A regularized inverted perturbation approach method: potential energy curve of the $4^1\Sigma^+_u$ state in $Na_2$

We describe a modification of the inverted perturbation approach method allowing to construct physically sensible potential energy curves for electronic states of diatomic molecules even when some parts of the potential are not adequately characterized by the experimental data. The method is based on a simple regularization procedure, imposing an additional constraint on the constructed potential curve. In the present work it is applied to the double minimum 4$^1\Sigma^{+}_{\mathrm u}$ state of Na$_2$, observed experimentally by polarization labeling spectroscopy technique.