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<H2><A ID="SECTION00053000000000000000">
4.3 Projection over atomic states, DOS, projected band structure</A>
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<P>
The code <TT>projwfc.x</TT> calculates projections of wavefunctions
over atomic orbitals. The atomic wavefunctions are those contained
in the pseudopotential file(s). The Löwdin population analysis (similar to
Mulliken analysis) is presently implemented. The projected DOS (or PDOS:
the DOS projected onto atomic orbitals) can also be calculated and written
to file(s). More details on the input data are found in file
<TT>Doc/INPUT_PROJWFC.*</TT>. The ordering of the various
angular momentum components (defined in routine <TT>ylmr2.f90</TT>)
is as follows:
<!-- MATH
$P_{0,0}(t)$
-->
<I>P</I><SUB>0, 0</SUB>(<I>t</I>), <!-- MATH
$P_{1,0}(t)$
-->
<I>P</I><SUB>1, 0</SUB>(<I>t</I>), <!-- MATH
$P_{1,1}(t)cos\phi$
-->
<I>P</I><SUB>1, 1</SUB>(<I>t</I>)<I>cosφ</I>, <!-- MATH
$P_{1,1}(t)sin\phi$
-->
<I>P</I><SUB>1, 1</SUB>(<I>t</I>)<I>sinφ</I>,
<!-- MATH
$P_{2,0}(t)$
-->
<I>P</I><SUB>2, 0</SUB>(<I>t</I>), <!-- MATH
$P_{2,1}(t)cos\phi$
-->
<I>P</I><SUB>2, 1</SUB>(<I>t</I>)<I>cosφ</I>, <!-- MATH
$P_{2,1}(t)sin\phi$
-->
<I>P</I><SUB>2, 1</SUB>(<I>t</I>)<I>sinφ</I>,
<!-- MATH
$P_{2,2}(t)cos2\phi$
-->
<I>P</I><SUB>2, 2</SUB>(<I>t</I>)<I>cos</I>2<I>φ</I>, <!-- MATH
$P_{2,2}(t)sin2\phi$
-->
<I>P</I><SUB>2, 2</SUB>(<I>t</I>)<I>sin</I>2<I>φ</I>
and so on, where <I>P</I><SUB>l, m</SUB>=Legendre Polynomials,
<!-- MATH
$t = cos\theta = z/r$
-->
<I>t</I> = <I>cosθ</I> = <I>z</I>/<I>r</I>, <!-- MATH
$\phi= atan(y /x)$
-->
<I>φ</I> = <I>atan</I>(<I>y</I>/<I>x</I>).
<P>
Data produced by code <TT>projwfc.x</TT> can be further
analysed using auxiliary codes <TT>sumpdos.x</TT> (sums selected PDOS
by specifying the names of files containing the desired PDOS: type
<TT>sumpdos.x -h</TT> or look into the source code for more details)
and <TT>plotproj.x</TT> . A more sophisticated tools is the script
<TT>tools/sum_states.py</TT>, by Julen Larrucea: documentation in
<TT>http://larrucea.eu/sum_states-py-2/</TT>.
<P>
The total electronic DOS can also be calculated by code <TT>dos.x</TT>,
whose complete input documentation is in <TT>Doc/INPUT_DOS.*</TT>
See Example 02 for total and projected electronic DOS calculations,
-and for projected band structure;
see Example 03 for projected and local DOS calculations.
<P>
The DOS projected over <EM>molecular</EM> states (e.g. for a molecule on
a surface system) can be computed using code <TT>molecularpdos.x</TT>
(courtesy of Guido Fratesi). See file <TT>Doc/INPUT_MOLDOS.*</TT>
for input documentation and directory <TT>MolDos_example/</TT> for
an example.
<P>
The calculation of magnetic anisotropy using the Force Theorem is described
in the following paper:
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.205409. An
example and a README can be found in <TT>ForceTheorem_example/</TT>
<P>
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