The isotope dependence of diatomic Dunham coefficients

The isotope dependence of the Dunham vibration-rotation coefficients Y_kl of a diatomic molecule is studied. Rovibronic interactions between different electronic states are taken into account by transformation to an effective vibration-rotation Hamiltonian for each electronic state. This contains modified vibrational and rotational reduced masses as well as the adiabatic correction to the potential energy. The effects of these contributions on the vibration-rotation energies are expressed in terms of two functions and for each atom i. The resultant formula for Y_kl is Y_kl=μ_c^−(k+2l)/2U_kl{1+m_eΔ_kl^a/M_a+m_eΔ_kl^b/M_b+O(m_e²/M_i²)}, where U_kl, Δ_kl^a, and Δ_kl^b are isotopically invariant, M_a and M_b are the atomic masses, and μ_c = M_aM_b/(M_a + M_b − Cm_e) is the atomic reduced mass, modified by the molecular charge number C for charged species. The U_kl with l ≥ 2 can be calculated from those with l = 0 and 1. The corrections U_klΔ_klⁱ are related to the functions and and to the Dunham corrections. Recent data for the CO molecule are discussed, and it is suggested that some large Δ_klⁱ values are associated with accidentally small U_kl values, since the size of U_klΔ_klⁱ is not directly related to that of U_kl.