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Collective jumps of a Pt adatom on fcc-Pt (001): Nudged Elastic Band Calculation

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Description: calculate the energy barrier for the self-diffusion (of a Pt-adatom) on Pt (001): The most stable adsorption site of the adatom Pt@Pt(001) is the hollow (h) position. Simple models of the diffusion of the adatom from h to the neighboring h site include two diffusion paths: hollow-top-hollow (hth, eg along [1-10]) or hollow-bridge-hollow (hbh, eg along [100]). A collective jump mechanism involving 2 Pt atoms diffusing along [1-10] is proposed to be the diffusion mechanism with the lowest energy barrier [1]

The calculation of the barrier heights involves the following steps:

1. calculation of the bulk a0 of Pt for the chosen functional

2. a clean Pt (001) surface, with a 2D supercell of -at minimum- (2x2) reconstruction

3. the energies of the surface including the Pt-adatom in h, b, and t position

4. a Nudged Elastic Band (NEB) calculation [2] for the proposed collective jump mechanism

steps 1-3 are straightforward

inputs for a fast, preliminary estimate are given here and in Pt_NEB_fast.tgz (mind this "quick and dirty" setup is only suitable to learn about principles of the setup of a NEB calculation; the results of the NEB run with this minimal set of parameters do not reproduce the experimentally found behaviour), for a more time-consuming, but more accurate setup (larger number of Pt layers, denser k-mesh, higher PREC and ENCUT) please use the files untarred from Pt_NEB.tgz:

System: fcc Pt (001), 3layers

ISTART = 0
EDIFF = 1e-6              # electronic convergence
PREC = Normal
IBRION = 1                # DIIS algorithm
POTIM = 0.5
NSW = 20
EDIFFG = -0.01            # max forces: 0.1eV/AA
NELMIN = 5                 # at least 5 el. scf steps  for each ionic step


K-Points
 0
Gamma
 3  3  1
 0  0  0
fcc Pt, paw-PBE
5.62024
  1.0 0.0 0.0
  0.0 1.0 0.0
  0.0 0.0 3.0
  Pt
  12
Selective
Direct
0.25 0.25 0.11785       F  F  F
0.75 0.25 0.11785       F  F  F
0.25 0.75 0.11785       F  F  F
0.75 0.75 0.11785       F  F  F
0.00 0.00 0.23570       F  F  T
0.00 0.50 0.23570       F  F  T
0.50 0.00 0.23570       F  F  T
0.50 0.50 0.23570       F  F  T
0.25 0.25 0.35355       F  F  T
0.75 0.25 0.35355       F  F  T
0.25 0.75 0.35355       F  F  T
0.75 0.75 0.35355       F  F  T
 fcc Pt, paw-PBE
   5.62024000000000
     1.0000000000000000    0.0000000000000000    0.0000000000000000
     0.0000000000000000    1.0000000000000000    0.0000000000000000
     0.0000000000000000    0.0000000000000000    3.0000000000000000
   Pt 
   13
 Selective dynamics
 Direct
  0.2500000000000000  0.2500000000000000  0.1178499999999971   F   F   F
  0.7500000000000000  0.2500000000000000  0.1178499999999971   F   F   F
  0.2500000000000000  0.7500000000000000  0.1178499999999971   F   F   F
  0.7500000000000000  0.7500000000000000  0.1178499999999971   F   F   F
  0.0000000000000000  0.0000000000000000  0.2341409911878811   T   T   T
  0.0000000000000000  0.5000000000000000  0.2344158754007225   T   T   T
  0.5000000000000000  0.0000000000000000  0.2377721273226986   T   T   T
  0.5000000000000000  0.5000000000000000  0.2341409911878811   T   T   T
  0.2500000000000000  0.2500000000000000  0.3517982322412672   T   T   T
  0.7500000000000000  0.2500000000000000  0.3517982322412672   T   T   T
  0.2500000000000000  0.7500000000000000  0.3517982322412672   T   T   T
  0.7500000000000000  0.7500000000000000  0.3517982322412672   T   T   T
  0.0000000000000000  0.5000000000000000  0.4492270704381683   T   T   T
 fcc Pt, paw-PBE
   5.62024000000000
     1.0000000000000000    0.0000000000000000    0.0000000000000000
     0.0000000000000000    1.0000000000000000    0.0000000000000000
     0.0000000000000000    0.0000000000000000    3.0000000000000000
   Pt
   13
 Selective dynamics
 Direct
  0.2500000000000000  0.2500000000000000  0.1178499999999971   F   F   F
  0.7500000000000000  0.2500000000000000  0.1178499999999971   F   F   F
  0.2500000000000000  0.7500000000000000  0.1178499999999971   F   F   F
  0.7500000000000000  0.7500000000000000  0.1178499999999971   F   F   F
  0.0002686432543183  0.0000000000000000  0.2356407813553420   T   T   T
  0.0014220524373488  0.5000000000000000  0.2356795143373628   T   T   T
  0.4997313567456815  0.0000000000000000  0.2356407813553420   T   T   T
  0.4985779475626512  0.5000000000000000  0.2356795143373628   T   T   T
  0.2500000000000000  0.2341977119064422  0.3525947402192897   F   T   T
  0.7500000000000000  0.2518717446753760  0.3518647397661007   T   T   T
  0.2500000000000000  0.7658022880935580  0.3525947402192897   F   T   T
  0.7500000000000000  0.7481282553246233  0.3518647397661007   T   T   T
  0.2500000000000000  0.5000000000000000  0.4716518885541170   F   F   T
 fcc Pt, paw-PBE
   5.62024000000000
     1.0000000000000000    0.0000000000000000    0.0000000000000000
     0.0000000000000000    1.0000000000000000    0.0000000000000000
     0.0000000000000000    0.0000000000000000    3.0000000000000000
   Pt
    13
 Selective dynamics
 Direct
  0.2500000000000000  0.2500000000000000  0.1178499999999971   F   F   F
  0.7500000000000000  0.2500000000000000  0.1178499999999971   F   F   F
  0.2500000000000000  0.7500000000000000  0.1178499999999971   F   F   F
  0.7500000000000000  0.7500000000000000  0.1178499999999971   F   F   F
 -0.0014262288827347 -0.0014262288827347  0.2348121710889565   T   T   T
 -0.0014262288827347  0.5014262288827348  0.2348121710889565   T   T   T
  0.5014262288827348 -0.0014262288827347  0.2348121710889565   T   T   T
  0.5014262288827348  0.5014262288827348  0.2348121710889565   T   T   T
  0.2500000000000000  0.2500000000000000  0.3433443664932221   F   F   T
  0.7500000000000000  0.2500000000000000  0.3546231232810972   T   T   T
  0.2500000000000000  0.7500000000000000  0.3546231232810972   T   T   T
  0.7500000000000000  0.7500000000000000  0.3516055254412989   T   T   T
  0.2500000000000000  0.2500000000000000  0.4861522106341429   F   F   T

the NEB calculation should be done a follows:

1. run the job from a parent directory containing the files INCAR, POTCAR,KPOINTS and the run-script of the job

2. consider how many intermediate geometries (N) should be chosen between the initial and the final state of the jump in INCAR, this corresponds to the parameter IMAGES

3. generate sub-directories 00 (containing the POSCAR of the initial geometry i), ... 0(N+1) (containing the POSCAR of the final geometry f of the jump). The POSCAR files of the intermediate steps, to be interpolated between POSCARi and POSCARf are stored in the directories 01 .. 0N. Calculations are only done for these intermediate steps, the optimization of the geometries is done under the constraint that the relaxing atoms remain on a plane perpendicular to the hypertangent of the diffusion path. All all output files OUTCAR, CONTCAR, OSZICAR .. of the NEB-steps run are written to these subdirectories.

in the present excercise, the required precision,... is reduced to a minimum (the files are found in Pt_NEB_fast.tgz) to save computing time, a more reliable setup is saved in Pt_NEB.tgz)


System: fcc Pt (001), 3layers

ISTART = 0
EDIFF = 1e-6              # electronic convergence
PREC = Normal
IBRION = 1                # DIIS algorithm
NSW = 10
EDIFFG = -0.01            # max forces: 0.1eV/AA
NELMIN = 5                 # at least 5 el. scf steps  for each ionic step
IMAGES = 2                # 2 intermediate geometries for  the NEB
SPRING = -5               # spring constant


K-Points
 0
Gamma
 3  3  1
 0  0  0
  • POSCAR (of the initial state, in directory 00)
 fcc Pt, paw-PBE
    5.62024000000000 
     1.0000000000000000    0.0000000000000000    0.0000000000000000
     0.0000000000000000    1.0000000000000000    0.0000000000000000
     0.0000000000000000    0.0000000000000000    3.0000000000000000
   13
 Direct
   0.250000    0.250000   0.117850
   0.750000    0.250000   0.117850
   0.250000    0.750000   0.117850
   0.750000    0.750000   0.117850
   0.000000    0.000000   0.230682
   0.000000    0.500000   0.230971
   0.500000    0.000000   0.234757
   0.500000    0.500000   0.230682
   0.256381    0.243619   0.347171
   0.743619    0.243619   0.347171
   0.256381    0.756381   0.347171
   0.743619    0.756381   0.347171
   0.000000    0.500000   0.444316
  • POSCAR (of the final state, in directory 03)

 fcc Pt, paw-PBE
   5.62024000000000
     1.0000000000000000    0.0000000000000000    0.0000000000000000
     0.0000000000000000    1.0000000000000000    0.0000000000000000
     0.0000000000000000    0.0000000000000000    3.0000000000000000
   13
 Direct
   0.250000    0.250000   0.117850
   0.750000    0.250000   0.117850
   0.250000    0.750000   0.117850
   0.750000    0.750000   0.117850
   0.000000    0.000000   0.230682
   0.000000    0.500000   0.230971
   0.500000    0.000000   0.234757
   0.500000    0.500000   0.230682
   0.500000    0.000000   0.444316
   0.756381    0.256381   0.347171
   0.243619    0.743619   0.347171
   0.756381    0.743619   0.347171
   0.243619    0.256381   0.347171

4. concatenate the POSCAR files of i and f to the file POSCAR1_POSCAR2 MIND:

-- these files must not include the lines with the names of the atoms (vasp.5.2 only) and 'Selective Dynamics',

-- there must be no blank line between the POSCARS

-- the block with the velocities of the atoms must be deleted

-- be careful to check that in POSCARi and POSCARj all atoms are on the same side of the supercell to avoid that an atom that actually jumps across the origin of the cell is dragged through the cell by the interpolation of the positions.

5. interpolate the starting geometries of the IMAGES, this can be done by using the following script

interpolatePOSCAR POSCAR1_POSCAR2, the interpolated files are written into the respective subdirectories 00 ... 0(N+1)


  • interpolatePOSCAR
file=$1
if [ ! -x $file ]
then
  usage: interpolatePOS POSCAR1_POSCAR2
fi

awk <$file '
BEGIN { rep=4; center=0 }
/center/ { center=1}
/rep/ { rep=$2 }
 { line=line+1
   if ( second != 1 ) {
       if ( line == 6 )  {
          lines = $1 + $2 + $3 + 7
          print "found ",lines," ions"
          head[line] = $0
       } else if ( line < 8 )
          head[line] = $0
       else
          {
             x[line-7] = $1 ; y[line-7] = $2 ; z[line-7] = $3
             if (line==lines) {
                   line=0; second=1;
                   print "first set read"
             }
          }
    } else {
       if ( line >= 8 )
          {
              x2[line-7] = $1; y2[line-7] = $2 ; z2[line-7] = $3  }
             if (line==lines) {
                   print "second set read"
             }
    }
}
END  {
   lines=lines-7
   for ( line=1; line<=lines ; line ++ )  {
        cx1=cx1+ x[line] ; cy1=cy1+ y[line] ; cz1=cz1+ z[line]
        cx2=cx2+ x2[line]; cy2=cy2+ y2[line]; cz2=cz2+ z2[line]
   }
   if (center) {
     cx=(cx2-cx1)/lines
     cy=(cy2-cy1)/lines
     cz=(cz2-cz1)/lines
     print "center of mass for second cell will be shifted by",cx,cy,cz
   }

   for ( i=0; i<rep ; i++ ) {
       file="0" i "/POSCAR"
       print "writing to " file
       for (line=1; line<=7 ; line++ )
          print head[line]  >file
       for ( line=1; line<=lines ; line ++ )  {
          b=i/(rep-1)
          a=(rep-1-i)/(rep-1)
          dx=a*x[line] + b*(x2[line]-cx)
          dy=a*y[line] + b*(y2[line]-cy)
          dz=a*z[line] + b*(z2[line]-cz)

          printf " %10.6f  %10.6f %10.6f\n",dx,dy,dz >file
       }
   }
}'

NOTE: the total number of steps is explicitely given in line 8 of the script (rep=, rep = IMAGES+2). If a dfferent number of IMAGES is chosen, this parameter has to be changed.

alternatively the name of the input file and the number of images can be passed as options to interpolatePOSCAR: interpolatePOSCAR <fn> <IMAGES+2>

6. run vasp:

MIND: the number of CPUs to be used has to be an integer multiple of IMAGES

7. if convergence is not reached within NSW steps, the calculation can be continued by a continuation run, just like for a standard ionic relaxation.

8. HINT: better convergence is usually achieved if the number of IMAGES is rather low (up to 4). If the region close to the transition state is to be refined, one can do another NEB-calculation, using the ionic configurations of the IMAGES adjacent to the transition state as the new initial and final states for the follow-up run.

9: obtain the barrier along diffusion path 00-03 by interpolation (spline)

Downloads

Pt_NEB.tgz, Pt_NEB_fast.tgz

References

  1. G.L.Kellogg and Peter J.Feibelman, Phys. Rev. Lett. 64 (26), 3143 (1990)
  2. G. Mills, H. Jonsson and G. K. Schenter, Surface Science, 324, 305 (1995); H. Jonsson, G. Mills and K. W. Jacobsen, `Nudged Elastic Band Method for Finding Minimum Energy Paths of Transitions', in `Classical and Quantum Dynamics in Condensed Phase Simulations', ed. B. J. Berne, G. Ciccotti and D. F. Coker (World Scientific, 1998)

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