Tautomerism free energy calculations

Figure 4 Heterocycles for which the tautomeric equilibrium in aqueous solution has been studied using free energy calculations including explicit solvent. Tautomerism occurs by exchanging a proton between the labeled atoms.

The 2-substituted system has proven especially attractive to modelers because the experimental equilibrium constants are known both in the gas phase and in many different solutions. As a result, the focus of the modeling study can be on the straightforward calculation of the differential solvation free energy of the two tautomers, without any requirement to first accurately calculate the relative tautomeric free energies in the gas phase. However, in 1992 Les et al. [290] suggested that prior experimental data [240,266,288], primarily in the form of ultraviolet spectra in the gas phase and in low-temperature matrices, had been misinterpreted and that the reported equilibrium constants referred to homomeric dimers of tautomers (i.e., (42)2 (43)2). Parchment et al. [291] contested this... 

The gas-phase and aqueous basicities of six 1,2,3-triazoles (71-76), have been determined, the former by FTICR and the latter by spectrophotometry and II NMR. The gas-phase experiments are in good agreement with the Gibbs free energies calculated at the B3LYP/6-31G level. In contrast, only semiquantitative ascertainments are possible when basicities in the gas phase and in solution are compared. The equilibria involved are complex due to tautomerism [87],... 

Worth GA, King PM. Tautomerization and ionisation studies using free energy methods. In Reddy MR, Erion MD, eds. Free Energy Calculations in Rational Drug Design. New York Kluwer/Plenum, 2001 119-140. 

Reddy et al. calculated relative tautomerization free energies for Ng, Ng-dimethyl 2,6-diaminobenz[cd]indole (a) and its anti (b) and syn (b ) imino tautomers in aqueous solution (Figure 4) using FEP (AMBER) and ab initio MP2/6-31G //3-21G (Gaussian 88/90) methods. The relative tautomer free... 

Durant and coworkers used FEP (BOSS 3.1) and ab initio 6-31G (Gaussian 90) calculations to determine the tautomeric/conformational equilibrium of histamine and (aR,pS)-aP-dimethylhistamine in neutral and proto-nated forms. The relative tautomerization free energy for the neutral species, tMc( e-N3H-histamine (g3H), tra s-N3H-histamine (t3H), and tra s-NlH-histamine (tlH) with respect to gawcfee-NlH-histamine (glH) was -1.94 0.19, -3.08 0.26, and -1.28 + 0.32 kcal/mol, respectively. The percentage in solution for neutral glH, g3H, t3H, and tlH was predicted to be 1%, 12%, 83%, and 4%, respectively. The authors concluded that the preference for t3H may be due to the large number of polar sites available for hydration. The relative tautomerization free energy for protonated t3H, tlH, and glH with... 

Similar FEP/QM combinational calculations were performed to study tautomerism " and relative basic-ities/acidities in solution. Other applications of free energy simulation methods in solution include the study of the conformational equilibria of sugars " and determination of the solvation of protein cavities. Accurate determination of absolute or relative solvation free energies of simple molecules in a solvent has become an essential test for any new force field or free energy calculation method. 

The second aspect is more fundamental. It is related to the very nature of chemistry (quantum chemistry is physics). Chemistry deals with fuzzy objects, like solvent or substituent effects, that are of paramount importance in tautomerism. These effects can be modeled using LFER (Linear Free Energy Relationships), like the famous Hammett and Taft equations, with considerable success. Quantum calculations apply to individual molecules and perturbations remain relatively difficult to consider (an exception is general solvation using an Onsager-type approach). However, preliminary attempts have been made to treat families of compounds in a variational way [81AQ(C)105]. 

Whilst this Chapter is primarily concerned with the methods of determining the free energies of tautomeric or ionisation equilibria via computer simulation of free energy differences, many of the issues raised relate also to the determination of other molecular properties upon which behaviour of the molecule within the body may depend, such as the redox potential or the partition coefficient.6 In the next section, we shall give a brief explanation of the methods used to calculate these free energy differences -namely the use of a thermodynamic cycle in conjunction with ab initio and free energy perturbation (FEP) methods. This enables an explicit representation of the solvent environment to be used. In depth descriptions of the various simulation protocols, or the accuracy limiting factors of the simulations and methods of validation, have not been included. These are... 

Although the tautomeric ratios of the 4 species have not been measured directly, it is known that in aqueous solution the keto-N2H form dominates, while the keto-NlH form is only detectable in non-polar solvents. An analysis of experimental data concluded that in aqueous solution the stability (lowest free energy) is in the order keto-N2H > imino-N2H > enol-NlH > keto-NIH. In the gas phase, calculations predict that the keto-N2H form is the least stable. While solvation is found to favour this species, which is the most polar, this stabilisation is not enough to reverse the order of stability. It is thus clearly predicted that the keto-NIH tautomer is the most stable in... 

Finally, Nagaoka et al have made a very interesting study applying MC-FEP techniques to the vinyl alcohol - acetaldehyde tautomerism.32 Using a cluster of the solute with three water molecules as a solute , the free energy for the tautomerism was calculated along different reaction pathways, which had been previously found by ab initio calculations including an SCRF solvation term. They were able to deduce that a two-step mechanism is favoured over a concerted one for the transfer of the proton. 

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