Rate Coefficients For Rotational Transitions Research Articles

The rotational excitation of the water isotopologues by molecular hydrogen

ABSTRACT We present cross-sections and rate coefficients for rotational transitions in the water isotopologues D2O, H$_2^{18}$O, and HDO induced by collisions with para-H2(j2 = 0) and ortho-H2(j2 = 1). Quantum scattering calculations are performed at the full close-coupling level with the isotopic variants of an accurate full-dimensional H2O−H2 interaction potential. The D2O, H$_2^{18}$O, and HDO cross-sections are compared to the corresponding cross-sections for H2O. Large isotopic effects are observed in the case of D2O and HDO, in particular for collisions with p-H2(j2 = 0), while the 18O isotopic substitution is found to be negligible. Rate coefficients are provided for rotational transitions among all para-D2O, ortho-D2O, and HDO levels with internal energy below 300 cm−1 and for kinetic temperatures in the range 5–300 K. Non-LTE radiative transfer calculations show that the HDO 225.9 GHz and H$_2^{18}$O 203.4 GHz transitions recently detected with ALMA in the young proto-planetary disc V883 Ori should be inverted (weak masers) in a large fraction of the disc.

Interaction of methanol with molecular hydrogen: Ab initio potential energy surface and scattering calculations.

The potential energy surface (PES) describing the interaction of the methanol molecule with molecular hydrogen has been calculated by the use of the explicitly correlated coupled cluster method, including single, double, and (perturbative) triple excitations [CCSD(T)-F12a] and a correlation-consistent aug-cc-pVTZ basis, with the assumption of fixed molecular geometries. The computed points were fit to a functional form appropriate for time-independent quantum scattering calculations of rotationally inelastic cross sections and rate coefficients. Stationary points on the PES were located, and the global minimum was found to have an energy equal to -254.7 cm-1 relative to the energy of the separated molecules. This PES was used in time-independent close coupling quantum scattering calculations to determine state-to-state cross sections and rate coefficients for rotational transitions within the A- and E-type nuclear spin torsional ground states.

Temperature dependence of collisional rate coefficients for rotational transitions: a-type asymmetric top molecules

On realizing that the rate coefficients for rotational transitions in the H2CS, H2CO, H2CC, H2CSi, due to collisions with He atom, under the IOS approximation, increase with the increase of kinetic temperature, we have looked analytically for 9 transitions in a-type asymmetric top molecules, because the results of Green et al. (1978) for H2CO do not increase for all the transitions, though they also are calculated under the IOS approximation. We tried to understand the source of discrepancy, but could not succeed, as the details of the work of Green et al. (1978) are not available. Data for other three molecules (H2CS, H2CC, H2CSi) are not available in the literature. Since our investigation is analytical, there is no reason not to believe our results.

Collisional excitation of thioformaldehyde and of Silylidene

For analysis of spectrum of a molecule in the interstellar medium, radiative and collisional transition probabilities for rotational transitions in the molecule are required. We have calculated collisional rate coefficients for rotational transitions in ortho and para thioformaldehyde (H2CS), and in ortho and para Silylidene (H2CSi) due to collisions with He atom for kinetic temperatures 10, 20, 30, 40 and 50K, following the procedure discussed in our earlier work. The accuracy of collisional rate coefficients may be within a factor of 2.

Collisional excitation of vinylidene (H2CC)

Though H2CO, H2CS, H2CCC, H2CCCC, H2CCO have been identified in cool interstellar molecular clouds, identification of H2CC is still awaited. To analyze its spectrum, collisional rate coefficients are required. We have calculated collisional rate coefficients for rotational transitions between 23 levels of ortho and para H2CC for kinetic temperatures 10, 20, 30, 40, and 50K. The scattering problem is analyzed using the computer code MOLSCAT where the colliding partner is He atom. The interaction between H2CC and He has been calculated with GAUSSIAN 2003. For the interaction potential obtained with GAUSSIAN 2003, MOLSCAT is used to derive the parameters q(L,M,M′|E) as a function of energy E of the colliding partner. After averaging the parameters q(L,M,M′|E) over a Maxwellian distribution, the parameters Q(L,M,M′|T) as a function of the kinetic temperature T in the cloud are obtained. Finally, the collisional rate coefficients have been calculated.We have also calculated radiative transition probabilities for the transitions between the rotational levels. Finally, for ortho-H2CC, we have solved a set of statistical equilibrium equations coupled with the equations of radiative transfer and found that the H2CC may be identified through anomalous absorption of its transition 111–110 at 4.89GHz.

Collisional rates for rotational transitions in H2CO and their application

Formaldehyde (H2CO) has always been of great importance for physicists. To analyze its spectrum collisional rate coefficients are required. Their computation is quite tedious job. We have calculated collisional rate coefficients for rotational transitions between 23 levels of each of the ortho and para species of H2CO for kinetic temperatures 10, 20, 30, 40, and 50K. The scattering problem is analyzed with the help of the computer code MOLSCAT where the colliding partner is taken as the He atom. The required potential for interaction between H2CO and He is calculated with the help of the software gaussian 2003 where the coupled-cluster CCSD(T) method and cc-pVTZ basis set are used. The Basis Set Superposition Errors (BSSE) are accounted for. The wave functions for the asymmetric top molecule H2CO are expressed in terms of the Wigner D-functions and the expansion coefficients gJτK are obtained. For the interaction potential obtained with the help of gaussian 2003, MOLSCAT is used to derive the parameters q(L,M,M′|E) as a function of energy E of the colliding partner. After averaging the parameters q(L,M,M′|E) over the Maxwellian distribution, the parameters Q(L,M,M′|T) as a function of the kinetic temperature T in the cloud are obtained. The results are compared with the available data.We have also calculated radiative transition probabilities (Einstein A-coefficients) for transitions between 23 rotational levels for each of the ortho and para species of H2CO. Finally, for ortho-H2CO, we have solved a set of 23 statistical equilibrium equations coupled with 39 equations of radiative transfer and discussed anomalous absorption of the 111-110 transition of H2CO at 4.830GHz.

Potential energy surface and rovibrational energy levels of the H2-CS van der Waals complex

Owing to its large dipole, astrophysicists use carbon monosulfide (CS) as a tracer of molecular gas in the interstellar medium, often in regions where H(2) is the most abundant collider. Predictions of the rovibrational energy levels of the weakly bound complex CS-H(2) (not yet observed) and also of rate coefficients for rotational transitions of CS in collision with H(2) should help to interpret the observed spectra. This paper deals with the first goal, i.e., the calculation of the rovibrational energy levels. A new four-dimensional intermolecular potential energy surface for the H(2)-CS complex is presented. Ab initio potential energy calculations were carried out at the coupled-cluster level with single and double excitations and a perturbative treatment of triple excitations, using a quadruple-zeta basis set and midbond functions. The potential energy surface was obtained by an analytic fit of the ab initio data. The equilibrium structure of the H(2)-CS complex is found to be linear with the carbon pointing toward H(2) at the intermolecular separation of 8.6 a(o). The corresponding well depth is -173 cm(-1). The potential was used to calculate the rovibrational energy levels of the para-H(2)-CS and ortho-H(2)-CS complexes. The present work provides the first theoretical predictions of these levels. The calculated dissociation energies are found to be 35.9 cm(-1) and 49.9 cm(-1), respectively, for the para and ortho complexes. The second virial coefficient for the H(2)-CS pair has also been calculated for a large range of temperature. These results could be used to assign future experimental spectra and to check the accuracy of the potential energy surface.

Rotational excitation of mono- and doubly-deuterated water by hydrogen molecules

Rate coefficients for rotational transitions in HDO and D2O induced by H2 collisions below 300 K are presented. Calculations have been performed at the close-coupling and coupledstates levels with the deuterated variants of the H2O–H2 interaction potential of Valiron et al. The HDO–H2 and D2O–H2 rate coefficients are compared to the corresponding rate coefficients for HDO–He and H2O–H2, respectively. Significant differences are observed. In particular the new HDO rate coefficients are found to be significantly larger (by up to three orders of magnitude) than the corresponding HDO–He rate coefficients. The impact of the new HDO rate coefficients is examined with the help of non-LTE radiative transfer calculations. A number of potential HDO maser lines are finally identified, in particular the 80.6 GHz (11,0–11,1) transition.

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.

Rovibrational excitation of HD molecules by He atoms

We present rate coefficients for rotational transitions induced in collisions between HD and He. Rotational levels and kinetic temperatures T 1000 K are considered. The in- teraction potential surface calculated by Muchnick & Russek (1994) has been used, together with the quantal coupled-channel method for calculating the cross-sections. Very good agreement with previous calculations by Schaefer (1990) is obtained. The present work goes beyond the latter in that collision rates are cal- culated for all available rotational levels below the first excited vibrational level.

Collisional rates for asymmetrical top molecules

Collisional rate coefficients for rotational transitions in C3 H2 and SiC2 due to collisions with H2 molecules are calculated. The C3 H2 has two distinct species, ortho and para, whereas the SiC2 has only ortho specie due to spin statistics for the identical carbon nuclei. For ortho- and para-C3 H2 we accounted for 47 and 48 energy levels, respectively. The calculations are done for the kinetic temperatures 30, 60, 90, and 120 K. For ortho-SiC2 , we accounted for 40 energy levels and the calculations are done for the kinetic temperatures 25, 50, 75, 100, and 125 K. The results are reported here for the transitions in the upward direction. The values for the downward direction can easily be calculated with the help of the detailed equilibrium equation.

Rovibrational excitation of HD in collisions with atomic and molecular hydrogen

We have computed cross-sections and rate coefficients for rovibrational transitions in HD, induced by collisions with atomic and molecular hydrogen. We employed fully quantum-mechanical methods and the potential of Boothroyd et al. for H–HD, and that of Schwenke for H2–HD. The rate coefficients for vibrational relaxation v=10 of HD are compared with the corresponding values for H2. The influence of vibrationally excited channels on the rate coefficients for rotational transitions within the v=0 vibrational ground state of HD is shown to be small at T=500 K, where T is the kinetic temperature. The rate coefficients, for 100T2000 K, are available from http://ccp7.dur.ac.uk/.

The rotational excitation of H2 by H2

We present rate coefficients for rotational transitions induced in collisions between H2 molecules. Rotational levels J ≤ 8 and kinetic temperatures T ≤ 1000 K are considered. The interaction potential computed by Schwenke has been used, together with the quantal coupled channels method of calculating the cross-sections. Comparison is made with the more recent of previous results.

Quantum Mechanical Calculations of Rotational Transitions in H‐H2Collisions

We report quantum mechanical cross sections and rate coefficients for rotational transitions due to collisions of hydrogen atoms with hydrogen molecules. The sensitivity of the results to the nature of the potential energy surface and to the scattering formulation is investigated. We find that the rigid rotor and harmonic oscillator approximations are inadequate to describe the dynamics. We make use of the most reliable of the potential energy surfaces in a close-coupled description of the nonreactive scattering that takes the vibrational motion into account, and we calculate rate coefficients for rotational transitions at temperatures below 1000 K, where the reactive channels may be neglected.