quantum-espresso/PP/examples/CLS_FS_example

This example shows how to calculate final-state core-level-shift (CLS)
using the core-excited pseudo-potential technique. The procedure has
been used in several works and references for the underlying theoretical
concepts can be found in the articles listed below.

E. Pehlke and M. Scheffler - http://link.aps.org/doi/10.1103/PhysRevLett.71.2338
J. N. Andersen, D. Hennig, E. Lundgren, M. Methfessel, R. Nyholm, and
M. Scheffler  - http://link.aps.org/doi/10.1103/PhysRevB.50.17525

The definition of a FS core-level-shift is based on a difference
of energies and it's then necessary to take a reference atom in the
configuration studied to obtain the relative core level shifts. In this
example a very simple calculation regarding the SCLS (surface core level
shift) in the rhodium 011 slab is presented.

First the slab has to be defined with the correct parameters (how many
layers are needed to find a bulk-like atom, the separation between the
periodic repetitions of the slab, DFT convergence parameters, ecc...) and
the atomic positions have to be relaxed. All these steps are described
in detail in other examples and are not treated here. The structure
used in this example should not be taken as reference for an accurate
calculation but the parameters are chosen in order to keep the example
fast and instructive.

In the slab geometry it's natural to take the atom in the central layer,
that mimics the bulk environment, as reference and calculate all CLS from
the difference w.rt. this one. In this example the other interesting
atoms are the atoms in the surface layer and  the one in the first
subsurface layer.  Once the desired atoms are identified the procedure
is straightforward and can be defined in few steps:

 1) Make a regular SCF calculation of the slab where the core-excited
 pseudo-potential is used for the reference atom.

 2) Make several other SCF calculations, one for each selected atom in
 which only this one is described by the core-excited pseudo-potential

 3) Calculate the ground state (GS) energy difference between each
 of these SCF calculations and the one for the reference atom.
 These differences are the FS core-level shifts.

----------------

1) For this simulation, and all the following ones, it's necessary to
define a normal pseudo-potential and a core-excited one for Rhodium. The
two potentials have to be consistent with each other (functional,
parameters, ecc..), being the core-excited one a PP for the same atomic
type with a different, core-excited, electronic configuration. (The
instructions to generate of a core-excited PP can be found in the ld1.x
manual.)

Once the PP and the core-excited PP are defined the calculation is
a regular SCF run with the only difference that the bulk atom, the
reference, is defined by the core-excited PP. ONLY the reference atom
is defined in this way and ntyp variable in the &system namelist has to
be defined including the new core-excited type. All the other parameter
are defined following the normal guidelines for a SCF calculation.

*** Keep in mind that the core-excited atom is a new atomic type in
the configuration and all the precautions of possible interaction have
to be considered. In the example a slab 1x1 is used only to let the
example run on an average single CPU, again this is just a reference
structure. It's possible, and in fact true, that a bigger supercell is
needed, for example a 2x2 or a 3x3, to keep all the core-excited atoms
enough separated, avoid an interaction between them.

    (input=rh011bulk.scf.in, output=rh011bulk.scf.out)

2) All the other simulations are identical to the bulk-reference one but
this time the atom defined with the excited PP is different. For every
simulation ONLY ONE atom has to be defined by the core-excited PP and
no relaxation as to be done, only one SCF calculation. (If one wants
to calculate the CLS of three different atoms three SCF calculations
are needed).

It's clear that to keep consistency all the other SCF parameters
(k-points, energy cut-offs, ecc..)  of these new calculations have to
be identical to the reference SCF calculation.

    (input=rh011surf.scf.in, output=rh011surf.scf.in)

3) Once obtained the energy for all the atoms identified the CLS are
defined as the difference between the GS energy of the particular SCF
calculation and the GS energy of the reference SCF one:

    SCLS = energy_gs(surface core-excited) - energy_gs(bulk core-excited)
    CLS = energy_gs(other atom core-excited) - energy_gs(bulk core-excited)

    (see final-state.txt)