There is nothing magic about Covariance NMR. I think that this plot shows the power of the Covariance NMR method. I have created a stacked plot representation with the 1D projections obtained from the different processing methods described in this post (Zero-Filling, Linear Prediction and Direct Covariance NMR). So direct Covariance NMR allows us to produce a 2D spectrum in which the resolution in both dimensions is determined by the resolution of the spectrum along the direct dimension. Taking the square root of C matrix is in practice done using standard linear algebra methods (in short, diagonalizing the matrix and then reconstructing C^(1/2) using eigenvectors and the square roots of eigenvalues). Root squaring may also suppress false correlations which may be present in F'F due to resonance overlaps.
In order to approximate the intensities of the covariance spectrum to those of the idealized 2D FT spectrum, the square root of C should be taken. We might get more data points per hertz, but no new information is achieved as it’s shown in the figure above. In theory, zero filling by at least a factor of two is highly recommended because it enforces causality but beyond that, the gain in resolution is purely cosmetic. In this case we have zero filled from 128 to 1024 data points (e.g. Zero Filling is certainly a good technique to improve resolution but, of course, it cannot invent new information from where it does not exist. It can be observed now that the resolution along f1 is slightly higher than in the previous case but we still cannot distinguish the inner structure of the multiplets (e.g. For example, in this particular case we could try to extrapolate the FID (along t1) from 128 to 1024 points in order to match the number of points along f2. A well known and very simple technique is simply to add zeros, a process called zero-filling, which basically is equivalent to a kind of interpolation in the frequency domain.
How could this be improved? We could try to extrapolate the FID (somehow) along the columns (F1) to a higher number of points (e.g. The very high performance of Mnova makes Covariance NMR computationally affordable and open to a wide range of routine applications.
#Inmr 2d processing full#
The new implementation of Covariance NMR in Mnova is much more efficient and for this particular example, full calculation of the Indirect Covariance spectrum takes less than 3 seconds in the same computer. The computation of the covariance matrix requires O(N1N2^2/2) floating point operations, whereas the square-root operation based on diagonalization of C requires O(N2^3) floating point operations (see this for more details).įor example, calculation of the indirect covariance NMR spectrum (including square root computation) of the HSQC-TOCSY spectrum showed above (1024x1024 data points) took about 60 seconds in my laptop (Sony VAIO, Intel Core, Duo Processor, 2.40 GHz, 2 GB RAM) in MestReC. The first time I implemented Indirect Covariance NMR in MestReC, I found that the computational effort required was quite high. Of course, in indirect covariance NMR spectroscopy, the spectral resolution along both frequency axes is determined by the sampling along the evolution t1 time. In other words, it brings in a sensitivity increase of 8 over a 13C detected experiment. The advantage is obvious: Indirect Covariance NMR yields a 13C-13C TOCSY correlation without having to detect the 13C nucleus. It is important to mention that both experiments must be acquired and processed under identical conditions, temperature, number of scans etc. In the other EXSY experiment, the EXSY reference experiment, no cross peaks due to magnetization exchange should be observed (thermal equilibrium) and the amplitudes of just the diagonal peaks of those signals in exchange, A(0), have to be measured. In this experiment the amplitudes (intensities) of those signals in exchange, A(tm), have to be quantified for both diagonal and cross peaks. In the former experiment the mixing time (tm) need to be large enough for the magnetization exchange process to take place. For the calculation of rate constants, the program requires that the user supplies the experimental amplitudes of certain NMR peaks obtained in two different EXSY experiments, one is an EXSY experiment acquired at a certain mixing time (tm), and the other is an EXSY experiment acquired at 0 or very short mixing time (reference experiment).
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