Divergence Treatment in Calculating Molecular Normal Vibrations and Adjusting Molecular Force Field

So far, while solving the vibrational problems of molecules, one usually needs to do the following work:First, a set of initial values of force constants must be assumed. Then, the frequencies which are calculated with these initial values of the force constants using Wilson's GF metrix method are compared to those observed values and the molecular force field is adjusted to minimize the differences between the two values by means of least-squares methods. Finally, these adjusted force constants can be used to calculate the normal vibrations, give band assignments and so on. Unfortunately, divergent difficulties may arise when doing these works with conputers. For this reason, Marquart's method was given to overcome such difficulties. Here we introduce a new method to treat this problem. More satisfactory results are obtained when we apply it to water molecule and its isotope.