In this subsection, the simple molecules, the hydrogen molecule ion,
H 
, the water molecule, H 
O and
the hydronium ion, H 
O 
are examined.
For H , no Hartree or exchange and correlation
energies are included (it is a one-electron problem),
while for the water molecule and the hydronium ion,
studies under LDA [23] and GG-LDA [27, 28] are presented.
In each case the value of
was fixed,
and the screening function was evaluated on an FFT mesh determined by
a plane-wave cutoff 1.1 times the value used for the electron density
(4.4 times the Kohn-Sham orbital cutoff).
In Table 6, the convergence of the electronic energy
of the H ion with cubic box edge, L, is shown for different choices of
plane-wave cutoff.
The results show a uniform convergence with
box edge, L, at fixed plane-wave cutoff. In Tables 7 and 8,
the behavior of the total energy difference between
an H O molecule and an H O ion as a function of box size
for LDA [23] and GG-LDA [27, 28], respectively,
are given.
Uniform convergence with box size at fixed plane-wave cutoff
is again observed. In addition,
although different functionals and pseudopotentials
are used in the calculations presented in
the two tables, the total energy difference is reproduced
accurately (within 70 Kelvin). At fixed box edge, L=9 Å , the energy
difference convergences rapidly with cutoff. For example, under LDA,
(180 Ry) = 0.268921 Hartree, (240 Ry) = 0.269400 Hartree
and (300 Ry) = 0.269497 Hartree. Note, energy differences
between systems with different total charge are ill defined when
the screening function is neglected [2, 3].
Indeed, the results indicate that neglecting the screening function
increases the error, particularly, in the charged systems.