# gridfree.m

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.

## Contents

## 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

- 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.
- Rotational correlation times for SLE go into parameters.tau_c, not inter.tau_c (the latter is only used by the Redfield theory module).
- The state projector assumes a powder - single crystal MAS is not supported, use singlerot.m instead.
- 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*