This volume aims to provide a consistent mathematical and physical treatment of empirical data processing in vibrational spectroscopy, based on the modern theory of nonlinear ill-posed problems. The authors offer a clear description of the foundation of the theory and also look at its applications. The straightforward mathematical formulation of model constraints as well as the use of experimental data form the main issues in the book. Ab initio methods are briefly discussed, since these are likely to provide a good starting point for subsequent empirical data fitting. The data processing methods developed in the book provide empirical force fields which are compatible with experimental data as well as with certain model assumptions. Numerical methods and results of applications to different statements of inverse problems of spectroscopy are also given.
Physical model of molecular vibrations; full statement of the vibrational problem; consideration of the mathematical model for molecular vibration analysis - direct and inverse problems; vibrational problems in internal coordinates - use of the redundant coordinate system; vibrational problems in symmetry coordinates; ill-posed problems and the regularization method - regularizing algorithms for constructing force fields of poly-atomic molecules on the base of experimental data; numerical methods; analysis of band intensities in vibrational spectra of poly-atomic molecules; numerical implementation of algorithms for solving problems of vibrational spectroscopy; examples of molecular force field calculations on the basis of experimental data; joint treatment of ab initio and experimental data in molecular force field calculations with Tikhonov's method of regularization. Appendix: systems of units used in vibrational spectroscopy.
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- ID: 9789067643047
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