Effective potentials in molecular collisions

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Procedures are developed for obtaining effective potentials Veff between two linear molecules. The potential Veff couples the internal rotational states of the molecules, regardless of the spatial effects associated with the projection quantum numbers M. Since just Veff is not sufficient for treating the dynamics, an effective Hamiltonian H eff = H0eff+Veff is obtained from the original Hamiltonian H = H0+V, where Ha describes the unperturbed motion of the molecules. A consistent procedure is presented for finding both effective operators H0eff and Veff, where the matrix elements of an effective operator Qeff are written as 〈J1J2|Qeff|J1′J 2′〉. The effective states 1/1/2) are orthonormal eigenstates of the rotational portion of H0eff with the same level spacings as for H0. The effective potential is shown to have the form of a radial function times an internal state coupling matrix, or in general a sum of such terms. The effective close-coupled equations are developed from Heff, and it is demonstrated that there is a decoupling of the orbital and internal rotational angular momenta. The significantly reduced dimensionality of the effective equations is shown by comparison with the corresponding equations derived from H. A numerical example using Veff in semiclassical time-dependent perturbation theory is presented.

Original languageEnglish (US)
Pages (from-to)1718-1725
Number of pages8
JournalThe Journal of chemical physics
Issue number4
StatePublished - 1972

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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