This is an open access article published under a Creative Commons Attribution (CC-BY) License, which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited. pubs.acs.org/JCTC Article Kinetic Isotope Effect in Low-Energy Collisions between Hydrogen Isotopologues and Metastable Helium Atoms: Theoretical Calculations Including the Vibrational Excitation of the Molecule Mariusz Pawlak,* Piotr S. Żuchowski, and Piotr Jankowski Cite This: J. Chem. Theory Comput. 2021, 17, 1008−1016 Read Online ACCESS Metrics & More Article Recommendations *sı Supporting Information ABSTRACT: We present very accurate theoretical results of Penning ionization rate coefficients of the excited metastable helium atoms (4He(23S) and 3He(23S)) colliding with fi the hydrogen isotopologues (H2, HD, D2) in the ground and rst excited rotational and vibrational states at subkelvin regime. The calculations are performed using the current best ab initio interaction energy surface, which takes into account the nonrigidity effects of the molecule. The results confirm a recently observed substantial quantum kinetic isotope effect (Nat. Chem. 2014, 6, 332−335) and reveal that the change of the rotational or vibrational state of the molecule can strongly enhance or suppress the reaction. Moreover, we demonstrate the mechanism of the appearance and disappearance of resonances in Penning ionization. The additional model computations, with the morphed interaction energy surface and mass, give better insight into the behavior of the resonances and thereby the reaction dynamics under study. Our theoretical findings are compared with all available measurements, and comprehensive data for prospective experiments are provided. 1. INTRODUCTION composition and formation of interstellar clouds and 16,17 A chemical reaction is a fundamental process in chemistry. structure. Hydrogen and helium are the lightest and most abundant External control of its dynamics is crucial to understand many chemical elements in the Universe, while molecular hydrogen physical and chemical phenomena, especially at the quantum is the lightest and the most common molecule.18,19 For level. Recent sophisticated merged beams experiments for low- instance, molecular hydrogen and helium are the prime energy atom−molecule collisions revealed the possibility of 20 − constituents of gas giants. New ground- and space-based controlling molecular reactions.1 10 These experiments were − high-resolution telescopes enable the observation of light groundbreaking achievements in cold chemistry.11 15 The first elements, which was previously inaccessible. Very recently, merged neutral supersonic beams technique was demonstrated 3 Downloaded via 81.190.23.145 on February 10, 2021 at 00:25:14 (UTC). scientists have made the first-ever detection of 2 S helium in in 2012 by the group of Narevicius,1 approaching a collision the atmosphere of one of the planets (WASP-107b) beyond temperature below 10 mK. Narevicius and co-workers 19 the solar system. Soon after, excited metastable helium was − investigated the Penning ionization (PI) reactions by colliding confirmed on other exoplanets.21 29 The measurements of the excited metastable helium atoms 4He* (≡ 4He(23S)), See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. helium absorption signal in exoplanet atmospheres are now contained in one beam, with ground-state molecular hydrogen important markers of a variety of planetary processes. They H2, contained in another beam have become a unique probe for assessing exoplanetary compositions and understanding the formation of exoplanetary He*+ H → He + H+ + e− 22 systems. The observation of long-lived metastable helium atoms has changed the way astronomers look at exoplanets and They observed a few shape resonances by measuring reaction fi ffi has raised the signi cance of theoretical chemistry for rate coe cients, systematically decreasing collision energy astrophysical domains. Undoubtedly, the collisions of 23S from a few tens of kelvins down to millikelvins. In follow-up ff 2 helium with various atomic and molecular partners, especially studies, they focused on the isotope e ect, where the with hydrogen isotopologues, are of primary importance for hydrogen molecule was substituted by hydrogen deuteride fi (HD) and deuterium (D2). This was the rst observation of such an effect in low-energy collisions. It turned out that the Received: October 26, 2020 positions of the resonances were different for the hydrogen Published: January 21, 2021 isotopologues, far from intuitive expectations. The substitution strongly affected the PI process with an order of magnitude increase in the reaction rate coefficient at certain collision energies. This effect may significantly matter to the isotopic © 2021 The Authors. Published by American Chemical Society https://dx.doi.org/10.1021/acs.jctc.0c01122 1008 J. Chem. Theory Comput. 2021, 17, 1008−1016 Journal of Chemical Theory and Computation pubs.acs.org/JCTC Article astrochemistry. It is also worth noting that there are a vibrationally averaged surface, one needs to know a full- considerable number of experimental studies for He* in dimensional surface for a given complex,42 however, the collisions with more complex molecules (for example, surface averaged over the vibrational state v can be obtained hydrogen sulfide,30 nitrous oxide,31 benzene,32 naphthalene,33 approximated43 using a Taylor expansion of the interaction anthracene,33 [2,2]-paracyclophane,34 pyrene,35 chrysene,35 potential V(R, θ, r) with respect to the intramonomer 35 36 37 37 coronene, glycine, anisole, thioanisole, and selenoani- coordinate r, around some reference value rc sole37). ff ⟨⟩θθθ ≈ + ⟨⟩− As was shown in ref 2, the kinetic isotope e ect in the VRjv, (, ) fR01 (, ) fRr (, )( jv,c r ) 4 * collisions between light subsystems (such as He with H2, 1 HD, and D ) is dramatic, fundamentally changing the reactivity +⟨⟩−⟨⟩+fR(,θ )( r2 2 r r r2 ) 2 2 jv,,cc jv (1) of the PI process. A high level of theory is required to evaluate 2 fi θ θ θ ∂ θ ∂ the experimental ndings. The main motivation of our present where f 0(R, )=V(R, , rc), f1(R, )= V(R, , r)/ r at r = rc, fi ff θ ∂2 θ ∂ 2 ⟨ ⟩ ⟨ 2⟩ studies was to con rm the strong isotope e ect in cold and f 2(R, )= V(R, , r)/ r at r = rc. The r j,v and r j,v chemistry reactions based on our recently developed, very symbols denote the averaged values of r and r2 for the 38 fi accurate interaction energy surface. This ab initio surface rovibrational states of H2 de ned by the quantum numbers j includes nonrigidity effects of the molecule, which play an and v. In our investigations, we took r equal to the H−H 38 c important role in low-energy molecular anisotropic collisions. distance averaged over the rovibrational ground state, i.e., rc = ⟨ ⟩ Additionally, this surface also allows us to predict resonance r 0,0 = 1.4487 Bohr. The values of f1 and f 2 can be calculated structures for experimentally uncharted cases. Since we can on the grid of the intermolecular coordinates with the finite- account for nonrigidity effects, complexes with the vibration- difference method. The vibrationally averaged surfaces ally excited hydrogen molecule or its isotopologues can be obtained within this approximation were used in bound-state − 44−46 − 47 − 48 considered. Such complexes have become easier to access calculations for the H2 CO, Ar HF, and N2 HF experimentally due to recent progress in the production and complexes, and an excellent, or at least, very good agreement of 39−41 the control of the excited hydrogen isotopologues. Thus, the theoretical spectra with experimental ones was observed. ffi − in the present work, we compute reaction rate coe cients of For the H2 CO complex, scattering calculations were also 49 the H2/HD/D2 molecules in the ground and excited rotational performed with the surface defined through eq 1, and an 4 (j = 0/1) and vibrational (v = 0/1) states with He*, and excellent agreement with the experimental data50,51 and the 3 additionally with He*. We demonstrate that by changing the full-dimensional results was achieved. ff quantum state of the molecule, one can turn on or o In the present study, we have used the values of the f i particular low-energy resonances, thereby strongly modify the expansion functions, where i = 0, 1, 2, calculated in ref 38. The PI. It enables us better control over reactions in the subkelvin details can be found in that paper, but here we would like to regime. mention that the leading f 0 term was obtained using the coupled cluster method with singles, doubles, and perturbative 2. THEORY triples (CCSD(T)), and improved with a full configuration 2.1. Interaction Energy Surface. Our theoretical interaction (FCI) correction. The f1 and f 2 derivatives were approach consists of two parts: the first is to prepare the calculated with the symmetry-adapted perturbation theory 53 4 * best possible interaction energy surface, and the second is to (SAPT) method. As was demonstrated for the He +H2 perform quantum-dynamical calculations of the PI rate complex, the diagonal Born−Oppenheimer (DBO) correc- ffi * 54 fi coe cients. To parameterize the He +H2 complex, we use tion is signi cantly smaller than other contributions to f 0,so Jacobi coordinates: the distance R between He* and center of we neglected this correction in that work. Moreover, for the θ 4 * 4 * mass (COM) of H2, the angle between the H2 bond and the He + HD and He +D2 complexes, the DBO correction − * 4 * COM He direction, and the distance r between the can be expected to be even smaller than for He +H2 due to hydrogen nuclei. Thus, the full-dimensional energy surface the larger masses of HD and D2 in comparison to H2. Thus, we θ can be written as a function of these coordinates, V(R, , r).