Overtone cp.m

Overtone cross-polarisation experiment that applies a cross-polarisation pulse pair and then performs frequency-domain acquisition at the overtone frequency; because time-domain overtone spectroscopy is difficult (see http://dx.doi.org/10.1039/C4CP03994G), this acquisition mode is preferable in practice, and simulations assumptions should be set to 'qnmr'.

Syntax

    spectrum=overtone_cp(spin_system,parameters,H,R,K)

Parameters

    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.spins        -  overtone-active nucleus, specified as a
                               single-element cell array

    parameters.spc_dim      -  Fokker-Planck spatial dimension

    parameters.method       -  pulse simulation method, either
                               'average' or 'fplanck'

    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), rad/s

    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

Returns

The function returns the resulting spectrum.

Examples

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

Notes

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_a.m, slowpass.m, assume.m, Built-in_experiments

Version 2.9, authors: Ilya Kuprov