CLS Next Gen: Accurate Frequency–Frequency Correlation Functions from Center Line Slope Analysis of 2D Correlation Spectra Using Artificial Neural Networks

The center line slope (CLS) observable has become a popular method for characterizing spectral diffusion dynamics in two-dimensional (2D) correlation spectroscopy because of its ease of implementation, robustness, and clear theoretical relationship to the frequency–frequency correlation function (FFCF). The FFCF relates the frequency fluctuations of an ensemble of chromophores to coupled bath modes of the chemical system and is used for comparison to molecular dynamics simulations and for calculating 2D spectra. While in the appropriate limits, the CLS can be shown to be the normalized FFCF, from which the full FFCF can be obtained, in practice the assumptions that relate the CLS to the normalized FFCF are frequently violated. These violations are due to the presence of homogeneous broadening and motional narrowing. The generalized problem of relating the CLS to the FFCF is reanalyzed by introducing a new set of dimensionless parameters for both the CLS and FFCF. A large data set was generated of CLS parameters derived from numerically modeled 2D line shapes with known FFCF parameters. This data set was used to train feedforward artificial neural networks that act as functions, which take the CLS parameters as inputs and return FFCF parameters. These neural networks were deployed in an algorithm that is able to quickly and accurately determine FFCF parameters from experimental CLS parameters and the fwhm of the absorption line shape. The method and necessary inputs to accurately obtain the FFCF from the CLS are presented.