Charge Balanced Unit Cells

Obviously, the net charge in a unit cell is zero. A less obvious need is for the dipole of the unit cell to be as small as possible. Consider the highly artificial system:

+     +     +     +     +     +     +     +
                        -     -     -     -     -     -     -     -
                        |     |     |     |     |     |     |     |
                       / \   / \   / \   / \   / \   / \   / \   / \
                      /   \_/   \_/   \_/   \_/   \_/   \_/   \_/   \_
                      A                           C D                B

This system represents a simple hydrocarbon backbone with anionic sites covalently bound. The anionic charge is balanced by cation counterions. However, although there is one cation for each anion, and the unit cell is uncharged, the unit cell does have a large dipole.

Why is this undesirable? For the purpose of this discussion, let CUTOFP be infinite. Then electrons in atom A would be stabilized by every cationic charge and destabilized by every anionic charge. With increasing distance the effect of the cations and anions would more-or-less cancel out. However, at large distances an asymmetry in the charge distribution is introduced. To the left of A there would be 8 anions and 12 cations, while to the right of A there would be 16 anions and 12 cations. The potential effect of this asymmetry would be a net positive potential at A. Similarly, at B there would be a net negative potential arising from the charges.

As a result of the Born-von Kármán periodic boundary conditions, atom A is bonded to atom B. Because of the symmetry of this system, A and B should have the same charge (roughly zero), but because of the large unit cell dipole, there will be an induced dipole in the bond A-B. There will be induced dipoles in all bonds of the A-B type, for example C-D, but these will be very small compared to that in the A-B bond.

The overall effect of this induced bond dipole is that the molecular geometry in the region of A and B is deformed. In a correctly optimized system, the effect of having a large dipole in the unit cell is to induce gradient effects at the ends of the unit cell.

To avoid these effects, the unit cell should be chosen in such a way as to make the dipole of the unit cell as small as possible. For most systems, the default value of CUTOFP used by the program will prevent this problem from occurring.