Mid- and Far-IR Spectra of H5(+) and D5(+) Compared to the Predictions of Anharmonic Theory

Vibrational spectroscopy of Cu+(H2)4: about anharmonicity and fluxionality

The vibrational spectra of the copper(I) cation-dihydrogen complexes Cu⁺(H₂)₄, Cu⁺(D₂)₄ and Cu⁺(D₂)₃H₂ are studied using cryogenic ion trap vibrational spectroscopy in combination with quantum chemical calculations. The infrared photodissociation (IRPD) spectra (2500-7300 cm^-1) are assigned based on a comparison to IR spectra calculated using vibrational second-order perturbation theory (VPT2). The IRPD spectra exhibit ≈60 cm^-1 broad bands that lack rotational resolution, indicative of rather floppy complexes even at an ion trap temperature of 10 K. The observed vibrational features are assigned to the excitations of dihydrogen stretching fundamentals, combination bands of these fundamentals with low energy excitations as well as overtone excitations of a minimum-energy structure with C_s symmetry. The three distinct dihydrogen positions present in the structure can interconvert via pseudorotations with energy barriers less than 10 cm^-1, far below the zero-point vibrational energy. Ab initio Born-Oppenheimer molecular dynamics (BOMD) simulations confirm the fluxional behavior of these complexes and yield an upper limit for the timeframe of the pseudorotation on the order of 10 ps. For Cu⁺(D₂)₃H₂, the H₂ and D₂ loss channels yield different IRPD spectra indicating non-ergodic behavior.

Infrared spectroscopy of the protonated HCl dimer and trimer

The protonated HCl dimer and trimer complexes were prepared by pulsed discharges in supersonic expansions of helium or argon doped with HCl and hydrogen. The ions were mass selected in a reflectron time-of-flight spectrometer and investigated with photodissociation spectroscopy in the IR and near-IR regions. Anharmonic vibrational frequencies were computed with VPT2 at the MP2/cc-pVTZ level of theory. The Cl-H stretching fundamentals and overtones were measured in addition to stretch-torsion combinations. VPT2 theory at this level confirms the proton-bound structure of the dimer complex and provides a reasonably good description of the anharmonic vibrations in this system. The trimer has a HCl-HClH⁺-ClH structure in which a central chloronium ion is solvated by two HCl molecules via hydrogen bonding. VPT2 reproduces anharmonic frequencies for this system, including several combinations involving core ion Cl-H stretches, but fails to describe the relative band intensities.

Infrared spectroscopy and anharmonic theory of H3 +Ar2,3 complexes: The role of symmetry in solvation

The vibrational spectra of H₃ ⁺Ar_2,3 and D₃ ⁺Ar_2,3 are investigated in the 2000 cm^-1 to 4500 cm^-1 region through a combination of mass-selected infrared laser photodissociation spectroscopy and computational work including the effects of anharmonicity. In the reduced symmetry of the di-argon complex, vibrational activity is detected in the regions of both the symmetric and antisymmetric hydrogen stretching modes of H₃ ⁺. The tri-argon complex restores the D_3h symmetry of the H₃ ⁺ ion, with a concomitant reduction in the vibrational activity that is limited to the region of the antisymmetric stretch. Throughout these spectra, additional bands are detected beyond those predicted with harmonic vibrational theory. Anharmonic theory is able to reproduce some of the additional bands, with varying degrees of success.

The Role of Tunneling in the Spectra of H5+ and D5+ up to 7300 cm-1

The spectra for H₅⁺ and D₅⁺ are extended to cover the region between 4830 and 7300 cm^-1. These spectra are obtained using mass-selected photodissociation spectroscopy. To understand the nature of the states that are accessed by the transitions in this and prior studies, we develop a four-dimensional model Hamiltonian. This Hamiltonian is expressed in terms of the two outer H₂ stretches, the displacement of the shared proton from the center of mass of these two H₂ groups, and the distance between the H₂ groups. This choice is motivated by the large oscillator strength associated with the shared proton stretch and the fact that the spectral regions that have been probed correspond to zero, one, and two quanta of excitation in the H₂ stretches. This model is analyzed using an adiabatic separation of the H₂ stretches from the other two vibrations and includes the non-adiabatic couplings between H₂ stretch states with the same total number of quanta of excitation in the H₂ stretches. Based on the analysis of the energies and wave functions obtained from this model, we find that when there are one or more quanta of excitation in the H₂ stretches the states come in pairs that reflect tunneling doublets. The states accessed by the transitions in the spectrum with the largest intensity are assigned to the members of the doublets with requisite symmetry that are localized on the lowest-energy adiabat for a given level of H₂ excitation.

The smallest proton-bound dimer H5+: theoretical progress

The protonated hydrogen dimer, H5+, is the smallest system including proton transfer, and has been of long-standing interest since its first laboratory observation in 1962. H5+ and its isotopologues are the intermediate complexes in deuterium fractionation reactions, and are of central importance in molecular astrophysics. The recently recorded infrared spectra of both H5+ and D5+ reveal a rich vibrational dynamics of the cations, which presents a challenge for standard theoretical approaches. Although H5+ is a four-electron ion, which makes highly accurate electronic structure calculations tractable, the construction of ab initio-based potential energy and dipole moment surfaces has proved a hard task. In the same vein, the difficulties in treating the nuclear motion could also become cumbersome due to their high dimensionality, floppiness and/or symmetry. These systems are prototypical examples for studying large-amplitude motions, as they are highly delocalized, interconverting between equivalent minima through internal rotation and proton transfer motions requiring state-of-the-art treatments. Recent advances in the computational vibrational spectroscopy of the H5+ cation and its isotopologues are reported from full quantum spectral simulations, providing important information in a rigorous manner, and open perspectives for further future investigations. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.

A theoretical study on the infrared signatures of proton-bound rare gas dimers (Rg-H+-Rg), Rg = {Ne, Ar, Kr, and Xe}

The infrared spectrum of proton-bound rare gas dimers has been extensively studied via matrix isolation spectroscopy. However, little attention has been paid on their spectrum in the gas phase. Most of the Rg₂H⁺ has not been detected outside the matrix environment. Recently, Ar_nH⁺ (n = 3-7) has been first detected in the gas-phase [D. C. McDonald et al., J. Chem. Phys. 145, 231101 (2016)]. In that work, anharmonic theory can reproduce the observed vibrational structure. In this paper, we extend the existing theory to examine the vibrational signatures of Rg₂H⁺, Rg = {Ne, Ar, Kr, and Xe}. The successive binding of Rg to H⁺ was investigated through the calculation of stepwise formation energies. It was found that this binding is anti-cooperative. High-level full-dimensional potential energy surfaces at the CCSD(T)/aug-cc-pVQZ//MP2/aug-cc-pVQZ were constructed and used in the anharmonic calculation via discrete variable representation. We found that the potential coupling between the symmetric and asymmetric Rg-H⁺ stretch (ν₁ and ν₃ respectively) causes a series of bright n₁ν₁ + ν₃ progressions. From Ne₂H⁺ to Xe₂H⁺, an enhancement of intensities for these bands was observed.

Communication: Infrared photodissociation spectroscopy of the H6+ cation in the gas phase

The H₆⁺ cation was generated in a pulsed-discharge supersonic expansion of hydrogen and mass-selected in a time-of-flight spectrometer. Its vibrational spectrum was measured in the region of 2050-4550 cm^-1 using infrared photodissociation with a tunable OPO/OPA laser system. The H₆⁺ photodissociates, producing H₅⁺, H₄⁺, and H₃⁺ fragments; each of these fragment channels has a different spectrum. Computational studies identify two low-lying isomers described in previous work, whose energies were evaluated at the CCSD(T)/cc-pVTZ//MP2/cc-pVTZ level of theory. A D_2d species having an H₂⁺ cation bridging between two perpendicular H₂ molecules is the global minimum structure. A C_s structure with an H₃⁺ core ion bound to both H₂ and an H atom lies 4.0 kcal mol^-1 higher in energy. Anharmonic vibrational spectra were computed for each of these isomers with second-order vibrational perturbation theory (VPT2) in combination with density functional theory at the B2PLYP/cc-pVTZ level. The comparison between experimental and predicted spectra confirms the presence of both the D_2d and C_s structures and explains the spectra in different fragmentation channels. Although we find reasonable agreement between the experiment and the spectra predicted by VPT2 computations, a more sophisticated computational approach is needed to better understand this complex system.

Spectroscopy of Proton Coordination with Ethylenediamine

Protonated ethylenediamine monomer, dimer, and trimer were produced in the gas phase by an electrical discharge/supersonic expansion of argon seeded with ethylenediamine (C₂H₈N₂, en) vapor. Infrared spectra of these ions were measured in the region from 1000 to 4000 cm^-1 using laser photodissociation and argon tagging. Computations at the CBS-QB3 level were performed to explore possible isomers and understand the infrared spectra. The protonated monomer exhibits a gauche conformation and an intramolecular hydrogen bond. Its parallel shared proton vibration occurs as a broad band around 2785 cm^-1, despite the formally equivalent proton affinities of the two amino groups involved, which usually leads to low frequency bands. The barrier to intramolecular proton transfer is 2.2 kcal mol^-1 and does not vanish upon addition of the zero-point energy, unlike the related protonated ammonia dimer. The structure of the dimer is formed by chelation of the monomer's NH₃⁺ group, thereby localizing the excess proton and increasing the frequency of the intramolecular shared proton vibration to 3157 cm^-1. Other highly fluxional dimer structures with facile intermolecular proton transfer and concomitant structural reorganization were computed to lie within 2 kcal mol^-1 of the experimentally observed structure. The spectrum of the trimer is rather diffuse, and a clear assignment is not possible. However, an isomer with an intramolecular proton transfer like that of the monomer is most consistent with the experimental spectrum.

IR Spectroscopy of Protonated Acetylacetone and Its Water Clusters: Enol-Keto Tautomers and Ion→Solvent Proton Transfer

Protonated ions of acetylacetone, H⁺(Hacac), and their argon-tagged analogues are produced via a pulsed discharge and cooled in a supersonic expansion. These ions are mass analyzed, selected in a time-of-flight spectrometer, and studied with infrared laser photodissociation spectroscopy using the method of rare-gas atom tagging. Computational studies at the DFT/B3LYP level are employed to elucidate the structures and spectra of these ions, which are expected to exist as either enol- or keto-based tautomers. The protonated acetylacetone ion is found to form a single enol-based isomer. Adding one or two water molecules to this ion, for example, H⁺(Hacac)(H₂O)_1,2, produces primarily enol-based structures, although a small concentration of keto structures also contribute to the spectra. The vibrational patterns resulting from hydrogen bonding in these systems are not well-described by theory. Addition of a third water molecule to form the H⁺(Hacac)(H₂O)₃ ion causes a significant change in the spectroscopy, attributed to proton transfer from the H⁺(Hacac) ion into the water solvent.

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.

Mapping gas phase dipeptide motions in the far-infrared and terahertz domain

Vibrational signatures of Ac-Phe-AA-NH₂ dipeptides are recorded and analysed in the far IR/THz spectral domain (100–800 cm⁻¹, 3–24 THz), with the ‘AA’ amino acid chosen within the series ‘AA’ = Gly, Ala, Pro, Cys, Ser, Val. Phe stands for phenylalanine.

Probing the Relationship Between Large-Amplitude Motions in H5(+) and Proton Exchange Between H3(+) and H2

Understanding the spectroscopy and dynamics of H5(+) is central in gaining insights into the H3(+) + H2 → H5(+) → H2 + H3(+) proton transfer reaction. This molecular ion exhibits large-amplitude vibrations, which allow for the transfer of a proton between H3(+) and H2 even in its ground vibrational state. With vibrational excitation, the number of open channels for permutations of protons increase. In this work, the minimized energy path variant of diffusion Monte Carlo is used to investigate how the energetically accessible proton permutations evolve as H5(+) is dissociated into H3(+) + H2. Two mechanisms for proton permutation are investigated. The first is the proton hop, which correlates to large-amplitude vibrations of the central proton in H5(+). The second is the exchange of a pair of hydrogen atoms between H3(+) and H2. This mechanism requires several proton hops along with a 120° rotation of H3(+) within the H5(+) molecular ion. This analysis shows that while there is a narrow region of configuration space over which both isomerization processes are energetically accessible, full permutation of the five protons in H5(+) more likely occurs through a stepwise mechanism. Such full permutation of the protons becomes accessible when the shared proton stretch is excited to the vpt = 2 or 3 excited state. The effects of deuteration and rotational excitation of the H2 and H3(+) products are also investigated. Deuteration inhibits permutation of protons, while rotational excitation has only a small impact on these processes.

Theoretical predictions on the role of the internal H3(+) rotation in the IR spectra of the H5(+) and D5(+) cations

The IR spectra of the H5(+) and D5(+) cations in the mid- and far-IR spectral regions have been recently reported by experimentalists. These spectra show very rich vibrational patterns representing a challenge for state-of-the-art theoretical methods to provide definitive interpretations of them. Using a full-dimensional quantum anharmonic treatment, within the MCTDH approach, together with ab initio potential and dipole moment surfaces, the predominant features in the spectra are assigned, completing an important part in previous theoretical and experimental comparisons. The internal rotation of the H3(+) unit by exciting the H3(+)-H2 stretching mode is found to correspond to the new calculated features at 1182, 1876, and 2139 cm(-1) of the H5(+) spectrum, leading to a consistent assignment with the experimental spectra. In the calculated spectra of both H5(+) and D5(+) clusters, the progressions in the H3(+)-H2 stretch of the shared proton and the in- and out-of- plane H3(+) rotation are demonstrated to be the main features. Such states are expected to play a central role in the low temperature hydrogen/deuterium proton hop/exchange H3(+) + H2 reactions.

First-principles simulations of vibrational states and spectra for H5(+) and D5(+) clusters using multiconfiguration time-dependent Hartree approach

Simulations of the infrared (IR) spectra of the H5(+) and D5(+) clusters are carried out in the whole energy range, using a recent, reliable "on the fly" DFT-based potential energy surface, and its corresponding dipole moment surface. For the present study we adopted a recently proposed four-dimensional quantum model to describe the proton transfer motion between the two vibrating H2 or D2 units. Time-dependent and time-independent approaches within the multiconfiguration time-dependent Hartree method are employed for investigating the vibrational dynamics of the complexes. The obtained spectra are compared with recent experimental data available for energies up to 4500 and 3500 cm(-1) for the H5(+) and D5(+), respectively. Even though the present results are based on a reduced dimensional model, the infrared spectra are shown to be in good qualitative accord with those observed experimentally. Also as the reported data are subject to the potential energy surface, comparisons with previous theoretical calculations based on an analytical ab initio parameterized surface are also presented. The differences on the topology of the potentials are discussed in connection with their effect on the spectral features. We found that the main characteristics of the experimentally observed spectra are reproduced by both surfaces, evaluating in this way the sensitivity of such computations on the quality of the underlying potential. This finding serves to connect aspects of the potential surface of these systems to their spectral complexity, and could be indicative to calibrate intrinsic errors in their calculation for future studies.

Full-dimensional quantum calculations of the dissociation energy, zero-point, and 10 K properties of H7+/D7+ clusters using an ab initio potential energy surface

Diffusion Monte Carlo (DMC) and path-integral Monte Carlo computations of the vibrational ground state and 10 K equilibrium state properties of the H7 (+)/D7 (+) cations are presented, using an ab initio full-dimensional potential energy surface. The DMC zero-point energies of dissociated fragments H5 (+)(D5 (+))+H2(D2) are also calculated and from these results and the electronic dissociation energy, dissociation energies, D0, of 752 ± 15 and 980 ± 14 cm(-1) are reported for H7 (+) and D7 (+), respectively. Due to the known error in the electronic dissociation energy of the potential surface, these quantities are underestimated by roughly 65 cm(-1). These values are rigorously determined for first time, and compared with previous theoretical estimates from electronic structure calculations using standard harmonic analysis, and available experimental measurements. Probability density distributions are also computed for the ground vibrational and 10 K state of H7 (+) and D7 (+). These are qualitatively described as a central H3 (+)/D3 (+) core surrounded by "solvent" H2/D2 molecules that nearly freely rotate.

Full-dimensional quantum calculations of the vibrational states of H5(+)

Full-dimensional quantum calculations of the vibrational states of H5(+) have been performed on the accurate potential energy surface developed by Xie et al. [J. Chem. Phys. 122, 224307 (2005)]. The zero point energies of H5(+), H4D(+), D4H(+), and D5(+) and their ground-state geometries are presented and compared with earlier theoretical results. The first 10 low-lying excited states of H5(+) are assigned to the fundamental, overtone, and combination of the H2-H3(+) stretch, the shared proton hopping and the out-of-plane torsion. The ground-state torsional tunneling splitting, the fundamental of the photon hopping mode and the first overtone of the torsion mode are 87.3 cm(-1), 354.4 cm(-1), and 444.0 cm(-1), respectively. All of these values agree well with the diffusion Monte Carlo and multi-configuration time-dependent Hartree results where available.

Investigation of the structure and spectroscopy of H5(+) using diffusion Monte Carlo

The results of diffusion Monte Carlo (DMC) calculations of the ground and selected excited states of H5(+) and its deuterated analogues are presented. Comparisons are made between the results obtained from two recently reported potential surfaces. Both of these surfaces are based on CCSD(T) electronic energies, but the fits display substantial differences in the energies of low-lying stationary points. Little sensitivity to these features is found in the DMC results, which yield zero-point energies based on the two surfaces that differ by between 20 and 30 cm(–1) for all twelve isotopologues of H5(+). Likewise, projections of the ground state probability amplitudes, evaluated for the two surfaces, are virtually identical. By using the ground state probability amplitudes, vibrationally averaged rotational constants and dipole moments were calculated. On the basis of these calculations, all isotopologues are shown to be near-prolate symmetric tops. Further, in cases where the ion had a nonzero dipole moment, the magnitude of the vibrationally averaged dipole moment was found to range from 0.33 to 1.15 D, which is comparable to the dipole moments of H2D+ and HD2(+). Excited states with up to three quanta in the shared proton stretch and one quantum in the in-phase stretch of the outer H2 groups were also investigated. Trends in the energies and the properties of these states are discussed.

IR photodissociation spectroscopy of H7(+), H9(+), and their deuterated analogues

Cluster ions of H7(+)/D7(+) and H9(+)/D9(+) produced in a supersonic molecular beam with a pulsed discharge source are mass selected and studied with infrared laser photodissociation spectroscopy. Photodissociation occurs by the loss of H2 (D2) from each cluster, producing resonances in the 2000-4500 cm(-1) region. Vibrational patterns indicate that these ions consist of an H3(+) (D3(+)) core ion solvated by H2 (D2) molecules. There is no evidence for the shared proton structure seen previously for H5(+). The H3(+) ion core vibrational bands are weakened and broadened significantly, presumably by enhanced rates of intramolecular vibrational relaxation. Computational studies at the DFT/B3LYP or MP2 levels of theory (including scaling) are adequate to reproduce qualitative details of the vibrational spectra, but neither provides quantitative agreement with vibrational frequencies.