# Ilpcs.m

Fits experimental PCS data using the distributed paramagnetic centre model described in http://dx.doi.org/10.1039/c6cp05437d

Syntax:

     [mxyz,chi,Ilm,pred_pcs,s_mxyz,s_chi,s_Ilm]=ilpcs(nxyz,expt_pcs,ranks,mguess)


Parameters:

     nxyz  - nuclear coordinates as [x y z] with multiple rows,
at which PCS is to be evaluated, in Angstroms.

expt_pcs  - a column vector of experimental pseudocontact shifts
in ppm

ranks - row of multipole expansion ranks to be used in the
fitting procedure

mguess - guess value for the paramagnetic centre position,
a three-element vector in Angstrom



Output:

    mxyz   - optimized paramagnetic centre coordinates as [x y z],
in Angstroms.

chi    - optimized magnetic susceptibility tensor in cubic
Angstroms.

Ilm    - {[],[]} cell array of numbers corresponding to the multipole
moments defined in the paper cited above:

for L=0,  Ilm=N/2/sqrt(pi)

for L=1,  Ilm=[real(I11) I10 imag(I11)]

for L=2,  Ilm=[real(I22) real(I21) I20 imag(I21) imag(I22)]

et cetera.

pred_pcs  - predicted pseudocontact shift (in ppm) at each of
the nuclei.

chi    - optimized magnetic susceptibility tensor in cubic
Angstroms.

s_mxyz - standard deviations of paramagnetic centre
coordinates as [x y z], in Angstroms.

s_chi  - standard deviations of magnetic susceptibility
tensor elements in cubic Angstroms.

s_Ilm  - standard deviations of the multipole moments, arranged in
the same order as the moments themselves.


Note: a good initial guess for the paramagnetic centre location is essential for a successful fit.

Version 1.9, authors: Elizaveta Suturina, Ilya Kuprov