Overtone cp.m

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Overtone cross-polarisation experiment with frequency-domain acquisition.




The function executes a cross-polarisation pulse pair followed by frequency-domain acquisition at the overtone frequency. Because time-domain overtone spectroscopy is difficult (see http://dx.doi.org/10.1039/C4CP03994G for details), this mode of acquisition is preferable in practice. Simulations assumptions should be set to 'qnmr'.


    parameters.sweep        -  vector with two elements giving the spectrum frequency extents
                               in Hz around the overtone frequency

    parameters.npoints      -  number of points in the spectrum

    parameters.rho0         -  initial state

    parameters.coil         -  detection state

    parameters.Nx           -  X Zeeman operator on the quadrupolar nucleus

    parameters.Hx           -  X Zeeman operator on the spin-1/2 nucleus

    parameters.rf_frq       -  spin-lock frequency offset from the overtone frequency on the quadrupolar nucleus, Hz

    parameters.rf_pwr       -  a vector of spin-lock powers on the quadrupolar nucleus (first element) and the 
                               spin-1/2 nucleus (second element), Hz

    parameters.rf_dur       -  spin-lock pulse duration, seconds

    parameters.method       -  'average' uses the average Hamiltonian theory, 'fplanck' uses Fokker-Planck formalism
                               for the calculation of the pulse evolution.

    H                       -  Hamiltonian commutation superoperator

    R                       -  unthermalised relaxation superoperator 

    K                       -  chemical kinetics superoperator


The function returns the populations of the detection state at the frequencies specified.


The following 15N overtone spectrum is produced by examples/nmr_overtone/cpmas_glycine_plain.m example file:

Ot example 3.png


  1. Relaxation must be present in the system dynamics, or the matrix inverse-times-vector operation performed by the frequency domain detection module would fail to converge. The relaxation superoperator should not be thermalised.
  2. Relaxation theory is not applied during the pulses.
  3. Average Hamiltonian and Fokker-Planck pulses produce signals in different phases. We are trying to figure out why, but it looks non-trivial. The average Hamiltonian theory option is faster.
  4. Irrespectively of the pulse algorithm option selection, the magic angle spinning is always handled with the Fokker-Planck formalism.
  5. There's some really weird difference between the experimental data obtained on Bruker and Agilent spectrometers that goes beyond the spinning direction difference. While this is of no direct relevance to the simulations, at the moment Spinach seems to agree with the Agilent output.

See also

overtone_pa.m, overtone_dante.m, overtone_hmqc.m, overtone_a.m, slowpass.m

Revision 3284, authors: Ilya Kuprov, Phil Williamson, Marina Carravetta