Periodic calculations with non-periodic solutions

[Andy Van Yperen-De Deyne]

Dear CP2K users,

A goal of our current research is to optimize a defect and its
environment in a NaCl crystal.
We noticed that some things are going really wrong with the
optimization. The problem is already present at the first SCF cycle,
so to solve the problem, we tested on single point calculations.

We concentrated on an easier defect to investigate the problem: two
vacancies (Na and Cl) next to each other.

CP2K seems to calculate different single point energies for a defect
placed at the middle of the supercell and a defect at the edges of the
supercell. The differences are about 1e-3 Hartree (= 2.6255 kJ/mol)
for the ‘easy’ defect and about 1e-2 to 1e-1 Hartree for the defect we
want to optimize.

The orientation of the defect does not influence the energy, there is
only a computational error (1e-8 Hartree).

Since CP2K is a periodic code, we thought the position of the defect
should not affect the energy, but we noticed that the energy does
depend on the position. The result seems to be "non-periodic", while
we are using periodic boundary conditions.

We varied the cellsize, cutoff and basisset, without any improvement.
The functional used is PBE and we always use the GTH pseudopotentials
(the interesting defect contains a transition metal).


Cellsize
-----------
We increased the number of atoms (6x6x6, 8x8x8 and 10x10x10) and off
course increased the size of the cubic cell from 16.95 to 22.6 to
28.25 Angstrom. There was no improvement.


Cutoff
--------
Since we thought the cutoff could be a problem, we varied it from 300
to 1000 Rydberg by steps of 100 Rydberg (cubic cell size = 16.95).
These calculations were preformed on a NaCl lattice without
vacancies.
Instead the energy rises once the cutoff frequency becomes larger then
400 Rydberg.

Cutoff	Energy in Hartree
280		-6729.967521
300		-6729.96693
350		-6730.399649
400		-6730.539355
500		-6730.471037
600		-6730.342918
700		-6730.370525
800		-6730.320033
900		-6730.258037
1000		-6730.291928

Energy differences are typical 0.05 Hartree. This is unacceptable.

We also varied the cutoff for a NaCl lattice with two vacancies on the
edge and in the middle of the cell. There is no convergence for the
difference in energy between the ‘center’ and ‘edge’ calculation.

Cutoff	Energy difference (E(edge)-E(centre)) in Hartree
300		2.14577E-06
600		0.001135582
800		-1.58246E-05


Basis set
--------------
We tried both the BASIS_MOLOPT and  the GTH_BASIS_SETS. It seems that
the difference in energy is of a comparable magnitude for both
basissets.


Does anyone has any experience with this kind of systems or had
similar problems?

Please find at http://groups.google.com/group/cp2k/web/NaCl.tar.gz two
typical inputfiles we used. (cutoff = 600, basisset = MOLOPT and size
is 6x6x6 atoms (16.95 by 16.95 by 16.95 Angstrom).

Sincerely yours,

Andy Van Yperen-De Deyne