In the experimental section, they write that they cut conformers after a second optimization after the scan for conformers by a few values. The take from the twenty structures they get only those with energies up to 0.59 kcal/mol. This should be a limit of conformational stability at 300 K. But they don't cite a reference for this fact. Is this something everybody knows through their academic education?
This is a hand-waving argument. If you calculate what is $k_B T$ for $T=$300 K in units of cal/mol, you'll find the value $k_B T \approx$ 595.762 cal, which rounds to 0.60 kcal/mol.
But, there are some problems with this argument. First, the intrinsic error in DFT (especially M06-2X/6-311++G** as used in the paper!) is likely much larger. I think usually one would choose a much higher threshold, something like 3-5 kcal/mol, to screen out conformers from DFT for running more accurate calculations on them. M06-2X also has no dispersion; I would dispersion corrections might be significant for conformer energies.
Of course, it is not the electronic energy but the free energy which is relevant, so the entropy term also plays an effect.
I taught Gaussian myself, and I read in the Gaussian manual that a stable conformed is a minimum of the potential energy surface (PES). In the paper 1, they show structures that look not like the PES minimum. Is it possible in reason of these cut-off values that the stable conformer is not automatically the minimum?
If I understand correctly, you've done a geometry optimization for imidacloprid. Geometry optimizations (like many other optimizations) typically converge onto the closest local minimum. However, the issue with conformers is that their number increases rapidly with the size of the molecule, and several of them may be thermodynamically accessible. For instance, melatonin has 52 unique conformers, see the study by Fogueri, Kozuch, Karton and Martin in J. Phys. Chem. A 117, 2269 ( 2013). Locating all the conformers is a global optimization problem, which is difficult, since size of the solution space grows rapidly with the size of the system. To find the conformers, you need to scan over all the dihedral angles, in principle.
Let's say you want to do find the global minimum conformer. If you scan the angles in steps of $30^\circ$ as in the paper (I'm not sure if this is small enough for all systems), to go from $0^\circ$ to $360^\circ$ you need 12 steps, but since $0^\circ=360^\circ$, there are only $N=11$ unique angles. This means that your procedure would be
- scanning over all dihedral angles: $N=11$ calculations
- scan over all pairs of dihedral angles: $N^2 = 121$ calculations
- scan over all triplets of dihedral angles : $N^3 = 1331$ calculations
- scan over all quartets of dihedral angles : $N^4 = 14641$ calculations
- scan over all quintets of dihedral angles : $N^5 = 161051$ calculations
If you're lucky, you can safely truncate the procedure at a small number of simultaneous dihedral changes. Otherwise you may not find the global minimum. Still, my colleagues in the chemical industry tell me that doing conformational analysis is really important for chemistry.