Close-coupling Calculations Research Articles

Collision excitation of c-C3H-(X1A1) by He.

Accurate modeling of anionic abundances in the interstellar and circumstellar media requires calculations of collisional data with the most abundant species that are usually He atoms and H2 molecules. In this paper, we focus on smaller cyclic molecular anion, c-C3H-, an astrophysical candidate, following the detection of larger CnH- carbon chains. From a new three-dimensional potential energy surface, the rotational (de-)excitation of the c-C3H-(X1A1) anion by collision with He is investigated. The surface is obtained in the supermolecular approach at the CCSD(T)-F12/aug-cc-pVTZ level of theory. Fully quantum close-coupling calculations of inelastic integral cross sections are performed on a grid of collisional energies large enough to ensure the convergence of the state-to-state rate coefficients for the 34 first rotational levels up to jKa,Kc = 77,0 of c-C3H- and temperatures ranging from 5 to 100K. For this collisional system, rate coefficients exhibit a strong dominance in favor of 21,2 → l1,1 downward transition. This transition was previously used for the detection of the cyclic parent c-C3H. The c-C3H--He rate coefficients (∼10-11cm3s-1) are of the same order of magnitude as those of the detected anions CnH- (as C2H-, C4H-, and C6H-) in collision with He and one order of magnitude smaller than those with H2. The critical densities of H2 were also estimated, and a discussion on the validity of the local thermodynamic equilibrium conditions is carried out. This work represents the contribution to understanding and modeling abundances and chemistry of hydrocarbon radicals, CnH, in astrophysical media.

HeH+ Collisions with H2: Rotationally Inelastic Cross Sections and Rate Coefficients from Quantum Dynamics at Interstellar Temperatures.

We report for the first time an accurate ab initio potential energy surface for the HeH+–H2 system in four dimensions (4D) treating both diatomic species as rigid rotors. The computed ab initio potential energy point values are fitted using an artificial neural network method and used in quantum close coupling calculations for different initial states of both rotors, in their ground electronic states, over a range of collision energies. The state-to-state cross section results are used to compute the rate coefficients over a range of temperatures relevant to interstellar conditions. By comparing the four dimensional quantum results with those obtained by a reduced-dimensions approach that treats the H2 molecule as an averaged, nonrotating target, it is shown that the reduced dimensionality results are in good accord with the four dimensional results as long as the HeH+ molecule is not initially rotationally excited. By further comparing the present rate coefficients with those for HeH+–H and for HeH+–He, we demonstrate that H2 molecules are the most effective collision partners in inducing rotational excitation in HeH+ cation at interstellar temperatures. The rotationally inelastic rates involving o-H2 and p-H2 excitations are also obtained and they turn out to be, as in previous systems, orders of magnitude smaller than those involving the cation. The results for the H2 molecular partner clearly indicate its large energy-transfer efficiency to the HeH+ system, thereby confirming its expected importance within the kinetics networks involving HeH+ in interstellar environments.

Measurements of charge transfer and target-electron-loss cross sections forH+,D+, andHe+impact on lithium at low energies

Experimental cross section measurements for charge transfer and for electron loss from lithium via charge transfer and direct ionization are reported for collisions between light ions and lithium atoms. Beams of protons, deuterium ions, and helium ions intersect a lithium atom beam, and collision cross sections are inferred by measuring the number of lithium ions produced in the collisions. The collision energy ranges studied are 0.13--3.5 keV for proton impact, 0.13--0.83 keV for deuterium ion impact, and 0.28--3 keV for helium ion impact. At proton collision energies below 0.7 keV our charge transfer cross sections are in excellent agreement with the theoretical predictions, resolving a long-standing discrepancy between theory and experiment in this energy range. Cross sections for proton and for deuterium ion impact on lithium are measured to be identical when scaled to the same collision velocity, indicating that quantum effects are not significant in the energy range studied. Comparison between our cross section measurements for lithium electron loss due to helium ion impact and previously measured charge transfer cross sections show that ionization is a negligible process in ${\mathrm{He}}^{+}+\mathrm{Li}$ collisions at energies below 3 keV. Undulations in the measured collision cross sections at low energy are observed for both proton and helium ion impact and are compared to molecular orbital close-coupling calculations.

Collisional excitation of isotopologs of H2S by molecular hydrogen: D2S and HDS

ABSTRACT Rate coefficients for transitions between the lower rotational levels of two isotopologs of hydrogen sulphide, specifically HDS and D2S, induced by collisions with para-H2 and ortho-H2 are presented in this work. The availability of these rate coefficients will allow accurate estimates to be made of the abundance of these species in the interstellar medium to be made from astronomical observations. The rate coefficients were computed in close-coupling calculations using potential energy surfaces (PESs) obtained by transformation of the H2S–H2 PES previously calculated with the explicitly correlated CCSD(T)-F12a coupled-cluster method. Rate coefficients for transitions between rotational levels with energies less than 196 cm−1 and temperatures from 5 to 400 K have been calculated for HDS, ortho-D2S, and para-D2S. The rate coefficients for the H2S–H2, HDS–H2, and D2S–H2 systems are compared

Deexcitation rate coefficients of C3 by collision with H2 at low temperatures

Context. An accurate analysis of the physical-chemical conditions in the regions of the interstellar medium in which C3 is observed requires knowing the collisional rate coefficients of this molecule with He, H2, electrons, and H. Aims. The main goals of this study are to present the first potential energy surface for the C3 +H2 complex, to study the dynamics of the system, and to report a set of rate coefficients at low temperature for the lower rotational states of C3 with para- and ortho-H2. Methods. A large grid of ab initio energies was computed at the explicitly correlated coupled-cluster with single-, double-, and perturbative triple-excitation level of theory, together with the augmented correlation-consistent quadruple zeta basis set (CCSD(T)-F12a/aug-cc-pVQZ). This grid of energies was fit to an analytical function. The potential energy surface was employed in close-coupling calculations at low collisional energies. Results. We present a high-level four-dimensional potential energy surface (PES) for studying the collision of C3 with H2. The global minimum of the surface is found in the linear HH-CCC configuration. Rotational deexcitation state-to-state cross sections of C3 by collision with para- and ortho-H2 are computed. Furthermore, a reduced two-dimensional surface is developed by averaging the surface over the orientation of H2. The cross sections for the collision with para-H2 using this approximation and those from the four-dimensional PES agree excellently. Finally, a set of rotational rate coefficients for the collision of C3 with para- and ortho-H2 at low temperatures are reported.

Broadening and shifting of the carbon monoxide rotational lines in a wide temperature range: calculations in the framework of the classical impact theory for CO-He

The classical impact theory of Gordon is used to calculate half-widths and shifts of spectral lines of the pure rotational band of 12C16O isotopologue broadened by He. Two rotational transitions are examined: J=0-> J=1 and J=1-> J=2 in the wide temperature range from 1.3 to 600 K. The main purpose of this work is the study of the validity limits of classical impact theory at low temperatures. Dynamical calculations were performed on the accurate CO-He ab initio potential energy surface. The results of calculations are in good agreement with experimental data with the exception of very low temperatures. The contributions of collisions of different types (elastic, inelastic, quasibound complexes) are clearly examined in the classical picture frame. It is shown that the mismatches between classical theory and measurements are caused by the too high contribution of elastic collisions into broadening and shift in the present variant of theoretical model. The idea in the spirit of the Weisskopf theory is applied to try to diminish this contribution. The classical results are also compared with the results of fully quantum close coupling calculations made with using four CO-He interaction potentials. The roots of discrepancies at low temperatures as well as the virtues and the shortcomings of a classical approach are discussed. Keywords: collisional line broadening and shift, intermolecular interactions, classical impact theory, classical trajectory method, quasibound complexes.

Уширение и сдвиг вращательных линий оксида углерода в широком диапазоне температур: расчеты в рамках классической ударной теории для CO-He

The classical impact theory of Gordon is used to calculate half-widths and shifts of spectral lines of the pure rotational band of 12C16O isotopologue broadened by He. Two rotational transitions are examined: J=0J=1 and J=1J=2 in the wide temperature range from 1.3 to 600 K. The main purpose of this work is the study of the validity limits of classical impact theory at low temperatures. Dynamical calculations were performed on the accurate CO-He ab initio potential energy surface. The results of calculations are in good agreement with experimental data with the exception of very low temperatures. The contributions of collisions of different types (elastic, inelastic, quasibound complexes) are clearly examined in the classical picture frame. It is shown that the mismatches between classical theory and measurements are caused by the too high contribution of elastic collisions into broadening and shift in the present variant of theoretical model. The idea in the spirit of the Weisskopf theory is applied to try to diminish this contribution. The classical results are also compared with the results of fully quantum close coupling calculations made with using four CO-He interaction potentials. The roots of discrepancies at low temperatures as well as the virtues and the shortcomings of a classical approach are discussed.

Modeling the Mg I from the NUV to MIR

Context. Semi-empirical models of the solar atmosphere are used to study the radiative environment of any planet in our Solar System. There is a need for reliable atomic data for neutral atoms and ions in the atmosphere to obtain improved calculated spectra. Atomic parameters are crucial to computing the correct population of elements through the whole stellar atmosphere. Although there is very good agreement between the observed and calculated spectra for the Sun, there is still a mismatch in several spectral ranges due to the lack of atomic data and the inaccuracies thereof, particularly for neutrals such as Mg I. Aims. To represent many spectral lines of Mg I from the near-ultraviolet to the mid-infrared correctly, it is necessary to add and update the atomic data involved in the atomic processes that drive their formation. Methods. The improvements made to the Mg I atomic model are as follows: i) 127 strong lines, including their broadening data, were added. ii) To obtain these new lines, we increased the number of energy levels from 26 to 85. iii) Photoionization cross-section parameters were added and updated. iv) Effective collision strength (ϒij) parameters were updated for the first 25 levels using the existing data from the convergent close-coupling calculations. One of the most significant changes in our model is given by the new ϒij parameters for transitions involving levels between 26 and 54, which were computed with a multiconfiguration Breit–Pauli distorted-wave (DW) method. For transitions involving superlevels, we calculated the ϒij parameters with the usual semi-empirical formulas. Results. More than 100 transitions were added to our calculations, increasing our capability of reproducing important features observed in the solar spectra. We found a remarkable improvement in matching the solar spectra for wavelengths higher than 30 000 Å when our new DW ϒij data were used in the model.

Collisional excitation of NH by H2: Potential energy surface and scattering calculations.

Collisional data for the excitation of NH by H2 are key to accurately derive the NH abundance in astrophysical media. We present a new four-dimensional potential energy surface (PES) for the NH-H2 van der Waals complex. The ab initio calculations of the PES were carried out using the explicitly correlated partially spin-restricted coupled cluster method with single, double, and perturbative triple excitations [RCCSD(T)-F12a] with the augmented correlation-consistent polarized valence triple zeta basis set. The PES was represented by an angular expansion in terms of coupled spherical harmonics. The global minimum corresponds to the linear structure with a well depth De = 149.10 cm-1. The calculated dissociation energy D0 is found to be 30.55 and 22.11 cm-1 for ortho-H2 and para-H2 complexes, respectively. These results are in agreement with the experimental values. Then, we perform quantum close-coupling calculations of the fine structure resolved excitation cross sections of NH induced by collisions with ortho-H2 and para-H2 for collisional energies up to 500 cm-1. We find strong differences between collisions induced by ortho-H2 and para-H2. Propensity rules are discussed. The cross sections are larger for fine structure conserving transitions than for fine structure changing ones, as predicted by theory. These new results should help in interpreting NH interstellar spectra and better constrain the abundance of NH in interstellar molecular clouds.

Collisional excitation of methylene by molecular hydrogen

ABSTRACT Accurate estimates of the abundance of methylene (CH2) in the interstellar medium require knowledge of both the radiative and collisional rate coefficients for the transfer of population between rotational levels. In this work, time-independent quantum close coupling calculations have been carried out to compute rate coefficients for the (de-)excitation of ortho- and para-CH2 in collisions with ortho- and para-H2. These scattering calculations have employed a recently computed, high-quality potential energy surface, based on the coupled cluster level of theory [RCCSD(T)-F12a], for the interaction of CH2 in its ground $\tilde{X} ^3B_1$ electronic state with H2. The collisional rate coefficients were obtained for all fine-structure transitions among the first 22 and 24 energy levels of ortho- and para-CH2, respectively, having energies less than 277 cm−1. These rate coefficients are compared with previous calculated values, obtained by scaling data for CH2–He. In the case of ortho-CH2, whose levels display hyperfine structure, rate coefficients for transitions between hyperfine levels were also computed, by the MJ randomization approximation. Finally, some simple radiative transfer calculations are presented.

Benchmark Angle-Differential Cross-Section Ratios for Excitation of the 4p5s Configuration in Krypton

Benchmark intensity ratio measurements of the energy loss lines of krypton for excitation of the 4p61S0→4p55s[3/2]2, 4p55s[3/2]1, 4p55s′[1/2]0, and 4p55s′[1/2]1 transitions are reported, these being the lowest electronic excitations for krypton. The importance of these ratios as stringent tests of theoretical electron scattering models for the noble gases is discussed, as well as the role of spin-exchange and direct processes regarding the angular dependence of these ratios. The experimental data are compared with predictions from fully-relativistic B-spline R-matrix (close-coupling) calculations.

Resolved fine and hyperfine state-to-state rate coefficients for the rotational transitions of C3N induced by collision with He

ABSTRACT The fine and hyperfine resolved state-to-state rate coefficients for the rotational (de)excitation of C3N by collision with helium are computed. To this aim a 2D potential energy surface is calculated for this system. The recoupling method is used to obtain the fine and hyperfine structure resolved rate coefficients from spin-free close-coupling calculations. These results are compared with those given by the infinite-order sudden approximation and the M-randomizing limit. General propensity rules for the transitions are also found and analysed.

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.

Extraction of Ps-formation cross-sections from single-centre positron-scattering calculations

Positron scattering on atomic and molecular targets is a two-centre problem due to the possibility of rearrangement (Ps-formation) processes. In certain kinematic regions, single-centre expansion methods can be applied to two-centre scattering problems. In such approaches, however, information about Ps-formation and direct ionization processes are combined into excitation amplitudes of positive-energy pseudostates. In this report we show that Ps-formation amplitudes can be extracted using the total scattering wave function, which we reconstruct from single-centre convergent close-coupling calculations. The method is applied to positron scattering from hydrogen and lithium atomic targets. Excellent agreement with the two-centre theoretical benchmark results show the validity of the proposed technique.

Rainbow scattering in rotationally inelastic collisions of HCl and H2.

We examine rotational transitions of HCl in collisions with H2 by carrying out quantum mechanical close-coupling and quasi-classical trajectory (QCT) calculations on a recently developed globally accurate full-dimensional ab initio potential energy surface for the H3Cl system. Signatures of rainbow scattering in rotationally inelastic collisions are found in the state resolved integral and differential cross sections as functions of the impact parameter (initial orbital angular momentum) and final rotational quantum number. We show the coexistence of distinct dynamical regimes for the HCl rotational transition driven by the short-range repulsive and long-range attractive forces whose relative importance depends on the collision energy and final rotational state, suggesting that the classification of rainbow scattering into rotational and l-type rainbows is effective for H2 + HCl collisions. While the QCT method satisfactorily predicts the overall behavior of the rotationally inelastic cross sections, its capability to accurately describe signatures of rainbow scattering appears to be limited for the present system.

Convergent close-coupling calculations of electrons scattering on electronically excited molecular hydrogen

We use the adiabatic-nuclei molecular convergent close-coupling method to perform calculations of 0.01--1000 eV electrons scattering on the $c^{3}\mathrm{\ensuremath{\Pi}}_{u}$, $a^{3}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$, $B^{1}\mathrm{\ensuremath{\Sigma}}_{u}^{+}$, $C^{1}\mathrm{\ensuremath{\Pi}}_{u}$, and $EF^{1}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$ states of ${\mathrm{H}}_{2}$ in the $v=0$ vibrational level. Elastic, superelastic, ionization, and grand-total cross sections are presented, as well as cross sections for excitation of the $n=2$--3 singlet and triplet states of ${\mathrm{H}}_{2}$ (where $n$ is the atomic-limit principle quantum number). Comparison with available theoretical results is made. Good agreement is found with the recent $R$-matrix results [J. Phys. B 53, 245203 (2020)] for most of the exchange and dipole-forbidden transitions, but not for the dipole-allowed transitions. The sources of disagreement were found to be an unconverged partial-wave expansion and the utilization of the fixed-nuclei approximation (as opposed to adiabatic-nuclei) in the $R$-matrix calculations.

Rate coefficients for H2:H2 inelastic collisions in the ground vibrational state from 10 to 1000 K

Aims. In this work, we present a pruned set of state-to-state rate coefficients (STS rates) for inelastic H2:H2 collisions in the thermal range from 10 to 1000 K. The set includes all relevant rates needed for diagnostics based on the simulation of quadrupole infrared spectra of H2. Methods. The reported set was obtained from a quantum scattering close-coupling calculation employing a recent version of the MOLSCAT code, a high-level potential energy surface, and rotational energies of the H2 molecules with spectroscopic accuracy. These improvements have led to a significant increase in the accuracy with respect to previous computational results. The accuracy of the present STS rates is tested against recently reported experimental rates. Most dominant rates agree with the experiment within a 2σ uncertainty (2 to 6%). Results. In addition to the tables given in the main text, three machine-readable tables are available at the CDS. These tables include all the relevant numerical results of the paper, namely, the excitation and de-excitation STS rates for H2:H2 inelastic collisions at selected temperatures between 10 and 1000 K, and their functional description for interpolation at any intermediate temperature.

Isotopic and vibrational-level dependence of H2 dissociation by electron impact

The low-energy electron-impact dissociation of molecular hydrogen has been a source of disagreement between various calculations and measurements for decades. Excitation of the ground state of H$_2$ into the dissociative $b ^3\Sigma_u^+$ state is now well understood, with the most recent measurements being in excellent agreement with the molecular convergent close-coupling (MCCC) calculations of both integral and differential cross sections (2018 Phys. Rev. A 98 062704). However, in the absence of similar measurements for vibrationally-excited or isotopically-substituted H$_2$, cross sections for dissociation of these species must be determined by theory alone. We have identified large discrepancies between MCCC calculations and the recommended $R$-matrix cross sections for dissociation of vibrationally-excited H$_2$, D$_2$, T$_2$, HD, HT, and DT (2002 Plasma Phys. Contr. F. 44 1263-1276,2217-2230), with disagreement in both the isotope effect and dependence on initial vibrational level. Here we investigate the source of the discrepancies, and discuss the consequences for plasma models which have incorporated the previously recommended data.

Collision-Induced Rotational Excitation of CO2 by N(4S) Atoms: A New Ab Initio Potential Energy Surface and Scattering Calculations.

Collisional excitations of CO2 molecules are significant to fully understand the physical and chemical processes of astrophysical and atmospheric environments. Rotational excitations of CO2 molecules induced by N(4S) atoms have been studied for the first time. First, we have computed a new highly accurate ab initio potential energy surface (PES) of a CO2-N(4S) van der Waals complex. The PES has been obtained by employing the partially spin-restricted coupled cluster with open-shell single, double, and perturbative triple excitation method with aug-cc-pVQZ basis sets. The full close-coupling calculations have been performed to compute cross sections for kinetic energies up to 800 cm-1. For all of the excitations, rotational cross sections exhibit an overall decrease with the increase of the energy gaps. Rate coefficients are calculated by averaging the cross sections over a Maxwell-Boltzmann distribution for temperatures ranging from 1 to 150 K. The trends in rate coefficients are in good agreement with those of similar collision systems. The decrease in energy gaps and the increase in temperature are the key factors to enhance the rate coefficients of CO2 excitation. Our study will be useful for accurately establishing the atmospheric model of terrestrial planets and determining the abundance of CO2 and N(4S) in space.

Rotational excitation of C2H- anion in collision with H2.

The discovery of anions in the interstellar medium has shown that they are very reactive species. This gave them great importance in the modeling of the chemical and astrophysical evolution of the interstellar medium. The detection of the first anion C6H− followed by the other anions C4H−, C8H− and CN− in the interstellar medium has encouraged research on other detectable anions. The C2H− anion was observed for the first time in the circumstellar envelope of IRC+10216 and in TMC-1. In these cold and low-density regions, precise modeling of the chemical and physical conditions of the observed emission lines requires knowledge of the radiative and collisional excitation rates. We present here the first new two-dimensional Potential Energy Surface (PES) for C2H–H2 interaction. Rotational excitation of the anion by collision with para-H2(jH2 = 0) is investigated. The PES is obtained in the super-molecular approach based on a single and double excitation coupled cluster method with perturbative contributions from triple excitations (CCSD(T)). In all our calculations, all atoms were described using the augmented correlation-consistent triple zeta (aug-cc-pVTZ) basis sets and bond f unctions. Fully-quantum close-coupling calculations of inelastic integral cross sections are done on a grid of collision energies large enough to ensure converged state-to-state rate coefficients for the 16 first rotational levels of C2H− and for temperatures ranging from 5 to 120 K. For this collisional system, rate coefficients exhibit a strong propensity in favor of even Δj transitions.