High-order anharmonicity parameters in various representations of the diatomic potential function and exact relations between spectroscopic constants. application to the co molecule

Closed formulae for Born—Oppenheimer anharmonicity parameters a_n in terms of isotopically invariant constants U_mj are derived for Dunham, Simons—Parr—Finlan, Ogilvie—Tipping and Thakkar representations and are applied to the CO molecule. Models for a fit of vibration—rotation and pure rotational transitions based on the exact relations U_mj = f(U_k,o, U_k-1.1) and U_mj = α(U_k,1, U_k,2) are discussed.