A general model-based approach to two-dimensional infrared correlation spectroscopy incorporating the global phase angle

We describe a theoretical framework for a model-based approach to two-dimensional correlation spectroscopy that is generally applicable to any arbitrary model function. The method is based on the correlation between spectral data and a set of model waveforms with a varying correlation index, the global phase angle Theta. When experimental spectral intensity variations are expressed as sinusoidal, exponential, Lorentzian, or quadratic functions, the proposed approach allows us to estimate the quantitative values of the target parameters in those expressions. In addition, this method enables us to assess the sequential order in a series of bands undergoing non-identical intensity changes in a dynamic data set. We present both simulated and experimentally obtained data that illustrate that the deviations from linearity of the absorption band intensity waveforms are clearly detected and can be quantitatively estimated using quadratic functions.