Least-Squares Fitting of Multidimensional Spectra to Kubo Line-Shape Models.

Area of Science:

• Spectroscopy
• Chemical Physics
• Data Analysis

Background:

• Traditional methods like centerline-slope (CLS) fitting for spectral diffusion analysis suffer from limitations in precision and robustness.
• CLS fitting is susceptible to residual signals and has fundamental issues in uncertainty propagation.

Purpose of the Study:

• To evaluate the efficacy of least-squares fitting of multidimensional spectra to generalized Kubo line-shape models.
• To introduce a novel, reliable, and versatile fitting metric: the scale invariant gradient norm (SIGN).

Main Methods:

• Development of a novel least-squares fitting metric, the scale invariant gradient norm (SIGN).
• Application of nonlinear model fitting to generalized Kubo line-shape models for spectral diffusion analysis.
• Statistical analysis of uncertainty propagation in spectral fitting methods.

Main Results:

• The SIGN metric enables a highly reliable and versatile algorithm for spectral diffusion analysis.
• Nonlinear model fitting offers 8× to 50× better precision for dephasing parameters than CLS, increasing data acquisition efficiency by 1-2 orders of magnitude.
• Model fitting demonstrated superior robustness with only 10% variation in Kubo time constants versus 60% for CLS in experimental measurements.

Conclusions:

• Least-squares fitting to generalized Kubo models, particularly with the SIGN metric, provides a more robust and efficient method for spectral diffusion analysis than CLS.
• The developed algorithm accurately predicts linear spectra from nonlinear data and is freely available as a desktop application.
• This advancement significantly enhances the reliability and efficiency of measuring spectral diffusion dynamics.