- 1 XML specification for atomic PAW datasets
- 1.1 Introduction
- 1.2 What defines a dataset?
- 1.3 Specification of the elements
- 1.4 The header
- 1.5 A comment
- 1.6 The atom element
- 1.7 Exchange-correlation
- 1.8 Generator
- 1.9 Energies
- 1.10 Valence states
- 1.11 Radial grids
- 1.12 Shape function for the compensation charge
- 1.13 Radial functions
- 1.14 Zero potential
- 1.15 The Kresse-Joubert formulation
- 1.16 Kinetic energy differences
- 1.17 Meta-GGA
- 1.18 Exact exchange integrals
- 1.19 Optional elements
- 1.20 End of the dataset
- 1.21 How to use the datasets
- 1.22 Plotting the radial functions
- 1.23 References
XML specification for atomic PAW datasets
This page contains information about the PAW-XML data format for the atomic datasets necessary for doing Projector Augmented-Wave calculations . We use the term dataset instead of pseudo-potential because the PAW method is not a pseudo-potential method.
An example XML file for nitrogen PAW dataset using LDA can be seen here: n.lda.xml
- Note: Hartree atomic units are used in the XML file (
h= m = e = 1).
What defines a dataset?
The following quantities define a minimum PAW dataset (the notation from Ref.  is used here):
|Kinetic energy of the core electrons|
|Shape function for compensation charge|
|All-electron core density|
|Pseudo electron core density|
|Pseudo electron valence density|
|All-electron partial waves|
|Pseudo partial waves|
|Kinetic energy differences|
The following quantities can be optionally provided:
|Radius of the PAW augmentation region (max. of matching radii)|
|Kresse-Joubert local ionic pseudopotential|
|State-dependent shape function for compensation charge|
|Core kinetic energy density|
|Pseudo core kinetic energy density|
|Core-core contribution to exact exchange|
|Core-valence exact-exchange correction matrix|
Specification of the elements
An element looks like this:
<name> ... </name>
or for an empty element:
- Tip: An XML-tutorial can be found here
The first two lines should look like this:
<?xml version="1.0"?> <paw_dataset version="0.7">
The first line must be present in all XML files.
Everything else is put inside an element with name
and this element has an attribute called
It is recommended to put a comment giving the units and a link to this web page:
<!-- Nitrogen dataset for the Projector Augmented Wave method. --> <!-- Units: Hartree and Bohr radii. --> <!-- http://www.where.org/paw_dataset.html -->
<atom symbol="N" Z="7" core="2" valence="5"/>
atom element has attributes
valence (chemical symbol, atomic number, number of core electrons
and number of valence electrons).
xc_functional element defines the exchange-correlation functional used for generating the dataset.
It has the two attributes
type attribute can be
name attribute designates the exchange-correlation functional and can be specified in the following ways:
Taking the names from the LibXC library.
The correlation and exchange names are stripped from their
XC_part and combined with a
+-sign. Here is an example for an LDA functional:
<xc_functional type="LDA", name="LDA_X+LDA_C_PW"/>
and this is what PBE will look like:
<xc_functional type="GGA", name="GGA_X_PBE+GGA_C_PBE"/>
Using one of the following pre-defined aliases:
type name LibXC equivalent Reference
LDA exchange; Perdew, Wang, PRB 45, 13244 (1992)
Perdew et al PRB 46, 6671 (1992)
Perdew, Burke, Ernzerhof, PRL 77, 3865 (1996)
Hammer, Hansen, Nørskov, PRB 59, 7413 (1999)
Zhang, Yang, PRL 80, 890 (1998)
Perdew et al, PRL 100, 136406 (2008)
Armiento, Mattsson, PRB 72, 085108 (2005)
Becke, PRA 38, 3098 (1988); Lee, Yang, Parr, PRB 37, 785 (1988)
<xc_functional type="LDA", name="PW"/>
<xc_functional type="GGA", name="PBE"/>
<generator type="scalar-relativistic" name="MyGenerator-2.0"> Frozen core: [He] </generator>
This element contains character data describing in words how the dataset was generated.
type attribute must be one of:
<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>
valence_states element contains several
defined by a unique
id as well as
n quantum numbers.
For each of them it is also required to provide the energy
f and the matching radius of the partial waves
The number of
state elements determines the size of the partial wave basis. It is equal to the number of radial functions
(radial parts of the , and )
and is noted in the rest of this document.
For this dataset, the first two lines describe bound eigenstates with occupation numbers and principal quantum numbers. Notice, that the three additional unbound states should have no
In this way, we know that only the first two bound states (with
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=d*i" d="0.1" istart="0" iend="9" id="g1"> <values> 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 </values> <derivatives> 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 </derivatives> </radial_grid>
This defines one radial grid as where i runs from 0 to 9.
<radial_grid> element we have the 10 values of
followed by the 10 values of the derivatives .
All functions (densities, potentials, ...) that use this grid are given as 10 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=d*i" d="0.01" istart="0" iend="99" id="lin"> <radial_grid eq="r=a*exp(d*i)" a="1.056e-4" d="0.05" istart="0" iend="249" id="log">
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 (i = 0, ..., 99).
Each number must be separated by a
<newline> character or by one or
<space>'s (no commas).
For numbers with scientific notation, use this format:
A program can read the values for and from the file
or evaluate them from the
eq and associated parameter attributes.
There are currently six types of radial grids:
iend attributes indicating the range of i should always be present.
Although it is possible to define as many radial grids as desired, it is recommended to minimize the number of grids in the dataset.
Shape function for the compensation charge
The general formulation of the compensation charge uses an expansion over the partial waves ij and the spherical harmonics:
where is a Gaunt coefficient.
The standard expression  for the shape function is a product of the multipole moment and a shape function :
<shape_function type="gauss" rc="3.478505426185e-01">
Another formulation  defines directly :
bessel the four parameters
must be determined from
rc for each value of as described in .
<shape_function type="bessel" rc="3.478505426185e-01">
There is also a more general formulation where
is given in a numerical form. Several shape functions can be set (with the
depending on and/or combinations of partial waves (specified using the optional
See for instance section II.C of .
Example 1, defining numerically in :
<shape_function type="numeric" l=0 grid="g1"> ... ... </shape_function>
Example 2, defining directly for states
=N-2s and =
N-2p, and =0:
<shape_function type="numeric" l=0 state1="N-2s" state2="N-2p" grid="g1"> ... ... </shape_function>
Continuing, we have now reached the all-electron (resp. pseudo core, pseudo valence) density:
<ae_core_density grid="g1"> 6.801207147443e+02 6.801207147443e+02 6.665042896724e+02 ... ... </ae_core_density> <pseudo_core_density rc="1.1" grid="g1"> ... ... </pseudo_core_density> <pseudo_valence_density rc="1.1" grid="g1"> ... ... </pseudo_valence_density>
The numbers inside the
pseudo_valence_density) element defines the radial part of
(resp. , ).
The radial part must be multiplied by to get the full density
( should integrate to the number of core electrons).
The pseudo core density and the pseudo valence density are defined similarly and
also have a
rc attribute specifying the matching radius.
elements contain the radial parts of the ,
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
<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>
Remember that the radial part of these functions must be multiplied by a spherical harmonics:
The zero potential, (see section VI.D of )
is defined similarly to the densities; the radial part must be multiplied by
to get the full potential.
zero_potential element has a
rc attribute specifying the cut-off
radius of ::
<zero_potential rc="1.1" grid="g1"> ... ... </zero_potential>
The Kresse-Joubert formulation
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 n is defined as:
where is the larger of and .
- Note: 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
that contains the function directly,
so that no conversion is necessary:
<kresse_joubert_local_ionic_pseudopotential rc="1.3" grid="log"> ... ... </kresse_joubert_local_ionic_pseudopotential>
kresse_joubert_local_ionic_pseudopotential element has a
attribute specifying the matching radius. This matching radius corresponds to the maximum
of all the matching radii used in the formalism.
Kinetic energy differences
<kinetic_energy_differences> 1.744042161013e+00 0.000000000000e+00 2.730637956456e+00 ... ... <kinetic_energy_differences>
This element contains the symmetric matrix:
where is the kinetic energy operator used by the generator.
With partial waves (see definition), we have a matrix listed as numbers.
Datasets for use with MGGA functionals must also include information on the core kinetic energy density and pseudo core kinetic energy density ; the latters are defined with these two elements:
<ae_core_kinetic_energy_density grid="g1"> ... ... </ae_core_kinetic_energy_density> <pseudo_core_kinetic_energy_density rc="1.1" grid="g1"> ... ... </pseudo_core_kinetic_energy_density>
These densities are defined similarly to the core and valence densities (see above).
pseudo_core_kinetic_energy_density element has a
specifying its matching radius.
Exact exchange integrals
The core-core contribution to the exact exchange energy and the symmetric core-valence PAW-correction matrix are given as:
The coefficients depend only on pairs of the radial basis functions and can be evaluated by summing over radial integrals times 3-j symbols according to:
is the number of core electrons corresponding to , namely ,
(resp. ) is the larger (resp. smaller) of and .
can be specified in the
attribute of the
With valence states
is a matrix.
It can be specified as numbers inside
<exact_exchange core="..."> ... ... </exact_exchange>
Although not necessary, it may be helpful to provide the following item(s) in the dataset:
- Radius of the PAW augmentation region
- This radius defines the region (around the atom) outside which all pseudo quantities are equal to the all-electron ones. It is equal to the maximum of all the cut-off and matching radii. Note that -- for better lisibility -- the
paw_radiuselement should be provided in the header of the file.
End of the dataset
How to use the datasets
Most likely, the radial functions will be needed on some other type of radial grid than the one used in the dataset. 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.
Plotting the radial functions
The first 10-20 lines of the XML-datasets, should be pretty much human readable, and should give an overview of what kind of dataset it is and how it was generated. The remaining part of the file contains 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.
- Note: The
pawxml.pyprogram 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] dataset[.gz]
||Show program's version number and exit.|
||Show this help message and exit.|
||Function to extract.|
||Select valence state.|
||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
- P. E. Blöchl, Projector Augmented-Wave method, Phys. Rev. B 50, 17953-19979 (1994)
- P. E. Blöchl, C. J. Forst and J. Schimpl, Projector Augmented-Wave method: Ab initio molecular dynamics with full wave functions, Bulletin of Materials Science 26, 33-41 (2003)
- N. A. W. Holzwarth, A. R. Tackett, and G. E. Matthews, A Projector Augmented Wave (PAW) code for electronics structure calculations: Part I atompaw for generating atom-centered functions, Computer Physics Communications 135, 329-347 (2001)
- G. Kresse and D. Joubert, Form ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758-1775 (1999)
- K. Laasonen, A. Pasquarello, R. Car, C. Lee and D. Vanderbilt, Car-Parrinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials, Phys. Rev. B 47, 10142-10153 (1993)