# 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.