"Sequential order" rules in generalized two-dimensional correlation spectroscopy

The widely used "sequential order" rules in the generalized two-dimensional (2D) correlation spectroscopy were adopted from the mechanical perturbation-based 2D infrared, where dynamic spectral intensity variation must be a simple sinusoid. 2D correlation analysis is fundamentally a form of parametrization of the integrated or overall relationship between two variable quantities. In generalized 2D correlation spectroscopy, however, the dynamic spectral intensity variations are generally nonperiodic and monotonic, and spectral intensity changes are largely instantaneous. The sequential orders in generalized situations are therefore localized. It is naturally necessary and important to testify whether the analysis result obtained by using the sequential order rules is consistent with the local sequential order of events, which reflects the real sequential order in generalized situations. Unfortunately, this test was not done yet. In this report, the sequential order rules have been tested in the generalized situations using simulated spectra with different local sequential orders and assuming the intensity changes of bands take the exponential forms. It has been found that the sequential order rules correctly identify the local sequential order of two events when spectral intensities of two bands increase or decrease at the same direction but fail when spectral intensities change at different directions. In addition, 2D correlation analysis cannot distinguish the local sequential order from the rate difference of events. A theoretical analysis demonstrates that the synchronous and asynchronous spectra in the generalized 2D correlation spectroscopy may also indicate the linear/nonlinear relationship, in addition to the integrated or overall sequential order of events. The synchronous and asynchronous spectra in the generalized 2D correlation spectroscopy do not necessarily provide the information on the local sequential order or rate difference of events.