Time-dependent DFT calculations for bulk silicon
Sample directory: band/e_Silicon/
The time-dependent DFT functionality is important new functionality in ADF2002.03. 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.
