Re: uniform charged background ( No.1 ) 
 Date: 2005/12/01 13:36
 Name: T.Ozaki
 Hi,
The charge compensation is implicitly made. The trick relies on the fact that the FFT is used for solving Poisson's equation in OpenMX.
In OpenMX the charge density is decomponsed into two contributions (see PRB 72, 045121): superposition of atomic charge and the difference chage, and the sum of two is exactly the same as that calculated from KS wave functions. Then, the difference charge is Fouriertransformed to find the Hartree potential arising from the difference charge. If the system is neutral, the Fourier component with q=0 is zero, since the Fourier component with q=0 corresponds to the integration of the difference charge over the unit cell.
On the other hand, if the system is charged up negatively or positively, the Fourier component with q=0 is not zero. This brings a problem in finding the Hartree potential because of the division by zero (1/q^2, where q=0). Thus, the Fourier component with q=0 is set in zero, which means that a uniform charge density with the opposite charge is assumed. This is the meaning for "The charge compensation is implicitly made" (see also Rev.Mod.Phys. 64, 1045).
However, it should be noted that in this 'implicit compensation' an artificial Coulomb interaction between charged atoms in the periodically copied cells could be a source of errors as discussed in PRB 51, 4014., while the remedy is not implemented in OpenMX.
In a practical sense, for molecular systems you will need to check how the energy diffience between different charged systems behaves as a function of the cell size.
Best regards,
T.Ozaki

