Ionic contributions to the frequency dependent dielectric function of NaCl: Difference between revisions

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Line 98: Line 98:
  Eigenvectors and eigenvalues of the dynamical matrix
  Eigenvectors and eigenvalues of the dynamical matrix
  ----------------------------------------------------
  ----------------------------------------------------
   1 f  =    5.130373 THz   32.235082 2PiTHz  171.130804 cm-1    21.217523 meV
   1 f  =    5.130373 THz   '''32.235082 2PiTHz''' 171.130804 cm-1    21.217523 meV
             X        Y        Z          dx          dy          dz
             X        Y        Z          dx          dy          dz
       0.000000  0.000000  0.000000    0.000000  -0.000000    0.779560
       0.000000  0.000000  0.000000    0.000000  -0.000000    0.779560
       2.777981  2.777981  2.777981    0.000000  -0.000000  -0.626328
       2.777981  2.777981  2.777981    0.000000  -0.000000  -0.626328
   2 f  =    5.130373 THz    32.235082 2PiTHz  171.130804 cm-1    21.217523 meV
   2 f  =    5.130373 THz    '''32.235082 2PiTHz''' 171.130804 cm-1    21.217523 meV
             X        Y        Z          dx          dy          dz
             X        Y        Z          dx          dy          dz
       0.000000  0.000000  0.000000    -0.697237  -0.348675    0.000000
       0.000000  0.000000  0.000000    -0.697237  -0.348675    0.000000
       2.777981  2.777981  2.777981    0.560186    0.280139    0.000000
       2.777981  2.777981  2.777981    0.560186    0.280139    0.000000
   3 f  =    5.130373 THz    32.235082 2PiTHz  171.130804 cm-1    21.217523 meV
   3 f  =    5.130373 THz    '''32.235082 2PiTHz''' 171.130804 cm-1    21.217523 meV
             X        Y        Z          dx          dy          dz
             X        Y        Z          dx          dy          dz
       0.000000  0.000000  0.000000    -0.348675    0.697237    0.000000
       0.000000  0.000000  0.000000    -0.348675    0.697237    0.000000

Revision as of 10:51, 18 July 2019

Task

Calculation of the ionic contruibutions to the frequency dependent dielectric function of NaCl.

Calculation

To get the full (electronic & ionic) frequency dependent dielectric function you will have to compute them separately.

Step 1. Do a standard DFT calculation

Step 2. Calculate the electronic contributions to the frequency dependent dielectric function.[1]

Step 3. Calculate the ionic contributions to the frequency dependent dielectric function.[2]

Step 4. Add the two dielectric functions together:

This approach can be used for semi-conductors and insulators, not for metals.

Input

POSCAR

NaCl FCC                               
  5.55596202    
    0.5000000000000000    0.5000000000000000    0.0000000000000000
    0.0000000000000000    0.5000000000000000    0.5000000000000000
    0.5000000000000000    0.0000000000000000    0.5000000000000000
  Na   Cl
    1     1
Direct
 0.0000000000000000  0.0000000000000000  0.0000000000000000
 0.5000000000000000  0.5000000000000000  0.5000000000000000

KPOINTS

A smaller 4x4x4 or 8x8x8 would also suffice in case you are running interactively on one core.

Gamma-centred 11x11x11 Monkhorst-Pack grid
 0 
G
11 11 11
0 0 0

INCAR

  • INCAR file for the static calculation:
PREC = High
ISMEAR = 0 ; ISIGMA = 0.01
EDIFF = 1.E-8
GGA = PS
  • INCAR electronic contributions to the frequency dependent dielectric function[1]

(see other tutorials for more advanced options: Dielectric_properties_of_SiC. The same procedures for the electronic contributions apply to this example.)

PREC = High
ISMEAR = 0 ; ISIGMA = 0.01
EDIFF = 1.E-8
GGA = PS
ALGO = Exact
LOPTICS = .TRUE.


  • INCAR ionic contributions to the frequency dependent dielectric function[2]:
PREC = High
ISMEAR = 0 ; ISIGMA = 0.01
EDIFF = 1.E-8
GGA = PS
EDIFF = 1.E-8
#The ionic dielectric function can be calculated in two ways:################
#1# DFPT (faster), but does not allow for METAGGA use. ######################
IBRION = 8; LEPSILON=.TRUE.
#2# Finite differences (slower). ############################################
#IBRION = 6; LPEAD=.TRUE; LCALCEPS=.TRUE.
#NFREE = 2 ; POTIM = 0.015
#In both 1 and 2 the calculated dielectric function is in vasprun.xml #######

Results

Download all necessary files and run doall.sh. An Awk script ("extract_diel_vasprun") is used to extract the dielectric function from the vasprun.xml file and write it into a easy to plot two-column format. If everything goes well you will obtain two files ("diel.electron.dat" and "diel.ion.dat"). The two dielectric functions have been plotted in the following figure:

Note that the units on the frequency axes are different, eV and 2THz. The high frequency 'ion-clamped' dielectric constant () was obtained with the LOPTICS calculation. The static field () contribution of the ionic lattice to the dielectric constant ( ) can be calculated by DFPT or by the finite-difference method. In both cases the phonon frequencies and the Born effective charges are calculated:

BORN EFFECTIVE CHARGES (including local field effects) (in e, cummulative output)
---------------------------------------------------------------------------------
ion    1
   1     1.07157     0.00000     0.00000
   2     0.00000     1.07157    -0.00000
   3    -0.00000    -0.00000     1.07157
ion    2
   1    -1.07157    -0.00000    -0.00000
   2    -0.00000    -1.07157     0.00000
   3     0.00000     0.00000    -1.07157
Eigenvectors and eigenvalues of the dynamical matrix
----------------------------------------------------
  1 f  =    5.130373 THz   32.235082 2PiTHz  171.130804 cm-1    21.217523 meV
            X         Y         Z           dx          dy          dz
     0.000000  0.000000  0.000000     0.000000   -0.000000    0.779560
     2.777981  2.777981  2.777981     0.000000   -0.000000   -0.626328
  2 f  =    5.130373 THz    32.235082 2PiTHz  171.130804 cm-1    21.217523 meV
            X         Y         Z           dx          dy          dz
     0.000000  0.000000  0.000000    -0.697237   -0.348675    0.000000
     2.777981  2.777981  2.777981     0.560186    0.280139    0.000000
  3 f  =    5.130373 THz    32.235082 2PiTHz  171.130804 cm-1    21.217523 meV
            X         Y         Z           dx          dy          dz
     0.000000  0.000000  0.000000    -0.348675    0.697237    0.000000
     2.777981  2.777981  2.777981     0.280139   -0.560186    0.000000


If a phonon mode is 'dipole-active', meaning that the dipole moment of all ions involved in the mode changes in size during one period, it will appear in the frequency dependent dielectric function. The total static dielectric constant is then the sum of the two contributions:

Plotting

Use xmgrace or your other favourite plotting tool to plot the two collumn files (diel.electron.dat and diel.electron.dat):

xmgrace -nxy diel.electron.dat &
xmgrace -nxy diel.ion.dat

Download

NaCl_dielectric.tgz

References