Benhui
Yang
*^{a},
P.
Zhang
^{b},
C.
Qu
^{c},
P. C.
Stancil
^{a},
J. M.
Bowman
^{c},
N.
Balakrishnan
^{d} and
R. C.
Forrey
^{e}
^{a}Department of Physics and Astronomy and Center for Simulational Physics, University of Georgia, Athens, GA 30602, USA. E-mail: yang@physast.uga.edu
^{b}Department of Chemistry, Duke University, Durham, NC 27708, USA
^{c}Department of Chemistry, Emory University, Atlanta, GA 30322, USA
^{d}Department of Chemistry and Biochemistry, University of Nevada, Las Vegas, NV 89154, USA
^{e}Department of Physics, Penn State University, Berks Campus, Reading, PA 19610, USA
First published on 31st October 2018
We report a six-dimensional (6D) potential energy surface (PES) for the CS–H_{2} system computed using high-level electronic structure theory and fitted using a hybrid invariant polynomial method. Full-dimensional quantum close-coupling scattering calculations have been carried out using this potential for rotational and, for the first time, vibrational quenching transitions of CS induced by H_{2}. State-to-state cross sections and rate coefficients for rotational transitions in CS from rotational levels j_{1} = 0–5 in the ground vibrational state are compared with previous theoretical results obtained using a rigid-rotor approximation. For vibrational quenching, state-to-state and total cross sections and rate coefficients were calculated for the vibrational transitions in CS(v_{1} = 1,j_{1}) + H_{2}(v_{2} = 0,j_{2}) → CS(v_{1}′ = 0,j_{1}′) + H_{2}(v_{2}′ = 0,j_{2}′) collisions, for j_{1} = 0–5. Cross sections for collision energies in the range 1 to 3000 cm^{−1} and rate coefficients in the temperature range of 5 to 600 K are obtained for both para-H_{2} (j_{2} = 0) and ortho-H_{2} (j_{2} = 1) collision partners. Application of the computed results in astrophysics is also discussed.
Due to its astrophysical importance, there have been many theoretical studies of pure rotational cross sections and rate coefficients for CS in collision with H_{2}. Green and Chapman^{11} calculated CS–H_{2} rotational excitation rate coefficients among first 13 rotational states of CS. Later Turner et al.^{12} extended the calculations to rotational levels through j_{1} = 20 for rate coefficient below 300 K. However these rate coefficients were computed using a CS–He PES obtained from an electron gas model.^{15} Vastel et al.^{10} performed local thermodynamic equilibrium (LTE) and non-LTE radiative transfer modeling using the NAUTILUS chemical code for the sulfur chemistry in the L1544 pre-stellar core; the rate coefficients of CS with para-H_{2} calculated by Green and Chapman^{11} were adopted to obtain the column density of CS. Albrecht presented approximate rate coefficients for CS–H_{2} (j_{2} = 0) using an empirical analytical expression^{16} and a fit to the rate coefficients of Green and Chapman.^{11} This approximation was also adopted to derive the collisional rate coefficients of linear molecules SiO, HCN, H_{2}O.^{17,18} Recently, a four-dimensional (4D) potential energy surface (PES) for CS–H_{2} was constructed by Denis-Alpizar et al.^{20} based on ab initio calculations within the coupled-cluster singles and doubles plus perturbative triples[CCSD(T)] method and the augmented correlation consistent polarized valence quadruple zeta (aug-cc-pVQZ) basis set. The interaction energy between CS and H_{2} was obtained by subtracting the sum of the monomer potentials of CS and H_{2} from the total energy of the CS–H_{2} complex, where CS and H_{2} were treated as rigid rotors with the bond length of H_{2} fixed at its vibrationally averaged value, r_{0} = 1.4467a_{0} in the vibrational ground state and the bond length of CS fixed at its equilibrium value (r_{e} = 2.9006a_{0}). The PES was fitted with a least squares procedure for the angular terms and interpolation of the radial coefficients with cubic splines.^{19} This 4D rigid rotor PES was applied to compute the rotational (de)excitation rate coefficients for the first 30 rotational levels of CS by collision with para-H_{2} (j_{2} = 0) and ortho-H_{2} (j_{2} = 1).^{13,14} Additionally, the CS–para-H_{2} rate coefficients obtained by mass-scaling the CS–He results of Lique et al.^{21} are also available in the Leiden Atomic and Molecular Database.^{23} These scaled results were also adopted by Neufeld et al.^{8} in their turbulent dissipation region models to determine the equilibrium level populations of CS in diffuse molecular clouds, where CS j_{1} = 2–1 line was observed using the IRAM 30 m telescope. For CS vibrational excitation, Lique and Spielfiedel^{22} performed the scattering calculations of rovibrational excitation cross sections and rate coefficients of CS by He. However, to our knowledge, there are no theoretical results available for vibrational excitation of CS with H_{2}. The only available measurements are for the removal rate constants for vibrationally excited CS(v_{1} = 1) with H_{2}, reported about a half century ago.^{24,25}
Quantum close-coupling (CC) calculations are the primary source of rate coefficients for astrophysical modeling. Full-dimensional quantum CC formalism has been developed^{26,27} for collisions involving two diatomic molecules. With the development of the quantum CC scattering code TwoBC,^{28} diatom–diatom systems in full-dimensionality can be treated and was first used for CC calculations of rovibrational collisions of H_{2} with H_{2}.^{29–32} Rovibrational CC calculations were also performed for the collisional systems CO–H_{2},^{33,34} CN–H_{2},^{35} SiO–H_{2},^{36} along with coupled-states approximation calculations in 5D and 6D.^{37–39}
Here we report the first full-dimensional PES and the first vibrational inelastic scattering calculations for the CS–H_{2} system. The paper is organized as follows. A brief description of the Theoretical methods for the electronic structure and scattering calculations are given in Section 2. The results are presented and discussed in Section 3 followed by Astrophysical applications in Section 4. Section 5 summarizes the results and presents an outlook on future work.
The ab initio electronic structure computations of potential energies were performed using the explicitly correlated coupled-cluster (CCSD(T)-F12b) method.^{43,44} All the calculations employed aug-cc-pV5Z (for H and C atoms)^{45} and aug-cc-pV(5+d)Z (for S atom) orbital basis set,^{46} and the corresponding MP2FIT (for H and C atoms) and aug-cc-pwCV5Z (for S atom) auxiliary bases^{47,48} for density fitting. The aug-cc-pV6Z-RI auxiliary bases (without k functions)^{49} were used for the resolutions of the identify and density-fitted Fock matrices for all orbital bases. No scaled triples correction was used in the CCSD(T)-F12 calculation. The interaction PES was corrected for basis set superposition error (BSSE)^{50} using the counter-poise (CP)^{51} method. Benchmark calculations at this CCSD(T)-F12 level were carried out on selected molecular configurations and results were compared with those from the conventional CCSD(T) method using aug-cc-pV5Z. The CP corrected interaction energy agrees closely with those derived from CCSD(T)/aug-cc-pV5Z.
The full-dimensional CS–H_{2} interaction potential, referred to as VCSH2, is a hybrid one combining a fit to the full ab initio data set (denoted V_{I}) and a fit to the long-range data (denoted V_{II}) and is expressed by
V = (1 − s)V_{I} + sV_{II}, | (1) |
(2) |
(3) |
In Fig. 2 the R dependence of VCSH2 PES is compared with the PES of Denis-Alpizar et al.^{20} for (θ_{1}, θ_{2}, ϕ) = (0°, 0°, 0°), (180°, 0°, 0°), (180°, 90°, 0°), and (90°, 90°, 90°). Good agreement between our PES and the PES of Denis-Alpizar et al.^{20} is displayed, except that our PES is a little shallower at the global minimum. Our fitted PES has a depth of −162.56 cm^{−1} at the collinear structure with the C atom towards to H_{2} and R = 8.6a_{0}. The minimum of the PES of Denis-Alpizar et al.^{20} is about −173 cm^{−1} and also corresponds to a collinear geometry with same R value. Fig. 3 shows a two-dimensional contour plot of the VCSH2 PES in θ_{1}, θ_{2} space for fixed values of r_{1} = 2.9006a_{0}, r_{2} = 1.4011a_{0}, R = 8.5a_{0}, and ϕ = 0°.
Fig. 2 The R dependence of the CS–H_{2} interaction potential, VCSH2 for (θ_{1}, θ_{2}, ϕ) = (0°, 0°, 0°), (180°, 90°, 0°), (90°, 90°, 90°), and (180°, 0°, 0°). The bond lengths of CS and H_{2} are fixed at equilibrium value and vibrationally averaged value in the rovibrational ground state, respectively. Symbols are for the PES of Denis-Alpizar et al.^{20} (D–A). |
Fig. 3 Contour plots of the potential VCSH2 as a function of θ_{1} and θ_{2} for r_{1} = 2.9006a_{0}, r_{2} = 1.4011a_{0}, R = 8.5a_{0}, and ϕ = 0°. |
(4) |
(5) |
We use a combined molecular state (CMS)^{30} notation, (v_{1}j_{1}v_{2}j_{2}), to describe a combination of rovibrational states for CS(v_{1}j_{1}) and H_{2}(v_{2}j_{2}), where j_{i} and v_{i} (i = 1, 2) are the rotational and vibrational quantum numbers of CS and H_{2}. For a rovibrational transition the state-to-state cross section can be obtained as a function of the collision energy E_{c} from the corresponding scattering matrix S:
(6) |
The total quenching cross section of CS from initial state (v_{1}j_{1}v_{2}j_{2}) → (v_{1}′;v_{2}′j_{2}′) is obtained by summing the state-to-state quenching cross sections over the final rotational state of j_{1}′ of CS in vibrational state v_{1}′,
(7) |
From the state-to-state cross section the corresponding rate coefficient at a temperature T can be obtained by averaging it over a Boltzmann distribution of collision energies.
(8) |
In the full-dimensional rovibrational scattering calculations with the TwoBC code^{28} the log-derivative matrix propagation method of Johnson^{55} was employed to propagate the CC equations from R = 4.5a_{0} to 25a_{0}. The number of Gauss–Hermite quadrature points N_{r1}, N_{r2}; the number of Gauss–Legendre quadrature points in θ_{1} and θ_{2}, N_{θ1}, N_{θ2}; and the number of Chebyshev quadrature points in ϕ, N_{ϕ} adopted to project out the expansion coefficients of the PES are listed in Table 1. In the scattering calculations, the monomer potentials of Paulose et al.^{56} and Schwenke^{57} are used to describe the rovibrational motions of CS and H_{2}, respectively.
Basis set | N _{ θ 1 }(N_{θ2}) | N _{ ϕ } | N _{ r 1 }(N_{r2}) | λ _{1} | λ _{2} | ||
---|---|---|---|---|---|---|---|
a Basis set is presented by the maximum rotational quantum number and included in each relevant vibrational level v_{1} and v_{2} for CS and H_{2}, respectively. b Maximum values of the total angular momentum quantum number J(J_{E1},J_{E2},J_{E3},J_{E4}) used in scattering calculations for collision energies E_{1} = 10, E_{2} = 100, E_{3} = 1000, and E_{4} = 3000 cm^{−1}, respectively. | |||||||
6D rotation | |||||||
para-H_{2}–CS | j ^{max}_{1} = 30, j_{2} = 0,2 | 12 | 8 | 18 | 8 | 4 | (16, 30, 80, 160)^{b} |
ortho-H_{2}–CS | j ^{max}_{1} = 30, j_{2} = 1,3 | 12 | 8 | 18 | 8 | 4 | (18, 32, 82, 162)^{b} |
6D rovibration | |||||||
para-H_{2}–CS | [(0,35;1,20)(0,2)]^{a} | 12 | 8 | 18 | 8 | 4 | (16, 30, 80, 160)^{b} |
ortho-H_{2}–CS | [(0,35;1,20)(0,3)]^{a} | 12 | 8 | 18 | 8 | 4 | (18, 32, 82, 162)^{b} |
Fig. 4 Rotational state-to-state de-excitation cross sections for CS(j_{1}) + H_{2}(j_{2}) → CS(j_{1}′) + H_{2}(j_{2}′), j_{1} = 5, j_{1}′ < j_{1}. Lines are for the present results and symbols are for the results of Denis-Alpizar et al.^{13} (a) CS in collision with para-H_{2}, j_{2} = j_{2}′ = 0; (b) CS in collision with ortho-H_{2}, j_{2} = j_{2}′ = 1. |
Fig. 5(a and b) display the total rotational quenching cross sections from initial states j_{1} = 1–5 of CS with para-H_{2} (j_{2} = 0) and ortho-H_{2} (j_{2} = 1), respectively. It is found that for both para-H_{2} and ortho-H_{2}, except for collision energies below ∼ 3 cm^{−1}, the total rotational quenching cross sections increase with increasing initial j_{1}. For para-H_{2}, the resonance features observed in the state-to-state cross sections can also be noted in the total quenching cross sections, particularly in the j_{1} = 1 state.
In Fig. 6, we provide a comparison between the para-H_{2} and ortho-H_{2} cross sections for initial rotational states j_{1} = 1 and 2. For Δj_{1} = −1, the cross section of ortho-H_{2} are larger than that of para-H_{2} over the whole range of collision energy. While for the j_{1} = 2 → 0 transition, the cross sections of para-H_{2} and ortho-H_{2} are of comparable magnitude, though the resonance dominated region for para-H_{2} shows significant differences.
Fig. 6 Comparison of the rotational state-to-state de-excitation cross sections for CS in collision with para- and ortho-H_{2}. (a) From initial state j_{1} = 1; (b) from initial state j_{1} = 2. |
In Fig. 7(a and b) we show the temperature dependence of the rate coefficients for rotational quenching of CS from j_{1} = 2 induced by para- and ortho-H_{2} collisions, respectively, in the temperatures range of 5 to 600 K. For comparison, the corresponding rate coefficients of Denis-Alpizar et al.^{14} are also included. The temperature dependence is the steepest for the j_{1} = 2 → 0 rate coefficient for para-H_{2} collisions. While for j_{1} = 2 → 1, the rate coefficient first decreases with temperature from T = 5–20 K, then increases gradually with increasing temperature. Compared to the results of Denis-Alpizar et al.,^{14} good agreement is observed for the j_{1} = 2 → 0 rate coefficients. However, for the j_{1} = 2 → 1 transition, our rate coefficient is larger than the results of Denis-Alpizar et al. but the differences tend to vanish as the temperature is increased. As shown in Fig. 2, the VCSH2 PES and the PES of Denis-Alpizar et al.^{20} have different well depths with VCSH2 being the shallower one. This leads to different resonance structures in the cross sections on the two PESs, particularly, at low collision energies. The differences in the rate coefficients at low temperatures may be attributed to the different resonance structures. Fig. 8 provides a comparison of the state-to-state rate coefficients from the present work for j_{1} = 5 with that of Denis-Alpizar et al..^{14} The para-H_{2} results shown in Fig. 8(a) are in reasonable agreement with the results of Denis-Alpizar et al. while the ortho-H_{2} results presented in Fig. 8(b) are in excellent agreement.
Fig. 7 Rotational state-to-state de-excitation rate coefficients compared with the results of Denis-Alpizar et al. (D–A)^{14} for CS(j_{1} = 2) in collision with (a) para-H_{2} (j_{2} = 0) and (b) ortho-H_{2} (j_{2} = 1). |
Fig. 8 Rotational state-to-state de-excitation rate coefficients compared with D–A for CS(j_{1} = 5) in collision with (a) para-H_{2}(j_{2} = 0) and (b) ortho-H_{2}(j_{2} = 1). |
When rate coefficients for a particular collision complex are lacking, it has been argued that rate coefficients from chemically similar systems could be at adopted.^{58} We test this idea by comparing the current results from CS to prior work on SiO^{36} and SiS.^{59,60} In Fig. 9, the state-to-state rate coefficients for rotational quenching from initial state j_{1} = 3 for para-H_{2} collisions are shown. The rate coefficients differ by a factor of ∼5 with no clear trend. Adoption of such an approximation is clearly not advisable.
The state-to-state quenching cross sections were computed for CS rovibrational transitions from v_{1} = 1, CS(v_{1} = 1, j_{1}) + H_{2}(v_{2} = 0, j_{2}) → CS(v_{1}′ = 0, j_{1}′) + H_{2}(v_{2}′ = 0, j_{2}′), i.e., (1j_{1}0j_{2}) → (0j_{1}′0j_{2}′). In our calculations, initial j_{1} = 0–5 and final j_{1}′ = 0, 1, 2,⋯, 35. For para-H_{2}, j_{2} = 0, j_{2}′ = 0 and 2, while for ortho-H_{2}, j_{2} = 1, j_{2}′ = 1 and 3 are considered. We only consider the rotational excitations of H_{2} within its ground vibrational state, i.e., v_{2} = v_{2}′ = 0 for all of the results presented here. The basis sets employed in the scattering calculations are given in Table 1. All vibrational quenching cross sections were calculated for collision energies between 1 and 3000 cm^{−1}.
As examples, we show in Fig. 10 the state-to-state quenching cross sections from initial CMS (1000) and (1001) into selected final rotational states in v_{1}′ = 0, j_{1}′ = 0, 2, 4, 6, 8, 10, 15, 20, and 25. These results correspond to rotationally elastic scattering of the H_{2} molecule, i.e., j_{2} = 0 → j_{2}′ = 0. As seen from Fig. 10, for both para-H_{2} and ortho-H_{2} colliders, a large number of resonances are observed in the cross sections at collision energies between 1 and 50 cm^{−1}. We also notice that the resonances persist to higher energies with increasing j_{1}′. Additionally, the state-to-state quenching cross sections increase with collision energy for energies above ∼50 cm^{−1}. Overall, the cross sections corresponding to j_{1}′ ≤ 15 show similar resonance structures and exhibit similar energy dependence. The cross sections for j_{1}′ = 20 and 25 are about two to three orders of magnitude smaller than other transitions for both para- and ortho-H_{2} for collision energies below 300 cm^{−1}, however they increase rapidly with energy, and the cross section of j_{1}′ = 25 becomes the largest at an energy of 3000 cm^{−1}.
Next we discuss the effect of vibrational excitation of CS on its pure rotational quenching. This is provided in Fig. 11 for v_{1} = 0 and 1 for rotational levels j_{1} = 1 and 5 to all j_{1}′ < j_{1} for para-H_{2} with H_{2} scattered elastically. It can be seen that the cross sections are nearly identical for v_{1} = 0 and 1, over the whole range of energies considered in this work demonstrating the negligible effect of vibrational excitation of CS on pure rotational quenching. This is due to the almost harmonic nature of the v = 0 and 1 vibrational levels of CS. Similar results are found for ortho-H_{2} collisions. This also means that, effect of vibrational excitation of CS can be ignored for pure rotational transitions in CS in collisions with ortho- and para-H_{2}, at least for low vibrational levels. A similar conclusion was also drawn for the SiO–H_{2} system.^{36}
Using eqn (7) the total vibrational quenching cross section of CS from initial CMS (1000) and (1001) was obtained by summing the state to state quenching cross sections over the final rotational state j_{1}′ of CS in vibrational state v_{1} = 0. These total quenching cross section were calculated for elastic and inelastic transitions in H_{2}.
Fig. 12(a) presents the energy dependence of the total v_{1} = 1 → v_{1}′ = 0 quenching cross section with para-H_{2} from CMSs (1000) for elastic (j_{2} = 0 → j_{2}′ = 0) and inelastic (j_{2} = 0 → j_{2}′ = 2) transitions in H_{2}. While they exhibit similar energy dependencies and similar resonance structures at low energies, the cross sections for elastic transition in H_{2} are about a factor of two larger than its inelastic counterpart in the entire energy range. For ortho-H_{2} and initial CMS (1001), Fig. 12(b) shows that the total vibrational quenching cross sections for elastic (j_{2} = 1 → j_{2}′ = 1) and inelastic (j_{2} = 1 → j_{2}′ = 3) transitions in H_{2} are comparable for collision energies below ∼200 cm^{−1}. For energies above ∼200 cm^{−1}, the cross section for H_{2} rotation preserving transition becomes increasingly dominant.
We also calculated the state-to-state and total vibrational quenching rate coefficients of CS(v_{1} = 1, j_{1}) in collisions with para-H_{2} (j_{2} = 0) and ortho-H_{2} (j_{2} = 1) for j_{1} = 0–5. State-to-state rate coefficients are obtained for j_{1}′ = 0, 1, 2,⋯, 35 and j_{2}′ = 0 and 2 for para-H_{2} and j_{2}′ = 1 and 3 for ortho-H_{2}. Unfortunately, there are no published experimental or theoretical state-to-state rate coefficients available for comparison. As an example, in Fig. 13 we show the total vibrational quenching rate coefficients for temperatures between 1 and 600 K for CMS (1000) to (v_{1}′ = 0) and j_{2}′ = 0, and CMS (1001) to (v_{1}′ = 0) and j_{2}′ = 1.
Fig. 13 Total rate coefficients for the vibrational quenching of CS compared to the same transitions for CO from ref. 33 and SiO from ref. 33. (a) from (1000) to v_{1}′ = 0 + para-H_{2}(v_{2}′ = 0, j_{2}′ = 0). (b) From (1001) to v_{1}′ = 0 + ortho-H_{2}(v_{2}′ = 0, j_{2}′ = 1). |
Previously we have provided a comparison of CS–H_{2} rate coefficients with that of CO–H_{2} (ref. 33) and for SiO–H_{2} (ref. 36). It was shown that for the same transitions, the total quenching rate coefficients of CO–H_{2} are typically ∼2–3 orders of magnitude smaller than that of CS–H_{2} and SiO–H_{2}. The large magnitude of SiO–H_{2} rate coefficients are likely due to the high anisotropy of the SiO–H_{2} PES. Interestingly, at high temperatures the CS–H_{2} rate coefficients merge with those of SiO–H_{2}. Furthermore, generally the rate coefficients increase with increasing well depth of the interaction PES, the SiO–H_{2} rate coefficients are largest with a well depth of 293.2 cm^{−1} and CO–H_{2} rate coefficients are smallest with a well depth of 93.1 cm^{−1}.
Carbon monosulfide and its isotopic species have been detected in a large range of astrophysical environments. As a high-density tracer of dense gas, CS emission is normally used in the study of star forming regions. Using the IRAM Plateau de Bure interferometer Guilloteau et al.^{62} observed two CS transitions j_{1} = 3–2 and j_{1} = 5–4 in the DM Tau disk. The line intensities were used to determine the magnitude of the turbulent motions in the outer parts of the disk. Maxted et al.^{63} detected emission j_{1} = 1–0 and j_{1} = 2–1 of CS and its isotopologues in four of the densest cores towards the western rim of supernova remnant RX J1713.7-3946 and confirmed the presence of dense gas ≥10^{4} cm^{−3} in the region. More recently, CS emission (1–0) was used in the investigation of the nature of the supernova remnant HESS J1731-347.^{64} Line emission from rotational transition j_{1} = 7–6 within the vibrationally excited state v = 1 was observed in IRAS 16293-2422.^{65} Gómez-Ruiz et al.^{66} detected CS and isotopologues ^{12}C^{32}S, ^{12}C^{34}S, ^{13}C^{32}S, ^{12}C^{33}S, for a total of 18 transitions with Herschel/HIFI and IRAM-30m at L1157-B1. With Herschel/HIFI spectral line survey^{67} CS transitions were detected toward the Orion Bar, tracing the warm and dense gas with temperatures of 100–150 K and densities of 10^{5}–10^{6} cm^{−3}. NLTE analysis was also performed with RADEX, where the CS–H_{2} rate coefficients were obtained by reduced-mass scaling the rate coefficients with He of Lique et al.^{21} Using the IRAM 30 m telescope, Aladro et al.^{68} performed a molecular line survey towards the circumnuclear regions of eight active galaxies, CS and its isotopologues were identified in M83, M82, M51, and NGC 253. Using the Atacama Large Millimeter/submillimeter Array (ALMA), Takano et al.^{69} performed a high resolution imaging study of molecular lines near the supermassive black hole at the center of galaxy NGC 1068. CS emission of j_{1} = 2–1 was distributed both in the circumnuclear disk and the starburst ring. Walter et al.^{70} investigated dense molecular gas tracers in the nearby starburst galaxy NGC 253 using ALMA, CS(j_{1} = 2–1) was detected in the molecular outflow.
Vibrationally excited molecules, which are excited by collision or infrared radiation, can be used to probe extreme physical conditions with high gas densities and temperatures. The first observation of vibrationally excited CS in the circumstellar shell of IRC + 10216 was reported by Turner^{71} through transitions j_{1} = 2 → 1 and 5 → 4 in v_{1} = 1. In 2000, Highberger et al.^{72} reobserved these lines and also detected new transitions of j_{1} = 3–2, 6–5, and 7–6 of vibrationally excited CS(v = 1) toward IRC + 10216. Using Submillimeter Array, Patel et al.^{73} detected the CS v_{1} = 2, j_{1} = 7–6 transition from the inner envelope of IRC + 10216. Finally, vibrational absorption lines for CS have been detected for its fundamental band near 8 μm in IRC + 10216.^{74} These observations used the Texas Echelon-cross-Eschelle Spectrograph (TEXES) on the 3 m Infrared Telescope facility.
Our present full-dimensional scattering calculation will be able to provide accurate rovibrational state-to-state CS–H_{2} collisional data for future modeling of protostars, the infrared sources discussed above, and future FIR and submillimeter observations with Herschel and ALMA. Furthermore, CS vibrational bands in the 1–5 μm region will be accessible by the James Webb Space Telescope (JWST) to be launched in 2021 and currently with SOFIA using the EXES (5–28 μm) or FORCAST (5–40 μm) instruments. In PPDs, CS vibrational lines probe the inner warm regions which are exposed to the UV radiation from the protostar.
Cross sections and rate coefficients for pure rotational transitions from the present study are found to be in good agreement with the rigid-rotor approximation calculations of Denis-Alpizar et al.^{13,14} using a 4-dimensional potential surface. The vibrational quenching cross sections and rate coefficients have been reported for the first time. In future work, we plan to extend the current calculations to higher rotational and vibrational states of CS and include the effect of vibrational excitation of the H_{2} molecule.
Footnote |
† Electronic supplementary information (ESI) available: The potential energy surface subroutine. See DOI: 10.1039/c8cp05819a |
This journal is © the Owner Societies 2018 |