Ionic contributions to the frequency dependent dielectric function of NaCl: Difference between revisions
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[[File:NaCl-diel-ion.png|500px]] | [[File:NaCl-diel-ion.png|500px]] | ||
The high frequency 'ion-clamped' dielectric constant (<math>\varepsilon_{\infty}</math>) was obtained with the LOPTICS calculation. The static field (<math>\omega=0</math>) contribution of the ionic lattice to the dielectric constant ( <math>\varepsilon_{\rm ion}</math>) can be calculated by DFPT or by the finite-difference method. In both cases the phonon frequencies and the Born effective charges are calculated: | Note that the units on the frequency axes are different, eV and 2<math>\pi</math>THz. The high frequency 'ion-clamped' dielectric constant (<math>\varepsilon_{\infty}</math>) was obtained with the LOPTICS calculation. The static field (<math>\omega=0</math>) contribution of the ionic lattice to the dielectric constant ( <math>\varepsilon_{\rm ion}</math>) 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) | BORN EFFECTIVE CHARGES (including local field effects) (in e, cummulative output) | ||
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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 |
Revision as of 10:50, 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:
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \varepsilon (\omega )=\varepsilon _{{{\rm {elec}}}}(\omega )+\varepsilon _{{{\rm {ion}}}}(\omega )
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
(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.
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 2Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \pi THz. The high frequency 'ion-clamped' dielectric constant (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \varepsilon _{{\infty }} ) was obtained with the LOPTICS calculation. The static field (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \omega =0 ) contribution of the ionic lattice to the dielectric constant ( Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \varepsilon _{{{\rm {ion}}}} ) 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: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \varepsilon _{{0}}=\varepsilon _{{\infty }}+\varepsilon _{{{\rm {ion}}}}
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
References