Article pubs.acs.org/JPCA
Cite This: J. Phys. Chem. A XXXX, XXX, XXX−XXX
Low-Energy Water−Hydrogen Inelastic Collisions Published as part of The Journal of Physical Chemistry virtual special issue “F. Javier Aoiz Festschrift”. Astrid Bergeat,*,§ Alexandre Faure,‡ Sébastien B. Morales,§ Audrey Moudens,§,† and Christian Naulin§ §
Univ. Bordeaux, CNRS, Bordeaux INP, ISM, UMR 5255, F-33405 Talence, France Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France
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‡
ABSTRACT: New molecular beam scattering experiments are reported for the water−hydrogen system. Integral cross sections of the first rotational excitations of para- and orthoH2O by inelastic collisions with normal-H2 were determined by crossing a beam of H2O seeded in He with a beam of H2. H2O and H2 were cooled in the supersonic expansion down to their lowest rotational levels. Crossed-beam scattering experiments were performed at collision energies from 15 cm−1 (below the threshold for the excitation to the lowest excited rotational state of H2O: 18.6 cm−1) up to 105 cm−1 by varying the beam crossing angle. The measured state-to-state crosssections were compared to the theoretical cross-sections (close-coupling quantum scattering calculations): the good agreement found further validates both the employed potential energy surface describing the H2O−H2 van der Waals interaction and the state-to-state rate coefficients calculated with this potential in the very low temperature range needed for the modeling of interstellar media.
1. INTRODUCTION The ubiquity of water in the Universe has been demonstrated over the last 50 years through many astronomical observations by ground- and space-based telescopes.1−4 In the interstellar medium (ISM), water vapor was detected for the first time in 1969 toward the Orion nebula.5 Since then, gaseous water is known to be present in the various objects of ISM, such as dense clouds, protostars, stars, and planet-forming regions, as it has been recently observed by Herschel Space Observatory (see review from van Dishoeck et al.3 and references therein). Water is a key molecule for understanding of the energy balance and the physical−chemical processes that occur in these environments. Its principal collision partner is obviously H2 because of its predominant abundance in ISM. Therefore, an accurate description of H2O−H2 collision dynamics is required in order to fully interpret spectral features recorded by astronomers at infrared and sub-millimeter wavelengths. Populations of each observed rotational level of gaseous water are determined by the competition between collisional and radiative excitation−relaxation processes. In the context of dense clouds in ISM, because of the low collision frequency, gaseous molecules are not at local thermodynamic equilibrium, with populations of each state being mainly controlled by collision dynamics. Potential energy surfaces (PESs) used to compute (de)excitation collision cross-sections and rate coefficients are determined by ab initio quantum methods, describing the intermolecular interaction between the two collision partners. For the benchmark system H2O−H2, several © XXXX American Chemical Society
intermolecular PESs have been calculated, including fulldimensional ones.6−10 The accuracy of the PES of Valiron et al.9 (hereafter V08) has been checked against various experiments including inelastic state-to-state differential cross-sections,11,12 pressure broadening cross-sections,13−15 elastic integral cross-sections,16 second virial coefficients,17 and bound states of the complex.18−21 These comparisons between theory and experiment have all demonstrated the high accuracy of V08 in the short-range and well regions of the potential. The present study provides the first experimental check of V08 at long range by measuring scattering crosssections of the first rotational excitations, both at the state-tostate level and at very low collision energy (near rotational thresholds).
2. THEORETICAL CALCULATIONS The scattering quantum calculations were conducted at the full close-coupled level using the MOLSCAT program22 combined with the V08 PES of Valiron et al.9 Briefly, this fivedimensional (5D) PES was obtained as an explicit vibrational average of the full-dimensional (9D) PES over the ground rovibrational states of H2O and H2. Full details can be found in Special Issue: F. Javier Aoiz Festschrift Received: May 20, 2019 Revised: July 2, 2019 Published: July 8, 2019 A
DOI: 10.1021/acs.jpca.9b04753 J. Phys. Chem. A XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry A Valiron et al.9 We note that such a vibrational averaging was recently assessed for CO−H2, and it was found to provide an excellent approximation to full-dimensional scattering calculations.23 The spherical harmonics expansion of the 5D PES includes 149 angular basis functions, as described in Valiron et al.9 The coupled differential scattering equations were solved using the hybrid modified log-derivative Airy propagator.24 Total energies up to 345 cm−1 were considered using a very fine energy grid (increments of 0.05 cm−1) for a proper description of rotational thresholds and an accurate assessment of resonances. Calculations were performed for H2 in its ground para (jH2 = 0) and ortho (jH2 = 1) states, and crosssections for normal-H2 (n-H2) were obtained with an ortho-topara ratio of 3 (see the upper panels of Figures 3 and 4). The highest rotational angular momentum of H2O in the basis set was JH2O = 5 (corresponding to the inclusion of 18 para and 18 ortho levels), whereas two rotational levels of H2 were included for the para (jH2 = 0, 2) and ortho (jH2 = 1, 3) symmetries of H2. Higher levels were found to affect the investigated crosssections by less than 1% (in the experimental energy range). Convergence was also checked as a function of the propagator step size (parameter STEPS), and the other propagation parameters were taken as the default MOLSCAT values. The maximum value of the total angular momentum Jtot used in the calculations was Jtot = 52 at the highest collisional energy. The rotational constant for H2 was taken as B0 = 59.322 cm−1. The H2O energy levels were described using the effective Hamiltonian of Kyrö et al.,25 as done previously by Dubernet and co-workers.26 Finally, the reduced mass of the system is 1.81277 a.m.u.
spectrum of the water in the supersonic beam is shown in Figure 1.
Figure 1. (2 + 1) REMPI spectrum of the C̃ 1B1, v′ = 0 ← X̃ 1A1, v = 0 transition of H2O in the supersonic beam (blue line) or in the chamber (black line). Assignments (J′K′a,K′c ← JKa,Kc) of the transitions are given. See Yang et al.29 for more details.
Water is an asymmetric top molecule, and its rotational levels are conventionally labeled JKa,Kc, where J is the rotational angular momentum quantum number, and Ka and Kc are formally the projections of the rotational angular momentum vector on the molecular axes a and c, respectively.30 The analysis of our experimental spectrum was performed by using the molecular constants of Yang et al.:29 in the supersonic expansion, the only rotational levels populated are 101 at 64− 70%, 000 at 23−25%, and 110 and 111 at a few percent. No evidence of water clusters was found: there was no signal recorded at the time delay for a mass-to-charge ratio of 36 at any laser wavelength in the 247.5−248.5 nm range. For H2O and H2 in their ground vibronic states, the presence of two identical hydrogen atoms results in two nuclear spin states: ortho (Ka + Kc odd or jH2 odd) and para (Ka + Kc even or jH2 even). It is clear from our spectra, that the ortho/para ratio of water remained unchanged during the supersonic expansion,29,31 at the value of 3:1. This is also the case for H2. A weak signal due to background from thermal water cations is hardly observable in Figure 1, but is the major one, even the only one observable in the spectrum of the excited states in the lower panel of Figure 2, where the amplification of the signal has been increased. It should be noticed that the signal of these excited states starts to increase with the collision energy. Thus, this background signal, which is the main source of the signal uncertainty, was offset by shot-to-shot background subtraction when triggering the probe laser and the H2O beam at 10 Hz with the H2 beam at 5 Hz. After subtraction, populations of only few percent of the first excited rotational levels were found. The experimental integral cross-sections (ICSs) shown in Figures 3 and 4 are derived from the difference in REMPI signals obtained when probing the H2O 110 (or 111) state with and without the H2 beam. Each data point corresponds to 36 (or 24 scans) of the beam intersection angle acquired between 27.5° (or 35°) and 12.5° with a −0.5° decrement and 100 laser shots per angle, across several days. This procedure ensures a
3. EXPERIMENTAL SECTION The experimental setup used to obtain low collision energies is a crossed-molecular beam apparatus,27,28 under single collision conditions. The relative translational energy can be varied when scanning the beam crossing angle, the lowest value being for the lowest angle when the reactant beams have nearly the same velocities. The H2O beam was formed by expanding through an Even−Lavie valve at 320 K; water vapor seeded in He as carrier gas, from a high-pressure reservoir (13 bar) maintained at the temperature of 315 K. The velocity distribution of the H2O beam was centered at (1825 ± 50) m s−1 with speed and angular spreads of 59 m s−1 and 0.85°, corresponding to the half-width at 1/e (HWE) of the fitted Gaussian profiles. The H2 molecular beam was produced by supersonic expansion through a second pulsed Even−Lavie valve and cryo-cooled at a set point of 145 K, to obtain a Gaussian velocity distribution centered at (1930 ± 54) m s−1 with speed and angular spreads at HWE of 52 m s−1 and 2.7°, respectively. The rotational populations of H2O vapor, seeded in He in the supersonic beam, were measured using (2 + 1) resonanceenhanced multiphoton ionization (REMPI) at ca. 248 nm, via the C̃ 1B1 Rydberg state.29 Laser pulse energies of 2−3.5 mJ per pulse at a repetition rate of 10 Hz were generated by doubling the output of a dye laser operating with Coumarin 500 dye in methanol, pumped by the third harmonic (355 nm) of a Nd:YAG laser. The laser beam was directed perpendicular to the collision plane, and a wavemeter was used to monitor the wavelength. The output of the frequency doubled dye laser was monitored with a photodiode to select data acquired with a laser pulse energy at ±15% of the average. A representative B
DOI: 10.1021/acs.jpca.9b04753 J. Phys. Chem. A XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry A
Figure 2. (2 + 1) REMPI spectrum of the C̃ 1B1, v′ = 0 ← X̃ 1A1, v = 0 transition of H2O in the supersonic beam. Assignments JKa,Kc refer to the ground vibronic state. See Yang et al.29 for more details. (a) Spectra of excited H2O with (green solid line) and without (gray dashed line) the water beam: the signal is essentially due to the background water. (b) Spectra of excited H2O without the H2 beam (gray dashed line) as well as with the H2 beam at 25° or a collision energy of 55 cm−1 (magenta solid line) and at 35° or a collision energy of 104 cm−1 (blue solid line). The value at each wavelength probed is an average of only 50 laser shots.
sufficiently short scan duration (
