Theory- Bader Analysis -> FCC Electron poor materials research group Group meeting Nov 11, 2010 Theory- Bader Analysis -> FCC This is version 2 with larger NG(X,Y,Z)F values for more accurate charge density grids

Pre-Procedure Very accurate Equation of state (EOS) calculations are preformed to find the optimum relaxed volume of the structure. This EOS is fitted to a Birch-Murnaghan equation. 11X11X11 kpoint gamma grid PREC=ACCURATE ENCUT=1.3*(ENMAX in POTCAR) Psuedo-potential is PAW_PBE A final very accurate final relaxation if preformed to bring the structures to their final relaxation volume given by EOS see next slide for INCAR for relaxation

INCAR for final relaxation System = Si relaxsetup.sh NSW = 20 | number of ionic steps ISIF = 4 | (ISIF=2 Relax ions only, ISIF=3 Relax everything) IBRION = 1 | ionic relaxation algorithm EDIFF = 1E-9 | break condition for elec. SCF loop EDIFFG = -1E-8 | break condition for ionic relaxation loop MAXMIX = 80 | keep dielectric function between ionic movements NELMIN = 8 | minimum number of electronic steps NFREE = 20 | number of degrees of freedom (don't go above 20) #RECOMMENDED MINIMUM SETUP #GGA= #xchange-correlation #VOSKOWN= #=1 if GGA=91; else = 0 PREC = ACCURATE #PRECISION, sets fft grid ENCUT = 320 #energy cutoff, determines number of lattice vectors LREAL = .FALSE. #.FALSE. MEANS USE RECIPROCAL LATTICE ISMEAR = 0 #determines how partial occupancies a set.

Procedure Static Calculations of the 4 FCC structures were computed from accurate relaxation (see previous slides) Calculations were done on a Gamma 11X11X11 grid USED NG(X,Y,Z)F of 6XNG(X,Y,Z) for accurate charge density grid. An extra flag was used in the INCAR file: LAECHG = .TRUE. Turns on All Electron CHGCAR file outputs and outputs 3 files AECCAR0: core charge density AECCAR1: atomic AE charge density (overlapping atomic charge density) AECCAR2: AE charge density The files AECCAR0 and AECCAR2 are added together for bader analysis per instructions: http://theory.cm.utexas.edu/bader/vasp.php chgsum.sh AECCAR0 AECCAR2, chsum is a shellscript Outputs CHGCAR_sum Bader analysis is done on the vasp CHGCAR from the static run bader.x -p atom_index -p bader_index CHGCAR -ref CHGCAR_sum atom_index: Write the atomic volume index to a charge density file bader_index: Write the Bader volume index to a charge density file

NOTES Only the PAW potentials can output there core charges for bader analysis A fine fft grid is needed to accurately reproduce the correct total core charge. It is essential to do a few calculations, increasing NG(X,Y,Z)F until the total charge is correct. The outputs from bader.x are: ACF.dat – Atomic Coordinate file. Shows the location and charge of the atoms BCF.dat – Bader Coordinate file. AVF.dat – Atomic Volume file. Used to keep track of other files that may be output with the bader program with flag –p all_atom AtIndex.dat (only with –p atom_index) – charge density file which contains the atomic borders BvIndex.dat (only with –p bader_index) –charge density file which contains the bader borders

INCAR_static System = Si SIGMA = 0.01 #RECOMMENDED MINIMUM SETUP PREC = ACCURATE #PRECISION ENCUT = 320 LREAL = .FALSE. #.FALSE. MEANS USE RECIPROCAL LATTICE ISMEAR = 0 #USE GAUSSIAN SMEARING #FOR GW CALCULATIONS #LOPTICS = .TRUE. #NBANDS = 96 #FOR BADER ANALYSIS LAECHG=.TRUE. NGXF = 120 #USE 6X NGX for bader analysis NGYF = 120 NGZF = 120 .

Electronegativity (EN) using Pauling Scale

GaAs ACF.dat : # X Y Z CHARGE MIN DIST ATOMIC VOL -------------------------------------------------------------------------------- 1 0.0000 0.0000 0.0000 2.3763 1.0539 18.1315 2 1.4409 1.4409 1.4409 5.6237 1.2766 29.7299 VACUUM CHARGE: 0.0000 VACUUM VOLUME: 0.0000 NUMBER OF ELECTRONS: 8.0000 ENAs – ENGa = 0.37 Bader charge shift = 0.6237

GaAs Bader Volume Bounding Boxes All other FCC bounding boxes look virtually identical to this one

InSb ACF.dat : # X Y Z CHARGE MIN DIST ATOMIC VOL -------------------------------------------------------------------------------- 1 0.0000 0.0000 0.0000 2.6001 1.2796 29.8830 2 1.6622 1.6622 1.6622 5.3999 1.4473 43.5992 VACUUM CHARGE: 0.0000 VACUUM VOLUME: 0.0000 NUMBER OF ELECTRONS: 8.0000 ENSb – ENIn = 0.27 Bader charge shift = 0.3999

GaSb ACF.dat : # X Y Z CHARGE MIN DIST ATOMIC VOL -------------------------------------------------------------------------------- 1 0.0000 0.0000 0.0000 2.7022 1.1483 22.2941 2 1.5563 1.5563 1.5563 5.2978 1.4227 38.0197 VACUUM CHARGE: 0.0000 VACUUM VOLUME: 0.0000 NUMBER OF ELECTRONS: 8.0000 ENSb – ENGa = 0.24 Bader charge shift = 0.2978

ZnSe ACF.dat : # X Y Z CHARGE MIN DIST ATOMIC VOL -------------------------------------------------------------------------------- 1 0.0000 0.0000 0.0000 11.2714 1.0616 15.9986 2 1.4358 1.4358 1.4358 6.7286 1.3224 31.3555 VACUUM CHARGE: 0.0000 VACUUM VOLUME: 0.0000 NUMBER OF ELECTRONS: 18.0000 ENSe – ENZn = 0.9 Bader charge shift = 0.7286

ZnTe ACF.dat : # X Y Z CHARGE MIN DIST ATOMIC VOL -------------------------------------------------------------------------------- 1 0.0000 0.0000 0.0000 11.4898 1.1104 18.5303 2 1.5464 1.5464 1.5464 6.5102 1.4456 40.6387 VACUUM CHARGE: 0.0000 VACUUM VOLUME: 0.0000 NUMBER OF ELECTRONS: 18.0000 ENTe – ENZn = 0.45 Bader charge shift = 0.5102

Si - For Comparison ACF.dat : # X Y Z CHARGE MIN DIST ATOMIC VOL -------------------------------------------------------------------------------- 1 0.0000 0.0000 0.0000 3.9681 1.1316 20.2891 2 1.3672 1.3672 1.3672 4.0319 1.1051 20.6007 VACUUM CHARGE: 0.0000 VACUUM VOLUME: 0.0000 NUMBER OF ELECTRONS: 8.0000 ENTe – ENZn = 0.0 Bader charge shift = 0.0319

FCC Comparisons Compound Name EN1-EN2 Bader Si 0.0319 GaSb 0.24 0.2978 0.0319 GaSb 0.24 0.2978 InSb 0.27 0.3999 ZnTe 0.45 0.5102 GaAs 0.37 0.6237 ZnSe 0.9 0.7286