## Abstract

Procedures are developed for obtaining effective potentials V^{eff} between two linear molecules. The potential V_{eff} couples the internal rotational states of the molecules, regardless of the spatial effects associated with the projection quantum numbers M. Since just V^{eff} is not sufficient for treating the dynamics, an effective Hamiltonian H ^{eff} = H_{0}^{eff}+V^{eff} is obtained from the original Hamiltonian H = H_{0}+V, where Ha describes the unperturbed motion of the molecules. A consistent procedure is presented for finding both effective operators H_{0}^{eff} and V^{eff}, where the matrix elements of an effective operator Q^{eff} are written as 〈J_{1}J_{2}|Q^{eff}|J_{1}′J _{2}′〉. The effective states 1/1/2) are orthonormal eigenstates of the rotational portion of H_{0}^{eff} with the same level spacings as for H_{0}. 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 H^{eff}, 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 V^{eff} in semiclassical time-dependent perturbation theory is presented.

Original language | English (US) |
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Pages (from-to) | 1718-1725 |

Number of pages | 8 |

Journal | The Journal of chemical physics |

Volume | 57 |

Issue number | 4 |

DOIs | |

State | Published - 1972 |

## All Science Journal Classification (ASJC) codes

- General Physics and Astronomy
- Physical and Theoretical Chemistry