Quantum-dynamics study of the H5+ cluster: full dimensional benchmark results on its vibrational states

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 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'.

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.

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.

Vibrational dynamics of the H5(+) and its isotopologues from multiconfiguration time-dependent Hartree calculations

Full-dimensional multiconfiguration time-dependent Hartree (MCTDH) computations are reported for the vibrational states of the H(5)(+) and its H(4)D(+), H(3)D(2)(+), H(2)D(3)(+), HD(4)(+), D(5)(+) isotopologues employing two recent analytical potential energy surfaces of Xie et al. [J. Chem. Phys. 122, 224307 (2005)] and Aguado et al. [J. Chem. Phys. 133, 024306 (2010)]. The potential energy operators are constructed using the n-mode representation adapted to a four-combined mode cluster expansion, including up to seven-dimensional grids, chosen adequately to take advantage in representing the MCTDH wavefunction. An error analysis is performed to quantify the convergence of the potential expansion to reproduce the reference surfaces at the energies of interest. An extensive analysis of the vibrational ground state properties of these isotopes and comparison with the reference diffusion Monte Carlo results by Acioli et al. [J. Chem. Phys. 128, 104318 (2008)] are presented. It is found that these systems are highly delocalized, interconverting between equivalent minima through rotation and internal proton transfer motions even at their vibrational ground state. Isotopic substitution affects the zero-point energy and structure, showing preference in the arrangements of the H and D within the mixed clusters, and the most stable conformers of each isotopomer are the ones with the H in the central position. Vibrational excited states are also computed and by comparing the energies and structures predicted from the two surfaces, the effect of the potential topology on them is discussed.

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.

Full-dimensional (15-dimensional) ab initio analytical potential energy surface for the H7+ cluster

Full-dimensional ab initio potential energy surface is constructed for the H(7)(+) cluster. The surface is a fit to roughly 160,000 interaction energies obtained with second-order MöllerPlesset perturbation theory and the cc-pVQZ basis set, using the invariant polynomial method [B. J. Braams and J. M. Bowman, Int. Rev. Phys. Chem. 28, 577 (2009)]. We employ permutationally invariant basis functions in Morse-type variables for all the internuclear distances to incorporate permutational symmetry with respect to interchange of H atoms into the representation of the surface. We describe how different configurations are selected in order to create the database of the interaction energies for the linear least squares fitting procedure. The root-mean-square error of the fit is 170 cm(-1) for the entire data set. The surface dissociates correctly to the H(5)(+) + H(2) fragments. A detailed analysis of its topology, as well as comparison with additional ab initio calculations, including harmonic frequencies, verify the quality and accuracy of the parameterized potential. This is the first attempt to present an analytical representation of the 15-dimensional surface of the H(7)(+) cluster for carrying out dynamics studies.