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QM9 dataset contains about $134000$ small organic molecules with following properties computed using DFT approaches:

A = "rotational_constant_A"
B = "rotational_constant_B"
C = "rotational_constant_C"
mu = "dipole_moment"
alpha = "isotropic_polarizability"
homo = "homo"
lumo = "lumo"
gap = "gap"
r2 = "electronic_spatial_extent"
zpve = "zpve"
U0 = "energy_U0"
U = "energy_U"
H = "enthalpy_H"
G = "free_energy"
Cv = "heat_capacity"

In many papers, fundamental vibrational modes $\omega_1$ is also mentioned along with these properties. I was wondering:

  1. Can we calculate $\omega_1$ given the properties above?
  2. Are rotational constants used for computing $\omega_1$?
  3. Do we need DFT calculations to compute $\omega_1$ and zero point vibrational energy (ZPVE)?
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  1. Only for a diatomic molecule and only assuming the vibration is harmonic. In this case, $\mathrm{ZPVE}=\omega_1/2$. If its anharmonic or has rovibrational coupling, even the expression for a diatomic doesn't not allow you to determine $\omega_1$ from just the ZPVE. With polyatomic molecules, the ZPVE has contributions from all the vibrations, so you can't just extract a single vibrational frequency.
  2. Rotational constants are not used in computing $\omega_1$ (unless you are considering forms of rovibrational coupling).
  3. You can determine $\omega_1$ from other electronic structure methods and even classical molecular dynamics, but assuming you don't want to compare against experimental data, you would need to repeat these DFT calculations to get the corresponding $\omega_1$. For this dataset to include ZPVE, the underlying calculations would have had to determine all the vibrational frequencies of the molecule, but they seem not to have included this data in the QM9 set.
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