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XSPECTRA
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2009: First version of XSpectra
 by Christos Gougoussis, Matteo Calandra, Ari P. Seitsonen and Francesco Mauri

2014: Restyling of I/O, 
 by Delphine Cabaret and Nadejda Mas

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2015: L23 edge XAS calculation by O. Bunau and M. Calandra
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-----------------------------------------------------------------------
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The theoretical approach on which XSpectra is based was
described in: 

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L23 edges,

O. Bunau and M. Calandra
Projector augmented wave calculation of x-ray absorption spectra at the L2,3 edges
Phys. Rev. B 87, 205105 (2013) 

K/L1-edge,
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C. Gougoussis, M. Calandra, A. P. Seitsonen, F. Mauri,
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"First principles calculations of X-ray absorption in an ultrasoft 
pseudopotentials scheme: from $\alpha$-quartz to high-T$_c$ compounds",
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Phys. Rev. B 80, 075102 (2009) 
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M. Taillefumier, D. Cabaret, A. M. Flank, and F. Mauri
"X-ray absorption near-edge structure calculations with the pseudopotentials:
Application to the K edge in diamond and αalpha-quartz"
Phys. Rev. B 66, 195107 (2002)

You should cite these three works in all publications using this software.
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The implementation of the DFT+U approximation and its application to
K-edge XAS in NiO was performed in:

C. Gougoussis, M. Calandra, A. Seitsonen, Ch. Brouder, A. Shukla, F. Mauri
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" Intrinsic charge transfer gap in NiO from  Ni K -edge x-ray absorption spectroscopy",
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Phys. Rev. B 79, 045118 (2009)
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If you use DFT+U, you should cite this work too.
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Finally you should cite properly the Quantum ESPRESSO distribution.
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-----------------------------------------------------------------------
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XSpectra is a post-processing tools that relies on the output 
(the charge density) of the PWscf code (pw.x). 
Thus a scf calculation needs to be done before running 
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xspectra.x.

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To simulate core-hole effects, a pseudopotential with a hole in the s
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state (1s for K-edges, 2s for L1-edges, 2p1/2 for L2-edges, 2p3/2 for
L3-edges) needs to be generated for the absorbing atom. 
Some of these pseudopotentials are available 
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in the XSpectra examples directory, some others are available on 
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the pseudopotential web-page at www.quantum-espresso.org/ with the
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label "*star1s*_gipaw*" for K-edges, "*star2s*_gipaw*" for L1-edges and so on. 

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The self-consistent calculation is then performed on a supercell including
the absorbing atom. The size of the supercell needs to be verified from
system to system, since fairly large supercells are necessary for convergence.
If core-hole effects need not to be taken into account then a calculation on
a single cell with a standard pseudopotential (i.e. without the core-hole) 
is enough. 

Since xspectra.x uses GIPAW reconstruction of the all electron wavefunction
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the pseudopotential needs to contain information about GIPAW reconstruction.
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There is no limit to the number of GIPAW projector that can be included. 
Note however that at least two projectors are needed to obtain XAS spectra
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converged up to 30-40 eV from the Fermi level.
The use of a single projector is discouraged, particularly when semicore
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states are present. If more than two projectors are used, linear independence
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of the projectors should be explicitly verified (verbosity='high'). 
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Once the scf charge density has been obtained, the xspectra.x code can be 
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used as a post-processing tool. Note that the X-ray absorption spectra
can be calculated on a larger mesh, different from that used in the 
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PWscf scf run. Convergence need to be tested also for this second mesh.
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XSpectra calculates then the XAS electric dipole (for K and L edges)
or electric quadrupole contributions (for K and L1 edges only),
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using the Lanczos method and the continued fraction.
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This approach does not require the explicit calculation of empty states
and it is consequently very fast (only the charge density is needed).
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The code needs the radial core wavefunction of the initial core state
in input. This wavefunction is included in the pseudo
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and can be extracted using the script upf2plotcore.sh
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in the directory ~/espresso/XSpectra/tools/ .
Note that this script works only for UPF version 1.
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This is necessary to calculate the XAS matrix element.

The output spectrum can be separated in its spin-up and 
spin-down polarizations.
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DFT+U calculations  and collinear magnetism are possible.
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Ultrasoft pseudopotentials are allowed.
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Hybrid functionals not yet allowed.
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--------------------------------------------------------------------------

=======================================================================
NAMELIST / input_xspectra /


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calculation  	 character (len=8)				  DEFAULT=''
               	 'xanes_dipole', Perform dipolar calculation
               	 'xanes_quadrupole', Perform quadrupolar 
		       		      calculation
                 'hpsi', Perform the test H*psi=E*Psi (debug option)

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edge             character (len=16)                                 DEFAULT='K',
                 specifiy the edge to be calculated. 
                 'K' specify the standard K-edge calculation
                 'L2' calculates the L2 edge, 
                 'L3' calculates the L3 edge,
                 'L23' calculates both.
                 However, it should be noted that in the single particle
                 approximation the L3/L2 branching ration is exactly equal two 2.
                 Thus a calculation of one of the edges is enough.

lplus            logical                                           DEFAULT=.false.
                 if lpus=.true. only transition 2p ---> d are allowed
                 in the dipolar cross section for L23 edges.
                  
lminus           logical                                           DEFAULT=.false.
                 if lminus=.true. only transition 2p ---> s are allowed
                 in the dipolar cross section for L23 edges.

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prefix		 character (len=256) 
               	 prefix of the pwscf output files

outdir		 character (len=256)				   DEFAULT='./'
               	 directory tmp_dir or where the pwscf output files are stored

verbosity    	 character (len=4)				  DEFAULT='low'
               	 'high',it checks linear dependence of PAW projectors 
                        and write details about the projectors. 
                 Note that GIPAW already perform a check on the linear 
                  dependence of the projectors even without this option.

xiabs        	 integer				              DEFAULT=1
               	 type of the absorbing atom:
                 position within the ATOMIC_SPECIES in pwscf input

xkvec(1:3)       real(DP)				  DEFAULT=(1.0,0.0,0.0)
		 coordinates of the X-ray wave-vector k		  

xepsilon(1:3)	 real(DP)    	     	                  DEFAULT=(0.0,0.0,1.0)
                 coordinates of the incident X-ray polarization vector	  

xcoordcrys	 logical				         DEFAULT=.true.
		 .true. to use crystal coordinates for xkvec and xepsilon

xonly_plot	 logical					DEFAULT=.false.
		 .false. the continued fraction is calculated
		         for each k-point and at the end written
                         on the save file
		 .true.  uses a previously calculated continued
                         fraction (x_save_file) to re-plot the
		         spectrum with different parameters
		         (gamma broadening parameter,with occupied state,etc.)	  

x_save_file      character (len=256)                          DEFAULT=xanes.sav
                 save file where results of the Lanczos 
                 calculation (a,b coefficients, etc.) are written
		 If xonly_plot=.true., the x_save_file is read (read only) 
                 to get the Lanczos parameters calculated in a previous run
                 Current version number is 2

ef_r             (obsolete use xe0)
                 The Fermi energy is determined from the SCF save directory.
                 For an insulator, it is set to the energy of the highest occupied level.
                 If the calculation is spin polarized, the largest
                 of the Fermi energies corresponding to spin up and down is kept.
                 If the zero of the spectrum needs to be changed, use xe0 (see below).


xe0		 real(DP)				           DEFAULT=1.d4
                 energy-zero for the spectrum in eV 
                 - must be set to the Fermi level if xonly_plot is .true. 
		   and the version of x_save_file is 1
                   (written with a previous version of the code).
                   If x_save_file is 2 and xe0 is not specified then the zero 
                   energy of the spectrum is set at the Fermi level.
                 - can also be used to set the zero energy for the calculation
                   of the spectrum at an other value than the Fermi energy
                   (for example, for an insulator, in the middle of the gap) 

xniter		 integer					   DEFAULT=2000
                 maximum number of iterations for Lanczos.
		 The maximum number of iterations allowed must be lower 
                 than the number of vectors in the Hilbert space
                 (i.e. the number of plane waves).

xcheck_conv   	 integer					      DEFAULT=5
               	 number of iterations between 2 convergence tests:
                 Xspectra checks convergency of the spectrum every 
                 xcheck_conv iterations of the Lanczos-basis construction.

xerror           real(DP)                                          DEFAULT=0.01
                 convergence threshold for Lanczos calculation (eV)
                 If the difference of two successive spectra 
                 (for a given k-point) is smaller than xerror, 
                 the convergence is achieved.


show_status      logical			                DEFAULT=.false.
                 flag to show the status of the code

U_projection_type character(len=16)			       DEFAULT='atomic'
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		  type of projection for DFT+U calculations
		  (see the PWscf input file for more info)

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time_limit       integer                                          DEFAULT=1.d8
                 time in seconds before stopping the calculation.
                 If XSpectra stops because of the time limit, 
                 a and b coefficients of the incomplete continued fraction 
                 are stored in the .sav file. 
                  
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restart_mode     character (len=32)                     DEFAULT='from_scratch'
                 'restart' if you want to restart from a .sav file 
                           where a and b coefficients of an incomplete 
                           continued fraction are stored.
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===============================================================================

NAMELIST / plot /

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xnepoint         integer					    DEFAULT=100
                 number of energy points in the plot of the XAS spectrum
		 
xemax            real(DP)     	 				   DEFAULT=10.0
                 maximum energy in eV for the plot of the XAS spectrum
		 
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xemin            real(DP)			                    DEFAULT=0.0
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                 minimum energy in eV for the plot of the 
		 XAS spectrum

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cut_occ_states   logical				         DEFAULT=.false.
                 .false. the occupied states are visualized
                 .true.  the occupied states are smoothly cut
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			from the plot

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terminator       logical					DEFAULT=.false.
                 .true. to use the terminator function for the
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		               continued fraction
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                 .false. no terminator is used.

gamma_mode       character (len=256)		             DEFAULT='constant'
                 'constant': a constant broadening parameter (xgamma) 
                                is used for the XAS spectrum.
                 'variable': an energy-dependent broadening parameter 
                                  is used: constant and equal to gamma_value(1)
                                  from xemin to gamma_energy(1), 
                                  constant and equal to gamma_value(2)
                                  from gamma_energy(2) to xemax and linear 
                                  from gamma_energy(1) to gamma_energy(2).
	         'file': the continued fraction uses an energy-dependent
                              broadening parameter stored in file gamma_file.

                 The broadening parameter (gamma of the continued fraction)
                 is equivalent to the half width at half maximum
                 of a Lorentzian used for a convolution


xgamma	       real(DP)                                             DEFAULT=0.1
               constant broadening parameter to be used in the spectrum (eV)
               used for convergence and if gamma_mode='constant'
               
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gamma_energy(1:2) real(DP)
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                  energy values in eV of the 2 points of reference for variable gamma
                  used if gamma_mode='variable'
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gamma_value(1:2) real(DP)
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                 gamma values in eV of the 2 points of reference
                 used if gamma_mode='variable'

gamma_file     character (LEN=256)			    DEFAULT='gamma.dat'
               The file has to be formatted in two columns :
                            energy1  gamma1
	       		    energy2  gamma2
	       where at energy1 the broadening parameter is gamma1.
               used if gamma_mode='file'
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==============================================================================
NAMELIST / pseudos /

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filecore,      character (len=256)                           DEFAULT='Core.wfc'
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               core wavefunction file

r_paw(1:...)   real(DP)		                                 DEFAULT=1.5*rc
               paw radii to be used in paw reconstruction.
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               rpaw(1) corresponds to l quantum number=1 (electric dipole)
               rpaw(2) corresponds to l quantum number=2 (electric quadrupole)
               
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==============================================================================

 In order to cut the occupied states, the program performs an integration
 over the variable t in ] 0, infinity [. 
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 For more details see ref. 
  Ch. Brouder, M. Alouani, K. H. Bennemann, Phys. Rev. B 54 (1996) p.7334-49.
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 The integration is done with t going in two opposite directions, 
 from the start value cut_startt. So, the integration
 is done over ]cut_tinf,cut_startt] at least with step cut_stepl, and
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 over [cut_startt,cut_tsup[ at least with step cut_stepu. 
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 There are two arrays of size cut_nmeml and cut_nmemu 
 in order to save Green functions values. There is an area near
 the Fermi level of size cut_desmooth (in eV) where the cross section 
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 is interpolated in order to avoid a divergence.
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NAMELIST / cut_occ /

cut_ierror     real(DP)						 DEFAULT=1.d-7
               convergence tolerance for one step in the integral

cut_stepu      real(DP)  					 DEFAULT=1.d-2
               integration initial step, upper side

cut_stepl      real(DP)						 DEFAULT=1.d-3
               integration initial step, lower side

cut_startt     real(DP)						 DEFAULT=1.d0
               integration start value of the t variable

cut_tinf       real(DP)						 DEFAULT=1.d-6
               maximum value of the lower integration boundary

cut_tsup       real(DP)						 DEFAULT=100.d0
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               minimum value of the upper integration boundary
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cut_desmooth   real(DP)						 DEFAULT=1.d-2
               size of the interval near the fermi energy
               in which cross section is smoothed

cut_nmemu      integer						 DEFAULT=100000
               size of the memory of the values of the
               green function, upper side

cut_nmeml      integer						 DEFAULT=100000
               size of the memory of the values of the
               green function, lower side



=================================================================================