Computational Calculation of Equilibrium Constants: Addition to Carbonyl Compounds Rafael Go ´mez-Bombarelli, Marina Gonza ´lez-Pe ´rez, Marı ´a Teresa Pe ´rez-Prior, Emilio Calle, and Julio Casado* Departamento de Quı ´mica Fı ´sica, Facultad de Ciencias Quı ´micas, UniVersidad de Salamanca, Plaza de los Caı ´dos, s/n E-37008 Salamanca, Spain ReceiVed: July 28, 2009; ReVised Manuscript ReceiVed: September 1, 2009 Hydration reactions are relevant for understanding many organic mechanisms. Since the experimental determination of hydration and hemiacetalization equilibrium constants is fairly complex, computational calculations now offer a useful alternative to experimental measurements. In this work, carbonyl hydration and hemiacetalization constants were calculated from the free energy differences between compounds in solution, using absolute and relative approaches. The following conclusions can be drawn: (i) The use of a relative approach in the calculation of hydration and hemiacetalization constants allows compensation of systematic errors in the solvation energies. (ii) On average, the methodology proposed here can predict hydration constants within ( 0.5 log K hyd units for aldehydes. (iii) Hydration constants can be calculated for ketones and carboxylic acid derivatives within less than ( 1.0 log K hyd , on average, at the CBS-Q level of theory. (iv) The proposed methodology can predict hemiacetal formation constants accurately at the MP2 6-31++G(d,p) level using a common reference. If group references are used, the results obtained using the much cheaper DFT-B3LYP 6-31++G(d,p) level are almost as accurate. (v) In general, the best results are obtained if a common reference for all compounds is used. The use of group references improves the results at the lower levels of theory, but at higher levels, this becomes unnecessary. Introduction For more than a century, aldehydes have been known to undergo hydration, such that for example the equilibrium of formaldehyde hydration is strongly displaced toward the hydrate, to the extent that less than 0.1% of formaldehyde is present as the carbonyl compound in aqueous solution. Ketones and other carbonyl compounds also add a water molecule to form gem- diols. 1 Hydration reactions represent one of the simplest addition reactions to the carbonyl group and are of great importance in understanding many organic reactions. Since the formation of a tetrahedral intermediate is a step in some possible hydrolysis mechanisms, the hydration of carboxylic acid derivatives, esters, thioesters, and amides, is also important. Hemiacetalization may also form part of certain alcoholysis mechanisms. 2-9 Much attention has been devoted to the measurement and calculation of hydration rates. 10-13 Hydration free energies can be used to calculate hydration rate constants in neutral, acidic, and basic media, using multidimensional Marcus theory and the no-barrier theory. 14,15 Since aldehydes in their hydrate form cannot react with nucleophilic sites in DNA, the hydration of aldehydes is also significant in their role as alkylating and potentially mutagenic and carcinogenic agents. For instance, 99.997% of chloral is in its hydrate form, which significantly reduces its potential reactivity as an electrophile, and this in turn influences its genotoxic potential. 16-22 Because carbohydrates show intramolecular hemiacetal equi- libria, and since the reactivity of aldehydes as alkylating agents may be strongly influenced by the formation of cyclic and linear hemiacetals, hemiacetal formation is also of biological importance. Hydration and hemiacetalization equilibrium constants have been measured with a variety of methods, most commonly UV and NMR spectroscopy. 1 H, 13 C, 17 O, and 19 F have been used. 23-25 The experimental determination of hydration and hemiac- etalization equilibrium constants is complex. The sensitivity of NMR spectroscopy makes it difficult to measure very displaced equilibria directly, and the use of UV spectroscopy forces the assumption that the molar absorption coefficient is solvent- independent, which is an important source of error. 26 Therefore, indirect methods are often used: linear free energy relationships, equilibrium constant extrapolations, acetalization constants or hemiacetalization constants, calculation of formation and sol- vation free energies, and so forth. 14,15 Since computational calculations are now a plausible alterna- tive to the experimental determination of equilibrium constants such as pK a 27-29 and to our knowledge no first-principle approaches have been proposed for the calculation of hydration and hemiacetalization constants, here, we were prompted to address this issue. Methods of Calculation The computational calculation of equilibrium constants in solution is very demanding. It may be seen from the thermo- dynamic definition of K (eq 1) that an error of 5.7 kJ mol -1 in ΔG° results in a deviation of 1 logarithmic unit in K. * To whom correspondence should be addressed. Phone: +34 923 294486. Fax: +34 923 294574. E-mail: jucali@usal.es. log K )- ΔG o ln 10RT (1) J. Phys. Chem. A 2009, 113, 11423–11428 11423 10.1021/jp907209a CCC: $40.75  2009 American Chemical Society Published on Web 09/17/2009