Analysis of 2D NMR relaxation data using Chisholm approximations.

Area of Science:

• Nuclear Magnetic Resonance (NMR) Spectroscopy
• Computational Chemistry
• Data Analysis

Background:

• Analyzing 2D NMR relaxation data is crucial for understanding molecular dynamics.
• Existing methods for relaxation map analysis can be limited in accuracy and resolution.
• The Padé-Laplace method is a powerful tool for inverse Laplace transforms but requires adaptation for 2D data.

Purpose of the Study:

• To extend the Padé-Laplace method for analyzing two-dimensional (2D) NMR relaxation data.
• To introduce a novel algorithm based on the Chisholm approximation for 2D relaxation map analysis.
• To evaluate the performance and reliability of the new method compared to existing techniques.

Main Methods:

• Extension of the Padé-Laplace method to two dimensions.
• Approximation of the forward Laplace transform using a 2D rational polynomial (Chisholm approximation).
• Comparison of inversion results with Tikhonov regularization as a function of signal-to-noise ratio (SNR).

Main Results:

• The developed algorithm reliably analyzes 2D NMR relaxation data for SNRs greater than 50.
• The Chisholm approximation method demonstrates competitive performance against Tikhonov regularization.
• The method successfully detects simulated relaxation compartments with narrow Gaussian distributions (width ≤ 0.05 s⁻¹).
• Experimental data analysis at SNR 750 showed resolution of two relaxation compartments in 80% of cases when differing by a factor of 1.7.

Conclusions:

• The extended 2D Padé-Laplace method using Chisholm approximation is a reliable tool for 2D NMR relaxation data analysis.
• This method offers a viable alternative to Tikhonov regularization, particularly for specific SNR ranges and distribution widths.
• The algorithm demonstrates significant potential for resolving complex relaxation behaviors in experimental NMR data.