This article answers a frequent question about Spectral Hard Modeling methods for quantitative NMR spectra analysis, implemented in the PEAXACT software from S-PACT. It shows how nuclear magnetic resonance (NMR) spectroscopy can benefit from the modeling approach.
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Spectral Hard Modeling for NMR
Direct peak integration is still the method of choice for many scientists when it comes to quantitative analysis of NMR spectra. However, non-linear effects such as peak shifts, peak broadening and baseline distortions add more complexity and make it difficult to capture all NMR signals with appropriate integration ranges (e.g. 64 times the half-width of the signal).
This is where Spectral Hard Modeling comes into the game… Spectral Hard Modeling is a physically motivated method for quantitative analysis of spectroscopic data. It makes use of first principles information within the NMR spectrum, i.e., counting nuclear spins. In an ideal case, NMR peaks have a shape that is called Lorentzian. This line shape is broadened by inhomogeneities of the magnetic and electro-magnetic field or by coupling effects, which can be described as a Gaussian function which is broadening the Lorentzian.
|Flexibility of peak functions|
For Hard Modeling, the spectrum of a component is modeled with peak-shaped signals, expressed mathematically by peak functions, e.g. a combination of Lorentzian and Gaussian lines. Within a Hard Model, individual peaks are just a means to the end of representing the shape of each component. Multiplets or even higher-order spectra can be described as such combinations of peak functions. Peaks of the Hard Model are automatically fitted to new mixture spectra, i.e. you don't have to process each spectrum from the scratch.
Hard Modeling is especially beneficial for low-field NMR instruments that are making their way into real-time process analysis. In contrast to high-field NMR instruments these spectra often suffer from overlapping signals and more pronounced relative shifts.
|Hard Model (red) is a weighted sum of Component Models (blue).|
Each Component Model is composed of superimposed peaks (grey)
The relevant quantity of a fitted Hard Model is the signal area which each component contributes to the mixture. Areas of NMR signals behave extremely linear and independent of the surrounding sample matrix. They can be used directly for quantification, without the need for a calibration model.
If your model is well set and flexibility is validated, you may apply it in an unsupervised manner to an instrument connected to your process. You come up with a real-time output of concentrations – what makes your benchtop NMR a proper Process Analyzer!
Comparison to Peak Deconvolution
The well-informed NMR analyst may immediately recognize the close relationship to global peak deconvolution techniques. Indeed, Indirect Hard Modeling can be considered a more advanced form of peak fitting which we call "component fitting". Because of the linking of peaks to components the fitting problem has much less degrees of freedom which results in a physically more reasonable fit... a very relevant benefit for the NMR community with its strong physical background.