Aqueous Solvation Modeling

Current efforts in solvation modeling in general follow one of two distinct approaches. The first involves the explicit consideration of hundreds or thousands of solvent molecules.The supermolecular system consisting of these 

Another disadvantage of the explicit-water type of approach is that entropy-dependent properties (e.g., free energy) are notoriously difficult to determine accurately in simulations, since it is rarely clear to what extent all the important regions of phase space are sampled in the simulation. 2 jg partly a 

Finally, at least for the present, explicit-water simulations treat heavy-body motions by the laws of classical mechanics this is not always valid. 

Furthermore, the explicit-water simulations do include the CDS terms to the extent that dispersion and hydrogen bonding are well represented by the force field. Finally, by virtue of the solvent being explicitly part of the system, it is possible to derive many useful non-entropy-based properties (radial distribution functions, average numbers of hydrogen bonds, size and stability of the first solvation shell, time-dependent correlation functions, etc.). Since many of these properties are experimentally observable, it is often possible to identify and correct at least some deficiencies in the simulation. Simulation is thus an extremely powerful tool for studying solvation, especially when focused on the response of the solvent to the solute. 

An alternative simulation procedure is to replace the explicit solvent molecules with a continuous medium having the bulk dielectric constant. - Once the solvent has been simplified, it is much easier to employ quantum mechanical techniques for the ENP relaxation of electronic and molecular structure in solution thus this approach is complementary to simulation insofar as it typically focuses on the response of the solute to the solvent. Since the properties of the continuum solvent must represent an average over solvent configurations, such approaches are most accurately described as quantum statistical models. 

---

The SMx aqueous solvation models, of which the most successful are called AM1-SM2,27 AMl-SMla, and PM3-SM3, °- adopt this quantum statistical approach, which takes account of the ENP and CDS terms on a consistent footing. The NDDO models employed are specified as the first element (AMI or PM3) of each identifier. It is worth emphasizing that the SMx models specifically calculate the absolute free energy of solvation—a quantity not easily obtained with other approaches. We have reviewed the development and performance of the models elsewhere.203 We anticipate our further observations later in this chapter by noting that the mean unsigned error in predicted free energies of solvation is about 0.6-0.9 kcal/mol for the SMx models for a data set of 150 neutral solutes that spans a wide variety of functionalities. A number of examples are provided later in this chapter. 

Chambers C C, G D Hawkins, C J Cramer and D G Tmlilar 1996. Model for Aqueous Solvation Ba sed on Class IC Atomic Charges and First Solvation Shell Effects. Journal of Physical Chemistry 100 16385-16398. 

Cramer C j and D G Truhlar 1992. AM1-SM2 and PM3-SM3 Parametrized SCF Solvation Models for Free Energies in Aqueous Solution. Journal of Computer-Aided Molecular Design 6 629-666. 

From the results described above it is clear that a different QSPR model can be obtained depending on what data is used to train the model and on the method used to derive the model. This state of affairs is not so much a problem if, when using the model to predict the solubility of a compound, it is clear which model is appropriate to use. The large disparity between models also highlights the difficulty in extrapolating any physical significance from the models. Common to all models described above is the influence of H-bonding, a feature that does at least have a physical interpretation in the process of aqueous solvation. 

Bulk effects of the aqueous solvent have been evaluated by C-PCM solvation model. The specific effect of the solvation on the alkylation pathways has also been... 

Despite the importance of the oxidative polymerization of 5,6-dihydroxyin-dole, in the biosynthesis of pigments, little experimental data are known on the oxidation chemistry of the oligomers of 1. For such reasons, three major dimers of 1, such as 2-4 (Scheme 2.9), have been computationally investigated at PBEO/ 6-31+G(d,p) level of theory both in gas and in aqueous solution (by PCM solvation model) to clarify the quinone methide/o-quinone tautomeric distribution. 

SCHEME 2.10 Structures and relative energies (kcal/mol) of several tautomers/conformers resulting from the bielectronic oxidation of 2-4, computed at the PBE0/6-31 + G(d,p) level in vacuum and in aqueous solution (in parenthesis, by PCM solvation model, data from Ref. [19]). 

The base catalysis and the monoelectronic reductive activation processes have been described by a computational investigation at the R(U)B3LYP/6-31 + G(d,p) level of theory for the model imide NI (Scheme 2.14) 47 both in the gas phase and in aqueous solution, using PCM solvation model.40... 

Whitfield TW, Varma S, Harder E, Lamoureux G, Rempe SB, Roux B (2007) Theoretical study of aqueous solvation of K+ comparing ab initio, polarizable, and fixed-charge models. J Chem Theory Comput 3(6) 2068-2082... 

Sukumar, N., and G. A. Segal. 1986. Effect of Aqueous Solvation upon the Electronic Excitation Spectrum of the Glycine Zwitterion A Theoretical Cl Study Using a Fractional Charge Model. J. Am. Chem. Soc. 108, 6880-6884. 

C. J. Cramer and D. G. Truhlar, AM1-SM2 and PM3-SM3 parameterized SCF solvation models for free energies in aqueous solution, J. Comput.-Aided Mol. Design 6 629 (1992). 

D. J. Giesen, G. D. Hawkins, D. A. Liotard, C. J. Cramer, and D. G. Truhlar, A universal solvation model for the quantum mechanical calculation of free energies of solvation in non-aqueous solvents, Theoret. Chem. Acc. 98 85-109 (1997) erratum 101 309 (1999). 

The present authors, using the SMx series of models, have considered aqueous solvation effects on proton transfer for these same amines, together with several other bases, and have arrived at similar conclusions to those detailed... 

Using the same theoretical model, Karelson et al. [269] and later Rzepa et al. [270] examined 4-nitroimidazole. The latter work corrected incomplete geometry optimizations present in the former study. In this instance, AMI predicts 5 to be 1.4 kcal/mol lower in relative energy than 6. However, the D02 model predicts the aqueous solvation free energies to be -25.3 and -7.1 kcal/mol for 6 and 5, respectively, rendering 6 considerably lower in energy than 5 in solution, which agrees with the experimental situation. 

Parchment et al. [271] have provided more recent calculations on the 3-hydroxypyrazole equilibrium at the ab initio level. They noted that tautomer 9, which was not considered by Karelson et al. [268], is the lowest-energy tautomer in the gas phase at levels of theory (including AMI) up to MP4/6-31G //HF/3-21G [271], Although 8 is the dominant tautomer observed experimentally in aqueous solution, in the gas phase 8 is predicted to be nearly 9 kcal/mol less stable than 9 at the MP4 level [271], Using a DO model with an unphysically small cavity radius of 2.5 A, Parchment et al. [271] were able to reproduce at the ab initio level the AMI-DO prediction of Karelson et al. [268], namely that 8 is the most stable tautomer in aqueous solution. With this cavity, though, 8 is predicted to be better solvated than 9 by -22.2 kcal/mol [271], This result is inconsistent with molecular dynamics simulations with explicit aqueous solvation [271], and with PCM and SCME calculations with more reasonable cavities [271] these predict that 8 is only about 3 kcal/mol better solvated than 9. In summary, the most complete models used by Parchment et al. do not lead to agreement with experiment... 

Finally, we note that Karelson et al. [295] have used the D02 model with small cavity radii to consider aqueous solvation effects on other tautomeric equilibria of substituted pyridines. In particular, they examined methyllmethylene, amino/imino, hydroxy/oxo, and mercapto/thiono substitution at the 2-, 3, and 4-positions of pyridine. They observed methyl/methylene equilibria to be only slightly perturbed by aqueous solvation. Amino/imino equilibria were slightly more perturbed, followed by hydroxy/oxo equilibria. Mercapto/thiono equilibria were very significantly affected by aqueous solvation Karelson et al. predicted pK shifts of up to 16 units. This sensitivity of the thiono group to solvation is also discussed in the next section. Overall, the tautomeric equilibria of 3- and 4-substituted pyridines were more sensitive to aqueous solvation than were those of 2-substituted pyridines. 

Truhlar and coworkers [29, 232, 233] have proposed a quantum-mechanical-continuum dielectric model for aqueous solvation. This method is discussed by Truhlar and coworkers in Chapter I. 

From a theoretical viewpoint, the effect of aqueous solvation in organic reactions has received considerable attention in recent years. These studies have gone a step beyond analysis of simple models to consider reactions such as SN1, SN2, cycloaddition reactions and Claisen rearrangement, for instance, with more realistic models. 

Tomasi, J. (1994) Application of continuum solvation models based on a Quantum Mechanical Hamiltonian.,in Cramer, C. J. and Truhlar, D. ( .(cds.). Structure and Reactivity in Aqueous Solution, American Chemical Society, Washington,pp. 10-23. 

Vitalis, A., Pappu, R.V. ABSINTH a new continuum solvation model for simulations of polypeptides in aqueous solutions. J. Comput. Chem. 2009, 30, 673-99. 

More generally, as seen in Figure 6-16, there is no correlation between calculated (Hartree-Fock 6-3IG ) and experimental aqueous-phase basicities of amines. (As shown earlier in this chapter, Hartree-Fock and other simple calculation models are quite successful in reproducing relative gas-phase basicities in amines. Therefore, a plot of measured gas-phase basicities vs. measured aqueous-phase basicities would be expected to show poor correlation.) On the other hand, calculated (6-3IG ) relative basicities of amines corrected for the effects of aqueous solvation using the Cramer/Truhlar SMS.4 model shows reasonable correlation with the experimental (aqueous-phase) data (Figure 6-17). This further confirms that the simple solvation model is at least qualitatively correct. 

---