Choice of basis

[serhan]

Hi,

What is the criterion for the choice of basis set type? Element type or geometry or so? To be spesific, can we use SZ sets for graphene calculations?

Cheers,
Serhan

[Nordland]

Again it is tough question if you ask me.

In a plane wave methodology a cutoff energy of 1000 Ry is much better than 100 Ry, which again is better than 10 Ry.
Therefore if you had the best computer in the world, you should always go for the 1000 Ry as the results are the most correct.

In the same it goes for ATK, there are 5 basis sets SZ,DZ,SZP,DZP & DZDP, where DZDP being the best, and if you have a super computer,
and alot of time to wait you should always go with the DZDP basis-set.
However since it is almost never the case where we have unlimited time to our work, it becomes a comprimise between accuracy and the number of calculation we want to do.

When I decide which basis set to use, I do it by the two following rules:

1) Quick screening calculations on a sample system, which could be a dimer. If I am into relaxation, I test how the equilibrium distance of a dimer depends on the basis set, and if it is converged for SZP, then I use SZP. If it is a transport calculation or bulk calculation, I look at how the band structure looks around the fermi level, if the first couple of bands near the fermi level looks the same, then I would go with the fastest basis set.
2) If I am too lazy to do some prestudies, I work by the rule, that I try to jugde how far is this system from the atomic calculation of the elements in the calculation. Therefore if I calculate on an single atom, then single zeta is perfect, if it is molecule with only a few elements then DZ and SZP, will be the just fine. If it is a strange, rare molecule with all kinds of strange bonds, I would go for DZP or DZDP.
So the larger the difference there is between the atomic calculation of the each of elements in the system, and a system view as whole, the better basis set is required.

Therefore to answer your question about graphene, if you are going to make graphene calculation in 2D system, possible with hydrogen termination, then I would go with the SZP basis set. ( And my choice in this case is based on both rule 1 and 2 : )

[serhan]

Thanks again.

[Anders Blom]

As a general rule, to add the above considerations, I would never use SZ for real calculations, unless I was really forced to by memory constraints. There is just too little freedom both radially and angularly to properly describe bonds except in very spherically symmetric cases.

For several elements (specifically, those with a full shell as the valence), ATK will in fact refuse to run a SZ calculation since it will converge very poorly, if at all.

My rule of thumb is: SZP as a work-horse when trying things out, and most of the time for C-based systems, and DZP whenever I can afford it otherwise. DZ can sometimes be a good alternative to SZP if the geometry is close to "elemental". The difference between DZDP and DZP is rarely important; other errors like exchange-correlation functional are probably larger.

[serhan]

Thanks Anders for adding.

In fact, I faced the memory problem as I have written in other threads. A (6,6) nanotube as two-probe with 4 electrode repetitions and 20 central repetitions gave badalloc error. I have not tried to use 6 MPIs in 6 PC yet. I think this will also solve the problem without going to change the basis.

Cheers,
Serhan

[privador]

  Hi!
 Can u briefly say what is SZ,DZ,SZP,DZP,DZDP?
And how these methods are correlated with Tight binding model?
How many neighbours atoms we take into account of calculating bands?

[Nordland]

ATK uses numerical atomic orbitals as basis set.
The best reference for understanding the basis set SZ and so on is the Siesta Paper.

Single Zeta is the valence orbitals of atomic calculation, and all the basis set is more and more excited and pertubated orbitals of the atomic calculation.

All the atomic orbitals have a finite range and have compact support. The full basis set used in ATK is a super-position of all the atoms in the calculation atomic orbitals ( + a extra orbital if it is not SZ). The main idea of the tight-binding approximation is that the wave function can be expressed in terms of a few localized orbitals. However this basis set is not a complete basis set like plane waves. However the choice of basis (SZ,DZ...) makes the basis set more and more complete and makes the approximation more correct.

The number of neighbours in ATK is not a fixed size, but determined by the compact support of the atomic orbitals, and therefore there is no futher approximation in the number of neighbours to consider. It depends on the range of the basis function for a specific element and it environment. A iron (Fe) FCC-crystal it is required to take nothing less than 72 neighbour atoms to calculate the correct bands, and for other material like a carbon-chain only 5 neighbours is needed.

Hope it makes something clear.

[privador]

ok i understand the basic.
Lets take simple carbon graphene layer.They should have 3 neighbour atoms.
Does it mean,that SZ deals with FIRST  neighbour atoms valence orbitaks(minimum conditions)
DZ deals with FIRST and SECOND neighbour atoms valence orbitals?


http://www.hot.ee/suurfail//neibourh%20atoms.PNG
Here is picture which reflects my thoughts

[Anders Blom]

There is a fundamental difference between TB and the orbitals that are used in e.g. DFT. In TB you focus on the bonds between neighboring atoms, while the orbitals used in ATK are used to expand the electron density in the vicinity of each atom. In this case, the "bonding" comes about from overlap of such orbitals between atoms within a certain range. In ATK we use orbitals with a finite range (hard cutoff), and atoms within this range have a chance to "bond" in this way. The range is independent of the basis set type, but can be controlled by the "energy shift", as described in the manual.

For more information, see also http://quantumwise.com/documents/manuals/ATK-2008.10/ref.atomicorbitals.html.

[privador]

Thx ,that explanantion was good.
But i have difficulties understand terms

DoubleZeta; two basis orbitals for each valence orbital

What is term "(two)basis" orbital?

DoubleZeta plus one basis orbital for the first unoccupied shell

What is term unoccupied "shell"?
Is it same as unoccupied (unit)cell?

[Nordland]

DoubleZeta means that you have two (n=2) basis functions in your basis set for each of the valence electrons in the atom.
DoubleZetaPolarized means that you have the same basis function as in DoubleZeta in your basis set, but you have an extra orbital in your basis set. This is a orbital corresponding to an exicted states of the atom.

For more information on the shells, I think that wikipedia has a good explanation: Wikipedia on Shells

[Anders Blom]

A concrete example should make it clear.

Hydrogen
Valence: 1s
SZ: s
DZ: s s'
SZP: s p
DZP: s s' p
DZDP: s s' p p'

Gold
Valence: 6s 5d^10
SZ: s d
DZ: s s' d d'
SZP: s d p
DZP: s s' d d' p
DZP: s s' d d' p p'

By s' we here mean a second s orbital (same major quantum number) to add more radial degrees of freedom; the polarization functions add angular degrees of freedom.

The major quantum number are excluded since the basis orbitals are based on the pseudocore atom. Thus, the 6s valence electrons in the basis set for gold really look like 1s wavefunctions.

For a list of the valence as used by ATK, see http://quantumwise.com/documents/manuals/ATK-2008.10/ref.atomdata.html.