Introduction to surface calculations

黃聖峰 中正大學物理系2003 年 3 月 22 日

POTCARKPOINTSPOSCARINCAR

Required input files for VASP

pseudopotentail fileBrillouin zone samplingstructural datasteering parameters

Choosing POTCAR file

LDAGGAPAW_LDAPAW_GGAPAW_PBE(VASP4.5)

Check following line in POTCAR LEXCH= CA or 91 GGA= LPAW= T

PAW Ni_pv 16.0000000000000000 parameters from PSCTR are: VRHFIN =Ni: LEXCH = 91 EATOM = 3503.4980 eV, 257.4998 Ry

TITEL = PAW Ni_pv LULTRA = F use ultrasoft PP ? IUNSCR = 1 unscreen: 0-lin 1-nonlin 2-no RPACOR = 1.500 partial core radius POMASS = 58.690; ZVAL = 16.000 mass and valenz RCORE = 2.000 outmost cutoff radius RWIGS = 2.000; RWIGS = 1.058 wigner-seitz radius (au A) ENMAX = 367.921; ENMIN = 275.941 eV RCLOC = 1.301 cutoff for local pot LCOR = T correct aug charges LPAW = T paw PP EAUG = 703.443 DEXC = .000 RMAX = 2.404 core radius for proj-oper RAUG = 1.300 factor for augmentation sphere RDEP = 2.103 core radius for depl-charge QCUT = -5.200; QGAM = 10.400 optimization parameters

GGA tag in INCAR: (default is determined by POTCAR) PB Perdew-Becke PW Perdew-Wang 86 LM Langreth-Mehl-Hu 91 Perdew-Wang 91 PE Perdew-Burke-Ernzerhof (PBE) RP revised PBE

If doing spin polarized PW91 calculations :ISPIN = 2MAGMON = (initial magnetic moment for each atom)GGA = 91VOSKOWN = 1S.H. Vosko, L. Wilk and M. Nusair, Can. J. Phys. 58, 1200(1980)

“typical” values (never trust them!) Metals (9x9x9)/atom Semiconductors (4x4x4)/atom

k-points for bulk 0Monkhorst11 11 11 0 0 0

commentautomatic generation (= 0)Monkhorst or Gammapoint (centered)mesh parametershift

Setting KPOINTS file

For molecules or atoms (large supercells) use 1 x 1 x 1 (Γ)

For surfaces (one long direction) use 2-D Brillouin-zone, nk1 x nk2 x 1

IALGO = 38(blocked Davidson algorithm)IALGO = 48(RMM-DIIS)IALGO = 38 for 5 initial steps than 48 after ions are moved: 38 for 1st step than 48

ALGO-tag determine how the wavefunctions are optimized

◎VASP4.5 does not support IALGO = 8 (preconditioned conjugated gradient) for copyright reasons◎RMM-DIIS is 1.5 to 2 times faster, but Davidson is more stable.◎Eigenstates can be missed using RMM-DIIS for large system.◎If the Davidson algorithm is used for the first steps, there is praticallynodanger of missing eigenstates.

NormalVery_FastFast

Searching the optimal lattice parameter

(1) Automatic batch jobINCAR: ISTART = 0 ICHARG = 2

initial charge-density from ovelapping atoms

#! /bin/bashfor a in 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4docat >POSCAR <<!bcc Fe $a -0.5 0.5 0.5 0.5 -0.5 0.5 0.5 0.5 -0.5 1direct 0.0 0.0 0.0!vaspE=`tail -1 OSZICAR`echo $a $E >> SUMMARYdone

Sample unix bash script for volume scan

2.3 1 F= -.33734901E+01 E0= -.33734901E+01 d E =0.000000E+00 mag =0.111346E+002.4 1 F= -.54258528E+01 E0= -.54258528E+01 d E =0.000000E+00 mag =0.713446E+002.5 1 F= -.67487749E+01 E0= -.67487749E+01 d E =0.000000E+00 mag =0.136680E+012.6 1 F= -.75334410E+01 E0= -.75334410E+01 d E =0.000000E+00 mag =0.169207E+012.7 1 F= -.79469252E+01 E0= -.79469252E+01 d E =0.000000E+00 mag =0.193771E+012.8 1 F= -.81030668E+01 E0= -.81030668E+01 d E =0.000000E+00 mag =0.211534E+012.9 1 F= -.80790747E+01 E0= -.80790747E+01 d E =0.000000E+00 mag =0.226119E+013.0 1 F= -.79505898E+01 E0= -.79505898E+01 d E =0.000000E+00 mag =0.253218E+013.1 1 F= -.77562691E+01 E0= -.77562691E+01 d E =0.000000E+00 mag =0.264343E+013.2 1 F= -.75101095E+01 E0= -.75101095E+01 d E =0.000000E+00 mag =0.274595E+013.3 1 F= -.72343924E+01 E0= -.72343924E+01 d E =0.000000E+00 mag =0.283323E+013.4 1 F= -.69416562E+01 E0= -.69416562E+01 d E =0.000000E+00 mag =0.290679E+01

Result of volume scan

(2) Relaxing the structureINCAR: ISIF = 3 IBRION = 2 NSW = 40 PREC = high (VASP4.4) ENMAX = 1.3*default value in POTCAR EDIFF = 10E-5 (smaller than default value)

Ex. diamond Si from volume scan a = 5.488 Å from structure relaxation a = 5.465 Å (difference is due to the Pulay stress)

BCC Fe from volume scan a = 2.849 Å from structure relaxation a = 2.827 Å from FLAPW (WIEN97, volume scan) a = 2.832 Å

Building surfaces(1)asymmetric setup (2)symmetric setup

Fixed layers(bulk)

coordinatesare optimized

unit cell

vacuum

FCC (100) fcc – (100) surface – 5 layers3.55 .500000 .500000 .000000-.500000 .500000 .000000 .000000 .000000 5.000000Selective DynamicsCartesian .00000 .00000 .00000 F F F .00000 .50000 .50000 F F F .00000 .00000 1.00000 F F F .00000 .50000 1.50000 T T T .00000 .00000 2.00000 T T TorDirect .00000 .00000 .00000 F F F .50000 .50000 .16667 F F F .00000 .00000 .33333 F F F .50000 .50000 .50000 T T T .00000 .00000 .66667 T T T

FCC (111) fcc – (111) surface – 5 layers3.55 .707106 .000000 .000000-.353553 .612372 .000000 .000000 .000000 5.1961524Selective DynamicsCartesian .00000 .00000 .00000 F F F .00000 .40825 .57735 F F F .00000 .20412 1.15470 F F F .00000 .00000 1.73205 T T T .00000 .40825 2.30940 T T TorDirect .00000 .00000 .00000 F F F .33333 .66667 .11111 F F F .66667 .33333 .22222 F F F .00000 .00000 .33333 T T T .33333 .66667 .44444 T T T

Ex. FCC (111) c(2x4)

Ex. BCC (100) p(2x2)

Adsorbing atoms / molecules Surface reconstruction

Surface energy

)(21

bulkatomsurf ENE

Geometry

getting relaxed structure from CONTCAR

Relaxation of surface layers : %100

idea

ideai

d

dd

Heat of formation of overlayers of A on substrate B

2

)2( )()()(2)()(

AbulkBslabAnBslabAn

nEEEH

(Should use the same energy cutoff for each calculation)

WIEN97F (ev) E (ev) F (ev) E (ev) E(Ry)

w-bulk -12.86 -12.85 -12.77 -12.77 -32332.27w5-100 -59.18 -59.13 -58.95 -58.89 -161660.99w5-110 -60.66 -60.62 -60.66 -60.62 -161661.17w7-111 -81.96 -81.89 -81.66 -81.59 -226325.32

WIEN97surf-F (ev) surf-E (ev) surf-F (ev) surf-E (ev) surf-E (ev)

w5-100 2.56 2.57 2.46 2.48 2.54w5-110 1.82 1.83 1.61 1.62 1.34w7-111 4.03 4.04 3.88 3.90 3.98

relax(%) WIEN97w5-100 -10.92

1.67w5-110 -2.63

1.39w7-111 -13.13

-14.676.55

VASP-PP VASP-PAW

VASP-PP VASP-PAW

VASP-PP VASP-PAW

-11.062.14 1.87

-10.42

6.74-15.496.68

-2.401.20-13.18

-16.02

-2.121.17-15.01

MethodHeat of

Formation (ev)

Co/7W(111) 1.23 -0.03 -0.50 -37.9 -11.1 5.4 0.32Co/7W(111) 1.68 1.04 0.01 0.01 -8.0 -47.9 13.7 -3.5 2.93Co/7W(111) 1.66 1.86 1.49 -0.01 0.57 -29.5 -12.4 -14.7 -7.4 -0.2 0.1

Co/7W(111) 1.13 -0.04 -0.57 -39.7 -12.3 5.7 0.3Co/11W(111) 0.68 0.03 -0.51 -42.1 -11.3 3.7 -6.0 6.7 0.02Co/7W(111) 1.70 1.09 -0.01 0.00 -12.8 -48.6 15.8 -2.3 2.0

2Co/11W(111) 1.70 0.93 -0.02 0.07 -12.3 -50.0 17.0 -3.5 -3.6 3.9 0.03Co/7W(111) 1.66 1.87 1.64 -0.01 0.45 -31.1 -19.4 -3.7 -7.4 0.6 2.1

3Co/11W(111) 1.62 1.83 1.58 0.03 0.54 -32.2 -18.4 -4.9 -6.8 -0.1 1.8 -0.7 0.0

Co/7W(111) 0.86 -0.02 -0.49 -42.8 -11.2 6.6 -0.5Co/11W(111) 0.01 0.00 -0.46 -44.0 -10.5 3.7 -5.6 4.8 1.92Co/7W(111) 1.55 0.84 0.00 0.06 -9.5 -55.3 18.4 -2.0 2.1

2Co/11W(111) 1.56 0.63 0.00 0.15 -9.8 -54.2 18.3 -3.3 -4.5 6.0 -1.23Co/7W(111) 1.58 1.75 1.39 0.03 0.59 -26.1 -15.1 -12.8 -4.3 -0.3 2.6

3Co/11W(111) 1.54 1.69 1.18 0.01 0.62 -25.8 -11.9 -17.7 -2.4 0.2 1.5 1.1 -0.8

k-points: d=

Moment Relaxation (percentage of d)

WIEN97-FLAPW

VASP-PP

0.915(A) for VASP-PP0.919(A) for VASP-PAW

VASP-PAW

12x12x1 0.919(A) for WIEN97

Method Heat of Formation(eV)

Co/5W(110) 1.40 -0.03 -0.10 -15.2 -2.2 1.9

2Co/5W(110) 2.00 1.69 0.02 0.28 -25.2 -8.0 2.0 2.8

Co/5W(110) 1.27 -0.02 -0.19 -18.9 1.2 0.6

Co/7W(110) 1.25 -0.02 -0.19 -19.0 1.1 0.8 0.8

2Co/5W(110) 1.90 1.42 -0.02 0.16 -28.4 -12.4 0.7 1.1

2Co/7W(110) 2.00 1.41 -0.02 0.16 -28.4 -12.4 0.8 1.2 1.0

Co/5W(110) 0.70 -0.03 -0.17 -21.4 1.5 0.7

Co/7W(110) 0.76 -0.02 -0.16 -21.3 1.2 0.8 0.6

2Co/5W(110) 1.92 1.30 -0.02 0.23 -30.3 -14.0 0.4 0.9

2Co/7W(110) 1.92 1.33 -0.02 0.23 -30.1 -13.2 0.8 1.6 1.4

k-points: d=

2.252(A) for VASP-PAW

WIEN97-FLAPW

VASP-PP

VASP-PAW

12x12x1 for VASP 2.250(A) for WIEN97

Moment Relaxation (percentage of d )

16x16x1 for WIEN97 2.242(A) for VASP-PP

Local Density of states

INCAR: RWIGS = γ Å (works only for NPAR = 1 or serial version) LORBIT = 11 (only for PAW) ISMEAR = -5 (use tetrahedron for DOS calculations) NPAR = 1Output file : DOSCAR (energy, s-dos, p-dos, d-dos for each atom) PROCAR (dos for each band and k-point)

LORBIT-tag

Band structure (after selfconsistent run)

1. Setup a k-point list along specific axis in KPOINTS2. Set ICHARG = 11, read charg density from CHGCAR3. Set FFT grid parameter manually to same value, to make sure that CHGCAR file is read properly (NGX, NGY, NGZ, NGXF, NGYF, NGZF)4. Analyze and plot data in EIGENVAL after job done

k-points for band structure 161C .00000 .00000 .00000 1.00000 .02500 .00000 .00000 1.00000 .05000 .00000 .00000 1.00000…

Ex. KPOINTS file for band structure

Si-bulk Band Structure

WIEN2k VASP

using 2-D Brillouin-zone for surfacesto get projected bandstructure

k-points for surface band structure 13R .00000 .00000 .00000 1.00000 .12500 .00000 .00000 1.00000 .25000 .00000 .00000 1.00000 .37500 .00000 .00000 1.00000 .50000 .00000 .00000 1.00000 .50000 .12500 .00000 1.00000 .50000 .25000 .00000 1.00000 .50000 .37500 .00000 1.00000 .50000 .50000 .00000 1.00000 .37500 .37500 .00000 1.00000 .25000 .25000 .00000 1.00000 .12500 .12500 .00000 1.00000 .00000 .00000 .00000 1.00000

Ex. K-points along line Γ-X-M-Γ

Work function

1. Search “E-fermi” in OUTCAR to get fermi-level2. Analyze and plot data in LOCPOT

INCAR: LVTOT = .TRUE.

Output file : LOCPOT (same format as CHGCAR) WRITE(IU,FORM) (((V(NX,NY,NZ),NX=1,NGX),NY=1,NGY),NZ=1,NGZ)

LOCPOT only contain electrostatic part of potential,if exchange correlation potential is to be included,change one line in main.F :

! comment out the following line to add exchange correlation! INFO%LEXCHG=-1

Cou

lomb

poten

tial (eV) C

oulom

b p

otential (eV

)C

oulom

b p

otential (eV

)

Cou

lomb

poten

tial (eV)

W(100) W(110)

W(111) W(211)

Fermi energy

Z-axis(Å) Z-axis(Å)

Z-axis(Å) Z-axis(Å)

Φ

Surface adsorption

Ni – (111)3.53 .707106 .000000 .000000-.353553 .612372 .000000 .000000 .000000 5.19615245 1 1Selective DynamicsDirect .00000 .00000 .00000 F F F .33333 .66667 .11111 F F F .66667 .33333 .22222 F F F .00000 .00000 .33333 T T T .33333 .66667 .44444 T T T .33333 .66667 .54029 T T T .33333 .66667 .60299 T T T

Ex. CO/Ni(111)

POSCAR: INCAR:EXMAX = 400ISMEAR = -5LORBIT = 1

NPAR = 1RWIGS = 1.40 1.29 1.11

LVTOT = .TRUE.IDIPOL = 3LDIPOL = .TRUE.(dipol corrections)

COcleantotalads EEEE

Adsorption energy

(use the same energy cutoff)

Dipol correction

cleanE = -25.730 eV (270eV)= -25.741 eV (400eV)

COcleantotalads EEEE = -40.830 + 25.741 + 14.833= -0.256 eV

Result of CO/Ni(111)

F

CO clean

= 1.66 eV

Vacuum-potential at 8.15 / 6.76 eV

= 6.49 eV = 5.10 eV

But in Ni(111) calculation

clean = 5.24 eV

due to too small vacuum in CO/Ni(111)

Other new feature and advantages

VASP4.5

◎non-collinear magnetic structure and spin orbital coupling◎PREC=Low/Medium/Normal/Accurate/High◎single precision WAVCAR (smaller)◎new MPI communication layer and FFT routines

VASP4.6

◎support L(S)DA+U calculations◎report orbital moment◎new output file “vasprun.xml” used in new vasp utility “p4v” (python for vasp)