Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 6496−6501
pubs.acs.org/JPCL
Probing Nonadiabatic Effects in Low-Energy C(3Pj) + H2 Collisions Jacek Kłos,† Astrid Bergeat,*,‡ Gianmarco Vanuzzo,‡,§ Sébastien B. Morales,‡ Christian Naulin,‡ and François Lique*,¶ †
Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742-2021, United States University of Bordeaux, CNRS, ISM, UMR 5255, Talence, France ¶ LOMC-UMR 6294, CNRS-Université du Havre, 25 rue Philippe Lebon, BP 1123−76 063 Le Havre cedex, France § Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, 06123 Perugia, Italy J. Phys. Chem. Lett. Downloaded from pubs.acs.org by KAOHSIUNG MEDICAL UNIV on 11/03/18. For personal use only.
‡
S Supporting Information *
ABSTRACT: Nonadiabatic effects are of fundamental interest in collision dynamics. In particular, inelastic collisions between open-shell atoms and molecules, such as the collisional excitation of C(3Pj) by H2, are governed by nonadiabatic and spin−orbit couplings that are the sole responsible of collisional energy transfer. Here, we study collisions between carbon in its ground state C(3Pj=0) and molecular hydrogen (H2) at low collision energies that result in spin−orbit excitation to C(3Pj=1) and C(3Pj=2). State-to-state integral cross sections are obtained experimentally from crossed-beam experiments with a source of almost pure beam of C(3Pj=0) and theoretically from highly accurate quantum calculations. We observe very good agreement between experimental and theoretical data that demonstrates our ability to model nonadiabatic dynamics. New rate coefficients at temperatures relevant to astrochemical modeling are also provided. They should lead to an increase of the abundance of atomic C(3P) derived from the observations of interstellar clouds and a decrease of the efficiency of the cooling of the interstellar gas due to carbon atoms.
T
he Born−Oppenheimer (BO) approximation1 is invaluable in the application of quantum mechanics to molecular spectroscopy and molecular reaction dynamics. This approximation postulates that electrons adapt adiabatically to the motion of the much-heavier nuclei, so that the forces on the nuclei are generated by variation of the geometrydependent electronic energy of a single electronic state. The BO approximation allows one to model molecular dynamics as the motion of multiple nuclei on a single electronic potential energy surface (PES). Since the introduction of this concept, valuable insights in many systems of increasing size could be retrieved, in remarkable agreement with experiments (i) at the macrocanonical level: quantitative determination of thermal reactive rate constants (transition state theory/kinetics experiments); and (ii) at the microcanonical level: state-to-state integral (ICS) and differential (DCS) cross sections (classical trajectory methods/crossed beam experiments). Introduction of quantum mechanical calculations (QM) also led to a much more detailed description of the collisional processes, such as resonances or tunnelling effects. The ICS of inelastic collisions of O2 molecules with H2 at very low collisional energies (a few cm−1) exhibited a remarkable agreement (including for the resonances) with QM calculations.2 Similarly, the measurements of the H + H2 reactive rate constants have been in excellent agreement with theoretical QM calculations, even at low temperatures where the reaction proceeds through tunnelling.3 © XXXX American Chemical Society
Despite its great success, the BO approximation breaks down whenever two (or more) electronic states become degenerate. This breakdown is responsible for fundamental molecular phenomena such as predissociation or internal conversion in an isolated molecule4 and is ultimately crucial in more-complex chemical processes. For many systems of interest in the chemistry of planetary atmospheres (including earth) or interstellar media (such as dense molecular clouds), collision partners can be atoms or radicals (i.e., open shell systems). In that case, collisions imply multiple PESs so that the BO approximation no longer holds (nonadiabatic dynamics), and the system can change its electronic configuration because of strong spin−orbit couplings, or in regions where two PESs cross. This is particularly relevant for low-energy C(3Pj) + H2 collisions. Indeed, the spin−orbit interaction splits the ground electronic state of carbon into a triplet of fine-structure levels 3 Pj with j = 0, 1, and 2, the lowest energy level being 3Pj=0. The total angular momentum j results from the coupling of L and S, the orbital and spin angular momenta, respectively. Hence, energy transfer induced by collisions of C(3Pj) by H2 is made possible only by nonadiabatic and spin−orbit couplings between the multiple interaction potentials involved. Received: October 1, 2018 Accepted: October 30, 2018 Published: October 30, 2018 6496
DOI: 10.1021/acs.jpclett.8b03025 J. Phys. Chem. Lett. 2018, 9, 6496−6501
Letter
The Journal of Physical Chemistry Letters
production of excited atoms. The relative (3P1)/(3P0) population ratio obtained for the present experiments is ca. 4%. To determine the theoretical inelastic cross sections (ICS), we used the exact Close Coupling approach of ref 15 Such an approach should allow the collisions to be studied without any approximation. To determine the experimental ICSs, we used a crossed-beam apparatus with variable beam intersection angle, χ,16,17 allowing the relative reactant translational energy to be finely tuned: 1 1 E T = μvr2 = μ(vC 2 + vH2 2 − 2vCvH2 cos χ ) 2 2 where μ stands for the reactant reduced mass, vr represents the relative velocity, vC is the C velocity, and vH2 represents the H2 velocity. Both beams were generated using cryogenically cooled Even−Lavie fast-pulsed valves.18 Experimental results are displayed in Figures 1 and 2, along with theoretical data. However, to allow for comparison, theoretical results (displayed in Figure 1A for the j = 0 → 1 transition and in Figure 2A for the j = 0 → 2 transition) need to be convoluted to the experimental energy resolution. As one can see, the theoretical and experimental data match extremely well. The variation of the experimental ICS as a function of kinetic energy is well reproduced by the theoretical data. We also note that the main findings of the experiments are supported by the theoretical results. First, the results are only weakly dependent on the rotational state of H2 since the ICS obtained using either p-H2 or n-H2 colliders are similar for both the two excitation transitions probed in this work. Such a finding, which is not usual for neutral collisional systems,19 can certainly be explained by the large well depth in the C(3P)−H2 PESs that is weakly dependent on the orientation of H2. Second, one observes that the ICS for the 3P0 → 3P1 transition is similar to that of the 3P0 → 3P2 transitions, contrary to what was found recently for the O(3P)−H2 collisional system.7 In principle, a selection rule forbidding the 3P0 → 3P1 transition should exist.20 However, because of the presence of an efficient indirect coupling between the 3P0 and 3P2 states, together with 3P2−3P1 coupling, there is an increase of the 3P0 → 3P1 ICS. The efficiency of this indirect coupling can be explained by the important well depth in the PESs. Finally, one can observe resonant structures in the theoretical ICS. These are a consequence of the quasibound states arising from tunneling through the centrifugal energy barrier (shape resonances), or from the presence of an attractive potential well that allows H2 to be temporarily trapped into the well, hence leading to the formation of quasibound states (Feshbach resonances) before the complex dissociates.21 The ICS for C spin−orbit relaxation in collision with n-H2 appears to have a smoother energy dependence than the cross section for collision with p-H2. This is a result of the fact that there are many moreand, hence, overlapping resonances for o-H2 than for p-H2. Hence, the resonance features are mostly washed out for n-H2. One can note that, because of the convolution, the resonant structure in the theoretical ICS is mostly washed out, when compared to the experimental ICS, despite some remaining oscillations are clearly visible. The overall agreement for the resonant structures is good: however, although the theory correctly reproduces some of the resonances, it fails for some others, the theoretical resonances
Exact QM modeling of the above reaction including nonadiabatic and spin−orbit couplings is a real challenge from both quantum chemistry and quantum dynamics points of view. Indeed, a detailed understanding of non-BO coupling of adiabatic electronic states and of the potential energy surfaces associated with them and the ability to predict the effect of this type of coupling for real chemical systems remain significant challenges to current theories. Then, very few theoretical polyatomic (more than two atoms) collisional studies have been performed considering accurately nonadiabatic and spin−orbit effects. However, let us cite the prototype chemical reaction H2 + X (X = F, Cl)5,6 and some of the recent inelastic scattering studies involving H2 molecules and open-shell atoms or molecules such as O(3P), NO(2Π), or OH(2Π)7−9 that have provided deep insight into nonadiabatic dynamics. Because of the reactive nature of the C(3Pj) + H2 scattering that can form the CH2 intermediate complex, the theoretical modeling of this process is even more challenging than those previously mentioned. Excitation cross sections for the fine-structure transitions of C(3Pj) in collisions with ortho- and para-H2 (designated hereafter as o-H2 and p-H2, respectively) were computed by Schroder et al.10 However, the calculations were based on approximate (reduced dimension) PES and couplings that lead to approximate data at low collisional energy, which is relevant for astrophysical applications. Indeed, in the interstellar medium (ISM), collisional excitation followed by radiative decay leads to the conversion of thermal energy to radiant energy (photons), which can escape from the medium. Since hydrogen and helium, the two most abundant species in space, have no fine structure in their ground electronic states, cooling in the “cold” ISM is dominated by collisions with the next most abundant elements, carbon and oxygen,11 which do have lowlying fine-structure levels. In addition, atomic carbon is particularly abundant in dense interstellar clouds12 and is a precursor for the synthesis of many carbon-rich molecules.13 Accurate inelastic collision rate coefficients are crucial for astrophysical modeling, since densities in the ISM are such that the collision frequency is neither negligible nor large enough to maintain thermodynamic equilibrium and deriving abundances of species requires to solve simultaneously the radiative transfer equation and a set of statistical equilibrium equations. This, in turn, requires the availability of the state-to-state rate coefficients for collisional (de)excitation. In this study, we report inelastic collision experiments and quantum scattering calculations performed on new C(3P)−H2 ab initio PESs for spin−orbit excitation of C(3P0) with H2. Both approaches show evidence for the quantum nature of the collision at energies relevant to interstellar cloud physical conditions. The experimental approach requires producing an almostpure beam of C atoms in their ground spin−orbit state, 3P0, which is quite challenging for the following reasons. First, spin−orbit splitting is small: 3P1 and 3P2 components lie at only 16.42 and 43.41 cm−1 above the 3P0 ground state, respectively.14 Second, the ground state has the lowest multiplicity (2j + 1 = 1). As a result, the thermal (3P1)/(3P0) population ratio would be ca. 28%, at 10 K, i.e., much higher than the expected amount of C(3P1) produced by inelastic collisions with H2. Furthermore, C atoms are produced by dissociation of a parent molecule (here, CO), thus requiring sufficiently high excitation energy, which can easily lead to the 6497
DOI: 10.1021/acs.jpclett.8b03025 J. Phys. Chem. Lett. 2018, 9, 6496−6501
Letter
The Journal of Physical Chemistry Letters
Figure 1. Comparison of experimental and theoretical cross sections for C(3P0) + H2 → C(3P1) + H2 inelastic collisions. Panel (A) shows theoretical results. Panel (B) shows data for C + n-H2, and panel (C) shows data for C + p-H2. (Open triangles in panels (B) and (C) represent experimental data whereas lines represent convoluted theoretical ICSs.) All possible transitions are taken into account, assuming a 4% initial population of C(3P1) state: C(3P1) is populated by j = 0 → 1 (main contribution), and is depopulated by 1 → 0 (relaxation) and 1 → 2 (excitation) transitions, resulting in a total ICStot = σ(0−1) − 0.04(σ(1−0) + σ(1−2)). Experimental ICSs (in arbitrary units) are normalized to the same area as theory in their common energy range. Vertical error bars represent the statistical uncertainties at 95% of the confidence interval: each data point corresponds to 101 (n-H2) and 43 (p-H2) scans of the beam intersection angle acquired between 90° and 20° with −1° decrement and 100 laser shots per angle. The plotted error bars on energy are estimated from velocity and crossing angle uncertainties. Note that, for this transition, the ICSexp are derived from the difference in REMPI signals obtained when probing the j = 1 state with and without the H2 beam.
Figure 2. Comparison of experimental and theoretical cross sections for C(3P0) + H2 → C(3P2) + H2 inelastic collisions. Panel (A) shows theoretical results. Panel (B) represents data for C + n-H2, and panel (C) represents data for C + p-H2. (Open triangles in panels (B) and (C) represent experimental data whereas lines represent convoluted theoretical ICSs.) All possible transitions are taken into account, assuming a 4% initial population of C(3P1) state: C(3P2) is populated by j = 0 → 2 (main contribution) and 1 → 2 excitation transitions, resulting in a total ICStot = σ(0−2) + 0.04σ(1−2). Experimental ICSs (in arbitrary units) are normalized to the same area as theory in their common energy range. Vertical error bars represent the statistical uncertainties at the 95% confidence interval; each point corresponds to 36 (n-H2) and 53 (p-H2) scans of the beam intersection angle acquired between 70° (n-H2) and 20° or between 90° (p-H2) and 20°, with −1° decrement and 100 laser shots per angle; both beams were triggered at 10 Hz. The plotted error bars on energy are estimated from velocity and crossing angle uncertainties.
appearing at slightly higher collisional energies. These slight discrepancies may originate from the lack of correlation energies in the potential well that would lead to theoretical bound states energy levels slightly higher than those observed in the experiments, whereas the quasi-bound states are correctly located. Another possibility for these discrepancies is the use of a fixed internuclear distance for the H2 molecule that prevents an exact description of the anisotropy in the potential well. The origin of such resonant structures could be analyzed in detail,2,22,23 based on an adiabatic bender model.24 However, analysis of the resonant structures in the present case would be extremely difficult, because they appear at relatively high collisional energies and a significant number of bound states are likely to contribute to them. The good agreement between theory and experiment validates the PESs used to describe these challenging nonadiabatic processes, thus allowing collisional thermal-rate
coefficients to be determined by a Boltzmann thermal average of the present cross sections. The corresponding rate coefficients ki→f were computed for temperatures up to 100 K by averaging over a Maxwell− Boltzmann distribution of collision energies, Ec: i 8k T y ki → f (T ) = jjjj B zzzz k πμ {
1/2
∫0
∞
σi → f (ϵ)ϵe−ϵ dϵ
(1)
where kB is the Boltzmann constant, μ is the reduced mass of the collision pair, σi→f is the ICS for a transition from state i to 6498
DOI: 10.1021/acs.jpclett.8b03025 J. Phys. Chem. Lett. 2018, 9, 6496−6501
Letter
The Journal of Physical Chemistry Letters state f, and ϵ = Ec/(kBT). Note that the term
8kBT πμ
constrained astrochemical models that are used to have the most-accurate census of the molecular content in molecular clouds.
1/2
( )
is the
■
thermal average value of the relative velocity. Resulting thermal rate coefficients for C(3Pj) relaxation by collisions with p- and o-H2 are displayed in Figure 3, along with
METHODS Theoretical Methods. New highly correlated C(3P)−H2 PESs were computed at multireference configuration interaction method with large atomic basis set and used in the dynamical calculations (see Section 1 and Figures S1−S3 in the Supporting Information). Briefly, we employed explicitly correlated variant of the multireference configuration interaction method (MRCI-F12),27 and we used all-electron augcc-pVQZ basis sets for the C and H atoms28 augmented with corresponding F12 auxiliary density fitting basis sets. The MRCI-F12 calculations included single and double excitations and Davidson correction29 to account for higher excitations. All the electronic structure calculations of the PESs were performed with the MOLPRO30 program. The H2 geometry was kept fixed at r0 = 1.448736 bohr, which is the diatomic distance corresponding to the average value for the ground vibrational state of hydrogen molecule. For a 3P open-shell atom interacting with closed-shell 1Σ molecule, such as H2, three adiabatic PESs are involved: 13A″, 23A″, and 13A′. The two adiabats of the same A″ symmetry will avoid crossing with each other, and for the full description of the dynamics of this system, one must calculate off-diagonal diabatic PES. The diabatization of these two A″ states is performed by quasidiabatization algorithm implemented in the MOLPRO program. The quantal coupled equations were solved using the HIBRIDON package.31 The cross sections were checked for convergence, with respect to the inclusion of a sufficient number of partial waves and energetically closed channels. The H2 basis included all levels with a rotational quantum number j ≤ 6 and the contribution of the first 200 partial wave was included in the ICS calculation at 500 cm−1. State-to-state excitation cross sections were obtained between all the fine structure levels of C(3P) over the collision energy range relevant to the experiments (0−500 cm−1) and to allow calculation of the rate coefficients in the temperature domain of interest: 0−100 K. Experimental Methods. The C atom beam was obtained by dissociation of CO molecules seeded in neon in a dielectric barrier discharge incorporated in one of the valves. It was characterized in the crossing region by 2 + 1 resonanceenhanced multiphoton ionization (REMPI) time-of-flight (TOF) mass spectrometry using two-photon 2p2 3Pj → 2p3p 3Pj transitions at ∼140.15 nm (laser tuned at 280.3 nm).32 Populations of ∼95% for j = 0, 4% for j = 1, and 95% for j = 0 and
