  This article continues the series of works by the authors on the
approximation of the electronic terms of diatomic molecules by the Morse
formula, which is the simplest anharmonic approximation of the real term U(r).
Depending on the choice of parameters, the approximation has two alternative
solutions M1(r) and M2(r), with different patterns of deviations from the real
term and its vibrational structure. The difference {\delta}(r)=U(r)-M(r)
quantitatively shows the changes in the shape of the terms during
approximation. We introduced an empirical anharmonicity function -2{\omega}_e
x(v), which characterizes the positions of vibrational levels in the potential
well; it demonstrates the distortion of the vibrational structure of the term
U(r) during the approximation. Based on the data from literature, the functions
{\delta}(r) and -2{\omega}_e x(v) were constructed for more than 20 molecules.
Here we present a group of simple terms with minimal deviations from the Morse
shape.
