Finite Differences

The simplest way to calculate the vibrational spectrum is by finite differences via the keyword VIBRATIONAL ANALYSISVIBRATIONAL ANALYSIS. This type of calculation supports that largest variety of system setups. The corresponding &CPMDcpmdsec:CPMD section can look like this.

&CPMD
  VIBRATIONAL ANALYSIS FD GAUSS
  RESTART WAVEFUNCTION COORDINATES
  CONVERGENCE ORBITALS
    1.0e-7
&END

The flag GAUSS tells CPMD to produce a fake Gaussian type output file, VIB1.log, which can be used for visualization with programs like Molded, Molekel, or gOpenMol.

After the initial wavefunction optimization (which will take only one step since we start here from an already optimization wavefunction), every atom is displaced in positive and negative x-, y-, and z-direction by a small distance and the gradient computed.

 ********************** FINITE DIFFERENCES **********************

 **** ATOM=      1       O       X    DISPLACEMENT=  -1.00000E-02
           1     1.809E-03     -17.195809     0.000E+00      2.67
           2     1.689E-03     -17.198540    -2.731E-03      5.36
           3     3.134E-04     -17.198788    -2.474E-04      8.01
           4     4.404E-04     -17.198866    -7.845E-05     10.77
           5     1.731E-04     -17.198882    -1.614E-05     13.36
           6     7.991E-05     -17.198885    -2.977E-06     16.08
           7     2.503E-05     -17.198886    -4.262E-07     18.79
           8     1.825E-05     -17.198886    -1.032E-07     21.35
           9     8.614E-06     -17.198886    -2.675E-08     23.92
          10     3.341E-06     -17.198886    -7.541E-09     26.53
          11     1.542E-06     -17.198886    -2.013E-09     29.22
          12     1.282E-06     -17.198886    -7.660E-10     31.89
          13     6.752E-07     -17.198886    -2.762E-10     34.58
          14     3.561E-07     -17.198886    -4.047E-11     37.28
          15     1.321E-07     -17.198886    -8.328E-12     40.01
          16     6.347E-08     -17.198886    -1.169E-12     42.73
 ITER=    16         ENERGY=                       -17.1988859572
 TCPU=    45.46      GRADIENT=                          2.867E-03
[...]

At the end the resulting dynamical matrix is diagonalized and the resulting vibrational spectrum in harmonic approximation is computed. Unless a very tight geometry optimization was performed, a few very low frequency modes will appear. Since in our case we didn't optimize, these frequencies are fairly large, and there are several imaginary (=negative) frequencies as indication of the geometry not being fully optimized. For higher accuracy of the results a

 ****************************************************************
 HARMONIC FREQUENCIES [cm**-1]:

       -209.8467       -102.0840        -58.0525        -37.5732
         42.6296        214.9993       1581.2523       3712.7275
       3821.3442

 PURIFICATION OF DYNAMICAL MATRIX

 ****************************************************************
 HARMONIC FREQUENCIES [cm**-1]:

         -0.0001         -0.0001          0.0000          0.0000
          0.0000          0.0001       1621.5287       3721.6537
       3814.9509

In the second output the code enforces translational and rotational invariance of in the dynamical matrix.