Postprocessing

One of the major problems that arise in the theoretical prediction of NMR spectra are errors in the input of the chemical shifts and J-couplings. This is, because the input is often already based on DFT calculations, which will provide the shifts up to an accuracy of around 0.3 ppm and the J-couplings to within a range of 1 Hz. Note that these are very rough error estimates. Similarly the broadening of the peaks due to the parameter $\eta$ might need additional fitting, if the calculated peaks are too broad or too narrow. In order to mitigate these issues we provide the postprocessing module, which allows to quickly approximate how a calculated spectrum would have been different if one or multiple of the input parameters were changed. We will not discuss the exact maths behind these methods but just lay out the general steps these procedures follow.

All of the postprocessing procedures require the evaluation of the Green's function rather than just the spectrum. It can easily be calculated using the calculate_greens_function method, which behaves in the exact same way as calculate_spectrum. It returns an object of datatype NMRResultGreensFunction1D, which now has an attribute greens_function rather than spectrum storing the result of the calculation. One could then calculate the spectrum as follows

from hqs_nmr.calculate import calculate_greens_function

nmr_result = calculate_greens_function(
    molecule_parameters,
    calculation_parameters
)

summed_spectrum = np.sum(
    - np.imag(nmr_result.greens_function.spin_contributions), axis=0
)

Once the spectrum has been obtained, the next step is to compare the calculated spectrum with some reference spectrum (for example from experiment). This can be done by simply plotting the spectra against one another. In case the spectra are not aligned to the desired accuracy one can now use the postprocessing methods to try to fit the calculated spectrum to the reference by altering the input parameters for the shifts, J-couplings, and/or the broadening. Though it is important to understand that these methods only give approximate results. Hence, they should be understood as iterative schemes, where after fitting one would take the altered input parameters and again perform a complete spectrum calculation, then check if the desired accuracy has been reached and so on.

As this was just a rough outline of the idea, you might want to consider the example notebooks for a more detailed description. Also note that this entire procedure is automatically available if you use the HQSpectrum frontend tool.