Quantum-scattering Calculations Research Articles

Accurate reference spectra of HD in an H2--He bath for planetary applications

The hydrogen deuteride (HD) molecule is an important deuterium tracer in astrophysical studies. The atmospheres of gas giants are dominated by molecular hydrogen, and the simultaneous observation of H$_2$ and HD lines provides reliable information on the D/H ratios on these planets. The reference spectroscopic parameters play a crucial role in such studies. Under the thermodynamic conditions encountered in these atmospheres, spectroscopic studies of HD require not only the knowledge of line intensities and positions but also accurate reference data on pressure-induced line shapes and shifts. Our aim is to provide accurate collision-induced line-shape parameters for HD lines that cover any thermodynamic conditions relevant to the atmospheres of giant planets, namely any relevant temperature, pressure, and perturbing gas composition (the H$_2$--He mixture). We performed quantum-scattering calculations on our new, highly accurate ab initio potential energy surface (PES) and we used scattering S matrices obtained in this way to determine the collision-induced line-shape parameters. We used cavity ring-down spectroscopy to validate our theoretical methodology. We report accurate collision-induced line-shape parameters for the pure rotational R(0), R(1), and R(2) lines, the most relevant HD lines for investigations of the atmospheres of the giant planets. Besides the basic Voigt-profile collisional parameters (i.e., the broadening and shift parameters), we also report their speed dependences and the complex Dicke parameter, which can influence the effective width and height of the HD lines up to almost a factor of 2 for giant planet conditions. The sub-percent-level accuracy reached in this work is a considerable improvement over previously available data. All the reported parameters (and their temperature dependences) are consistent with the HITRAN database format, hence allowing for the use of the HITRAN Application Programming Interface (HAPI) for generating the beyond-Voigt spectra of HD.

A single resonance Regge pole dominates the forward-angle scattering of the state-to-state F + H2 → FH + H reaction at Etrans = 62.09 meV.

The aim of the present paper is to bring clarity, through simplicity, to the important and long-standing problem: does a resonance contribute to the forward-angle scattering of the F + H2 reaction? We reduce the problem to its essentials and present a well-defined, yet rigorous and unambiguous, investigation of structure in the differential cross sections (DCSs) of the following three state-to-state reactions at a translational energy of 62.09 meV: F + H2(vi = 0, ji = 0, mi = 0) → FH(vf = 3, jf = 0, 1, 2, mf = 0) + H, where vi, ji, mi and vf, jf, mf are the initial and final vibrational, rotational and helicity quantum numbers respectively. Firstly, we carry out quantum-scattering calculations for the Fu-Xu-Zhang potential energy surface, obtaining accurate numerical scattering matrix elements for indistinguishable H2. The calculations use a time-independent method, with hyperspherical coordinates and an enhanced Numerov method. Secondly, the following theoretical techniques are employed to analyse structures in the DCSs: (a) full and Nearside-Farside (NF) partial wave series (PWS) and local angular momentum theory, including resummations of the full PWS up to second order. (b) The recently introduced "CoroGlo" test, which lets us distinguish between glory and corona scattering at forward angles for a Legendre PWS. (c) Six asymptotic (semiclassical) forward-angle glory theories and three asymptotic farside rainbow theories, valid for rainbows at sideward-scattering angles. (d) Complex angular momentum (CAM) theories of forward and backward scattering, with the Regge pole positions and residues computed by Thiele rational interpolation. Thirdly, our conclusions for the three PWS DCSs are: (a) the forward-angle peaks arise from glory scattering. (b) A broad (hidden) farside rainbow is present at sideward angles. (c) A single Regge pole contributes to the DCS across the whole angular range, being most prominent at forward angles. This proves that a resonance contributes to the DCSs for the three transitions. (d) The diffraction oscillations in the DCSs arise from NF interference, in particular, interference between the Regge pole and direct subamplitudes.

Accurate measurement of the loss rate of cold atoms due to background gas collisions for the quantum-based cold atom vacuum standard

We present the measurements of thermalized collisional rate coefficients for ultra-cold 7Li and 87Rb colliding with room-temperature He, Ne, N2, Ar, Kr, and Xe. In our experiments, a combined flowmeter and dynamic expansion system, a vacuum metrology standard, is used to set a known number density for the room-temperature background gas in the vicinity of the magnetically trapped 7Li or 87Rb clouds. Each collision with a background atom or molecule removes a 7Li or 87Rb atom from its trap, and the change in the atom loss rate with background gas density is used to determine the thermalized loss rate coefficients with fractional standard uncertainties better than 1.6% for 7Li and 2.7% for 87Rb. We find consistency—a degree of equivalence of less than one—between the measurements and recent quantum-scattering calculations of the loss rate coefficients [Kłos and Tiesinga, J. Chem. Phys. 158, 014308 (2023)], with the exception of the loss rate coefficient for both 7Li and 87Rb colliding with Ar. Nevertheless, the agreement between theory and experiment for all other studied systems provides validation that a quantum-based measurement of vacuum pressure using cold atoms also serves as a primary standard for vacuum pressure, which we refer to as the cold-atom vacuum standard.

High-precision cavity-enhanced spectroscopy for studying the H2-Ar collisions and interactions.

Information about molecular collisions is encoded in the shapes of collision-perturbed molecular resonances. This connection between molecular interactions and line shapes is most clearly seen in simple systems, such as the molecular hydrogen perturbed by a noble gas atom. We study the H2-Ar system by means of highly accurate absorption spectroscopy and ab initio calculations. On the one hand, we use the cavity-ring-down-spectroscopy technique to record the shapes of the S(1) 3-0 line of molecular hydrogen perturbed by argon. On the other hand, we simulate the shapes of this line using ab initio quantum-scattering calculations performed on our accurate H2-Ar potential energy surface (PES). In order to validate the PES and the methodology of quantum-scattering calculations separately from the model of velocity-changing collisions, we measured the spectra in experimental conditions in which the influence of the latter is relatively minor. In these conditions, our theoretical collision-perturbed line shapes reproduce the raw experimental spectra at the percent level. However, the collisional shift, δ0, differs from the experimental value by 20%. Compared to other line-shape parameters, collisional shift displays much higher sensitivity to various technical aspects of the computational methodology. We identify the contributors to this large error and find the inaccuracies of the PES to be the dominant factor. With regard to the quantum scattering methodology, we demonstrate that treating the centrifugal distortion in a simple, approximate manner is sufficient to obtain the percent-level accuracy of collisional spectra.

Ab initio quantum scattering calculations for the CO-O2 system and a new CO-O2 potential energy surface: O2 and air broadening of the R(0) line in CO.

We present ab initio calculations of the collisional broadening of the R(0) pure rotational line in CO (at 115GHz) perturbed by O2. Our calculations are done in a fully quantum way by solving close-coupling quantum-scattering equations without any approximations. We also report a new, highly accurate CO-O2 potential energy surface on which we did the quantum-scattering calculations. The calculated collisional broadening agrees with the available experimental data in a wide temperature range. The calculated collisional shift is negligible compared to the broadening, which is also consistent with the experimental data. We combine this result with our previous calculations for the same line in CO perturbed by N2 [Jóźwiak et al., J. Chem. Phys. 154, 054314 (2021)]; the obtained air-perturbed broadening of the R(0) pure rotational line in CO and its temperature dependence perfectly agree with the HITRAN database. This result constitutes an important step toward developing a methodology for providing accurate ab initio reference data on spectroscopic collisional line-shape parameters for molecular systems relevant to the Earth's atmosphere and for populating spectroscopic line-by-line databases.

Two-Center Interference in the Photoionization Delays of Kr_{2}.

We present the experimental observation of two-center interference in the ionization time delays of Kr_{2}. Using attosecond electron-ion-coincidence spectroscopy, we simultaneously measure the photoionization delays of krypton monomer and dimer. The relative time delay is found to oscillate as a function of the electron kinetic energy, an effect that is traced back to constructive and destructive interference of the photoelectron wave packets that are emitted or scattered from the two atomic centers. Our interpretation of the experimental results is supported by solving the time-independent Schrödinger equation of a 1D double-well potential, as well as coupled-channel multiconfigurational quantum-scattering calculations of Kr_{2}. This work opens the door to the study of a broad class of quantum-interference effects in photoionization delays and demonstrates the potential of attosecond coincidence spectroscopy for studying weakly bound systems.

CO-Ar collisions: ab initio model matches experimental spectra at a sub percent level over a wide pressure range

We use three independent spectroscopic techniques, operating in the millimeter-wavelength range, to study molecule-atom collisions, and validate our quantum-scattering calculations on two recent potential energy surfaces. We study the first pure rotational transition in a CO molecule perturbed by Ar. This molecular system is a good prototype of atmospherically relevant cases. It is, on the one hand, affordable for calculation of the line shape parameters by modern ab initio methods, and on the other hand, is very convenient for experimental studies because of its regular, well spaced rotational spectrum having a moderate intensity. We show that the simulated collision-perturbed spectra, which are based on our fully ab initio calculations, agree with the experimental line profiles at sub-percent level over a wide range (more than four orders of magnitude) of pressures. We demonstrate that the agreement between theory and experiment can be further improved if the model accounts for the collisional transfer of an optical coherence between different rotational transitions (the line-mixing effect). We show that the two surfaces tested in this work lead to a very similar agreement with the experiment. Capability of calculating line shape parameters in a broad range of temperatures is demonstrated.

Collisional excitation of deuterated hydroxyl (OD) by molecular hydrogen

ABSTRACT Cross sections and rate coefficients for transitions between hyperfine levels associated with the 14 lowest rotational/fine-structure levels of OD induced by collisions with ortho-H2 and para-H2 are presented. These collisional parameters have been computed in time-independent close-coupling quantum-scattering calculations with a potential energy surface (PES) describing the OD–H2 interaction, which was obtained by transformation of the OH–H2 PES. Rate coefficients have been computed for temperatures from 5 to 200 K. Cross sections for OD transitions between rotational/fine-structure levels are found to be significantly larger than the corresponding transitions in OH, mainly because of the reduced energy gaps in OD. The hyperfine-resolved rate coefficients were employed in simple radiative transfer calculations for OD and compared with analogous calculations for OH.

Inelastic scattering in isotopologues of O2-Ar: the effects of mass, symmetry, and density of states.

The two species considered here, O2 (oxygen molecule) and Ar (argon-atom), are both abundant components of Earth's atmosphere and hence familiar collision partners in this medium. O2 is quite reactive and extensively involved in atmospheric chemistry, including Chapman's cycle of the formation and destruction of ozone; while Ar, like N2, typically plays the nevertheless crucial role of inert collider. Inert species can provide stabilization to metastable encounter-complexes through the energy transfer associated with inelastic collisions. The interplay of collision frequency and energy transfer efficiency, with state lifetimes and species concentrations, contributes to the rich and varied chemistry and dynamics found in diverse environments ranging from planetary atmospheres to the interstellar and circumstellar media. The nature and density of bound and resonance states, coupled electronic states, symmetry, and nuclear spin-statistics can all play a role. Here, we systematically investigate some of those factors by looking at the O2-Ar system, comparing rigorous quantum-scattering calculations for the 16O16O-40Ar, 18O16O-40Ar, and 18O18O-40Ar isotope combinations. A new accurate potential energy surface was constructed for this purpose holding the O2 bond distance at its vibrationally averaged distance.

The first comprehensive dataset of beyond-Voigt line-shape parameters from ab initio quantum scattering calculations for the HITRAN database: He-perturbed H[formula omitted] case study

We demonstrate a new method for populating line-by-line spectroscopic databases with beyond-Voigt line-shape parameters, which is based on ab initio quantum scattering calculations. We report a comprehensive dataset for the benchmark system of He-perturbed H2 (we cover all the rovibrational bands that are present in the HITRAN spectroscopic database). We generate the entire dataset of the line-shape parameters (broadening and shift, their speed dependence, and the complex Dicke parameter) from fully ab initio quantum-scattering calculations. We extend the previous calculations by taking into account the centrifugal distortion for all the bands and by including the hot bands. The results are projected on a simple structure of the quadratic speed-dependent hard-collision profile. We report a simple and compact formula that allows the speed-dependence parameters to be calculated directly from the generalized spectroscopic cross sections. For each line and each line-shape parameter, we provide a full temperature dependence within the double-power-law (DPL) representation, which makes the dataset compatible with the HITRAN database. The temperature dependences cover the range from 20 to 1000 K, which includes the low temperatures relevant for the studies of the atmospheres of giant planets. The final outcome from our dataset is validated on highly accurate experimental spectra collected with cavity ring-down spectrometers. The methodology can be applied to many other molecular species important for atmospheric and planetary studies.

Evolution of a Molecular Shape Resonance along a Stretching Chemical Bond.

We report experiments on laser-assisted electron recollisions that result from strong-field ionization of photoexcited I_{2} molecules in the regime of low-energy electron scattering (<25 eV impact energy). By comparing differential scattering cross sections extracted from the angle-resolved photoelectron spectra to differential scattering cross sections from quantum-scattering calculations, we demonstrate that the electron-scattering dynamics is dominated by a shape resonance. When the molecular bond stretches during the evolution of a vibrational wave packet this shape resonance shifts to lower energies, both in experiment and theory. We explain this behavior by the nature of the resonance wave function, which closely resembles an antibonding molecular orbital of I_{2}.

Ab initio quantum calculations of collisional effects in molecular spectra

SynopsisWe present the methodology of obtaining the dataset of the beyond-Voigt line-shape parameters for spectroscopic databases from fully ab initio quantum-scattering calculations. It provides not only the pressure broadening and shift coefficients, but also their speed dependencies and the complex Dicke parameter. This approach is based on the calculations of the generalized spectroscopic cross section, resulting from the close-coupling equations solved for a given scattering system. The calculations were validated on accurate experimental spectra of the helium-perturbed hydrogen molecule.

Long-range versus short-range effects in cold molecular ion-neutral collisions

The investigation of cold interactions between ions and neutrals has recently emerged as a new scientific frontier at the interface of physics and chemistry. Here, we report a study of charge-transfer (CT) collisions of Rb atoms with N{}_{2}^{+} and O{}_{2}^{+} ions in the mK regime using a dynamic ion-neutral hybrid trapping experiment. We observe markedly different CT kinetics and dynamics for the different systems and reaction channels studied. While the kinetics in some channels are consistent with classical capture theory, others show distinct non-universal dynamics. The experimental results are interpreted with the help of classical-capture, quasiclassical-trajectory and quantum-scattering calculations using ab-initio potentials for the highly excited molecular states involved. The theoretical analysis reveals an intricate interplay between short- and long-range effects in the different reaction channels which ultimately determines the CT dynamics and rates. Our results illustrate salient mechanisms that determine the efficiency of cold molecular CT reactions.

Unexpected dynamical effects change the lambda-doublet propensity in the tunneling region for the O(3P) + H2 reaction.

One of the most relevant features of the O(3P) + H2 reaction is that it occurs on two different potential energy surfaces (PESs) of symmetries A' and A'' that correlate reactants and products. The respective saddle points, which correspond to a collinear arrangement, are the same for both PESs, whilst the barrier height rises more abruptly on the 3A' PES than on the 3A'' PES. Accordingly, the reactivity on the 3A'' PES should be always higher than on the 3A' PES. In this work, we present accurate quantum-scattering calculations showing that this is not always the case for rotationless reactants, where dynamical factors near the reaction threshold cause the 3A' PES to dominate at energies around the barrier. Further calculation of cross sections and Λ-doublet populations has allowed us to establish how the reaction mechanism changes from the deep tunneling regime to hyperthermal energies.

Long-lived complexes and signatures of chaos in ultracold K2 +Rb collisions

Lifetimes of complexes formed during ultracold collisions are of current experimental interest as a possible cause of trap loss in ultracold gases of alkali-dimers. Microsecond lifetimes for complexes formed during ultracold elastic collisions of K2 with Rb are reported, from numerically-exact quantum-scattering calculations. The reported lifetimes are compared with those calculated using a simple density-of-states approach, which are shown to be reasonable. Long-lived complexes correspond to narrow scattering resonances which we examine for the statistical signatures of quantum chaos, finding that the positions and widths of the resonances follow the Wigner-Dyson and Porter-Thomas distributions respectively.

Quantum Scattering Calculations of Transport Properties for the H-N2 and H-CH4 Collision Pairs.

Transport properties for collisions of hydrogen atoms with molecular nitrogen and methane were calculated through close-coupling quantum scattering calculations. For these calculations, potential energy surfaces for the interaction of H atoms with these molecules, with their geometries fixed at the respective equilibrium structures, were obtained with a coupled cluster method that included single, double, and (perturbatively) triple excitations [RCCSD(T)]. The computed transport properties for H-N2 were found to be similar in magnitude to those computed in a previous study but significantly different from those obtained through the conventional approach that employs isotropic Lennard-Jones (LJ) (12-6) potentials. The differences in the transport properties for H-CH4 computed in this work and those estimated with isotropic LJ potentials are somewhat smaller.

Low-temperature rate coefficients for vibrational relaxation of (3)Σ(u)(+)Rb2 molecules by (3)He and (4)He atoms.

We present quantum-scattering calculations of (4)He and (3)He colliding with (87)Rb2. For both helium isotopes, the elastic and inelastic rate coefficients are strongly influenced by the J = 1 partial wave. For the lighter isotope, a strong resonance feature of the J = 1 partial wave is responsible for an extremely efficient vibrational relaxation process. We also perform bound-state calculations of the Rb2He complex for even Rb permutation symmetry and nonzero total angular momentum. The global Rb2He (3)Σu(+) potential-energy surface used supports four bound states for (4)He and a single one for (3)He. We propose an analysis of the (87)Rb2(4)He spectrum separating the contributions of Rb2 rotation and helium motion.

Ion-neutral chemistry at ultralow energies: dynamics of reactive collisions between laser-cooled Ca+ ions and Rb atoms in an ion-atom hybrid trap †

Cold chemical reactions between laser-cooled Ca+ ions and Rb atoms were studied in an ion-atom hybrid trap. Reaction rate constants were determined in the range of collision energies ⟨E coll⟩/k B=20 mK-20 K. The lowest energies were achieved in experiments using single localised Ca+ ions. Product branching ratios were studied using resonant-excitation mass spectrometry. The dynamics of the reactive processes in this system (non-radiative and radiative charge transfer as well as radiative association leading to the formation of CaRb+ molecular ions) have been analysed using high-level quantum-chemical calculations of the potential energy curves of CaRb+ and quantum-scattering calculations for the radiative channels. For the present low-energy scattering experiments, it is shown that the energy dependence of the reaction rate constants is governed by long-range interactions in line with the classical Langevin model, but their magnitude is determined by short-range non-adiabatic and radiative couplings which only weakly depend on the asymptotic energy. The quantum character of the collisions is predicted to manifest itself in the occurrence of narrow shape resonances at well-defined collision energies. The present results highlight both universal and system-specific phenomena in cold ion-neutral reactive collisions.

Laser-induced fluorescence study of spin–orbit quenching of Cl(2P1/2) by H2, D2, and HD gases

Employing ultraviolet laser flash photolysis in combination with pulsed vacuum ultraviolet laser induced-fluorescence spectroscopy room-temperature rate constants kQ,H2=(5.8±0.6)×10−11cm3s−1, kQ,D2=(5.6±0.6)×10−12cm3s−1, and kQ,HD=(2.7±0.3)×10−11cm3s−1 for electronically non-adiabatic quenching of spin–orbit excited Cl(2P1/2) atoms in collisions with H2, D2, and HD gases were determined, which allow for comparison with results of recent quantum-scattering calculations [14,15].

Quenching of internal rotations versus collisional cooling at ultralow energies for weakly interacting partners: Cs2(3Σu+)withHe3,4

Quantum-scattering calculations at ultralow (close to 10{sup -6} cm{sup -1}) collision energies are carried out for the Cs dimer in its spin-stretched triplet state, interacting with helium. An ab initio potential energy surface is computed and employed, while the target molecule is kept in its ground vibrational state and several excitated initial rotational states are considered in the quantum dynamics. The highly anisotropic interaction is seen to cause, in spite of its weakness, internal energy quenching rates comparable with the efficiency of the collisional cooling of relative kinetic energies. The rates of spin-flip processes are also analyzed and compared with pure rotational quenching events.