NASA Goddard Institute for Space Studies
Datasets and Images

Molecular Collision Rates

Note: Due to the death of Dr. Sheldon Green in December 1995, this dataset page is no longer actively maintained.

Rotational and vibrational excitation rates are needed to interpret microwave and infrared observations of the interstellar gas. A research program at NASA/GISS under the direction of Sheldon Green was aimed at obtaining these rates by solving the quantum equations for molecular interactions and collision dynamics.

The MOLSCAT computer code was developed to perform the required molecular scattering calculations and is also available for distribution.

The Molecular Spectroscopy Web site at JPL contains frequency and linestrength data relevant to microwave and infrared astronomy.

Collision Rates Information Available Here

• water - helium
• monodeuterated water - helium
• water - hydrogen molecules
• formaldehyde - helium
• HCN - helium
• CS - hydrogen
• SiO - hydrogen
• sulfur monoxide (fine structure levels)
• sulfur dioxide
• HNCO
• HCl, including hyperfine structure levels
• CO excited by water

All of the collision rate files can be obtained via anonymous ftp from ftp.giss.nasa.gov in directory pub/sgreen/astrophys These files are generally available directly from this Web site. However, in future, files for additional molecular systems may become available there before they are added to the Web site. The file names are reasonably descriptive of their contents and the files are (I hope) self-explanatory.

water - helium

Excitation of water by helium has been studied in a series of increasingly more sophisticated calculations:

• S. Green, "Collisional excitation of interstellar molecules: water", Ap. J. (Suppl.) 42, 103-141 (1980)
• A. Palma, S. Green, D.J. DeFrees, and A.D. McLean, "Intermolecular potential for thermal water-helium collisions", J. Chem. Phys. 89, 1401-1407 (1988).
• A. Palma, S. Green, D.J. DeFrees, and A.D. McLean, "Collisional excitation of interstellar water", Ap. J. (Suppl.) 68, 287-318 (1988); addendum: 70, 681-685 (1989).
• S. Green, "Collisional excitation of interstellar molecules: deuterated water, HDO", Ap. J. (Suppl.) 70, 813-832 (1989).
• S. Green, D.J. DeFrees, and A.D. McLean, "Calculations of water microwave line broadening in collisions with He atoms: sensitivity to potential energy surfaces", J. Chem. Phys. 94, 1346-1359 (1991).
• S. Maluendes, A.D. McLean, and S. Green, "Comment on broadening of water microwave lines by collisions with He atoms", J. Chem. Phys. 96, 8150-8156 (1992).
• S. Green, S. Maluendes, and A.D. McLean, "Improved collisional excitation rates for interstellar water", Ap. J. (Suppl.) 85, 181-185 (1993).

Resulting collisional excitation rates appear to be reasonably well converged. Comparison with the best available experimental data which sample the same physical process, microwave line broadening, is fairly satisfactory and it is believed that remaining discrepancies are likely to reflect experimental difficulties.

Collisions do not interconvert para- and ortho-H₂O levels and calculations have been done among the lowest 49 ortho-H₂O levels and the lowest 50 para-H₂O levels providing rate constants in each case for kinetic temperatures between 20 and 2000 K. Plain text (ascii) files describing the rotational levels and rate constants are provided for

• ortho-water
• para-water

monodeuterated water - helium

The interaction potential does not depend on the nuclear isotopes (to a very good approximation) and one of the ab initio interactions for water - helium was transformed into the HDO center of mass and used in molecular scattering calculations (S. Green, "Collisional excitation of interstellar molecules: deuterated water, HDO", Ap. J. (Suppl.) 70, 813-832 (1989)). Excitation rates were obtained among the lowest 34 rotational levels for temperatures between 50 and 500 K. A plain text (ascii) file of the published table of rates is available.

water - hydrogen molecules

Since hydrogen molecules outnumber He atoms by 4 or 5 to 1 in the interstellar gas excitation by hydrogen molecules is the process of most interest. Calculations for this case, however, are much more expensive than calculations for excitation by He atoms. Increases in computation abilities finally permit some calculations for hydrogen molecules, however.

An accurate ab initio potential energy surface for H₂O-H₂ was reported by T.R. Phillips, S. Maluendes, A.D. McLean, and S. Green, J. Chem. Phys. 101, 5824-5830 (1994). A FORTRAN subroutine which generates the potential and which is compatible with the MOLSCAT code, is available.

Preliminary molecular scattering calculations were reported by T.R. Phillips, S. Maluendes, and S. Green, J. Chem. Phys. 102, 6024-6031 (1995). The main conclusion was that excitation by ortho-H₂ is significantly different from excitation by H₂ in its lowest, j=0, rotational level, with some rates enhanced by an order of magnitude.

A manuscript reporting more extensive calculations to temperatures of 140 K is in press in the Ap. J. Suppl. Rates for excitation of water out of its lowest (j=0-2) levels by both ortho- and para-hydrogen are given. The manuscript is available here as a PostScript file or tex file.

Tables describing these rate constants are available as several files

• ortho-water levels
• para-water levels
• ortho-water rates excited by hydrogen in j=0
• ortho-water rates excited by hydrogen in j=1
• para-water rates excited by hydrogen in j=0
• para-water rates excited by hydrogen in j=1

formaldehyde - helium

Excitation of formaldehyde by helium was studied in an early work by B.J. Garrison, et al., Ap. J. (Lett.) 200, L175-L177 (1975) which demonstrated that the observed "anomalous absorption" could be explained by a collisional "pump" effect. This work computed the interaction forces with then state-of-the-art quantum molecular structure methods (self-consistent field and configuration interaction) and used accurate coupled channel calculations for collision dynamics.

More extensive molecular scattering calculations with the same potential energy surface were subsequently done by these authors, Ap. J. (Suppl.) 36, 483-496 (1978) to obtain rate constants among more rotational levels and for a wider range of temperatures.

These calculations were significantly extended by S. Green, Ap. J. 76, 979-983 (1991) to obtain rates among the lowest 40 para-H₂CO levels and among the lowest 41 ortho-H₂CO levels (collisions do not couple ortho- and para-levels).

Plain text (ascii) files are available below which describe the rotational levels and tabulate rates for downward collisions (upward rates can be obtained by detailed balance).

• para-formaldehyde
• ortho-formaldehyde

hydrogen cyanide

One of the first astrophysical systems for which collision rates were calculated was HCN. An approximate (electron gas) interaction potential for HCN-He was used with essentially exact coupled channel molecular scattering calculations to obtain rates among the lowest 8 levels for temperatures of 5 - 100 K. Results were published in S. Green and P. Thaddeus, Ap. J. 191, 653 (1974).

More recent observations require rates for higher rotational levels and higher temperatures. The earlier calculations were extended in 1993 to obtain rate constants among the lowest 30 rotational levels and for temperatures of 100 - 1200 K. These results are not published but are available here as a plain text (ascii) file.

carbon monosulfide

Excitation rates among the lowest 13 rotational levels for temperatures of 10 - 100 K were presented by S. Green and S. Chapman, Ap. J. (Suppl.) 37, 169 (1978). The intermolecular potential was estimated by a relatively crude electron gas approximation for CS-He modified in the region of the well and at long-range for expected differences between He and H₂ and collision dynamics were done with this interaction potential for CS-H₂.

In order to interpret more recent observations of higher rotational levels in warmer sources, these calculations have been extended as described by B.E. Turner, K.-W. Chan, S. Green, and D.A. Lubowich, Ap. J. 399, 114 (1992). Rate constants are available among the lowest 21 rotational levels and for temperatures between 20 and 300 K as a plain text (ascii) file.

silicon monoxide

Maser emission among rotational levels in excited vibrational states of SiO is observed in the outer atmospheres of some stars. Understanding of this phenomenon requires knowledge of collision rates and, in particular, the relative rates for vibrational and pure rotational excitation at temperatures of a few thousand kelvin. These rates were obtained by R.J. Bieniek and S. Green, Ap. J. (Lett.) 265, L29 (1983) using an interaction potential estimated within an electron gas approximation (R.J. Bieniek and S. Green, Chem. Phys. Lett. 84, 380 (1981)) and treating collision dynamics within the vibrational close coupling rotational infinite order sudden approximation.

SiO is also observed in lower temperature interstellar gas. Interpretation of these observations requires collision rates among rotational levels in the ground vibrational state at temperatures to about 300 K. The earlier potential of Bieniek and Green was refitted to give a representation more appropriate for low energy rotational excitation and collision dynamics were treated within the coupled states approximation as described in B.E. Turner, K.-W. Chan, S. Green, and D.A. Lubowich, Ap. J. 399, 114 (1992). Rate constants are available among the lowest 21 rotational levels and for temperatures between 20 and 300 K as a plain text (ascii) file.

Neither of the above papers provides rates for temperatures between 300 and 2000 K, and such rates would be useful in some studies of circumstellar gas. Rigid rotor values using the IOS approximation have therefore been calculated at energies required for this temperaature range. Resulting rates can be obtained with a self-contained FORTRAN code which generates rates for a specified (input) temperature and for rotational levels from j=0 to a specified (input) JMAX. Owing to approximations used, temperatures in the range 300 - 1500 K and JMAX < 31 are recommended. The required generalized IOS cross sections as a function of collision energy are included in the code. The program is straightforward and should be easily modified to produce rate constants in a format convenient for further processing.

sulfur monoxide

sulfur dioxide

HNCO

hydrogen chloride

Using an intermolecular potential which was inferred from pressure broadening measurements on DCl - He and accurate coupled channel molecular scattering calculations, collisional excitation rates were computed for HCl rotational levels through j=7 and temperatures from 10 to 300 K. Nuclear hyperfine structure is resolved in some of the interstellar observations, and rates among the hyperfine levels have been obtained from the state-to-state rates by using IOS scaling relationships. Details of the molecular scattering calculation and also a discussion of line formation in interstellar sources are given in D.A. Neufeld and S. Green, "Excitation of interstellar hydrogen chloride", Ap. J. 432, 158 (1994).

Plain text (ascii) files are available with rotational state-to-state rates and also with rates among hyperfine structure levels.

CO excited by water

Analysis of observations of CO in cometary spectra requires rates of collisional excitation by water molecules. CO-H₂O collisions are too complex to be treated by current theoretical methods. However, these collision rates are related to linewidths in Coherent Anti-Stokes Raman Spectra and models exist for fitting these linewidths in terms of collision rate models. A method of obtaining CO-H₂O excitation rates from spectra of related systems was described in S. Green, Ap. J. 412, 436 (1993). Resulting collision rates can be obtained from a simple FORTRAN program. To test that the program works correctly, sample output is also provided.