gridfree.m

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Fokker-Planck magic angle spinning and SLE context that uses full Wigner D-function basis and therefore solved directly for the powder average - a spherical grid is not required. This function generates the Fokker-Planck Hamiltonian, external relaxation superoperator, kinetics superoperator, applies the necessary offsets, updates the parameter set, and passes all of that to the pulse sequence, which should be supplied as a handle.

Syntax

    answer=gridfree(spin_system,@pulse_sequence,parameters,assumptions)

Arguments

    @pulse_sequence     - pulse sequence function handle

    parameters.rate     - spinning rate in Hz

    parameters.axis     - spinning axis, given as a normalized
                          3-element vector

    parameters.spins    - a cell array giving the spins that 
                          the pulse sequence involves, e.g. 
                          {'1H','13C'}

    parameters.offset   - a cell array giving transmitter off-
                          sets in Hz on each of the spins listed
                          in parameters.spins array

    parameters.max_rank - maximum D-function rank to retain in
                          the solution (increase till conver-
                          gence is achieved, approximately
                          equal to the number of spinning si-
                          debands in the spectrum)

    parameters.tau_c    - correlation times (in seconds) for rotational 
                          diffusion. Single number for isotropic rotati-
                          onal diffusion, and a 3x3 matrix for anisotro-
                          pic rotational diffusion. 

Additional subfields may be required by the pulse sequence. The parameters structure is passed to the pulse sequence with the following additional parameters set:

    parameters.spc_dim  - matrix dimension for the spatial
                          dynamics subspace

    parameters.spn_dim  - matrix dimension for the spin 
                          dynamics subspace

Outputs

This function returns the powder average of whatever it is that the pulse sequence returns.

Examples

The following example files in the Spinach example set make use of this context function:

nmr_solids/mas_powder_trp_gridfree.m - large-scale simulation of tryptophan 13C MAS NMR

nmr_solids/mas_powder_gly_gridfree.m - glycine 13C MAS NMR spectrum

nmr_solids/mas_powder_suc_gridfree.m - large-scale simulation of sucrose 13C MAS NMR

nmr_solids/mas_powder_ala_gridfree.m - alanine 13C MAS NMR spectrum

nmr_solids/mas_powder_nqi_gridfree.m - deuterium NQI MAS NMR, no second-order rotating frame corrections

nmr_solids/mas_powder_dip_gridfree.m - MAS NMR on a pair of dipole coupled spins

nmr_solids/mas_powder_csa_gridfree.m - MAS NMR on a simple system with a CSA

Notes

  1. The choice of the Wigner D function rank truncation level depends on on the spinning rate (the slower the spinning, the greater ranks are required). The rank should be set approximately equal to the expected number of spinning sidebands. For diffusive dynamics, increase till the answer stops changing.
  2. Rotational correlation times for SLE go into parameters.tau_c, not inter.tau_c (the latter is only used by the Redfield theory module).
  3. The state projector assumes a powder - single crystal MAS is not supported, use singlerot.m instead.
  4. Perturbative corrections to the rotating frame transformation are not supported - use singlerot.m instead.

See also

powder.m, liquid.m, roadmap.m, singlerot.m, doublerot.m, imaging.m, floquet.m, crystal.m


Version 2.2, authors: Ilya Kuprov