# Bare Coulomb potential for hydrogen¶

## Using plane waves¶

GPAW has a special PAW setup for hydrogen called ae for all-electron. It’s not really a PAW setup because it doesn’t make use of any PAW magic at all — it’s just the bare Coulomb potential ($$-1/r$$).

The convergence of the energy as a function of plane-wave cutoff energy will be very slow due to the divergence of the potential at the hydrogen nucleus and also because of the cusp in the wave function:

from ase import Atoms
from gpaw import GPAW, PW
h = Atoms('H', cell=(5, 5, 5))
h.center()
h.calc = GPAW(setups='ae', txt='H.ae.txt')
for ecut in range(200, 1001, 100):
h.calc.set(mode=PW(ecut))
e = h.get_potential_energy()


You can look at the energy convergence with this command: