Consistency check of frequency calculations

Okko · 2024-09-06 21:37:23

Dear all,

the molecule Si(OH)4 molecule has been optimized at MP2/ANO-RCC-VTZP level of theory. To check whether the converged structure can be characterized as a true minimum in terms of a normal mode analysis I started calculations using the following input file:

>> export OMP_NUM_THREADS=1
>> export MOLCAS_MEM = 3000

&GATEWAY
  Title= SiOH
  Coord= $CurrDir/SiOH.Opt.xyz
  Basis set
  ANO-RCC-VTZP
>> Do   While

&SEWARD
  cholesky
End of input

&SCF
End of input

&MBPT2
End of input

&MCKINLEY
End of input

>> EndDo

The structure shows a C1 symmetry:

++    Symmetry information:
      ---------------------
 
                    Character Table for C1 
 
                             E  
                    a        1  x, y, xy, Rz, z, xz, Ry, yz, Rx, I

and normally one would expect 27 frequencies (3*N = 27 degrees of freedom where N = 6) listed after the normal mode analysis whereas one can discard the first 6 modes, i.e., three translational and three rotational coordinates from the output. This is how it's explained in the OpenMolcas manual for the 1,3-cyclopentadiene molecule. However, 21 frequencies (not the expected 27 frequencies) are obtained for the Si(OH)4 molecule and additionally, there is a warning that 5 vibrational contributions have been removed:

  *** Warning:                      5  vibrational contributions removed.

whereas the first 5 frequencies out of 21 correspond to the imaginary frequencies:

++ Principal components of the normal modes
   ----------------------------------------
 
   (Only contributions larger than 0.50 times the maximum are printed)
 
 
      Mode      1
        Frequency:         i759.07 cm-1
      ---------------------------------
        Dihedral O5 SI1 O2 H6    1.0000
        Dihedral O3 SI1 O2 H6    0.9989
        Dihedral O4 SI1 O2 H6    0.9922
        Angle SI1 O2 H6         -0.6624
      ---------------------------------
 
      Mode      2
        Frequency:         i572.09 cm-1
      ---------------------------------
        Dihedral O2 SI1 O5 H9   -1.0000
        Dihedral O3 SI1 O5 H9   -0.9901
        Dihedral O4 SI1 O5 H9   -0.9844
        Dihedral O3 SI1 O2 H6   -0.9096
        Dihedral O4 SI1 O2 H6   -0.8749
        Dihedral O5 SI1 O2 H6   -0.8686
        Angle SI1 O5 H9          0.5282
      ---------------------------------
 
      Mode      3
        Frequency:         i420.00 cm-1
      ---------------------------------
        Dihedral O4 SI1 O5 H9   -1.0000
        Dihedral O2 SI1 O5 H9   -0.9949
        Dihedral O3 SI1 O5 H9   -0.9851
        Dihedral O4 SI1 O3 H7    0.8322
        Dihedral O5 SI1 O3 H7    0.8155
        Dihedral O2 SI1 O3 H7    0.8088
        Angle SI1 O4 H8         -0.7317
        Angle SI1 O5 H9          0.6838
        Dihedral O3 SI1 O2 H6    0.6777
        Dihedral O5 SI1 O2 H6    0.6563
        Dihedral O4 SI1 O2 H6    0.6549
        Dihedral O5 SI1 O4 H8    0.5224
        Dihedral O2 SI1 O4 H8    0.5207
      ---------------------------------
 
      Mode      4
        Frequency:         i228.05 cm-1
      ---------------------------------
        Dihedral O5 SI1 O2 H6   -1.0000
        Dihedral O4 SI1 O2 H6   -0.9602
        Dihedral O3 SI1 O2 H6   -0.9550
        Dihedral O5 SI1 O4 H8    0.8373
        Dihedral O2 SI1 O4 H8    0.7639
        Dihedral O3 SI1 O4 H8    0.7534
        Dihedral O2 SI1 O5 H9    0.7335
        Dihedral O3 SI1 O5 H9    0.7268
        Dihedral O4 SI1 O5 H9    0.6715
        Angle SI1 O5 H9          0.5366
      ---------------------------------
 
      Mode      5
        Frequency:         i132.13 cm-1
      ---------------------------------
        Dihedral O2 SI1 O4 H8    1.0000
        Dihedral O3 SI1 O4 H8    0.9595
        Dihedral O5 SI1 O4 H8    0.9408
        Dihedral O2 SI1 O3 H7   -0.5863
        Dihedral O4 SI1 O3 H7   -0.5511
        Dihedral O5 SI1 O3 H7   -0.5502
      ---------------------------------
 
      Mode      6
        Frequency:          208.27 cm-1
      ---------------------------------
        Angle O2 SI1 O3         -1.0000
        Angle O3 SI1 O4          0.7863
        Angle O2 SI1 O5          0.5247
      ---------------------------------
...

Since I wasn't sure whether this structure is dynamically stable I took the geometry-optimized structure from OpenMolcas and performed an additional frequency calculation in Gaussian (without further optimization) using the same basis set ANO-RCC-VTZP, i.e., a user-specified basis set. Here, the calculation yields no imaginary frequency. In my opinion I would conclude that this structure gives a global minimum but I am still asking myself if this result is normal in OpenMolcas w.r.t. the warning as well as 5 imaginary frequencies irrespective of the Gaussian result?

Thank you in advance!

Last edited by Okko (2024-09-06 21:46:41)

Ignacio · 2024-09-09 08:15:27

OpenMolcas performs numerical frequency calculations in internal coordinates, so the translations and rotations are automatically excluded. I guess MP2 frequencies are numerical then, that will give lower accuracy. From the components, it looks like the orientation of the Hs might not be optimal. You could try performing single-point calculations for small displacements along the normal modes (their Cartesian components should be printed elsewhere) and see if the energy goes up or down.

When you do the calculation with Gaussian, do reproduce the energy? You may need to add a keyword for DKH2 or something.

Okko · 2024-09-19 17:48:21

Thank you for the reply!

Ignacio wrote:

OpenMolcas performs numerical frequency calculations in internal coordinates, so the translations and rotations are automatically excluded.

I am a bit puzzled by this statement. In the OpenMolcas manual (p. 562) it's stated that 33 degrees of freedom (3*11=33) are obtained for the 1,3-cyclopentadiene molecule due to the 11 atoms. Indeed, you get 33 frequencies which are listed in the corresponding output file even though one is only interested in the final 27 frequencies. In other words, one obtains 4 imaginary frequencies and 2 frequencies close to zero indicating that these can be attributed to the three translational and three rotational coordinates for the different symmetry species within the point group C2v.

If I apply this gained knowledge to the Si(OH)4 case I would claim that the emergence of the first 5 imaginary frequencies is normal and can be discarded similar to what is shown in the OpenMolcas manual or am I mistaken? However, I was just confused that the calculation resulted in 21 frequencies and not the expected 27 frequencies (see previous post related to the warning message).

Ignacio wrote:

When you do the calculation with Gaussian, do reproduce the energy? You may need to add a keyword for DKH2 or something.

Yes, the energies are reproduced in Gaussian which are almost the same:
Gaussian: E(MP2) = -593.030596 a.u.
OpenMolcas: E(MP2) = -593.030493 a.u.

when using the "integral=DKH2" keyword and identical number of frozen cores (by default a different number of frozen cores was set in the Gaussian calculation). The energies only differ in the last three digits which is probably related to numerical inaccuracies (such as different handling of floating-point precision or rounding behavior etc.) used in both software packages.

Last edited by Okko (2024-09-19 18:10:26)

Ignacio · 2024-09-20 08:04:56

Okko wrote:

In the OpenMolcas manual (p. 562) it's stated that 33 degrees of freedom (3*11=33) are obtained for the 1,3-cyclopentadiene molecule due to the 11 atoms.

But those are analytical frequencies, they are done in Cartesian coordinates, and therefore have the full 3N dimensionality. In your case you use MP2, for which analytical frequencies are not implemented and (semi)numerical frequencies are computed instead.

Okko · 2024-09-21 16:23:57

Thank you for the clarification. In order to understand where this warning message stems from I examined the subroutine "thermochem_.F90" which handles the vibrational frequencies contributing to the thermodynamic properties of the molecule, such as entropy, enthalpy etc. through vibrational modes. After breaking out of the loop the corresponding warning message is printed using an if-statement:

call mma_allocate(Freq,in_nFreq,label='Freq')
nFreq = 0
nTr2 = nTr
if (lSlapaf) nTr2 = 0
do i=1,in_nFreq
  dFreqI = EVal(i)
  if (dFreqI > 20.0_wp) then
    nFreq = nFreq+1
    Freq(nFreq) = dFreqI
  end if
end do
Freq(nFreq+1:) = Zero
if ((in_nFreq-nFreq-nTR2) > 0) write(u6,*) ' *** Warning: ',(in_nFreq-nFreq-nTR2),' vibrational contributions removed.'

In my understanding, very low frequencies (below a frequency threshold of 20 cm^-1 corresponding in this case to the obtained 5 imaginary frequencies) are removed from the thermochemical analysis because these frequencies are too low to be phyiscally meaningful. This should ensure that only valid and significant virbational modes contribute to the final thermodynamic properties.

In summary, from this analysis I understand that OpenMolcas uses a semi-analytical approach that incorporates both analytical and numerical elements (hybrid method) in the calculations of frequencies. In contrast, Gaussian uses numerical Hessians at the MP2 level, i.e., a purely numerical approach to the second derivatives. Thus, the key difference is that Gaussian uses fully numerical Hessians at MP2 (finite difference of analytical gradients) which probably leads to the differences in the handling of vibrational modes I observed in the Si(OH)4 frequency calculation especially for low-frequency or near-imaginary modes. Is this assumption correct?

Last edited by Okko (2024-09-21 16:24:37)

Ignacio · 2024-09-23 08:10:06

Probably, but OpenMolcas uses finite differences of analytical gradients, which is what I call seminumerical (typo above corrected). Gaussian, according to https://gaussian.com/freq/, supports fully analytical MP2 frequencies.

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#1 2024-09-06 21:37:23

Consistency check of frequency calculations

#2 2024-09-09 08:15:27

Re: Consistency check of frequency calculations

#3 2024-09-19 17:48:21

Re: Consistency check of frequency calculations

#4 2024-09-20 08:04:56

Re: Consistency check of frequency calculations

#5 2024-09-21 16:23:57

Re: Consistency check of frequency calculations

#6 2024-09-23 08:10:06

Re: Consistency check of frequency calculations

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