# Lpcs.m

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