**POINT CHARGE MODEL (PCM )**The point charge model is a simplified model of a crystal lattice in which ligands are presented as charged spheres with a uniform surface charge distribution that excludes the screening effects of the outer shell. This allows us to determine the A

^{m}

_{n}coefficients, which is equivalent to specifying the potential at a given point (i.e. in our case, the potential energy acting on the central ion). The coefficients are introduced due to the fact that the:

where: X_{i,} Y_{i,} Z_{i }– ligand coordinates, X,y,z – position of the central ion electron. By expanding it into a Maclaurin series

we will have reached an expansion whose coefficients are in line with our A^{m}_{n} parameters. The potentials for the three basic symmetries will have the following form:

- The potential of charges in the corners of the square away from the plane

Upon rotating the coordinate system by 45°, the signs of sections V^{4}_{4} and V^{4}_{6 }are altered

- The potential of charges located in the corners of a remote equilateral triangle

Upon reflecting in the horizontal plane, the signs of sections V^{3}_{4} and V^{3}_{6 } are altered

- The axial potential of a point charge

By rotation and superposition of these three components, we can compose the symmetry of the most highly symmetrical potentials carried by ligands in crystals.