Higher-order l-doubling of linear molecules

The centrifugal correction q_t^JJ( J + 1) to the l-doubling constant q_t corresponds to a term of type H∼₂₄ in the effective vibration-rotation Hamiltonian. A general sequential procedure for calculating H∼₂₄ is presented, and applied to the particular case of the constant q_t^J of linear molecules, which depends on the cubic but not the quartic potential constants. Reasonable agreement is obtained with observed values of q₂^J of CO ₂ and q₅^J of C ₂H ₂. The simple high- J behavior of rotational energies with V_t>1, when l-doubling dominates the ( g_tt - B_v) l_t² splittings, is discussed.