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--- absorbtion_spectra_by_fermi_golden_rule [2014/07/23 13:43]
prokop
+++ absorbtion_spectra_by_fermi_golden_rule [2014/07/24 14:30]
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-====== Absorbtion spectra by Fermi golden Rule ======
-There is a possibility to evaluate rught estimation of UV-VIS absorption spectra by [[http://en.wikipedia.org/wiki/Fermi's_golden_rule|Fermi golden rule]] between Kohn-Sham orbitals. For given range range of photon energy are selected all pairs of occupied and unoccupied gorund-state Kohn-Sham orbital with appropriate energy difference. This two orbitals are than projected onto real space grid and [[http://en.wikipedia.org/wiki/Transition_dipole_moment|transition dipole moment]] is computed. Oscilator strength (or probability of transition) is than proportional to squere of length of transition dipole moment. Absorbtion spectra  can be than plotted by summing up contributions of oscillator strength for occupied-unoccupied orbital pairs with energy difference falling into particular energy bins (like weighted histogram).
-Note that this method ( Fermi golden rule between ground state single particle states obtained from LDA-DFT ) is very crude approximation of true optical transitions. No beyond-DFT nor beyond-Hratree-Fock correction (such as RPA, TD-DFT, GW, BSE ... ) are used. For this reason transition energy ( positioning of peak ) is mostly not realistic. The method is, however, useful to explore dependence of electronic transition probability on symmetry breaking and changes in shape and localization of electronic states.
-=== Availability ===
-this is implemented only in Prokop's personal versions of Fireball located in
-  /data/home/hapala/Fireball_dev/src_1.0-BSfinal
-  /data/home/hapala/Fireball_dev/progs_Jellium_mod
-=== Usage ===
-The computation of transitions is activated by keyword ''iwrtexcit = 1'' in firebal.in. However, currently it is also necessary to activate ''iwrtewf = 1'' in order to initialize grid, even thought ''.xsf'' files written by ''iwrtewf'' option are not used at all and has nothing incommion with the computatuion of transitions ( this should be corrected in future). So the typical ''fireball.in'' looks like:
-  &OPTION
-  basisfile  = answer.bas
-  nstepf     = 1
-  icluster   = 1
-  ifixcharge = 1
-  &END
-  &OUTPUT
-  iwrtewf     = 1
-  iwrtexcit=1
-  &END
-  &MESH
-  iewform = 3
-  npbands = 1
-  pbands = 1
-  &END
-Than ''excitations.optional'' file should be provided to
-        ! write_out_transition_map ( default 0, moslty just for debuging )
-.0      ! dEmin ... minimum energy difference ( mostly 0)
-.5      ! dEmax ... maximim energy difference
-if  ''write_out_transition_map'' is set to '1', an '.xsf' file containing spatial distribution of transition dipole moment is outputed for each pair of orbitals. This may be usefull to identify parts of molecule which contribute most to the electronic transition. However, the number of transitions grow quadratically with energy range and each '.xsf' file needs typically more than 100MB of disk space. So in most of cases you would quickly consume HUGE amount of disk space ( like 1 terrabyte ) if you switch this option on.
-It is also recommended to chose reasonable small energy interval (dEmin,dEmax) oterwise the computation can take very long time.
-=== Outputs ===
-Excitations.dat file is writen out from the calculation. The file contains several columns of following meaingin:
-  - ''j,j'' index of ocupied and unoccupied orbital
-  - ''elta_Eij'' energy diffeence
-  - ''|D|'' length of transition dipole moment
-  - '' D_x,D_y,D_z'' cartesian components of transition dipole moment
-  - ''Ei,Ej'' energy eigenvalues corresponging to the Khon-Sham orbitals
-     i      j         delta_Eij               |D|                 D_x                 D_y                   D_z               Ei                     Ej
-    879        3.4862376070        0.9824594517        0.2759973643       -0.9336816482        0.1314937604       -3.0970434024       -6.5832810094
-    879        3.4791174668        0.9753364513       -0.4413174043        0.2404091902        0.8358968616       -3.0970434024       -6.5761608692
-    879        3.4582785159        0.5954896260        0.3594301771       -0.1688715641       -0.4437344220       -3.0970434024       -6.5553219183
-    879        3.4453548553        0.8057311791       -0.1487142116       -0.4625862731       -0.6427291469       -3.0970434024       -6.5423982578
-    879        3.4410779875        0.7684644226        0.0080712081       -0.6875508088       -0.3431418216       -3.0970434024       -6.5381213900
-    879        3.4257564875        0.4202213606        0.0892087920       -0.1778280360       -0.3701418282       -3.0970434024       -6.5227998899
-=== Making spectra ===
-For transformation of pairwise table of transition dipole moment into optical spectra for plotting can be used for example following bash/awk scripts.
-First script ''spectranice.sh'' accumulate (sum up) pairwise contributions of transition dipole moment into bins of given size and then blur them with gaussian filter (to make nice smooth spectra). The most importaint parameter is step size. For example with step size 0.001 eV:
-  spectranice.sh 0 3.5 0.001
-spectranice.sh code:
-  min=$1
-  max=$2
-  step=$3
-  awk -v min=$min -v max=$max -v step=$step '
-  BEGIN{for(i=0;min+i*step<max;i++){hist[i]=0}; minx=10000000; maxx=-10000000  }
-  (NR>0){
-  x=$3; y=$4; yy=y*y;
-  ei=int((x-min)/step)
-  if(x>maxx){maxx=x}
-  if(x<minx){minx=x}
-  hist[ei-5]+=yy*0.00098
-  hist[ei-4]+=yy*0.00977
-  hist[ei-3]+=yy*0.04395
-  hist[ei-2]+=yy*0.11719
-  hist[ei-1]+=yy*0.20508
-  hist[ei+0]+=yy*0.24609
-  hist[ei+1]+=yy*0.20508
-  hist[ei+2]+=yy*0.11719
-  hist[ei+3]+=yy*0.04395
-  hist[ei+4]+=yy*0.00977
-  hist[ei+5]+=yy*0.00098
-  }
-  END{
-  #print maxx,minx
-  for(i=0;min+i*step<max;i++){
-  if(((min+i*step)>minx) && ((min+i*step)<maxx) ) {print min+i*step,hist[i]}}
-  }
-  ' Excitations.dat > spectranice.dat
-in some cases you are not interested in the sum of all cotributions ( it would correspond to absorbtion spectra) but rather in the transition with highest oscillator strength in given interval of energy (energy bin). For this purpose script '''spectramax.sh'' can be used.
-  spectramax.sh 0.001
-  #! /bin/bash
-  step=$1
-  min=`awk '
-  BEGIN{Emin=100000}
-  (NR>0){if($3<Emin)Emin=$3}
-  END{print Emin}
-  ' Excitations.dat`
-  max=`awk '
-  BEGIN{Emax=0}
-  (NR>0){if($3>Emax)Emax=$3}
-  END{print Emax}
-  ' Excitations.dat`
-  echo $min $max
-  awk -v min=$min -v max=$max -v step=$step '
-  BEGIN{for(i=0;min+i*step<max;i++){hist[i]=0;num[i]=0;}}
-  (NR>0){
-  ei=int(($3-min)/step)
-  if(hist[ei]<($4*$4)){hist[ei]=($4*$4)}
-  }
-  END{for(i=0;min+i*step<max;i++){print min+i*step,hist[i]}}
-  ' Excitations.dat > spectramax.dat

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