VASP Tutorial: Dielectric properties and the Random-Phase ...

1 VASP Tutorial: Dielectric properties and theRandom-Phase-Approximation (RPA)University of Vienna,Faculty of Physics and Center for Computational Materials Science,Vienna, AustriaSetting up a VASP calculationVASP requires 4 input files to run a calculation: INCAR POSCAR KPOINTS POTCARI: The INCAR fileThe INCAR file contains the input parameters that steer the calculation: The default values set by VASP itself are a clever choice for moststandard calculations These standard settings may be modified to specify: What kind of calculation you want to do:SCF calculation, DOS, Dielectric properties , .. Basic inputs concering the required precision, the requestedlevel of convergence.

2 For a list of all INCAR-tags have a look at: The VASP manual: : The VASP wiki: : :INCARII: The POSCAR filefcc: NiHeader(comment) scaling (s)of atomic type(s)1 Number of atoms(of each type)Selective Dynamics(optional: selective dynamics)CartesianCartesian or Direct coordinates00 0 (T T T)positions of theatomsIn the POSCAR file you specify the structure (Bravaislattice and basis):III: The KPOINTS fileAutomaticmeshHeader(comment)0Nk=0:au tomatic mesh generationG (M) -centered(G) mesh or Monkhorst-Pack (M) grid4 4 4#of subdivisions along 0. shiftthe mesh ( )In the KPOINTS file you specify the points VASP will use to sample thefirst Brillouin zone in reciprocal spaceIV: The POTCAR fileThe POTCAR file has to contain the PAW datasets for all atomic types you havespecified in your POSCAR file:VASP comes with a library of PAW datasets, (one or more) for most elements of the periodic table: Each individual PAW data set starts with a descriptive section, specifying amongst other things: Parameters that were required to generate the dataset.

3 Number of valence electrons Atomic mass Default energy cutoffs When your unit cell contains more than one type of atom you have to concatenate the corresponding PAW datasets in the same order as you havespecified the different atomic types in your POSCAR file. You should not mix PAW datasets generated with different exchange-correlation filesOUTCAR detailed output of a VASP run, including: a summary of the input parameters information about the individual electronic steps:total energy, Kohn-Sham eigenvalues, Fermi-energy. stress tensors forces in the atoms local charges, magnetic moments Dielectric properties .. and a great many things more.

4 The amount of output written onto OUTCAR can be chosen by meansof the NWRITE-tag in the INCAR & stdout give a short summary of the self-consistency-cycle chosen SCF algorithm convergence of energy and charge density free energies, total magnetic moment of the cellOUTPUT filesCONTCAR& XDATCAR CONTCAR: updated geometry data at the end of a run lattice parameter Bravaismatrix ionic positions velocities the format of the CONTCAR is the same as for POSCAR:It can be directly be used for a continuation run (copy CONTCAR to POSCAR) XDATCAR: updated ionic positions of each ionic stepDOSCAR, CHGCAR & WAVECAR DOSCAR: total DOS andintegrated DOS, (local partial DOS) CHGCAR: the charge density WAVECAR: plane wavecoefficients of the be used to restart from a previous runDocumentation The VASP manual ( )Index: The VASP wiki ( )INCAR-tags: :INCART opicsFrequencydependentdielectricpropert iesRPA quasi-particlegaps(GW)GW bandstructureRPA totalenergies(ACFDT)TheBethe-SalpeterEqu ation(BSE): excitoniceffectsBSE: increasek-point samplingFrequency dependent Dielectric properties (ex.)

5 : SiC_dielectric)Goal: calculate the frequency dependent Dielectric function of SiCat two levelsof aproximation: Independent-Particle-Approximation (IPA) Random-Phase -Approximation (RPA)Minimal variety:cd dependent Dielectric properties (ex.: SiC_dielectric) Step 1: a standard DFT (PBE) groundstatecalculationsystem 6 60 0 0 ISMEAR= 0 SIGMA = smearingSet small smearingwidthEDIFF = tight convergencecriteriumINCAR:KPOINTS:POSCAR :Frequency dependent Dielectric properties (ex.: SiC_dielectric) Step 2: the Independent-Particle-Approximation (IPA), using LOPTICS=. = ExactExact diagonalisationof HamiltonianNBANDS = 64 Keep 64 bands after diagonalisationLOPTICS =.

6 = = 2000 Computefrequency dependent Dielectric function in the IPA, using a sum over unoccupied states (perturbation theory)Complex shift usedin Kramers-KronigtransformationNumber of bins in the DOS histogramISMEAR= 0 SIGMA = smearingSet small smearingwidthEDIFF = tight convergencecriteriumINCAR:In the OUTCAR (or ) file, you ll find the frequency dependentdielectric function, look : This calculation needs the orbitals (WAVECAR file) of Step dependent IMAGINARY Dielectric FUNCTION (independent particle, no local field effects)E(ev) X Y Z XY YZ ZX-------------------------------------- ---------------------------------------- --------frequency dependent REAL Dielectric FUNCTION (independent particle, no local field effects)E(ev) X Y Z XY YZ ZX-------------------------------------- ---------------------------------------- --------andFrequency dependent Dielectric properties (ex.)

7 : SiC_dielectric) Step 3: the Random-Phase -Approximation (RPA), using ALGO=CHIALGO = CHIC ompute Dielectric functionincluding local fieldeffects in the RPANBANDS = 64 Use the same#-of-bands as in Step 2. (LOPTICS=.TRUE.)otherwise the WAVEDER file is not read correctlyISMEAR= 0 SIGMA = smearingSet small smearingwidthEDIFF = tight convergencecriteriumLWAVE = .. writing WAVECAR and CHGCARINCAR:In the OUTCAR (or ) file, you ll find the frequency dependent dielectricfunction in the RPA, look : This calculation needs the orbitals (WAVECAR file) , and the derivative ofthe orbitals the Bloch wave vectors (WAVEDER file) written in Step MACROSCOPIC Dielectric TENSOR (including local field effects in RPA (Hartree))------------------------------ -------HEAD OF MICROSCOPIC Dielectric TENSOR (INDEPENDENT PARTICLE)------------------------------- ------and in the IPA, after:Frequency dependent Dielectric properties (ex.

8 : SiC_dielectric). quasi-particle gaps (GW)(ex.: Si_GW_gap)Goal: calculate quasi-particle (QP) bandgaps in the Random-Phase -Approximation Single-shot-GW (G0W0) Optional: partial the QP-energies in the Green s function (GW0).Minimal variety:cd quasi-particle gaps (GW) (ex.: Si_GW_gap)WORKFLOW of GW calculationsThe workflow of GW calculations consists of three consecutive steps:Step 1: a standard DFT groundstatecalculationStep 2: compute additional DFT virtual orbitals (empty states): Needs the WAVECAR from Step 3: the actual GW calculation: Needs WAVECAR and WAVEDER files from Step 2. : have a look at quasi-particle gaps (GW) (ex.

9 : Si_GW_gap) Step 1: a standard DFT (PBE) groundstatecalculationsystem 6 60 0 0 ISMEAR= 0 SIGMA = smearingSet small smearingwidthEDIFF = tight convergencecriteriumINCAR:KPOINTS:POSCAR :RPA quasi-particle gaps (GW) (ex.: Si_GW_gap) Step 2: compute additional DFT virtual orbitals (empty states):ALGO = ExactExact diagonalisationof HamiltonianNBANDS = 64 Keep 64 bands after diagonalisationLOPTICS = . = of the orbitals the Bloch wave vector (stored in the WAVEDER file)Complex shift usedin Kramers-KronigtransformationISMEAR= 0 SIGMA = smearingSet small smearingwidthEDIFF = tight : In this step one needs to set LOPTICS=.

10 TRUE. to have VASP calculate thederivative of the orbitals the Bloch wave vector (stored in the WAVEDER file).These are needed to correctly describe the long-wavelength limit of the : This calculation needs the orbitals (WAVECAR file) of Step quasi-particle gaps (GW) (ex.: Si_GW_gap) Step 3: RPA quasiparticles: single-shot GW (G0W0)ALGO = GW0 LSPECTRAL= . = 50 Algorithm used for G0W0 and GW0 calculations:for G0W0 set NELM=1 (Default)for GW0 set NELM=nNumber ofpoints used in the frequency integrationNBANDS = 64 Use the same#-of-bands as in Step 2. (LOPTICS=.TRUE.) otherwise the WAVEDER file is not read correctlyISMEAR= 0 SIGMA = smearingSet small smearingwidthEDIFF = tight : This calculation needs the orbitals (WAVECAR file) , and the derivative ofthe orbitals the Bloch wave vectors (WAVEDER file) written in Step the OUTCAR (or ) file, you ll find the RPA quasi-particle energiesafter:QP shifts <psi_nk| G(iteration)W_0 |psi_nk>: iteration 1for sc-GW calculations column KS-energies equals QP-energies in previous stepand V_xc(KS)= KS-energies -(<T + V_ion+ V_H > + <T+V_H+V_ion>^1 + <V_x>^1)k-point 1 : No.