Once we have obtained an optimized atomic configuration,we can perform electronic structure analysis. To obtain the detail information about energy spectra of the molecule, we perform one-time step run with fixed charges (our optimized structure is stored in ' answer.bas' file). Our fireball.in file looks like:
&OPTION basisfile = answer.bas nstepf = 1 icluster = 1 iqout = 1 ifixcharge = 1 dt = 0.5 &END &OUTPUT iwrteigen = 1 &END
Finishing the calculation, eigen.dat file appears in the working directory, which lists in ascending order all eigenvalues of molecular orbitals:
1 142
--- the energy eigenvalues ---
-20.77644 -20.17576 -19.32420 -18.49408
-18.49262 -17.56440 -17.48782 -16.37893
-16.35960 -14.45772 -13.77290 -12.91450
-12.55894 -12.31129 -11.72733 -10.57604
-10.47081 -10.27380 -9.84700 -9.75059
-9.28453 -9.25281 -8.86563 -8.08602
-7.86517 -7.84647 -7.63290 -7.56571
-7.38417 -7.07353 -6.59935 -5.95037
-5.93908 -5.79952 -4.77435 -3.52791
-1.31315 -0.15600 0.13238 0.36040
0.95653 0.98146 1.60240 2.20926
2.36855 2.46027 2.81924 3.35559
4.89158 5.47431 5.80665 5.83704
6.03328 6.93077 6.98308 7.45317
7.80996 9.21705 9.23329 9.72755
10.35864 10.52539 11.11532 11.31138
11.34314 11.65157 11.71850 11.98661
12.43798 12.47948 12.64843 13.13170
14.04051 14.19757 14.55861 15.06387
15.21110 15.30968 15.37279 15.99312
16.04862 16.43805 16.46738 16.88387
16.99408 17.25263 17.61341 18.59642
18.93562 19.46990 19.80628 20.31527
20.34526 21.40842 21.74713 22.24177
22.61195 22.76252 23.34774 24.49545
24.59028 24.93521 25.67988 25.78261
26.51534 27.32112 27.55584 28.04580
28.47919 28.76664 29.50683 30.65046
30.90050 31.21945 33.09324 34.44970
35.52433 35.86108 37.34994 37.88428
38.35645 41.40826 42.20641 43.29368
43.70757 47.36562 48.51939 50.04231
56.31003 56.38914 60.36281 66.30143
66.39706 73.75972 87.06108 87.07247
89.24974 91.64514 93.81909 95.64658
95.97695 99.09614
In addition, an occupancy 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:
... Band n = 24 k-points: ioccupy = 1 Band n = 25 k-points: ioccupy = 1 Band n = 26 k-points: ioccupy = 1 Band n = 27 k-points: ioccupy = 1 Band n = 28 k-points: ioccupy = 1 Band n = 29 k-points: ioccupy = 1 Band n = 30 k-points: ioccupy = 1 Band n = 31 k-points: ioccupy = 1 Band n = 32 k-points: ioccupy = 1 Band n = 33 k-points: ioccupy = 1 Band n = 34 k-points: ioccupy = 1 Band n = 35 k-points: ioccupy = 1 Band n = 36 k-points: ioccupy = 1 Band n = 37 k-points: ioccupy = 0 Band n = 38 k-points: ioccupy = 0 Band n = 39 k-points: ioccupy = 0 Band n = 40 k-points: ioccupy = 0 Band n = 41 k-points: ioccupy = 0 Band n = 42 k-points: ioccupy = 0 Band n = 43 k-points: ioccupy = 0 ...
It means last occupied level (HOMO) is no. 36 and first unoccupied level is no. 37. Their eigenvalues can be found in 'eigen.dat' file accounting appropriate number of levels (in ascending order).
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:</br>
(i) switch on 'iwrtdos' keyword in section '&OUTPUT', so 'fireball.in' looks like now:
&OPTION basisfile = answer.bas nstepf = 1 icluster = 1 iqout = 1 ifixcharge = 1 dt = 0.5 &END &OUTPUT iwrtdos = 1 &END
(ii) an extra new file called 'dos.optional' has to be created in the working directory with following syntax:
1.0 ! scale factor (leave 1.0) 1 22 ! list of atoms to analyze DOS 441 ! number of energy steps -22.0 0.05 ! initial energy, energy step 0 ! leave untouched 0.0 0.0 ! leave untouched 0.05 ! imaginary part of Green function (controls energy level smearing)
In this particular case, all 22 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.
Real-space electronic density
Sometimes is more illustrative visualize electron density in real-space. This can help can be of use as primitive estimation of STM images or it can provide more information about spacial (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:
&MESH iewform = 1 ! individual levels listed bellow will be plotted in separated files npbands = 2 ! number of molecular levels to be plotted pbands =36,37 ! list of molecular levels to be plotted &END
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].
real density of state of the HOMO molecular state
