Cross Sections For Rotational Transitions Research Articles

Electron-impact rotational excitation cross-sections and rate coefficients of molecular ion: HCO+

ABSTRACT HCO+ is one of the most abundant polyatomic ion in the Universe, also its presence in the planetary atmospheres and interstellar medium (ISM) makes it an interesting case to study. Low energy e−-HCO+ collisions result in rotational excitation and other molecular processes. In this study, the cross-sections for rotational transitions in HCO+ are evaluated for four rotational levels (j = 0, 1, 2, and 3) using the UK R-matrix method and the multichannel quantum defect theory (MQDT). The UK R-matrix method used to generate scattering matrices, through which cross-sections are computed. In past two decades, after developments and implementations of different theoretical approaches, the improved channel elimination procedure applied here is more promising to evaluate more accurate results near rotational thresholds important for the analysis of intensities of microwave region in plasma modelling. The rate coefficients are deduced from the computed cross-sections and studied over a wide electron temperature range.

Collisional Quenching of Highly Excited H2 due to H2 Collisions

Abstract Rate coefficients for pure rotational quenching in H2(ν 1 = 0, j 1) + H2(ν 2 = 0, j 2) collisions from initial levels of j 1 = 2–31 (j 2 = 0 or 1) to all lower rotational levels are presented. We carried out extensive quantum mechanical close-coupling calculations based on a recently published H2–H2 potential energy surface (PES) developed by Patkowski et al. that has been demonstrated to be more reliable than previous work. Rotational transition cross sections with initial levels of j 1 = 2–14, 18, 19, 24, and 25 were computed for energies ranging from 10−6 to 1000 cm−1, while the coupled-states approximation was adopted from 2000 to 20,000 cm−1. The corresponding rate coefficients were calculated for the temperature range 10−5 ≤ T ≤ 10,000 K. Scaling methods based on the ultra-cold data (10−5–1 K) were used to estimate rate coefficients for all other intermediate rotational states. Comparisons with previous work that adopted different PESs show small discrepancies at high temperatures and in low-energy resonance regions. The astrophysical applications of the current results are briefly discussed, including the rotational H2 critical densities due to para-H2 and ortho-H2 collisions.

Diabatic states, nonadiabatic coupling, and the counterpoise procedure for weakly interacting open-shell molecules

We study nonadiabatic coupling in systems of weakly interacting open-shell molecules which have nearly degenerate electronic states and hence significant nuclear derivative couplings. By comparison to numerically calculated nuclear derivatives of adiabatic electronic wave functions, we show that nonadiabatic couplings are represented accurately by diabatization using a recent multiple-property-based algorithm [T. Karman et al., J. Chem. Phys. 144, 121101 (2016)]. Accurate treatment of weakly interacting molecules furthermore requires counterpoise corrections for the basis-set superposition error. However, the generalization of the counterpoise procedure to open-shell systems is ambiguous. Various generalized counterpoise schemes that have been proposed previously are shown to be related through different choices for diabatization of the monomer wave functions. We compare these generalized counterpoise schemes and show that only two approaches accurately describe long-range interactions. In addition, we propose an approximate diabatization algorithm based on the asymptotic long-range interaction. This approach is appealingly simple to implement as it yields analytical expressions for the transformation to the diabatic representation. Finally, we investigate the effects of diabatizing intermolecular potentials on the nuclear dynamics by performing quantum scattering calculations for NO(X2Π)–H2. We show that cross sections for pure rotational transitions are insensitive to diabatization. For spin-orbit inelastic transitions, asymptotic diabatization and multiple-property-based diabatization are in qualitative agreement, but the quantitative differences may be observable experimentally.

Theoretical investigation of rotationally inelastic collisions of CH(X2Π) with hydrogen atoms.

We report calculations of state-to-state cross sections for collision-induced rotational transitions of CH(X2Π) with atomic hydrogen. These calculations employed the four adiabatic potential energy surfaces correlating CH(X2Π) + H(2S), computed in this work through the multi-reference configuration interaction method [MRCISD + Q(Davidson)]. Because of the presence of deep wells on three of the potential energy surfaces, the scattering calculations were carried out using the quantum statistical method of Manolopoulos and co-workers [Chem. Phys. Lett. 343, 356 (2001)]. The computed cross sections included contributions from only direct scattering since the CH2 collision complex is expected to decay predominantly to C + H2. Rotationally energy transfer rate constants were computed for this system since these are required for astrophysical modeling.

Theoretical investigation of rotationally inelastic collisions of CH(X2Π) with molecular hydrogen.

We report calculations of state-to-state cross sections for collision-induced rotational transitions of CH(X2Π) with molecular hydrogen. These calculations employed the diabatic matrix elements of the interaction potential determined by Dagdigian [J. Chem. Phys. 145, 114301 (2016)], which employed the multi-reference configuration-interaction method [MRCISD+Q(Davidson)]. Because of the presence of a deep well on the lower potential energy surface, the scattering calculations were carried out using the quantum statistical method of Manolopoulos and co-workers [Chem. Phys. Lett. 343, 356 (2001)]. The computed cross sections included contributions from direct scattering, as well as from the formation and decay of a collision complex. The magnitude of latter contribution was found to decrease significantly with increasing collision energy. Rotationally energy transfer rate constants were computed for this system since these are required for astrochemical modeling.

The first potential energy surfaces for the C6H(-)-H2 and C6H(-)-He collisional systems and their corresponding inelastic cross sections.

Molecular anions have recently been detected in the interstellar and circumstellar media. Accurate modeling of their abundance requires calculations of collisional data with the most abundant species that are usually He atoms and H2 molecules. In this paper, we focus on the collisional excitation of the first observed molecular anion, C6H(-), by He and H2. Theoretical calculations of collisional cross sections rely generally on ab initio interaction potential energy surfaces (PESs). Hence, we present here the first PESs for the C6H(-)-H2 and C6H(-)-He van der Waals systems. The ab initio energy data for the surfaces were computed at the explicitly correlated coupled cluster with single, double, and scaled perturbative triple excitations level of theory. The method of interpolating moving least squares was used to construct 4D and 2D analytical PESs from these data. Both surfaces are characterized by deep wells and large anisotropies. Analytical models of the PESs were used in scattering calculations to obtain cross sections for low-lying rotational transitions. As could have been anticipated, important differences exist between the He and H2 cross sections. Conversely, no significant differences exist between the collisions of C6H(-) with the two species of H2 (para- and ortho-H2). We expect that these new data will help in accurately determining the abundance of the C6H(-) anions in space.

Multichannel quantum defect theory for rovibrational transitions in ultracold molecule-molecule collisions

Multichannel quantum defect theory (MQDT) has been widely applied to resonant and nonresonant scattering in a variety of atomic collision processes. In recent years, the method has been applied to cold collisions with considerable success, and it has proven to be a computationally viable alternative to full close-coupling (CC) calculations when spin, hyperfine, and external field effects are included. In this paper, we describe a hybrid approach for molecule-molecule scattering that includes the simplicity of MQDT while treating the short-range interaction explicitly using CC calculations. This hybrid approach, demonstrated for ${\mathrm{H}}_{2}\text{\ensuremath{-}}{\mathrm{H}}_{2}$ collisions in full dimensionality, is shown to adequately reproduce cross sections for quasiresonant rotational and vibrational transitions in the ultracold $(1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K})$ and $\ensuremath{\sim}1\ensuremath{-}10\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ regime spanning seven orders of magnitude. It is further shown that an energy-independent short-range $K$ matrix evaluated in the ultracold regime $(1 \ensuremath{\mu}\mathrm{K})$ can adequately characterize cross sections in the mK-K regime when no shape resonances are present. The hybrid CC-MQDT formalism provides an alternative approach to full CC calculations at considerably less computational expense for cold and ultracold molecular scattering.

Theoretical investigation of rotationally inelastic collisions of the methyl radical with helium

Rotationally inelastic collisions of the CH(3) molecule in its ground X(2)A(2)'' electronic state have been investigated. We have determined a potential energy surface (PES) for the interaction of rigid CH(3), frozen at its equilibrium geometry, with a helium atom, using a coupled-cluster method that includes all single and double excitations, as well as perturbative contributions of connected triple excitations [RCCSD(T)]. The anisotropy of the PES is dominated by repulsion of the helium by the hydrogen atoms. The dissociation energy D(e) was computed to equal 27.0 cm(-1). At the global minimum, the helium atom lies in the CH(3) plane between two C-H bonds at an atom-molecule separation R = 6.52 bohr. Cross sections for collision-induced rotational transitions have been determined through quantum scattering calculations for both nuclear spin modifications. Rotationally inelastic collisions can cause a change in the rotational angular momentum n and its body-frame projection k. Because of the anisotropy of the PES due to the hydrogen atoms, there is a strong propensity for Δk = ±3 transitions. Thermal rate constants for state-specific total collisional removal have also been determined.

Rotational Quenching Rate Coefficients for H2in Collisions with H2from 2 to 10,000 K

Rate coefficients for rotational transitions in H2 induced by H2 impact are presented. Extensive quantum mechanical coupled-channel calculations based on a recently published (H2)2 potential energy surface were performed. The potential energy surface used here has been demonstrated to be more reliable than surfaces used in previous work. Rotational transition cross sections with initial levels of -->J ≤ 8 were computed for collision energies ranging between 10−4 and 2.5 eV, and the corresponding rate coefficients were calculated for the temperature range -->2 ≤ T≤ 10,000 K. In general, agreement with earlier calculations, which were limited to 100-6000 K, is good, although discrepancies are found at the lowest and highest temperatures. Low-density-limit cooling functions due to para- and ortho-H2 collisions are obtained from the collisional rate coefficients. Implications of the new results for nonthermal H2 rotational distributions in molecular regions are also investigated.

The He–CaH(2Σ+) interaction. II. Collisions at cold and ultracold temperatures

We present cross sections for rotational, vibrational, and fine-structure transitions in He–CaH(2Σ) collisions at cold and ultracold temperatures calculated using the ab initio potential energy surface reported in the preceding paper. Rotational quenching is fast, vibrational quenching is slow. The spin-rotational interaction, although small and having no influence at temperatures above 10 K, changes significantly the rate coefficients for rotational quenching at lower temperatures. The theoretical rotational, vibrational, and elastic cross sections are compared with the results of a buffer gas cooling experiment carried out at a temperature of about 0.4 K. The theoretical predictions for the vibrational and elastic cross sections are larger than the measured values. The sensitivity to the potential energy surface is explored. A modified surface diminishes but does not remove the differences between theory and experiment.

Laser-induced (5145 Å) B 1Πu→X 1Σ+g fluorescence of Na2

Laser-induced emission of the Na2 molecule consisting of discretemolecular fluorescence series was observed in the gas phase atan excitation wavelength of 5145.308 Å from anargon-ion laser. Eighteen fluorescence series for theB 1Πu→X 1Σ+g band system have beenobserved and analysed. Several fluorescence series are reported for thefirst time. The radiative transition probabilities for the observedfluorescence series were calculated using experimentally based hybridpotential energy curves for theB 1Πu and X 1Σ+g states constructed up todissociation and a B-X transition dipole moment function. Radiativelifetimes for the rovibrational levels of the upper states pumped by thelaser line have also been calculated. The transition probabilities andlifetimes agree with the corresponding observed measurements usuallywithin the experimental uncertainty. A strong rotational satellitestructure, with jumps withΔJ' = ±1,±2,...,±16 in some cases, for the mostintense bands of several fluorescence series was also analysed. Absoluteintegral cross sections for collision-induced rotational transitions,whenNa2*(v',J') in theB 1Πu state collides with Na atoms, for some v'-v''vibrational bands of intense fluorescence series, are also reported.

Differential cross sections for electron/positron scattering from polyatomic molecules

We describe a new computational code which allows for the calculation of elastic and rotationally inelastic differential cross sections (DCS) for electron/positron scattering from neutral polyatomic molecule with and without permanent dipole moments. The computation can deal both with linear and nonlinear systems. In the case of polar targets a procedure which corrects for the nonconvergence of the DCS in the Body-Fixed (BF) frame is described and implemented. The corresponding state-to-state rotationally inelastic and rotationally summed differential cross sections for rotational transitions involving spherical, symmetric and asymmetric top rotors are also given by the present code.

An analysis of rotational transition probabilities and cross sections using close coupling, hard shape, and classical trajectory methods

Classical and quantum transition probabilities were calculated applying the two (2D) and three (3D) dimensional close‐coupled and classical trajectory methods. The collision energy was 0.01 eV and, in this case, there are 12 classical accessible states for Xe−CO2 collisions. It was shown that for Δj≥8 the 2D and 3D transition probabilities agree quantitatively. The state‐to‐state total cross sections were also compared, in the same level of dimension, and the results showed similar trends. In addition, the hard shape quantum cross sections were compared with the 2D results and showed that the classical turning point cannot be used to obtain the semi‐axes of the ellipse, namely A and B. Moreover, the intensity of the hard shape cross sections showed to be different either for the 2D or 3D close coupling calculations. The comparison between the transition probabilities, carried out by the 2D and 3D quantum methods, showed the nature of the 2D results with accurate agreement for large Δj transitions.

Potential Parameters and Energy Dependence of Rotational Energy Transfer in Molecular Systems

The cross-sections for rotational transitions in a diatomic molecule due to collision with an atom were computed. An empirical relation is obtained that gives the dependence of cross-sections on the energy of the colliding system and the parameters of the interaction potential energy surface. The results are interpreted to investigate the mechanism of the rotational energy transfer process. The cross-sections are found to depend linearly on the torque, range of the potential, and the collision time. Depending on the variation in the location of classical turning point with change in energy, the cross-sections may increase or decrease with energy or cross-section versus energy curve may exhibit maxima or minima. PACS numbers: 35.20.-i

Effect of rovibrational coupling on the dynamics of ionic systems: the Kr-O2+ case

Various quantum decoupling and semiclassical methods are used to calculate cross sections for rotational and rovibrational transitions in O2+ colliding with Kr. A general analysis of time scales for rotational and vibrational excitations and of coupling strengths for the corresponding potentials is used to review the standard decoupling methods that treat separately vibrations and rotations in atom-molecule collisions. When such decoupling is applied to strongly interacting ionic systems and to heavy particles, it is found to fail rather dramatically and to be brought back to reliable values only when fully coupled rovibrational equations are used to treat the dynamics.

On the rotational angular momentum polarization in N+2–He. Classical trajectory and hard-ellipsoid model calculations

Classical trajectory and hard-ellipsoid methods are used to investigate collision-induced rotational alignment effects in N+2–He. Classical total, mf-resolved, and tensor cross sections for collision-induced rotational transitions are presented. Comparison of classical trajectory and quantum closed-coupled results show that total rotational inelastic cross sections are in good agreement, while mf-resolved and tensor cross sections agree only semiquantitatively. Velocity-averaged alignment parameters for N+2 ions drifting in a helium buffer gas are computed using a hard-ellipsoid model and a semiempirical two-dimensional velocity distribution. The alignment parameters are found to be smaller than the experimental values but lie in the range of the parameters obtained from a former quantum closed-coupled analysis.

Inelastic transitions in vibrationally excited Na2 induced by intermediate-energy-electron impact.

Differential cross sections for rotational transitions from vibrationally excited sodium dimers (v=2 and v=31) by electron impact at 150 eV have been measured. The rotational inelasticity increases with the initial vibrational quantum number. Analysis of the data provides clear evidence for vibrational transitions as well. The cross section for vibrational transitions increases with the vibrational quantum number and is not small compared to the cross section for rotational transitions. The experimental data are well reproduced by a simple two-center model.

Rotationally inelastic collisions of a molecule in a 1Δ electronic state: NH(a 1Δ)

The general theory for inelastic scattering of molecules 1Δ electronic states is outlined and applied to the specific case of 1Δ states arising from a π2 electron occupancy, e.g., NH(a 1Δ). Integral cross sections for rotational transitions out of the lowest rotational level (J=2) of NH(a 1Δ) v=0 are reported for several targets. A pulsed beam of rotationally cold NH(a 1Δ) was produced by 193 nm photolysis of a dilute mixture of hydrazoic acid in nitrogen seed gas at the tip of a nozzle. The target beam was also prepared as a pulsed supersonic beam. The final rotational state distribution was measured in the collision zone by laser fluorescence excitation. The state-to-state cross sections were found to decrease significantly with increasing final rotational quantum number J′. The magnitude of the J=2→J′=3 cross sections were compared for the different targets. Isotopic scrambling in NH(a 1Δ)–D2 collisions was also searched for but not observed.

Scaling relations in the rotational excitation of NH(X 3∑−) N=0 by argon

Integral cross sections for rotational transitions out of the lowest rotational level of NH(3∑−)v=0, namely N=0, J=1 F1, induced by collisions with argon have been measured in a crossed beam experiment. A pulsed beam of rotationally cold NH(3∑−) was produced by 193 nm photolysis of a dilute mixture of ammonia in nitrogen seed gas at the tip of a nozzle, the argon beam was also prepared in a pulsed source. The final rotational and spin–state populations were interrogated in the collision zone by laser fluorescence excitation in the A 3Π←X 3∑−(1,0) band of NH. Within a given N′ manifold, the F1 spin level had the largest values for the cross sections out of N=0. The spin–state distributions are, in fact, well described by the general formulas for inelastic collisions of a case (b) 3∑ molecule. The derived spin–free tensor opacities show a rapid decrease as a function of increasing N′.

State resolved cross sections for rotationally inelastic collisions of NH2(X̃ 2B1) with helium

Integral cross sections for rotational transitions from the lowest orthorotational level (00,0) of NH2 induced by collisions with helium have been measured in a crossed beam experiment. A pulsed supersonic beam of rotationally cold NH2 was produced by 193 nm photolysis of a dilute mixture of ammonia in argon seed gas at the tip of a nozzle; the helium target was also prepared as a pulsed beam. The final rotational state populations (without spin-state resolution) in the Ka=0 and 1 manifolds of NH2 were interrogated in the collision zone by dye laser fluorescence excitation in the à 2A1←X̃ 2B1 band system. Because of the rotational selection rules in this band system, it was not possible to put the cross sections for the two Ka manifolds on the same scale. Within a given Ka manifold, there is a marked preference for collisional transitions with the smallest ΔN change. These experimental results are compared to calculated close-coupling rotationally inelastic cross sections for H2O(00,0)–He collisions.