# zfs_sampling.m

Gadolinium ZFS probability distribution function for DOTA-type ligand complexes in cryogenic water-methanol glasses. This function returns Gauss-Legendre quadrature sampling points and weights for the ZFS parameter distribution described in http://dx.doi.org/10.1007/BF03166762 (see Figure 5). This function is necessary in the simulation of solid state EPR experiments involving gadolinium ions because there is always a distribution of zero-field splitting parameters that must be integrated over.

## Syntax

[D,E,W]=zfs_sampling(npoints_d,npoints_e,tol)

## Arguments

npoints_d - number of Gauss-Legendre quadrature points in D npoints_e - number of Gauss-Legendre quadrature points in E tol - tolerance for integration weights below which grid points are dropped

## Outputs

D - a vector of D values at each integration grid point E - a vector of E values at each integration grid point W - a vector of weights for each integration grid point

## Notes

The function also creates a figure with the distributions it has used for D and E parameters.

## See also

Integration grids, Appendix I: powder grids

*Version 2.6, authors: Ilya Kuprov, Nurit Manukovsky*