| Re: uniform charged background ( No.1 )|
- Date: 2005/12/01 13:36
- Name: T.Ozaki
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 Fourier-transformed 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.