Energy cut-off value for conformer calculations

I want to get familiar with the conformer calculation. I found a paper where they did the conformer calculations already for the molecule I work with. The paper can found here.

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? - or have they just forget to cite the reference? If this is the case, does somebody have a reference for this?

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?

1 Moreira et al., Computational electronic structure of the bee killer insecticide imidacloprid, New Journal of Chemistry, 2016, 40, 10353-10362

Add: I have not found a reference for the cut-off value for the stability of the conformers. Does someone have a similar problem? Or work on something which is similar?

• Welcome to our site! – Camps Dec 10 '20 at 11:54
• What is the meaning to study only a set of manually created conformers? I said manually because they determine not only which angles to use but also the number of steps in the PES scan. – Camps Dec 10 '20 at 12:33
• @Camps I like to find the lowest conformer for a dihydral scan. – Andrea Dec 11 '20 at 8:59
• If you only want the conformer with the lowest energy, what I would do is to run a molecular mechanics or semi-empirical scan (faster), select the conformers with lower energy, run a geometry optimization for each of them and then compare the final energies. – Camps Dec 11 '20 at 17:57
• @Camps But you would do the scan for conformer searching as well? - just with a method that is faster? – Andrea Dec 12 '20 at 18:57

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

1. scanning over all dihedral angles: $$N=11$$ calculations
2. scan over all pairs of dihedral angles: $$N^2 = 121$$ calculations
3. scan over all triplets of dihedral angles : $$N^3 = 1331$$ calculations
4. scan over all quartets of dihedral angles : $$N^4 = 14641$$ calculations
5. scan over all quintets of dihedral angles : $$N^5 = 161051$$ calculations
6. etc

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.

• "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. " - right, but I am wondering why in the reference not the minimum in the PES is marked as conformer. The structure right beside the minimum is marked. – Andrea Dec 15 '20 at 7:39
• @andrea it is not clear what you mean by "the structure right beside the minimum". Is it in the same basin, or a different one? Are you repeating the calculations at the same level of theory, i.e. M06-2X/6-311++G**? Note that the 6-311++G** is bad (pubs.acs.org/doi/10.1021/ja0630285); modern alternatives that lack this problem exist. – Susi Lehtola Dec 16 '20 at 1:33
• Sorry for the ambiguity. I mean the three stable conformers in the paper I cited above. In the PES, the three conformers IMI1-P, IMI2-P, and IMI3-P are marked in the PES the author published. Furthermore, these markups are not in the local minimum. Even when they decide for a bad functional and basis set, the stable conformers must sit at the PES's local minimum, or not? – Andrea Dec 16 '20 at 13:26
• @Andrea oh there was a plot. Yes, it's definitely sketchy: it looks like IMI1-P could move to the left and decrease in energy, same for IMI3-P to the right; as for IMI2-P it's hard to see whether there even is local minimum close to it. But it's also clear that the 30 degree sampling is not sufficient to get a smooth potential energy surface. However, the plot is for a rigid angle scan, whereas the real conformers are geometry optimized; this may explain the observed differences in the values of the dihedrals. – Susi Lehtola Dec 16 '20 at 15:03
• That is, the problem might just be in the visualization; the correct IMI positions would actually lie below the plotted surface since the geometry is fully relaxed. – Susi Lehtola Dec 16 '20 at 15:04