Obviously, there are general stability arguments that can be made to estimate relative pKas, such as evaluating the stability of the conjugate base of an acid, or thinking about how polarized the bond to hydrogen is.

However, is there a theory that can be absolute and account for the many exceptions to the above guidelines? What are the factors that are preventing a rigorous theory from being proposed?

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    $\begingroup$ Unfortunately acid/base strengths are still major weak points in quantum theory; there are no rigorous and affordable theories or approximations available. Most approaches have to be calibrated against highly accurate experimental measurements. $\endgroup$ Commented Jun 25, 2019 at 20:58
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    $\begingroup$ This 2015 review article is behind a paywall, but its abstract seems to provide a good summary of the state of the field, namely that it continues to be an active area of research, and there are two basic approaches researchers are pursing: onlinelibrary.wiley.com/doi/abs/10.1002/wcms.1218 $\endgroup$
    – theorist
    Commented Jun 26, 2019 at 1:38
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    $\begingroup$ @theorist the article you mention is available to the public, either on request on research gate (researchgate.net/publication/…) or directly and freely (no paywall), e.g., mercuryconsortium.org/furman/pubs/SeyboldsS2015.pdf $\endgroup$
    – Buttonwood
    Commented Jun 26, 2019 at 20:55
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    $\begingroup$ @NathanMatthieuTang It would be great if you could summarize the comments and your conversation with Seybold in an answer to your own question. $\endgroup$
    – Karsten
    Commented Nov 27, 2019 at 19:46
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    $\begingroup$ @KarstenTheis, Seybold wrote: "The central problem in predicting pKas comes from the difficulty in accounting for the interactions between the acid compounds and the surrounding solvent. Gas phase acidities, which are described in terms of delta Gs, can be rather accurately estimated if one applies sufficiently advanced quantum techniques. But solution acidity computations, which usually rely on continuum approximations for the solvent, aren't really up to the challenge. Remember that one now must account for thermodynamic alterations in both the solute compound and the surrounding solvent." $\endgroup$ Commented Dec 18, 2019 at 18:29


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