Arithmetic

Arithmetic (Not available in Mnova Lite):

This feature is used to carry out arithmetic operations with 'fid''s or processed spectra. Typically, you will use the arithmetic module implemented in MestReNova to sum 'fid''s  acquired under the same measurement conditions in order to improve the signal-to-noise ratio.

This tool is also very useful to remove impurities or solvent signals from a spectrum, to analize DEPT experiments. This feature will be enhanced in the oncoming versions of the software to be able to subtract FIDs of Selective Experiments (such as NOE or ROE).

How to sum or subtract spectra?

Application of Linear Combinations (sums, subtraction and multiplication) to spectra in the MestReNova interface is extremely simple. Just select the desired spectra (make sure they are acquired under same conditions) on the Page Navigator (by holding down 'CTRL key' or 'Cmd key' while clicking on each spectrum) and follow the menu 'Analysis/More Tools/Arithmetic':

This will display the 'Arithmetic' dialog box on screen. In this example, we want to add two times spectrum A to spectrum B, so we shall type the formula 'A+2B' in the applicable cell.

The 'Save' icon will allow you to save your formulas, which can be loaded by using the 'Load' button .

On pressing ‘OK’,  the result is a new spectrum which will consist of the sum of spectrum B plus two times spectrum A.

You can also subtract spectra, but in this case it is important that the user calculates the intensity ratio of both spectra. For example, in this spectrum we have a sample contaminated with a solvent.

Whilst the spectrum below corresponds to the solvent which we need to eliminate from the sample.

To successfully carry out the subtraction, we need to calculate the intensity ratio between the contaminated spectrum and the solvent spectrum. To obtain this ratio we can measure the intensity of a signal present in both spectra (by applying the command ‘Peak by peak’ and getting the result on the applicable table). For example, we measure the intensity of the singlet which appears at 1.32 ppm. For the first spectrum, we obtain an intensity of 22617 and for the second, 115031, indicating the the intensity ratio to be 1/5, or 0.2.

Typing the formula 'A-0.2B' (or 'A-0.2*B') in the 'Arithmetic' dialog box, we shall obtain the spectrum below, where the solvent signals have been removed:

Arithmetic and Covariance NMR

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. You can read the Covariance NMR chapter where it is shown 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 applicable 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.