Just to add to the discussion that started with the question about PDOS
projection radii:
Any definition of atomic charge is necessarily arbitrary. There are no atoms;
there are only nuclei and a wavefunction and charge density of electrons in the
field of those nuclei. There are various different schemes of partitioning this
charge density into "atoms". The ones I know are available for Siesta (two of
them mentioned in earlier posts) with easily accessible tools are:
- Mulliken charges
Project the wavefunction onto atom centred basis functions and count them
towards the atom the function is centred on.
Advantages: Trivial and cheap if you have an atom centred basis. No double
counting.
Disadvantages: It's not really a spatial partitioning. The charge in one point
is split between multiple atoms, which may be far away. A diffuse basis (which
improves the description of the wavefunction and may be otherwise desirable)
makes things worse.
- Atomic spheres
Draw a sphere around a nucleus and count all electron density within it towards
this nucleus.
Advantages: Relatively easy to implement. Intuitive (we all know that atoms are
little balls, right?).
Disadvantages: The radius is arbitrary. If the spheres are overlapping, you
count part of the charge twice. If they aren't, there are large parts of space
(and electron density) you don't count. In practice, you have a mixture of both
effects. If the sum of the volumes of spheres is the volume of the enclosed
space, it's called Wigner-Seitz radius. This is only uniquely defined for
monoatomic crystals, and even then the sum of atomic charges will differ from
the total charge.
- Bader charges (Atoms in Molecules)
Perhaps the most chemically intuitive partitioning. Assuming that you always
have a local maximum of electron density at a nucleus, the boundary between two
atoms is the surface of lowest density between the nuclei.
Advantages: Intuitive. Unique. Not basis set dependent.
Disadvantages: If using pseudopotentials, you only see the valence electrons.
The density maximum at a nucleus may not exist or be so shallow that it is not
found. Particularly hydrogen atoms have a habit of "disappearing", with their
electron density lumped into the charge of a neighbour.
If somebody knows of other schemes (Hirshfeld, NBO, ...) available for Siesta,
I'd be interested to hear about them.
Hope this helps,
Herbert
On 20/06/13 09:50, Emilio Artacho wrote:
And just to complete the story, some plane-wave codes
do not do the muffin-tin analysis, but do a full projection
onto atomic orbitals of the PW eigenstates, based on
Sanchez-Portal et al; Solid St. Commun. 95, 685 (1995), and
J. Phys. Condensed Matter 8, 3859 (1996). I think CASTEP and
CPMD do this. In this case both the Mulliken charges and
projected densities of states are conceptually the same as
in Siesta. Mind you, the results will not be quantitatively
comparable since in the case of PW they normally use
a minimal (SZ) atomic basis set to project upon, while
the original basis (PWs) is quite complete, while in Siesta
the basis for the Mulliken analysis is the same as was used
for the calculation.
Emilio
On Jun 20, 2013, at 10:13 AM, [email protected]
<mailto:[email protected]> wrote:
Hi Benedikt,
Alberto is right, SIESTA does not need projections,
but YOU might need them; exactly for the sake of comparing
the charges with those from "muffin-tin"-type codes
I wrote some time ago a primitive tool
http://www.home.uni-osnabrueck.de/apostnik/Software/grdint.f
which "integrates" grid properties, e.g. charge (spin) densities,
over given (atom-centered) spheres.
Some remarks:
1. It integrates functions defined on the grid, which are not
(l,m) resolved. That means, you can produce spin-up and spin-down
charges, but not partial s,p,d-charges. Of course you can first
generate LDOS within some energy interval, if you find it useful,
and then integrate it over a sphere.
2. The "integration" is in fact merely a counting of grid points
which either fall within, or not, of a given sphere. So the result
is not very accurate and prone to "noise". But it is usually OK
for the sake of comparison, and anyway becomes "better"
as the mesh density is increased.
3. The tool as not fast as you may expect it to be, for the task
it performs, because the algorithm used is very straightforward;
please feel free to improve.
Best regards
Andrei Postnikov
Hi Benedikt,
SIESTA does not need projections, as the basis orbitals are localized on
the atoms. You get naturally the "chemical" information one is used to.
Plane-wave codes such as vasp do need projections to get some kind of
"local" information from the delocalized basis.
Alberto
On Mon, Jun 17, 2013 at 4:28 PM, Benedikt Ziebarth <
[email protected]> wrote:
Hello,
I have a question about PDOS calculations with siesta. Is there a way to
specify the radius around the atoms in which the projection is carried
out?
This option exists in different other dft codes like vasp (
http://cms.mpi.univie.ac.at/**vasp/vasp/RWIGS.html<http://cms.mpi.univie.ac.at/vasp/vasp/RWIGS.html>
).
Any help would be very welcome.
Thanks
Benedikt Ziebarth
--
Emilio Artacho
CIC nanoGUNE Consolider, and Cavendish Laboratory, University of Cambridge
Tolosa Hiribidea 76, E-20018 Donostia - San Sebastián, Spain,
[email protected] <mailto:[email protected]>, +34 943 574039,
http://theory.nanogune.eu
--
Herbert Fruchtl
Senior Scientific Computing Officer
School of Chemistry, School of Mathematics and Statistics
University of St Andrews
--
The University of St Andrews is a charity registered in Scotland:
No SC013532
