Morse/Long-range potential
The Morse/Long-range potential (MLR potential) is an interatomic interaction model for the potential energy of a diatomic molecule. Due to the simplicity of the regular Morse potential (it only has three adjustable parameters), it is very limited in its applicability in modern spectroscopy. The MLR potential is a modern version of the Morse potential which has the correct theoretical long-range form of the potential naturally built into it. It has been an important tool for spectroscopists to represent experimental data, verify measurements, and make predictions. It is useful for its extrapolation capability when  data for certain regions of the potential are missing, its ability to predict energies with accuracy often better than the most sophisticated "ab initio" techniques, and its ability to determine precise empirical values for physical parameters such as the dissociation energy, equilibrium bond length, and long-range constants. Cases of particular note include: Historical origins. The MLR potential is based on the classic Morse potential which was first introduced in 1929 by Philip M. Morse. A primitive version of the MLR potential was first introduced in 2006 by Robert J. Le Roy and colleagues for a study on N. This  primitive form was used on Ca, KLi and MgH, before the more modern version was introduced in 2009 . A further extension of the MLR potential referred to as the MLR3 potential was introduced in a 2010 study of Cs, and this potential has since been used on HF, HCl, HBr and HI. Function. The Morse/Long-range potential energy function is of the form formula_1 where for large formula_2, formula_3 so formula_4 is defined according to the theoretically correct long-range behavior expected for the interatomic interaction. This long-range form of the MLR model is guaranteed because the argument  of the exponent is defined to have long-range behavior: formula_5 where formula_6 is the equilibrium bond length. There are a few ways in which this long-range behavior can be achieved, the most common is to make formula_7 a polynomial that is constrained to become formula_8 at long-range: formula_9 formula_10 where "n" is an integer greater than 1, which value is defined by the model chosen for the long-range potential formula_11. It is clear to see that: formula_12 Applications. The MLR potential has successfully summarized all experimental spectroscopic data (and/or virial data) for a number of diatomic  molecules, including: N, Ca, KLi, MgH, several electronic states of Li, Cs, Sr, ArXe, LiCa, LiNa, Br, Mg, HF, HCl, HBr, HI, MgD, Be, BeH, and NaH. More sophisticated versions are used for polyatomic molecules. It has also become customary to fit "ab initio" points to the MLR potential, to achieve a fully analytic "ab initio" potential and to take advantage of the MLR's ability to incorporate the correct theoretically known short- and long-range behavior into the potential (the latter usually being of higher accuracy than the molecular "ab initio" points themselves because it is based on atomic  ab initio calculations rather than molecular ones, and because features like spin-orbit coupling which are difficult to incorporate into molecular "ab initio" calculations can more easily be treated in the long-range). MLR has been used to represent "ab initio" points for KLi and KBe.