Purpose of band_interpolation.x:
This contains four band energies interpolation methods,
to be advantageously (but not necessarly) used for EXX band structure computations.
The PP/src/band_interpolation.x post-processing subprogram reads the band energies
stored in the pwscf.xml file after an SCF calculation on a uniform Monkhorst-Pack grid,
and interpolates the eigenvalues to an arbitrary set of k-points provided in input.
The workflow is just:
(1) do an SCF on a uniform grid
(2) call the interpolator from the folder in which the pwscf.xml
file is present (band_interpolation.x < input)
For large EXX calculations the first step can be splitted in two substeps:
(1) do an SCF calculation on a uniform grid with occupied bands only
(2) do a NSCF (or Bands) calculation on the same uniform grid adding virtual orbitals
(3) call the interpolator from the folder in which the pwscf.xml file is present
Four interpolation methods have been included (see method).
The interpolated band structure in eV units is written in a file named [method].dat
(e.g. fourier-diff.dat for the fourier-diff method) that is plottable with Grace or Gnuplot
(e.g. xmgrace -nxy fourier-diff.dat)
Structure of the input data:
============================
&INTERPOLATION
...
/
[ ROUGHNESS
RoughN
'automatic' or RoughC(1) RoughC(2) RoughC(3) ... RoughC(RoughN) ]
[ USER_STARS
NUser
vec_X vec_Y vec_Z ]
K_POINTS { tpiba_b }
nks
xk_x, xk_y, xk_z, wk
'fourier-diff'
The interpolation method to be used
Available options are:
band energies, as functions of k, are expanded in reciprocal space using a Star function basis set
(algorithm from Pickett W. E., Krakauer H., Allen P. B., Phys. Rev. B, vol. 38, issue 4, page 2721, 1988,
https://link.aps.org/doi/10.1103/PhysRevB.38.2721 ).
WARNING: The pwscf.xml file must be generated with nosym == .false. .
band energies, as functions of k, are expanded in reciprocal space using a Star function basis set
(algorithm from D. D. Koelling, J. H. Wood, J. Comput. Phys., 67, 253-262 (1986).
https://ui.adsabs.harvard.edu/abs/1986JCoPh..67..253K ).
WARNING: The pwscf.xml file must be generated with nosym == .false. .
inverse distance weighting interpolation with Shepard metric
(ACM 68: Proceedings of the 1968 23rd ACM national conference, January 1968, Pages 517–524,
https://doi.org/10.1145/800186.810616 ).
WARNING: The pwscf.xml file must be generated with nosym == .true. .
WARNING: This method is REALLY simple and provides only a very rough estimate of the band structure.
inverse distance weighting interpolation inside a sphere of given radius.
WARNING: The pwscf.xml file must be generated with nosym == .true. .
WARNING: This method is REALLY simple and provides only a very rough estimate of the band structure.
6
The maximum Miller index used to automatically generate the set of symmetry inequivalent Star vectors
(only for method == 'fourier-diff' or 'fourier')
.FALSE.
If .TRUE. a (time consuming) step is performed, to check whether all the Star functions have
the correct lattice periodicity (only for method == 'fourier-diff' or 'fourier') .
For automatically generated Star functions this should never occur by construction, and the program
will stop and exit in case one Star function with wrong periodicity is found (useful for
debugging and program sanity check).
If additional user-defined Star vectors are specified (see optional card USER_STARS),
the program will print a WARNING in case one Star function with wrong periodicity is found.
2
The exponent of the distance in the IDW method ( only for method == 'idw' or 'idw-sphere')
4.0d0
The search radius for method == 'idw-sphere', is Rmin * scale_sphere, where Rmin is the
minimum distance found between the uniform grid of k-points.
If scale_sphere is too small, some k-points of the path might not see enough uniform grid points
to average energies, whereas for large values the method becomes equal to method == 'idw'.
This card can be used to change the roughness functional that is minimized
in the method == 'fourier-diff' and 'fourier'.
In case method == 'fourier-diff', or 'fourier' and card ROUGHNESS is not specified the default
roughness will be used with RoughN == 1 and RoughC(1) == 1.0d0.
1
Number of terms included in the roughness functional
1.0d0
Coefficients for the terms included in the roughness functional.
They can be explicitely given or 'automatic' can be specified instead of numbers
to use default coefficients.
0
Number of supplied additional Star vectors.
Additional user-defined Star vectors that are added to the
automatically generated ones to augment the Star functions
basis set.
You might also want to check check_periodicity when providing
user-defined Star vectors.
tpiba_b
none
All K_POINTS options other than tpiba_b have been disabled in the interpolation.
Used for band-structure plots.
See Doc/brillouin_zones.pdf for usage of BZ labels;
otherwise, k-points are in units of 2 pi/a.
nks points specify nks-1 lines in reciprocal space.
Every couple of points identifies the initial and
final point of a line. pw.x generates N intermediate
points of the line where N is the weight of the first point.
Number of supplied special k-points.
Special k-points (xk_x/y/z) in the irreducible Brillouin Zone
(IBZ) of the lattice (with all symmetries) and weights (wk)
See the literature for lists of special points and
the corresponding weights.
If the symmetry is lower than the full symmetry
of the lattice, additional points with appropriate
weights are generated. Notice that such procedure
assumes that ONLY k-points in the IBZ are provided in input