# Ilpcs.m

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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*