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getting the center of mass of each part of a molecule


I need to get the center of mass (COM) of each half of the ligand shown in the figure (https://i.stack.imgur.com/dtdul.png). I get the main COM all the ligand, lets say it is close to C1 atom. In addition to the main COM of all the ligand, I need to find the COM of each half of the ligand. The atoms of the first part/half according to the main COM of the ligand are C2, C7, C8 and C9. As for the second part they are C3, C4, C5 and C6 atoms. The question is how can I divide the ligand in two parts according to the main COM and calculate the COM of each divided part (except for the atom closest to the main COM, C1)? By the way I have multiple ligands. The code should be user firendly. 

A short part of the input file is here:

1LIG     C1    1   4.434   5.366   1.780
1LIG     C2    2   4.317   5.301   1.940
1LIG     C3    3   4.430   5.286   1.888
1LIG     C4    4   4.380   4.942   2.467
1LIG     C5    5   4.148   4.929   2.443

A short snippet of the code used to get the main COM is here:

def heavy_atoms(atoms, xyz, ligand="LIG"):
    ids   = np.arange(len(atoms))
    names = [(i[10:15].strip(),i[5:10].strip()) for i,j in atoms]

    # Ligand atoms
    lig_atoms = np.array([ rname == ligand and not aname.startswith('H') for aname,rname in names ])
    lig_xyz = xyz[lig_atoms,:]

    # The main COM
    lig_com = xyz[lig_atoms, :].mean(axis=0)