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Estimation of pKa Values through Local Electrostatic Potential Calculations

Calculating the pKa value for a Brønsted acid is very hard, like really hard. A full thermodynamic cycle (fig. 1) needs to be calculated along with the high-accuracy solvation free energy for each of the species under consideration, not to mention the use of expensive methods which will be reviewed here in another post in two weeks time.

Fig 1. Thermodynamic Cycle for the pKa calculation of any given Bronsted acid, HA

Finding descriptors that help us circumvent the need for such sophisticated calculations can help great deal in estimating the pKa value of any given acid. We’ve been interested in the reactivity of σ-hole bearing groups in the past and just like Halogen, Tetrel, Pnicogen and Chalcogen bonds, Hydrogen bonds are highly directional and their strength depends on the polarization of the O-H bond. Therefore, we suggested the use of the maximum surface electrostatic potential (VS,max) on the acid hydrogen atom of carboxylic acids as a descriptor for the strength of their interaction with water, the first step  in the deprotonation process. 

We selected six basis sets; five density functionals; the MP2 method for a total of thirty-six levels of theory to optimize and calculate VS,max on thirty carboxylic acids for a grand total of 1,080 wavefunctions, which were later passed onto MultiWFN (all calculations were taken with PCM = water). Correlation with the experimental pKa values showed a great correlation across the levels of theory (R2 > 0.9), except for B3LYP. Still, the best correlations were obtained with LC-wPBE/cc-pVDZ and wB97XD/cc-pVDZ. From this latter level of theory the linear correlation yielded the following equation:

pKa = -0.2185(VS,max) + 16.1879

Differences in pKa turned out to be less than 0.5 units, which is remarkable for such a straightforward method; bear in mind that calculation of full thermodynamic cycles above chemical accuracy (1.0 kcal/mol) yields pKa differences above 1.0 units.

We then took this equation for a test with 10 different carboxylic acids and the prediction had a correlation of 98% (fig. 2)

fig 2. calculated v experimental pKa values for a test set of 10 carboxylic acids from equation above

I think this method can really catch on for a quick way to predict the pKa values of any carboxylic acid imaginable. We’re now working on the model extension to other groups (i.e. Bronsted bases) and putting together a black-box workflow so as to make it even more accessible and straightforward to use. 

We’ve recently published this work in the journal Molecules, an open access publication. Thanks to Prof. Steve Scheiner for inviting us to participate in the special issue devoted to tetrel bonding. Thanks to Guillermo Caballero for the inception of this project and to Dr. Jacinto Sandoval for taking the time from his research in photosynthesis to work on this pet project of ours and of course the rest of the students (Gustavo Mondragón, Marco Diaz, Raúl Torres) whose hard work produced this work.


Mexican Phys.Chem. Meeting XVth edition 

For the fifth year in a row my research group has participated in this traditional meeting on theoretical and computational chemistry, now at the beautiful city of Merida in southeastern Mexico.

Several distinguished international guests included Profs. Jose Luis Mendoza (Florida State University), Adrián Roitberg (University of Florida), Vincent Ortiz (Auburn University) and Paul Ayers (McMaster U. Canada); Their contributions rounded up nicely those of household names like Drs. Alberto Vela, Gabriel Merino (CINVESTAV) (the latter was also the main organizer), Jesus Hernández-Trujillo (UNAM), Jose Luis Gazquez (UAM-I), Óscar Jimenez (Guanajuato), and so many others who were also present.

My students presented four posters summarized below:

1) Maru Sandoval and Gustavo Mondragón on Photosynthesis, particularly the search for exciton transference mechanisms in both natural and theoretical arrangements of photosynthetic pigments. Some very exciting results have been observed; their publication is really near.

2) Raúl Torres and Gustavo Mondragón presented their work on arsenic removing calixarenes, published earlier this year, and the extension of said work to As(III) acids. Graphene oxide is now considered in our simulations as per the experimental work of our colleagues, Prof. Reyes Sierra and Prof. Eddie Lopez-Honorato.

3) Marco Diaz, Guillermo Caballero, Gustavo Mondragón and Raúl Torres had this poster on the calculation of sigma holes as descriptors for predicting pka values in organic acids. Their +1600 calculations project has found the best levels of theory (and ruled out some like B3LYP, of course) with some nice correlations. Yet, much work is still to be done but we’re on the right track.

4) Durbis Castillo presented his work on molecular docking and dynamics of a large library of HIV-1 entry inhibitors for which he uses the suite MAESTRO as a continuation of another project of ours. His enormous library is now in the hundredths of thousands and although we’re facing some technical difficulties, Durbis is thriving in his search. This is our first serious attempt towards a more mature drug discovery project; a manuscript should be ready in the first part of next year.

This guys and the rest of the lab who weren’t present are the ones who make our research flourish and they’ve all earned a day or two at the beach!

Here’s to fifteen more years of RMFQT!

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