Inverse Problems of Molecular Spectra Data Processing

There are considered ill-posed inverse problems which arise in molecular spectroscopy data processing. The main of them, the general inverse problem of structural chemistry for free molecules is nonlinear inverse problem of molecular vibrations. The modern view on this problem joins the study of molecular force field and geometry restoration using all available experimental data (vibrational (IR and Raman) spectroscopy, electron diffraction, etc.), a priori constraints and ab initio quantum mechanical calculations. The second inverse problem of determination of intermolecular potential from the second virial coefficient is also closely connected with molecular structure investigation. On the basis of formulation and formalization of possible obvious (and related to quantum mechanical results) model assumptions concerning the character of force fields which are widely used in vibrational spectroscopy we have constructed a principle for choosing a unique solution from the set of solutions in the framework of Tikhonov’s regularization theory. The solution is chosen as the nearest to the given matrix of force constants which satisfy all a priori assumptions concerning the model characteristics of the solution. Also there are presented stable numerical methods, based on Tikhonov’s regularization method for computing the force fields of polyatomic molecules from experimental data as well as some numerical illustrations using real data.