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--- benzen_eigenvalues [2017/03/06 14:55]
+++ benzen_eigenvalues [2017/03/06 14:55]
krejcio repair of plotted bands
@@ Line 1: / Line 1: @@
+===== Eigenvalue spectra =====
+Once we have obtained the ground state atomic configuration, we can perform electronic structure analysis. To obtain the detail information about the eigen-energy spectra of the benzene molecule, we perform one time-step run with the fixed ground state charges (we suppose our optimized structure is stored in  **''answer.bas''** file). Our **''fireball.in''** file looks like now:
+<code>
+  &OPTION
+  basisfile = answer.bas
+  nstepf = 1
+  icluster = 1
+  iqout = 3
+  ifixcharge = 1
+  dt = 0.5
+  &END
+  &OUTPUT
+  iwrteigen = 1
+  &END
+</code>
+Once the calculation is done, **''eigen.dat''** file appears in the working directory, which lists in ascending order all eigenvalues of molecular orbitals:
+<code>
+          36
+  ------ the energy eigenvalues ----
+      -20.56048    -18.37085    -18.36961    -15.07488
+    -15.07199    -12.69340    -12.00502    -10.79389
+    -10.27202    -10.26750     -8.72117     -8.66806
+     -8.66615     -6.29214     -6.29027     -1.29656
+     -1.29630      2.26245      3.42055      5.15577
+.15896      6.56990      7.02760      7.03623
+.08185     11.09818     11.94749     11.95269
+.15497     17.03885     81.57499     83.17471
+.19519     86.09707     86.11842     87.78916
+</code>
+Information about occupancies of individual molecular level can be written into output file, if keyword **''iwrtefermi''** is switched on. In this way energy levels of HOMO and LUMO orbitals can be identified. In our particular case we found in output file:
+<code>
+  ------ fermi ioccupy_k for k-point =            1
+  Band n =    1 k-points: ioccupy =  1
+  Band n =    2 k-points: ioccupy =  1
+  Band n =    3 k-points: ioccupy =  1
+  Band n =    4 k-points: ioccupy =  1
+  Band n =    5 k-points: ioccupy =  1
+  Band n =    6 k-points: ioccupy =  1
+  Band n =    7 k-points: ioccupy =  1
+  Band n =    8 k-points: ioccupy =  1
+  Band n =    9 k-points: ioccupy =  1
+  Band n =   10 k-points: ioccupy =  1
+  Band n =   11 k-points: ioccupy =  1
+  Band n =   12 k-points: ioccupy =  1
+  Band n =   13 k-points: ioccupy =  1
+  Band n =   14 k-points: ioccupy =  1
+  Band n =   15 k-points: ioccupy =  1
+  Band n =   16 k-points: ioccupy =  0
+  Band n =   17 k-points: ioccupy =  0
+  Band n =   18 k-points: ioccupy =  0
+  Band n =   19 k-points: ioccupy =  0
+  Band n =   20 k-points: ioccupy =  0
+  Band n =   21 k-points: ioccupy =  0
+  Band n =   22 k-points: ioccupy =  0
+  Band n =   23 k-points: ioccupy =  0
+  Band n =   24 k-points: ioccupy =  0
+  Band n =   25 k-points: ioccupy =  0
+  Band n =   26 k-points: ioccupy =  0
+  Band n =   27 k-points: ioccupy =  0
+  Band n =   28 k-points: ioccupy =  0
+  Band n =   29 k-points: ioccupy =  0
+  Band n =   30 k-points: ioccupy =  0
+  Band n =   31 k-points: ioccupy =  0
+  Band n =   32 k-points: ioccupy =  0
+  Band n =   33 k-points: ioccupy =  0
+  Band n =   34 k-points: ioccupy =  0
+  Band n =   35 k-points: ioccupy =  0
+  Band n =   36 k-points: ioccupy =  0
+</code>
+From the list, we can identify the last occupied molecular level (HOMO) is no. 15 and first unoccupied level (LUMO) is no. 16. Let note, the list of eigenvalues can be found in '''eigen.dat''' file accounting appropriate number of levels (in ascending order).
+===== Density Of States (DOS) =====
+Another way how to analyze energy spectra of molecule in Fireball is to calculate Density Of State (DOS). In addition,
+projected DOS on each atom is provided. To run this task for particular atomic configuration, two steps are necessary:
+(i) switch on '''iwrtdos''' keyword in section '''&OUTPUT''', so '''fireball.in''' looks like now:
+<code>
+  &OPTION
+  basisfile = answer.bas
+  nstepf = 1
+  icluster = 1
+  iqout = 1
+  ifixcharge = 1
+  dt = 0.5
+  &END
+  &OUTPUT
+  iwrtdos = 1
+  &END
+</code>
+(ii) an extra new file called **''dos.optional''** has to be created in the working directory with following syntax:
+<code>
+.0                   ! scale factor (leave 1.0)
+       12            ! list of atoms to analyze DOS
+                   ! number of energy steps
+  -22.0   0.05          ! initial energy, energy step
+                     ! leave untouched
+.0     0.0           ! leave untouched
+.05                  ! imaginary part of Green function (controls energy level smearing)
+</code>
+In this particular case, all 12 atoms will be involved in the DOS analysis and DOS will be calculated from energy -22.0 until 0.0 eV with energy step 0.05 eV. Several files will appear in the working directory **''dens_XXX.dat''** containing projected DOS on each atom labeled ''XXX'' and a file **''dens_TOT.dat''** including the total DOS.
+{{:benzen:dos_benzen.png?700|DOS benzen}}
+===== Real-space electronic density =====
+Sometimes is more illustrative to visualize the electron density in real-space. This can help as a primitive estimation of STM images or it can provide more information about spatial (de)localization certain molecular levels. Here we'll visualize HOMO and LUMO state of the molecule. To do this, we need to first switch on keyword **''iwrtewf''** in **''fireball.in''** file (the section **''&OUTPUT''**). As a next step, we need to create a new section in **''fireball.in''** called **''&MESH''** with following keywords:
+<code>
+  &MESH
+  iewform = 1               ! individual levels listed bellow will be plotted in separated files
+  npbands = 2               ! number of molecular levels to be plotted
+  pbands =15,16             ! list of molecular levels to be plotted
+  &END
+</code>
+Real-space densities of individual molecular levels are stored in **''bandplot_XXXX.xsf''** files, where ''XXXX'' means number of given molecular orbital. These files are stored in an internal format of visualization program [[http://www.xcrysden.org |Xcrysden]].
+the real-space distribution of the density of state of the HOMO molecular state
+{{:benzen:benzen_homo.png|HOMO Benzen}}
+the real-space distribution of the density of state of the LUMO molecular state
+{{:benzen:benzen_lumo.png|LUMO benzen}}
+<code>
+  &MESH
+  iewform = 2            ! sum density in energy window
+  ewfewin_min = -8.16    ! lower energy bound
+  ewfewin_max = -2.16    ! lower energy bound
+  &END
+</code>

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