The application of theoretical models of complex shape to the fitting of experimental spectra having closely overlapping bands

The problem of the uniqueness of parameters obtained during fitting of expe rimental spectra containing closely overlapping bands has been evaluated, s ince conventional methods of fitting do not produce reliable results. It is here shown that, despite the difficulties inherent in both the formal math ematical problem and its numerical solutions, typical and representative sp ectra can be resolved unambiguously within a reasonably chosen theoretical model. Reliable values of the parameters of the model, including parameters of band shape, can also be obtained. A random search method of global mini misation of a function with a significant number of arguments is derived. A program and algorithm to implement this method for spectra decomposition h ave been developed. The program allows the microdynamics of liquids to be o btained directly upon performing numerical Fourier transformations on a mod el (theoretical) time correlation function together with using model spectr a obtained thereby in each fitting step. A model spectrum for any desired a ccuracy and frequency range can hence be generated without the unavoidable errors inherent in conventional methods. The apparatus function of the spec trophotometer is also now readily incorporated. Using the algorithm, the pa rameters of the microdynamics of acetonitrile molecules are obtainable for the first time upon decomposition of its nu(2) Raman vibration, and a value of 0.069 was obtained for the dimensionless modulation speed in liquid ace tonitrile. This method has also enabled for the first time the detection of molecules in the second solvation shell around Li+ in acetonitrile, from w ithin its Raman spectrum.