SCM: Examples BAND

Time-dependent DFT calculations for bulk silicon

Sample directory: band/Silicon/

The time-dependent DFT functionality is an important functionality. It enables you to calculate frequency-dependent dielectric functions for 1-dimensional and 3-dimensional periodic systems. In the present example, a standard geometry for bulk Silicon is given. The accuracy and kspace variables can keep their normal values. The important part in this example is of course the RESPONSE block. It specifies that 7 frequencies should be treated, with an even spacing between 0.0 hartree and 0.25 hartree. In this example scalar ZORA relativistic effects are switched on with the isz line in the RESPONSE block.

$ADFBIN/band << eor
TITLE Silicon 

ACCURACY 5
KSPACE 2

DEPENDENCY BASIS 1e-10

UNITS 
 LENGTH ANGSTROM
END

RESPONSE
nfreq   7
strtfr  0d0
endfr   25d-2 
isz     1 
END


DEFINE
AAA=5.43
HA=AAA/2
END

LATTICE
0   HA  HA
HA  0   HA
HA  HA  0
END


ATOMS Si
0.0   0.0   0.0
HA/2  HA/2  HA/2
END
...
END INPUT
eor

For Silicon the real and imaginary parts of the dielectric function: epsilon(omega) = 1 + 4 Pi Chi(omega) are calculated.

In the output file, the results will look something like the fragment below. The output specifies for which frequency the dielectric function is determined, and then proceeds to print the values for the 3x3 tensors.

The real and imaginary parts are printed separately. At this frequency, the imaginary part is still zero. Because of the high symmetry of the system, the real part is a constant times the unit matrix except for numerical noise.

  ** Frequency **   0.833333E-01 au    2.26756     eV **
  ** Start the SCF procedure **  
  ***** Real ******  
  ** Chi_jj   X  **   -12.8363       0.142802E-18   0.547977E-17
  ** Chi_jj   Y  **   0.202883E-17   -12.8363       0.121052E-17
  ** Chi_jj   Z  **   0.124042E-16   0.215311E-17   -12.8363
  ***** Imag ******  
  ** Chi_jj   X  **   0.000000E+00   0.000000E+00   0.000000E+00
  ** Chi_jj   Y  **   0.000000E+00   0.000000E+00   0.000000E+00
  ** Chi_jj   Z  **   0.000000E+00   0.000000E+00   0.000000E+00
  *****************

After each frequency has been treated, the results are summarized in a table, for each component separately. For the xx-component, this looks as in the table below. The frequency/energy is again printed in two different units, the Dielectric Function is printed in a.u. The values for Chi, which are trivially related to those printed here, are summarized in a separate table.

 =================================================================
 ==         Frequency         ===       Dielectric Function     ==
 ==     a.u.   ==      e.V.   ===        Re    ==        Im     ==
 ============XX-dir===============================================
     0.416667E-01     1.13378         16.1119        0.000000E+00
     0.833333E-01     2.26756         23.7904        0.000000E+00
     0.125000         3.40134         15.8529         35.8574
     0.166667         4.53512        -3.49949         20.2221
     0.208333         5.66890        -6.60897         12.3661
     0.250000         6.80268        -6.42943         6.87957
 ============YY-dir===============================================
     0.416667E-01     1.13378         16.1119        0.000000E+00
     0.833333E-01     2.26756         23.7904        0.000000E+00
     0.125000         3.40134         15.8529         35.8574
     0.166667         4.53512        -3.49949         20.2221
     0.208333         5.66890        -6.60897         12.3661
     0.250000         6.80268        -6.42943         6.87957
 ============ZZ-dir===============================================
     0.416667E-01     1.13378         16.1119        0.000000E+00
     0.833333E-01     2.26756         23.7904        0.000000E+00
     0.125000         3.40134         15.8529         35.8574
     0.166667         4.53512        -3.49949         20.2221
     0.208333         5.66890        -6.60897         12.3661
     0.250000         6.80268        -6.42943         6.87957

Results of the test calculation (red/blue) are plotted in next Figure together with experimental data (yellow/green). The results for the seven specified frequencies are given. It should be obvious that more frequencies are needed (resulting in longer run times) to obtain a smooth curve in which peaks cannot be missed because of too coarse interpolation.

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