# Lpcs.m

From Spinach Documentation Wiki

Computes PCS from the multipole moments of the paramagnetic centre probability density as described in http://dx.doi.org/10.1039/c6cp05437d - Equation 33 is used under the assumption that all nuclei are outside the bounding sphere shown in Figure 1 of the paper. Syntax:

theo_pcs=lpcs(nxyz,mxyz,ranks,Ilm,chi)

Parameters:

nxyz - nuclear coordinates as [x y z] with multiple rows, at which PCS is to be evaluated, in Angstroms. mxyz - paramagnetic centre coordinates as [x y z], in Angstroms. ranks - array of multipole ranks supplied in Ilm Ilm - {[],[]} array of numbers corresponding to the integral Int(rho(r,theta,phi)Y*lm(theta,phi)r^ld^3r) for L=0 Ilm=N/2/sqrt(pi) for L=1 Ilm=[imag(I11) I10 real(I11)] for L=2 Ilm=[imag(I22) imag(I21) I20 real(I21) real(I22)] chi - the 3x3 matrix or the five independent elements of the susceptibility tensor in cubic Angstroms

Output:

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

*Version 1.9, authors: Elizaveta Suturina*