Synchronicity and linearity in generalized two-dimensional correlation spectroscopy: Concepts relevant to the analysis of nonperiodic, monotonically increasing or decreasing spectroscopic signals

The theory and terminology for two-dimensional (2D) infrared correlation spectroscopy were originally developed for the analysis of dynamic IR signals induced by periodic perturbations. The generalized 2D spectroscopy method defines synchronous and asynchronous relationships mathematically rigorously, both for periodic and nonperiodic perturbations. However, the concept of synchronicity may not be intuitively easy to understand when applying the generalized 2D spectroscopy method to the analysis of nonperiodic perturbations. We propose an alternative and novel measure and concept especially useful for nonperiodic perturbations. Our main proposal, when interpreting 2D maps, is to focus on linearity instead of synchronicity. We also propose a simple plot to reveal, verify, and identify linear and nonlinear relationships in the variable space. In addition, we are proposing the alternative use of four terms: (1) linearity as an alternative measure and concept to synchronicity; (2) covariance maps, peaks, etc. as an alternative term to synchronous maps, spectrum, peaks, etc.; (3) disvariance maps, peaks, etc., as an alternative term to asynchronous maps, spectrum, peaks, etc.; and (4) disrelation coefficient as an alternative term to normalized asynchronicity. In an example using FT-IR data from a three-component evaporation experiment, most peaks in the covariance or the traditional synchronous 2D map represented linear relationships, but also peaks representing nonlinear relationships between the involved spectroscopic bands were found. All larger peaks in the disvariance or the traditional asynchronous 2D map represented nonlinear relationships between the involved spectroscopic variables. Our proposed plot visually revealed the type and the degree of non-linearity.