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# Vibrational frequencies of CO on Ni 111 surface

## Contents

Calculation of the vibrational frequencies of CO@Ni(111) (on top).

## Input

### POSCAR

Ni - (111) + CO on-top
3.53000000000000
0.7071067800000000    0.0000000000000000    0.0000000000000000
-0.3535533900000000    0.6123724000000000    0.0000000000000000
0.0000000000000000    0.0000000000000000    5.1961523999999999
Ni   C    O
5     1     1
Selective dynamics
Direct
0.0000000000000000  0.0000000000000000  0.0000000000000000   F   F   F
0.3333333300000021  0.6666666699999979  0.1111111100000031   F   F   F
0.6666666699999979  0.3333333300000021  0.2222222199999990   F   F   F
-0.0000000000000000  0.0000000000000000  0.3326227833039623   F   F   F
0.3333333300000021  0.6666666699999979  0.4445699380869117   F   F   F
0.3333333300000021  0.6666666699999979  0.5403264650180125   F   F   T
0.3333333300000021  0.6666666699999979  0.6032949698060487   F   F   T

0.00000000E+00  0.00000000E+00  0.00000000E+00
0.00000000E+00  0.00000000E+00  0.00000000E+00
0.00000000E+00  0.00000000E+00  0.00000000E+00
0.00000000E+00  0.00000000E+00  0.00000000E+00
0.00000000E+00  0.00000000E+00  0.00000000E+00
0.00000000E+00  0.00000000E+00  0.00000000E+00
0.00000000E+00  0.00000000E+00  0.00000000E+00

• Frequencies only for the CO molecule and the z-direction (z- and (x,y) are independent).

N.B.: this POSCAR is essentially the result (CONTCAR file) of the relaxation performed in the CO on Ni 111 surface example.

### INCAR

 SYSTEM = CO on Ni111 - frequencies

general:
ENMAX  = 400
ISMEAR =    2  ; SIGMA = 0.2
ALGO   = Fast
EDIFF  = 1E-6
MAXMIX = 60  # reuse the mixer between ionic steps, saves time

dynamic:
NSW = 100
IBRION = 5
NFREE  = 2

• Small termination criterion (EDIFF).
• Automatic frequency calculation (displacement 0.04 ${\displaystyle \AA }$).
• Reuse of the mixer between ionic steps (MAXMIX) to save time.

### KPOINTS

k-points
0
Monkhorst-Pack
9 9 1
0 0 0


## Calculation

• Finite differences give the following additional output in the OUTCAR fiel for frequency calculations:
Finite differences progress:
Degree of freedom:   1/  2
Displacement:        1/  2
Total:               1/  4

• After the first calculation for the equilibrium geometry, NFREE displacements (${\displaystyle \pm }$POTIM) are performed for each degree of freedom. From these displacements the dynamical matrix is set up and diagonalized.
• At the end of the OUTCAR file the following are listed:
• Forces.
• The dynamical matrix and finally.
• The eigenfrequencies.
• Eigenvectors (first normalized and then mass-weighted).
• The example output for the eigenvectors and eigenvalues of the dynamical matrix from the OUTCAR file should look like the following:
Eigenvectors and eigenvalues of the dynamical matrix
----------------------------------------------------
1 f  =   63.914144 THz   401.584411 2PiTHz 2131.946301 cm-1   264.327748 meV
X         Y         Z           dx          dy          dz
0.000000  0.000000  0.000000            0           0           0
0.000000  1.441116  2.038046            0           0           0
1.248043  0.720558  4.076093            0           0           0
0.000000  0.000000  6.108743            0           0           0
0.000000  1.441116  8.153979            0           0           0
0.000000  1.441116  9.908620            0           0   -0.761748
0.000000  1.441116 11.063296            0           0    0.623594

2 f  =   12.467410 THz    78.335050 2PiTHz  415.868035 cm-1    51.561083 meV
X         Y         Z           dx          dy          dz
0.000000  0.000000  0.000000            0           0           0
0.000000  1.441116  2.038046            0           0           0
1.248043  0.720558  4.076093            0           0           0
0.000000  0.000000  6.108743            0           0           0
0.000000  1.441116  8.153979            0           0           0
0.000000  1.441116  9.908620            0           0   -0.623594
0.000000  1.441116 11.063296            0           0   -0.781748


As one can see the first vibrational mode is the so-called CO stretch mode (stretching and contracting the C-O bond), whereas the second mode shows the CO molecule moving w.r.t. to the metallic surface (CO-metal).

• Try to change the selective dynamics tag such that displacements

in x and y direction are allowed as well for CO (note that the selective dynamics flags always refer to cartesian coordinates), i.e,

 0.3333333300000021  0.6666666699999979  0.5403264650180125   F   F   T
0.3333333300000021  0.6666666699999979  0.6032949698060487   F   F   T


to

 0.3333333300000021  0.6666666699999979  0.5403264650180125   T   T   T
0.3333333300000021  0.6666666699999979  0.6032949698060487   T   T   T


Also test whether you need to decrease EDIFF to 1E-8.