift in the shared proton vibration and water bending vibration to be about 280 and 460 cm(-1), respectively, in good agreement with experimental observations.

Apparent stoichiometry of water in proton hydration and proton dehydration reactions in CH3CN/H2O solutions

Gradual solvation of protons by water is observed in liquids by mixing strong mineral acids with various amounts of water in acetonitrile solutions, a process which promotes rapid dissociation of the acids in these solutions. The stoichiometry of the reaction XH(+) + n(H(2)O) = X + (H(2)O)(n)H(+) was studied for strong mineral acids (negatively charged X, X = ClO(4)¯, Cl¯, Br¯, I¯, CF(3)SO(3)¯) and for strong cationic acids (uncharged X, X = R*NH(2), H(2)O). We have found by direct quantitative analysis preference of n = 2 over n = 1 for both groups of proton transfer reactions at relatively low water concentrations in acetonitrile. At high water concentrations, we have found that larger water solvates must also be involved in the solvation of the proton while the spectral features already observed for n = 2, H(+)(H(2)O)(2), remain almost unchanged at large n values up to at least 10 M of water.

Pseudo-Jahn-Teller origin of the low barrier hydrogen bond in N(2)H(7) (+)

The microscopic origin and quantum effects of the low barrier hydrogen bond (LBHB) in the proton-bound ammonia dimer cation N(2)H(7) (+) were studied by means of ab initio and density-functional theory (DFT) methods. These results were analyzed in the framework of vibronic theory and compared to those obtained for the Zundel cation H(5)O(2) (+). All geometry optimizations carried out using wavefunction-based methods [Hartree-Fock, second and fourth order Moller-Plesset theory (MP2 and MP4), and quadratic configuration interaction with singles and doubles excitations (QCISD)] lead to an asymmetrical H(3)N-H(+)cdots, three dots, centeredNH(3) conformation (C(3v) symmetry) with a small energy barrier (1.26 kcalmol in MP4 and QCISD calculations) between both equivalent minima. The value of this barrier is underestimated in DFT calculations particularly at the local density approximation level where geometry optimization leads to a symmetric H(3)Ncdots, three dots, centeredH(+)cdots, three dots, centeredNH(3) structure (D(3d) point group). The instability of the symmetric D(3d) structure is shown to originate from the pseudo-Jahn-Teller mixing of the electronic (1)A(1g) ground state with five low lying excited states of A(2u) symmetry through the asymmetric alpha(2u) vibrational mode. A molecular orbital study of the pseudo-Jahn-Teller coupling has allowed us to discuss the origin of the proton displacement and the LBHB formation in terms of the polarization of the NH(3) molecules and the transfer of electronic charge between the proton and the NH(3) units (rebonding). The parallel study of the H(5)O(2) (+) cation, which presents a symmetric single-well structure, allows us to analyze why these similar molecules behave differently with respect to proton transfer. From the vibronic analysis, a unified view of the Rudle-Pimentel three-center four-electron and charge transfer models of LBHBs is given. Finally, the large difference in the N-N distance in the D(3d) and C(3v) configurations of N(2)H(7) (+) indicates a large anharmonic coupling between alpha(2u)-alpha(1g) modes along the proton-transfer dynamics. This issue was explored by solving numerically the vibrational Schrodinger equation corresponding to the bidimensional E[Q(alpha(2u)),Q(alpha(1g))] energy surface calculated at the MP46-311++G(**) level of theory.

Eigen and Zundel Forms of Small Protonated Water Clusters: Structures and Infrared Spectra

The spectral properties of protonated water clusters, especially the difference between Eigen (H3O+) and Zundel (H5O2+) conformers and the difference between their unhydrated and dominant hydrated forms are investigated with the first principles molecular dynamics simulations as well as with the high level ab initio calculations. The vibrational modes of the excess proton in H3O+ are sensitive to the hydration, while those in H5O2+ are sensitive to the messenger atom such as Ar (which was assumed to be weakly bound to the water cluster during acquisitions of experimental spectra). The spectral feature around approximately 2700 cm-1 (experimental value: 2665 cm-1) for the Eigen moiety appears when H3O+ is hydrated. This feature corresponds to the hydrating water interacting with H3O+, so it cannot appear in the Eigen core. Thus, H3O+ alone would be somewhat different from the Eigen forms in water. For the Zundel form (in particular, H5O2+), there have been some differences in spectral features among different experiments as well as between experiments and theory. When an Ar messenger atom is introduced at a specific temperature corresponding to the experimental condition, the calculated vibrational spectra for H5O2+.Ar are in good agreement with the experimental infrared spectra showing the characteristic Zundel frequency at approximately 1770 cm-1. Thus, the effect of hydration, messenger atom Ar, and temperature are crucial to elucidating the nature of vibrational spectra of Eigen and Zundel forms and to assigning the vibrational modes of small protonated water clusters.

Infrared studies of ionic clusters: The influence of Yuan T. Lee

Beginning in the mid-1980s, a number of innovative experimental studies on ionic clusters emerged from the laboratory of Yuan T. Lee combining infrared laser spectroscopy and tandem mass spectrometry. Coupled with modern electronic structure calculations, this research explored many facets of ionic clusters including solvation, structure, and dynamics. These efforts spawned a resurgence in gas-phase cluster spectroscopy. This paper will focus on the major areas of research initiated by the Lee group and how these studies stimulated and influenced others in what is currently a vibrant and growing field.

Including quantum subsystem character within classical equilibrium simulations

A mixed quantum/classical density matrix approximation is derived. The density matrix makes use of quantum subsystem vibrational wave functions. The diagonal of the density matrix can be used as an equilibrium distribution in Monte Carlo simulations. The approximate distribution compares well with the path integral distribution for a model system. Since it includes quantum subsystem information, it performs much better than the quadratic Feynman-Hibbs distribution. These types of distributions can aid in including quantum vibrational information in otherwise classical simulations.

Vibrational Analysis of the H5O2+ Infrared Spectrum Using Molecular and Driven Molecular Dynamics

Standard molecular and driven molecular dynamics are used to analyze prominent spectral features in the H5O2+ infrared spectrum. In the driven method, the molecular Hamiltonian is augmented with a time-dependent term, mu x epsilon(0) sin(omegat), where mu is the dipole moment of H5O2+, epsilon0 is the electric field, and omega is the frequency. The magnitude of the electric field determines whether the driving is mild (the harmonic limit) or strong (anharmonic motion and mode coupling). We analyze the spectrum in the wavenumber range from 600 to 1900 cm(-1), where recent experimental measurements are available for H5O2+. On the basis of the simulations, we have assigned the broad feature around 1000 cm(-1) to the proton transfer coupled with the torsion motion. Intense absorption near 1780 cm(-1) is assigned to the H2O monomer bend coupled with proton transfer.

Mid-infrared characterization of the NH4+∙(H2O)n clusters in the neighborhood of the n=20 “magic” number

Vibrational predissociation spectra are reported for size-selected NH4+ (H2O)n clusters (n=5-22) in the 2500-3900 cm(-1) region. We concentrate on the sharp free OH stretching bands to deduce the local H-bonding configurations of water molecules on the cluster surface. As in the spectra of the protonated water clusters, the free OH bands in NH4+ (H2O)n evolve from a quartet at small sizes (n<7), to a doublet around n=9, and then to a single peak at the n=20 magic number cluster, before the doublet re-emerges at larger sizes. This spectral simplification at the magic number cluster mirrors that found earlier in the H+(H2O)n clusters. We characterize the likely structures at play for the n=19 and 20 clusters with electronic structure calculations. The most stable form of the n=20 cluster is predicted to have a surface-solvated NH4+ ion that lies considerably lower in energy than isomers with the NH4+ in the interior.

Quantum studies of the vibrations in H3O2− and D3O2−

The vibrations of H3O2- and D3O2- are investigated using diffusion Monte Carlo (DMC) and vibrational configuration-interaction approaches, as implemented in the program MULTIMODE. These studies use the potential surface recently developed by Huang et al. [ J. Am. Chem. Soc. 126, 5042 (2004)]. The focus of this work is on the vibrational ground state and fundamentals which occur between 100 and 3700 cm(-1). In most cases, excellent agreement is obtained between the fundamental frequencies calculated by the two approaches. This serves to demonstrate the power of both methods for treating this very anharmonic system. Based on the results of the MULTIMODE and DMC treatments, the extent and nature of the couplings in H3O2- and D3O2- are investigated.

Full-dimensional vibrational calculations for H5O2+ using an ab initio potential energy surface

We report quantum diffusion Monte Carlo (DMC) and variational calculations in full dimensionality for selected vibrational states of H(5)O(2) (+) using a new ab initio potential energy surface [X. Huang, B. Braams, and J. M. Bowman, J. Chem. Phys. 122, 044308 (2005)]. The energy and properties of the zero-point state are focused on in the rigorous DMC calculations. OH-stretch fundamentals are also calculated using "fixed-node" DMC calculations and variationally using two versions of the code MULTIMODE. These results are compared with infrared multiphoton dissociation measurements of Yeh et al. [L. I. Yeh, M. Okumura, J. D. Myers, J. M. Price, and Y. T. Lee, J. Chem. Phys. 91, 7319 (1989)]. Some preliminary results for the energies of several modes of the shared hydrogen are also reported.

Ab initio potential energy and dipole moment surfaces for H5O2+

Full-dimensional ab initio potential energy surface (PES) and dipole moment surface (DMS) are reported for H(5)O(2) (+). Tens of thousands of coupled-cluster [CCSD(T)] and second-order Moller-Plesset (MP2) calculations of electronic energies, using aug-cc-pVTZ basis, were done. The energies were fit very precisely in terms of all the internuclear distances, using standard least-square procedures, however, with a fitting basis that satisfies permutational symmetry with respect to like atoms. The H(5)O(2) (+) PES is a fit to 48 189 CCSD(T) energies, containing 7962 polynomial coefficients. The PES has a rms fitting error of 34.9 cm(-1) for the entire data set up to 110 000 cm(-1). This surface can describe various internal floppy motions, including the H atom exchanges, monomer inversions, and monomer torsions. First- and higher-order saddle points have been located on the surface and compared with available previous theoretical work. In addition, the PES dissociates correctly (and symmetrically) to H(2)O+H(3)O(+), with D(e)=11 923.8 cm(-1). Geometrical and vibrational properties of the monomer fragments are presented. The corresponding global DMS fit (MP2 based) involves 3844 polynomial coefficients and also dissociates correctly.

Infrared spectra of homogeneous and heterogeneous proton-bound dimers in the gas phase

Infrared multiphoton dissociation spectra of three homogeneous and two heterogeneous proton-bound dimers were recorded in the gas phase. Comparison of the experimental infrared spectra recorded in the fingerprint region of the proton-bound dimers with spectra predicted by electronic structure calculations shows that all modes which are observed contain motion of the proton oscillating between the two monomers. The O-H-O asymmetric stretch for the homogeneous dimers is shown to occur at around 800 cm-1. As expected, the O-H-O asymmetric stretching modes for the heterogeneous proton-bound dimers are observed to shift to significantly higher energy with respect to those for the homogeneous proton-bound dimers due to the asymmetry of the O-H-O moeity. This shift is shown to be predictable from the difference in proton affinities between the two monomers. Density functional predictions of the infrared spectra based on the harmonic oscillator model are demonstrated to predict the observed spectra of the homogeneous proton-bound dimers with reasonable accuracy. Calculations of the structure and infrared spectrum of protonated diglyme at the B3LYP/6-31+G** level and basis also agree well with an infrared spectrum recorded previously. For both heterogeneous proton-bound dimers, however, the predicted spectra are blue-shifted with respect to experiment.

A reduced dimensionality quasiclassical and quantum study of the proton transfer reaction H3O++H2O→H2O+H3O+

We report quantum and quasiclassical calculations of proton transfer in the reaction H(3)O(+)+H(2)O in three degrees of freedom, the two OH(+) bond lengths and the OH(+)O angle. The reduced dimensional potential energy surface is obtained from the full dimensional OSS3(p) energy function of H(5)O(2) (+) [L. Ojamae, I. Shavitt, and S. J. Singer, J. Chem. Phys. 109, 5547 (1998)], with an additional long-range correction to reproduce the correct ion-molecule interaction. This surface is used to perform both quasiclassical trajectory and quantum reactive scattering calculations of the zero total angular momentum cumulative reaction probability and cross sections for initial rotational states 0, 1, and 2. Comparison of these quantities are made to assess the importance of quantum effects in this reduced dimensional reaction. Additional quasiclassical cross sections are calculated to obtain the thermal rate constant for the reaction.