Prof. K. L. Sebastian

Principle of Maximum Hardness

The principle of maximum hardness, suggested by Pearson states:

"Molecules arrange their electronic structure so as to have the maximum possible hardness" [1].

If true, this is a very interesting concept.  The principle has been claimed to have been proved rigorously [2].  The proof has been given quite a bit of attention [3-9].  We have shown that the proof is in error [4].  Also a principle of maximum physical hardness also was claimed to be true [5], which again was pointed out to be in error [6].  This was expected  expected to change the current way of thinking on this topic.   Regarding our arguments, Parr and coworkers state [7]:

"Recently it has been correctly pointed out by Sebastian [4] that the proof of principle maximum hardness by two of us [2] is not true in general",

Inspite of this, even now,  claims are made that the principle of maximum chemical hardness has been given a general proof by Parr and Chattraj [1] and that the proof of the principle of maximum physical hardness is correct.    Pearson has written an article in Journal of Chemical Education [8], claiming these results.   He has even written a book on hardness [9], where the proof has been discussed [10] at length.  Unfortunately, all these are incorrect, though this has not been realised by the majority of workers in the field.  Clearly, this is a topic that needs many more investigations.


For more information, please see the listed publications below

  1. R. G. Pearson: J. Chem. Educ., 64, 561 (1987).
  2. R. G. Parr and P. K. Chattaraj: J. Am. Chem. Soc., 113, 1854 (1991).
  3. A. Dal Pino, M. Galvin, T. A. Arias and J. D. Joanopoulos: J. Chem. Phys., 98, 1606 (1993).
    R. G. Pearson: Accts. Chem. Res., 26, 250 (1993).
    R. G. Pearson and W. E. Palke: J. Phys. Chem., 96, 3283 (1992).
    D. Datta: J. Phys. Chem., 96, 2409 (1992).
    S. Pal, R. Roy and A. K. Chandra: J. Phys. Chem., 98, 2314 (1994).
  4. K. L. Sebastian: Chem. Phys. Lett., 231, 40 (1994).
  5. R. G. Pearson: J. Phys. Chem., 98, 1989 (1995).
  6. K. L. Sebastian: Comments on the principle of maximum physical hardness. Current Science , 71, 92 (1996).
  7. Verbatim quoted from - P. K. Chattraj, G. H. Liu and R. G. Parr: Chem. Phys. Lett., 237, 171 (1995).
  8. R. G. Pearson: Chemical Hardness: Applications from Molecules to Solids,   John Wiley & Sons, Inc, (1997).
  9. R. G. Pearson: Maximum Chemical and Physical Hardness. J. Chem. Ed., 76, 267 (1999).
  10. From the advertisement of the book: "Originally developed as an intuitive, qualitative concept, it is today firmly based on and justified by quantum chemistry......It also shows the links to quantum chemistry and especially density functional theory which have provided a theoretical basis for and at the same time have extended the range of applications of chemical hardness".

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