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

Isotope Effects on Ground and Excited States of Ethyl Cation, H+(C2H4)

The structure and spectra of ethyl cation, H⁺(C₂H₄), and its deuterated analogues are investigated using diffusion Monte Carlo (DMC). These calculations all show that the ground state wave function for H⁺(C₂H₄) is localized near the minimum energy configuration in which the excess proton is in a bridging configuration, although the amplitude of the vibrational motions of the bridging proton is large. Deuteration of the bridging proton reduces the amplitude of this motion, while deuteration of only the ethylenic hydrogen atoms in H⁺(C₂D₄) has little effect on the amplitude of the motion of the bridging proton. Excited states that are accessed by spectroscopically observed transitions in H⁺(C₂H₄) are calculated using fixed-node DMC. The calculated and measured frequencies for the states with one quantum of excitation in the ethylenic CH stretching vibrations show good agreement. We also explore the excited state with one quantum of excitation in the proton transfer vibration of the bridging proton and obtain a frequency of 616 cm^-1 for H⁺(C₂H₄). This frequency increases to 629 cm^-1 in H⁺(C₂D₄). Deuteration decreases this frequency to 491 and 495 cm^-1 in D⁺(C₂H₄) and D⁺(C₂D₄), respectively. The effects of partial deuteration on the frequencies of the CH stretching vibrations, and the corresponding probability amplitudes are also explored. Finally, we report the vibrationally averaged rotational constants for the four isotopologues of ethyl cation considered in this study.

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.

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'.

Calculation of Molecular Vibrational Spectra on a Quantum Annealer

Until recently molecular energy calculations using quantum computing hardware have been limited to gate-based quantum computers. In this paper, a new methodology is presented to calculate the vibrational spectrum of a molecule on a quantum annealer. The key idea of the method is a mapping of the ground state variational problem onto an Ising or quadratic unconstrained binary optimization (QUBO) problem by expressing the expansion coefficients using spins or qubits. The algorithm is general and represents a new revolutionary approach for solving the real symmetric eigenvalue problem on a quantum annealer. The method is applied to two chemically important molecules: O₂ (oxygen) and O₃ (ozone). The lowest two vibrational states of these molecules are computed using both a hardware quantum annealer and a software based classical annealer. Extension of the algorithm to higher dimensions is explicitly demonstrated for an N-dimensional harmonic oscillator (N ≤ 5). The algorithm scales exponentially with dimensionality if a direct product basis is used but will exhibit polynomial scaling for a nondirect product basis.

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.

Diffusion Monte Carlo simulations of gas phase and adsorbed D2-(H2)n clusters

We have computed ground state energies and analyzed radial distributions for several gas phase and adsorbed D₂(H₂)_n and HD(H₂)_n clusters. An external model potential designed to mimic ionic adsorption sites inside porous materials is used [M. Mella and E. Curotto, J. Phys. Chem. A 121, 5005 (2017)]. The isotopic substitution lowers the ground state energies by the expected amount based on the mass differences when these are compared with the energies of the pure clusters in the gas phase. A similar impact is found for adsorbed aggregates. The dissociation energy of D₂ from the adsorbed clusters is always much higher than that of H₂ from both pure and doped aggregates. Radial distributions of D₂ and H₂ are compared for both the gas phase and adsorbed species. For the gas phase clusters, two types of hydrogen-hydrogen interactions are considered: one based on the assumption that rotations and translations are adiabatically decoupled and the other based on nonisotropic four-dimensional potential. In the gas phase clusters of sufficiently large size, we find the heavier isotopomer more likely to be near the center of mass. However, there is a considerable overlap among the radial distributions of the two species. For the adsorbed clusters, we invariably find the heavy isotope located closer to the attractive interaction source than H₂, and at the periphery of the aggregate, H₂ molecules being substantially excluded from the interaction with the source. This finding rationalizes the dissociation energy results. For D₂-(H₂)_n clusters with n≥12, such preference leads to the desorption of D₂ from the aggregate, a phenomenon driven by the minimization of the total energy that can be obtained by reducing the confinement of (H₂)₁₂. The same happens for (H₂)₁₃, indicating that such an effect may be quite general and impact on the absorption of quantum species inside porous materials.

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.

Assessing the Performance of the Diffusion Monte Carlo Method As Applied to the Water Monomer, Dimer, and Hexamer

The diffusion Monte Carlo (DMC) method is applied to the water monomer, dimer, and hexamer using q-TIP4P/F, one of the most simple empirical water models with flexible monomers. The bias in the time step (Δτ) and population size (Nw) is investigated. For the binding energies, the bias in Δτ cancels nearly completely, whereas a noticeable bias in Nw remains. However, for the isotope shift (e.g, in the dimer binding energies between (H2O)2 and (D2O)2), the systematic errors in Nw do cancel. Consequently, very accurate results for the latter (within ∼0.01 kcal/mol) are obtained with moderate numerical effort (Nw ∼ 10(3)). For the water hexamer and its (D2O)6 isotopomer, the DMC results as a function of Nw are examined for the cage and prism isomers. For a given isomer, the issue of the walker population leaking out of the corresponding basin of attraction is addressed by using appropriate geometric constraints. The population size bias for the hexamer is more severe, and to maintain accuracy similar to that of the dimer, Nw must be increased by ∼2 orders of magnitude. Fortunately, when the energy difference between the cage and prism is taken, the biases cancel, thereby reducing the systematic errors to within ∼0.01 kcal/mol when using a population of Nw = 4.8 × 10(5) walkers. Consequently, a very accurate result for the isotope shift is also obtained. Notably, both the quantum and isotope effects for the prism-cage energy difference are small.

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.