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

Abstract

We report a comprehensive study of the efficacy of least-squares fitting of multidimensional spectra to generalized Kubo line-shape models and introduce a novel least-squares fitting metric, termed the scale invariant gradient norm (SIGN), that enables a highly reliable and versatile algorithm. The precision of dephasing parameters is between 8× and 50× better for nonlinear model fitting compared to that for the centerline-slope (CLS) method, which effectively increases data acquisition efficiency by 1–2 orders of magnitude. Whereas the CLS method requires sequential fitting of both the nonlinear and linear spectra, our model fitting algorithm only requires nonlinear spectra but accurately predicts the linear spectrum. We show an experimental example in which the CLS time constants differ by 60% for independent measurements of the same system, while the Kubo time constants differ by only 10% for model fitting. This suggests that model fitting is a far more robust method of measuring spectral diffusion than the CLS method, which is more susceptible to structured residual signals that are not removable by pure solvent subtraction. Statistical analysis of the CLS method reveals a fundamental oversight in accounting for the propagation of uncertainty by Kubo time constants in the process of fitting to the linear absorption spectrum. A standalone desktop app and source code for the least-squares fitting algorithm are freely available, with example line-shape models and data. We have written the MATLAB source code in a generic framework where users may supply custom line-shape models. Using this application, a standard desktop fits a 12-parameter generalized Kubo model to a 106 data-point spectrum in a few minutes.

Spectrophotometric Concentration Analysis Without Molar Absorption Coefficients by Two-Dimensional-Infrared and Fourier Transform Infrared Spectroscopy

“…Each effect is known across the literature of 2D-IR spectroscopy. ,,, Eq collectively accounts for them in a manner allowing each to be understood and assessed independently of the others. Equation is heuristic, and line shape terms χ and B might be better modeled using global fitting and first-principles 2D-IR line shape functions. ,− …”

“…Equation 7 is heuristic, and line shape terms χ and B might be better modeled using global fitting and first-principles 2D-IR line shape functions. 7 , 17 − 19 …”

An Evaluation of Maximum Determination Methods for Center Line Slope Analysis

“…As shown in Figure , all methods yielded a distribution of fit/true values centered near 1; however, the fast lifetime was recovered less accurately than the short lifetime, as the CLS method relies on the short-time approximation and is less reliable for relatively fast processes than for slow processes. ,, The full center of mass method was more precise for noise-free simulated CLS than all other methods. The direct method, which just uses the frequency of the pump slice where the signal is highest, was less precise than all other methods.…”

“…Multiple techniques exist for the extraction of FFCF parameters from t 2 -dependent 2D spectra, each with relative advantages and disadvantages. ,, The most widely used method to date is the center line slope (CLS) method, , which involves fitting a line to the ridge formed by the maxima of a 2D spectrum, calculating the slope of that line, and observing t 2 -dependent changes to the slope. The advantages of the CLS method include ease of implementation and insensitivity to several experimental complications in 2D spectroscopy, including apodization, anharmonicity, and broad background signals. , However, the CLS method can begin to lose accuracy with even small amounts of experimental noise . This represents a significant obstacle, as a full spectral diffusion experiment scans to long t 2 delays, at which it could take hours or days to get sufficient 2D spectra with acceptable signal-to-noise ratios (SNR), , limiting the type of sample that is viable for CLS measurements.…”

Increasing Pump–Probe Signal toward Asymptotic Limits

“…On the other hand, some room remains for fluence enhancement on weaker chromophores. For example, our recent reports with MeSCN (ε ≈ 150 M –1 cm –1 ) have ratios of false| ΔOD false| OD ( 0 ) ≈ 0.1 and 0.05, , which leaves room for ∼20× and ∼4× enhancement by increasing the pump fluence.…”