Developers Manual:Separation of the pseudopotential
We will separate the local part of the pseudpotential into a long-range and a short-range part. The long-range part will be the Coulomb potential associated with a radial Gaussian charge distribution:
The potential is
In Fourier space:
We want the potential generated by this charge to be smooth so we consider the associated potential (for simplicity we consider the 1D Poisson equation)
What we want is that must be smaller than a certain threshold:
Once we get , we can get the optimum value of :
For we get , which implies
This value will be used in the code. In principle there is a dependence on , but solving a transcendental equation in the code is not very reliable.
Note: this has been taken from the code; in case of discrepancies the code is more likely to be correct.