Discrepancy between vibrational frequencies computed using `xtb` and `xtb-python` (but not with `tblite`)

[Andrew-S-Rosen]

Overview

I'm getting different values for the vibrational frequencies when I use the standalone xtb executable with the --hess flag and when I use the Python API provided with python-xtb and the ASE Vibrations module. Interestingly, when I use the Python API of tblite, I get values that are consistent with the standalone xtb executable, suggesting that the root issue may reside with xtb-python.

Versions: xtb 6.4.1 from conda-forge (although 6.6.0 gives the same results), python-xtb 22.1 from pip, tblite 0.3.0 from pip, the master branch of ASE, Python 3.8.16, Ubuntu.

Reproducing the Discrepancy

Internal xTB vibrations

Input:

xtb c2h6.xyz --hess

c2h6.xyz.txt. Please drop the .txt extension.

Output:

 projected vibrational frequencies (cm⁻¹)
eigval :       -0.00    -0.00    -0.00     0.00     0.00     0.00
eigval :      341.39   873.74   873.75  1054.99  1203.59  1203.61
eigval :     1414.48  1447.57  1514.23  1514.30  1516.92  1517.01
eigval :     2971.79  2971.81  2989.26  2989.29  2989.29  2996.97

out.txt

xtb-python vibrations

Input:

from ase.build import molecule
from ase.vibrations import Vibrations
from xtb.ase.calculator import XTB

atoms = molecule('C2H6') # this is identical to c2h6.xyz
atoms.calc = XTB(method='GFN2-xTB')
vib = Vibrations(atoms)
vib.run()
vib.summary()

Output: The values with <--x should be dropped due to the 3N-6 rule for vibrations.

---------------------
  #    meV     cm^-1
---------------------
  0    2.3i     18.8i <--x
  1    0.0i      0.0i <--x
  2    0.0i      0.0i <--x
  3   50.6     408.0 <--x
  4   50.9     410.7 <--x
  5   87.8     708.0 <--x
  6   90.4     729.0
  7  108.3     873.6
  8  130.7    1053.8
  9  130.8    1055.1
 10  131.5    1060.6
 11  144.0    1161.1
 12  150.8    1216.1
 13  158.1    1274.9
 14  175.3    1414.2
 15  179.5    1447.4
 16  188.0    1516.7
 17  190.8    1538.6
 18  370.6    2989.0
 19  370.6    2989.1
 20  370.8    2990.8
 21  371.6    2996.9
 22  371.6    2997.5
 23  372.0    3000.4
---------------------

Note how the lowest real vibrational mode in the two codes do not match (341.39 vs. 729.0 cm^-1).

tblite vibrations

Input:

from ase.build import molecule
from ase.vibrations import Vibrations
from tblite.ase import TBLite

atoms = molecule('C2H6')
atoms.calc = TBLite(method='GFN2-xTB')
vib = Vibrations(atoms)
vib.run()
vib.summary()

Output:

---------------------
  #    meV     cm^-1
---------------------
  0    0.0i      0.1i <--x
  1    0.0i      0.1i <--x
  2    0.0i      0.1i <--x
  3   13.0     104.9 <--x
  4   13.0     105.0 <--x
  5   21.8     175.5 <--x
  6   42.2     340.7
  7  108.3     873.6
  8  108.3     873.7
  9  130.8    1055.1
 10  150.1    1210.4
 11  150.1    1210.4
 12  175.3    1414.3
 13  179.4    1447.2
 14  187.8    1514.4
 15  187.8    1514.7
 16  188.0    1516.6
 17  188.1    1516.9
 18  368.5    2972.3
 19  368.6    2972.6
 20  370.6    2988.9
 21  370.6    2989.2
 22  370.6    2989.3
 23  371.6    2997.1
---------------------

Note how this is largely in agreement with xtb but not with xtb-python.

Additional Debugging

Energies

As a sanity check, I have also computed the single-point energy with each code and get the following:

xtb: -7.336177090885 Eh

xtb-python: -7.3361770263 Eh

tblite: -7.3361770297 Eh

So, there is nothing obviously wrong with the energies.

Forces

I also compared forces. Again, this is all without any geometry optimization.

xtb-python:

array([[ 2.81356077e-15, -1.57075849e-05,  1.31289683e-01],
       [ 1.95063714e-14,  1.57075849e-05, -1.31289683e-01],
       [ 1.75860275e-15, -1.18139575e-01, -1.26627069e-01],
       [ 1.02323065e-01,  5.90773242e-02, -1.26632632e-01],
       [-1.02323065e-01,  5.90773242e-02, -1.26632632e-01],
       [-7.42620433e-15,  1.18139575e-01,  1.26627069e-01],
       [ 1.02323065e-01, -5.90773242e-02,  1.26632632e-01],
       [-1.02323065e-01, -5.90773242e-02,  1.26632632e-01]])

tblite:

array([[-7.43730571e-15, -1.52828580e-05,  1.31291022e-01],
       [-1.10273807e-14,  1.52828580e-05, -1.31291022e-01],
       [-3.56890669e-15, -1.18139858e-01, -1.26627303e-01],
       [ 1.02323311e-01,  5.90774659e-02, -1.26632866e-01],
       [-1.02323311e-01,  5.90774659e-02, -1.26632866e-01],
       [ 1.65071646e-15,  1.18139858e-01,  1.26627303e-01],
       [ 1.02323311e-01, -5.90774659e-02,  1.26632866e-01],
       [-1.02323311e-01, -5.90774659e-02,  1.26632866e-01]])

Again, there is nothing obviously different here.

[Andrew-S-Rosen]

@awvwgk, I'm curious if you have any initial guesses as for why this might be. Would you recommend just using tblite instead?

[awvwgk]

Having written tblite as a replacement for the xtb Python API I would of course recommend to prefer tblite ;).

[Andrew-S-Rosen]

Ah, I didn't know the context there! Thank you. That is very helpful to know.