Publication Abstracts

Heil et al. 1978

Heil, T.G., S. Green, and D.J. Kouri, 1978: The coupled states approximation for scattering of two diatoms. J. Chem. Phys., 68, 2562-2583, doi:10.1063/1.436115.

he coupled states (CS) approximation is developed in detail for the general case of two colliding diatomic molecules. The high energy limit of the exact Lippmann-Schwinger equation is used to obtain the CS equations so that the sufficiency conditions of Kouri, Heil, and Shimoni apply. In addition, care is taken to ensure correct treatment of parity in the CS, as well as correct labeling of the CS by an effective orbital angular momentum. The analysis follows that given by Shimoni and Kouri for atom-diatom collisions where the coupled rotor angular momentum j12 and projection λ12 replace the single diatom angular momentum j and projection λ. The result is an expression for the differential scattering amplitude which is a generalization of the highly successful McGuire-Kouri differential scattering amplitude for atom-diatom collisions. Also, the opacity function is found to be a generalization of the Clebsch-Gordon weight atom-diatom expression of Shimoni and Kouri. The diatom-diatom CS body frame T matrix TJ(j1'j2'j1212'|| j1j2 j12λ12) is also found to be nondiagonal in λ'12, λ12, just as in the atom-diatom case. The parity and identical molecule interchange symmetries are also considered in detail in both the exact close coupling and CS approximations. Symmetrized expressions for all relevant quantities are obtained, along with the symmetrized coupled equations one must solve. The properly labeled and symmetrized CS equations have not been derived before this present work. The present correctly labeled CS theory is tested computationally by applications to three different diatom-diatom potentials. First we carry out calculations for para-para, ortho-ortho, and ortho-para H2-H2 collisions using the experimental potential of Farrar and Lee (as modified by Zarur and Rabitz). Our results are compared with CC results due to Green. In addition, we have derived and tested the statistical and truncated coupled states approximations for this system. Next, we carried out calculations for ortho-para H2-H2 scattering using the configuration interaction surface of Ostlund. Calculations at seven energies from 2000 to 14,000 /cm are reported; the CS results are compared to CC results. The third system studied is H2-HCl, using a potential adapted from an HCl-He electron gas surface by Green. The results are again compared with CC studies due to Green. The results are quite encouraging and indicate that for systems (and specific transitions) satisfying the validity conditions of Kouri, Heil, and Shimoni, the CS is quantiative just as in the atom-diatom case. Furthermore, we expect the accuracy to improve as the energy of the collision increases.

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BibTeX Citation

@article{he01100t,
  author={Heil, T. G. and Green, S. and Kouri, D. J.},
  title={The coupled states approximation for scattering of two diatoms},
  year={1978},
  journal={J. Chem. Phys.},
  volume={68},
  pages={2562--2583},
  doi={10.1063/1.436115},
}

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RIS Citation

TY  - JOUR
ID  - he01100t
AU  - Heil, T. G.
AU  - Green, S.
AU  - Kouri, D. J.
PY  - 1978
TI  - The coupled states approximation for scattering of two diatoms
JA  - J. Chem. Phys.
VL  - 68
SP  - 2562
EP  - 2583
DO  - 10.1063/1.436115
ER  -

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