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# CO vibration

Calculation of the vibrational frequencies of a CO molecule.

## Input

### POSCAR

CO molecule in a box
1.0          ! universal scaling parameters
8.0 0.0 0.0  ! lattice vector  a(1)
0.0 8.0 0.0  ! lattice vector  a(2)
0.0 0.0 8.0  ! lattice vector  a(3)
1 1           ! number of atoms for each species
sel           ! selective degrees of freedom are changed
cart          ! positions in cartesian coordinates
0 0 0       F F T  ! first atom
0 0 1.143   F F T  ! second atom


Alternatively, try to fix one of the atoms completely.

### INCAR

SYSTEM = CO molecule in a box
ISMEAR = 0   ! Gaussian smearing
IBRION = 5   ! calculate second derivatives, Hessian matrix, and phonon frequencies
! from finite differences
NFREE = 2    ! central differences
POTIM = 0.02 ! 0.02 A stepwidth
NSW = 1      ! ionic steps > 0


### KPOINTS

Gamma-point only
0
Monkhorst Pack
1 1 1
0 0 0


## Calculation

• The selected degrees of freedom are displaced once in the direction ${\displaystyle {\hat {x}}}$ and once in ${\displaystyle -{\hat {x}}}$ by 0.02 ${\displaystyle \mathrm {\AA} }$ (POTIM).
• In the present case this makes 4 displacements plus the equilibrium positions (i.e. a total of five ionic configurations).

### OUTCAR

At the end of the OUTCAR file the following output should be obtained:

SECOND DERIVATIVES (NOT SYMMETRIZED)
------------------------------------
1Z          2Z
1Z  -114.737304  114.737304
2Z   114.458316 -114.458316

Eigenvectors and eigenvalues of the dynamical matrix
----------------------------------------------------

1 f  =   63.887522 THz   401.417139 2PiTHz 2131.058277 cm-1   264.217647 meV
X         Y         Z           dx          dy          dz
0.000000  0.000000  0.000000            0           0   -0.655280
0.000000  0.000000  1.143000            0           0    0.755386

  2 f/i=    0.038494 THz     0.241864 2PiTHz    1.284016 cm-1     0.159198 meV
X         Y         Z           dx          dy          dz
0.000000  0.000000  0.000000            0           0   -0.755386
0.000000  0.000000  1.143000            0           0   -0.655280