NMR Arithmetics

2D NMR spectra are simply 2D matrices (Note: these matrices can be real, complex or hypercomplex, but for the sake of simplicity, we will consider real matrices only) which can be subject to standard matrix algebra operations. I have presented in previous posts how Indirect and Direct Covariance NMR can be applied by proper matrix algebra. These methods are incorporated in Mnova as a dedicated module which also makes the filtering of spurious resonances possible . In order to show you that Covariance NMR actually involves these matrix operations, you can use Mnova’s powerful Arithmetic module which we have recently completed. This module has been designed in such a way that it operates as a simple spectral calculator. You enter the equation which the program parses and produces the expected result. For example, if we have a HSQC-TOCSY spectrum (A), we can enter the Indirect Covariance formula like this:

Where A corresponds to the real part of the original spectrum and TRANS indicates the transpose operation. This operation will produce the (unnormalized) Covariance NMR spectrum, in this case the 13C-13C correlation spectrum. Of course, in order to better approximate the covariance spectrum to the corresponding standard 2D FT counterpart, it’s necessary to calculate the square-root using, once more, matrix algebra. This is again very simple with our arithmetic module by just adding the square root operation (SQRT) into the equation:




This arithmetic module is not restricted to matrix operations within a single spectrum. We can freely combine as many spectra as we want. For instance, if we have, in the one hand a COSY spectrum and in the other a HSQC spectrum, we can combine both in an analogous way so that the indirect covariance NMR spectrum yields a HSQC-COSY 2D spectrum. More about this in a future post …