When is a bond broken? The polarizability perspective.

My pleasure, Diptarka Hait. I saw that your article has already been accepted in Angew., congratulations. By the way, in my previous email, I forgot to mention another relevant detail. The hardness profile also presents a similar behaviour that you display in your article. For instance, https://doi.org/10.1063/1.1742793 (I directly copy the abstract) We computed the energy and hardness profiles for a series of inter and intramolecular conformational changes at several levels of calculation. All processes studied have in common that the choice of a weak methodology or a poor basis set results in spurious stationary points in the energy profile. At variance with the energy profiles, the hardness profiles calculated as the difference between the vertical ionization potential and electron affinity always show the correct number of stationary points independently of the basis set and methodology used. For this reason, we concluded that hardness profiles can be used to check the reliability of the energy profiles for those chemical systems that, because of their size, cannot be treated with high-level ab initio methods. Related to this work, you can also find two additional works https://doi.org/10.1002/cphc.200700011 https://link.springer.com/article/10.1007/BF02708361 Thank you for reading my message, and best regards, Miquel

Congratulations on the excellent work, Diptarka Hait and Martin Head-Gordon. It brings me back to my PhD thesis (one of the main topics was the validity of the maximum hardness principle and the minimum polarizability principle) supervised by Miquel Solà and Josep Maria Luis, from nearly twenty years ago. Now, I feel like an old man. Thanks to your work, my memory has been refreshed :-). Here's a small discussion that you are probably aware of, just in case. In the DFT framework, MHP is exact under very strict conditions, where the external and chemical potentials remain constant (which, from a practical standpoint, is impossible to follow). MPP was defined using the inverse relationship between hardness and softness. However, both principles fail significantly, even under the best possible conditions, such as the vibrational distortions of a molecule. If the chemical distortion (in your case, breaking a chemical bond) primarily involves the HOMO and LUMO, it probably will work (also probably, in the Diels-Alder reactions, traditional systems that have been studied using conceptual DFT descriptors). Then, near the transition state geometry, a minimum of hardness and a maximum of polarizability will be present. But outside of these conditions, it becomes quite uncertain. For instance, please refer to Table 2 of https://pubs.acs.org/doi/10.1021/jp0470804 where we concluded, "These results cast serious doubts about the general validity of assuming the proportionality between polarizability and softness, which is the main assumption made in the formulation of the MPP." Taking advantage of this discussion, I will enclose some additional works that we did regarding the validity of MHP and MPP: - https://pubs.acs.org/doi/10.1021/ja015737i - https://doi.org/10.1063/1.1517990 - https://doi.org/10.1002/chem.202301294 Thank you for reading my message, congratulations again on your work, and best regards, Miquel