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