This page contains information about the PAW-XML data format for the atomic setups necessary for doing projector-augmented wave calculations. We use the term setup because the PAW method is not a pseudopotential method.
An example XML file for nitrogen PAW setup using LDA can be seen here: N.LDA.
Hartree atomic units are used in the XML file ().
The following quantities defines a minimum PAW setup (the notation from Ref.  is used here):
Quantity Description atomic number exchange-correlation functional kinetic energy of the core electrons shape function for compensation charge all-electron core density pseudo electron core density pseudo electron valence density zero potential all-electron partial waves pseudo partial waves projector functions kinetic energy differences
Contents of a PAW setup (in order of appearance).
An element looks like this:
<name> ... </name>
or for an empty element:
An XML-tutorial can be found here
The first two lines should look like this:
<?xml version="1.0"?> <paw_setup version="0.6">
The first line must be present in all XML files. Everything else is put inside an element with name paw_setup, and this element has an attribute called version. We are currently at version 0.6.
It is recommended to put a comment giving the units and a link to this web page:
<!-- Nitrogen setup for the Projector Augmented Wave method. --> <!-- Units: Hartree and Bohr radii. --> <!-- http://www.where.org/paw_setup.html -->
<atom symbol="N" Z="7" core="2" valence="5"/>
The atom element has attributes symbol, Z, core and valence (chemical symbol, atomic number, number of core electrons and number of valence electrons).
<xc_functional type="LDA", name="PW"/>
The xc_functional element defines the exchange-correlation functional used for generating the setup, and we currently have the following possibilities for LDA type functionals:
For type="GGA" we have these possibilities:
<generator type="scalar-relativistic" name="MyGenerator-2.0"> Frozen core: [He] </generator>
This element contains character data describing in words how the setup was generated. The type attribute must be one of: non-relativistic, scalar-relativistic or relativistic.
<ae_energy kinetic="53.777460" xc="-6.127751" electrostatic="-101.690410" total="-54.040701"/> <core_energy kinetic="43.529213"/>
The kinetic energy of the core electrons, , is used in the PAW method. The other energies are convenient to have for testing purposes and can also be useful for checking the quality of the underlying atomic calculation.
<valence_states> <state n="2" l="0" f="2" rc="1.10" e="-0.6766" id="N-2s"/> <state n="2" l="1" f="3" rc="1.10" e="-0.2660" id="N-2p"/> <state l="0" rc="1.10" e=" 0.3234" id="N-s1"/> <state l="1" rc="1.10" e=" 0.7340" id="N-p1"/> <state l="2" rc="1.10" e=" 0.0000" id="N-d1"/> </valence_states>
The valence_states element contains several state elements. For this setup, the first two lines describe bound eigenstates with occupation numbers and principal quantum numbers. Notice, that the three additional unbound states should have no f and n attributes. In this way, we know that only the first two bound states (with f and n attributes) should be used for constructing an initial guess for the wave functions.
There can be one or more definitions of radial grids:
<radial_grid eq="r=a*i/(n-i)" a="0.400000" n="300" istart="0" iend="299" id="g1"/>
This defines one radial grid as:
where runs from 0 to 299. All functions (densities, potentials, ...) that use this grid are given as 300 numbers defining the radial part of the function. The radial part of the function must be multiplied by a spherical harmonics: .
Each radial grid has a unique id:
<radial_grid eq="r=a*exp(d*i)" a="1.056e-4" d="0.05" istart="0" iend="249" id="log"/> <radial_grid eq="r=d*i" d="0.01" istart="0" iend="99" id="lin"/>
and each numerical function must refer to one of these ids:
<function grid="lin"> ... ... ... </function>
In this example, the function element should contain 100 numbers (). Each number must be separated by a <newline> character or by one or more <tab>‘s or <space>‘s (no commas). For numbers with scientific notation, use this format: 1.23456e-5 or 1.23456E-5 and not 1.23456D-5.
There are currently five types of radial grids:
eq parameters r=a*exp(d*i) a and d r=a*i/(1-b*i) a and b r=a*i/(n-i) a and n r=a*(exp(d*i)-1) a and d r=d*i d r=(i/n+a)^5/a-a^4 a and n
Types of radial grids. Note that the eq attribute is not meant to be parsed - only recognized.
The istart and iend attributes indicating the range of should always be present.
The compensation charge for an atom is expanded using the multipole moments :
where , and is the shape function defined in the file like this:
<shape_function type="gauss" rc="3.478505426185e-01"/>
Here, Gaussians are used, , as the basis for the compensation charges as described in Ref. .
Another choice would be type="bessel" rc="...", where a sum of two Bessel functions is used. Other possibilities are
as described in Ref. , and .
type parameters gauss rc bessel rc sinc rc exp rc and lamb
There is also the possibility that the shape function is given in numerical form. In that case, the shape function defined inside the shape_function element:
<shape_function grid="..."> ... ... </shape_function>
The grid attribute refers to one of the radial grids defined earlier.
Continuing, we have now reached the all-electron core density:
<ae_core_density grid="g1"> 6.801207147443e+02 6.801207147443e+02 6.665042896724e+02 ... ... </ae_core_density> <pseudo_core_density grid="g1"> ... </pseudo_core_density> <pseudo_valence_density grid="g1"> ... </pseudo_valence_density> <zero_potential grid="g1"> ... </zero_potential>
The numbers inside the ae_core_density element defines the radial part of . The radial part must be multiplied by to get the full all-electron core density (which should integrate to the number of core electrons). The pseudo core density, the pseudo valence density and the zero potential, , are defined similarly.
The ae_partial_wave, pseudo_partial_wave and projector_function elements contain the radial parts of the , and functions for the states listed in the valence_states element above (five states in the nitrogen example). All functions must have an attribute state="..." referring to one of the states listed in the valence_states element:
<ae_partial_wave state="N-2s" grid="g1"> -8.178800366898029e+00 -8.178246914143839e+00 -8.177654917302689e+00 ... ... </ae_partial_wave> <pseudo_partial_wave state="N-2s" grid="g1"> ... </pseudo_partial_wave> <projector_function state="N-2s" grid="g1"> ... </projector_function> <ae_partial_wave state="N-2p" grid="g1"> ... </ae_partial_wave> ... ...
<kinetic_energy_differences> 1.744042161013e+00 0.000000000000e+00 2.730637956456e+00 ... <kinetic_energy_differences> </paw_setup>
This element contains the symmetric matrix:
where is the kinetic energy operator used by the generator. With states, we have an matrix listed as numbers.
The Kresse-Joubert formulation of the PAW method is very similar to the original formulation of Blöchl. However, the Kresse-Joubert formulation does not use directly, but indirectly through the local ionic pseudopotential, . Therefore, the following transformation is necessary:
where is the number of core electrons, is the number of valence electrons, is the number of electrons contained in the pseudo core density and is the number of electrons contained in the pseudo valence density. The Hartree potential from the density is defined as:
where is the larger of and .
In the Kresse-Joubert formulation, the symbol is used for what we here call and in the Blöchl formulation, we have .
It is also possible to add an element kresse_joubert_local_ionic_pseudopotential that contains the function directly, so that no conversion is necessary:
<kresse_joubert_local_ionic_pseudopotential grid="log"> ... </kresse_joubert_local_ionic_pseudopotential>
Most likely, the radial functions will be needed on some other type of radial grid than the one used in the setup. The idea is that one should read in the radial functions and then transform them to the radial grids used by the specific implementation. After the transformation, some sort of normalization may be necessary.
The first 10-20 lines of the XML-setups, should be pretty much human readable, and should give an overview of what kind of setup it is and how it was generated. The remaining part of the files contain numerical data for all the radial functions. To get an overview of these functions, you can extract that data with the pawxml.py program and then pass it on to your favorite plotting tool.
The pawxml.py program is very primitive and is only included in order to demonstrates how to parse XML using SAX from a Python program. Parsing XML from Fortran or C code with SAX should be similar.
It works like this:
$ pawxml.py [options] setup[.gz]
|--version||Show program’s version number and exit.|
|-h, --help||Show this help message and exit.|
|-x <name>, --extract=<name>||Function to extract.|
|-s<channel>, --state=<channel>||Select valence state.|
|-l, --list||List valence states|
[~]$ pawxml.py -x pseudo_core_density N.LDA | xmgrace - [~]$ pawxml.py -x ae_partial_wave -s N2p N.LDA > N.ae.2p [~]$ pawxml.py -x pseudo_partial_wave -s N2p N.LDA > N.ps.2p [~]$ xmgrace N.??.2p
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