Free energies of solvation

Free energy perturbation (FEP) theory is now widely used as a tool in computational chemistry and biochemistry [91]. It has been applied to detennine differences in the free energies of solvation of two solutes, free energy differences in confonnational or tautomeric fonns of the same solute by mutating one molecule or fonn into the other. Figure A2.3.20 illustrates this for the mutation of CFt OFl CFt CFt [92]. 

Within the framework of the same dielectric continuum model for the solvent, the Gibbs free energy of solvation of an ion of radius and charge may be estimated by calculating the electrostatic work done when hypothetically charging a sphere at constant radius from q = 0 q = This yields the Bom equation [13]... 

Kirkwood generalized the Onsager reaction field method to arbitrary charge distributions and, for a spherical cavity, obtained the Gibbs free energy of solvation in tenns of a miiltipole expansion of the electrostatic field generated by the charge distribution [12, 1 3]... 

As with SCRF-PCM only macroscopic electrostatic contribntions to the Gibbs free energy of solvation are taken into account, short-range effects which are limited predominantly to the first solvation shell have to be considered by adding additional tenns. These correct for the neglect of effects caused by solnte-solvent electron correlation inclnding dispersion forces, hydrophobic interactions, dielectric saturation in the case of... 

McDonald, N. A., Carlson, H. A., Jorgensen, W. L. Free energies of solvation in chloroform and water from a linear response approach. J. Phys. Org. Chem. 10 (1997) 563-576... 

It is often the case that the solvent acts as a bulk medium, which affects the solute mainly by its dielectric properties. Therefore, as in the case of electrostatic shielding presented above, explicitly defined solvent molecules do not have to be present. In fact, the bulk can be considered as perturbing the molecule in the gas phase , leading to so-called continuum solvent models [14, 15]. To represent the electrostatic contribution to the free energy of solvation, the generalized Bom (GB) method is widely used. Wilhin the GB equation, AG equals the difference between and the vacuum Coulomb energy (Eq. (38)) ... 

The total electrostatic free energy G j of a system is given by the sum of the Coulomb energy and the Bom free energy of solvation (Eq. (39)) ... 

The Electrostatic Contribution to the Free Energy of Solvation The Born and Onsager Models... 

The solvent accessible surface area (SASA) method is built around the assumption that the greatest amount of interaction with the solvent is in the area very close to the solute molecule. This is accounted for by determining a surface area for each atom or group of atoms that is in contact with the solvent. The free energy of solvation AG° is then computed by... 

The accuracy of these methods is tested by finding the mean absolute error between the computed and experimental free energies of solvation. The SM4 method does well for neutral molecules in alkane solvents with a mean absolute error of 0.3 kcal/mol. For neutral molecules, the SM5 methods do very well with mean absolute errors in the 0.3 to 0.6 kcal/mol range, depending on the method and solvent. For ions, the SMI method seems to be most accurate with... 

The free energy of activation at the QCISD(T)/6-31 H-- -G(d,p) level amounts to 21.1 kcal/mol. According to the authors, the large electron density redistribution arising upon cyclization makes it necessary to use extended basis sets and high-order electron correlation methods to describe the gas-phase thermodynamics, which indicates clearly the gas-phase preference of the azido species. However, the equilibrium is shifted toward the tetrazole as the polarity of a solvent is increased. For instance, SCRF calculations (e = 78.4) yield a relative free energy of solvation with respect to the cw-azido isomer of —2.4 kcal/mol for the tmns-zziAo compound and of —6.8 kcal/mol for the tetrazole isomer. At a much lower level, the... 

R. Gomer, and G. Tryson, An experimental determination of absolute half-cell emfs and single ion free energies of solvation, J. Chem. Phys. 66, 4413-4424 (1977). 

Real Free Energy of Solvation of H+ and Absolute Potential of h( s) in Different Solvents ... 

Duffy, E. M., Jorgensen, W. L. Prediction of properties from simulations free energies of solvation in hexadecane, octanol, and water. J. Am. Chem. Soc. 2000, 122, 2878-2888. 

Totrov [31] developed a model to estimate electrostatic solvation transfer energy AGd" in Eq. (1) based on the Generalized Born approximation, which considers the electrostatic contribution to the free energy of solvation as ... 

MD simulations in expHcit solvents are stiU beyond the scope of the current computational power for screening of a large number of molecules. However, mining powerful quantum chemical parameters to predict log P via this approach remains a challenging task. QikProp [42] is based on a study [3] which used Monte Carlo simulations to calculate 11 parameters, including solute-solvent energies, solute dipole moment, number of solute-solvent interactions at different cutoff values, number of H-bond donors and acceptors (HBDN and HBAQ and some of their variations. These parameters made it possible to estimate a number of free energies of solvation of chemicals in hexadecane, octanol, water as well as octanol-water distribution coefficients. The equation calculated for the octanol-water coefficient is ... 

To calculate free energies of solvation for several organic molecules, Fortunelli and Tomasi applied the boundary element method for the reaction field in DFT/SCRF framework173. The authors demonstrated that the DFT/SCRF results obtained with the B88 exchange functional and with either the P86 or the LYP correlation functional are significantly closer to the experimental ones than the ones steming from the HF/SCRF calculations. The authors used the same cavity parameters for the HF/SCRF and DFT/SCRF calculations, which makes it possible to attribute the apparent superiority of the DFT/SCRF results to the density functional component of the model. The boundary element method appeared to be very efficient computationally. The DFT/SCRF calculations required only a few percent more CPU time than the corresponding gas-phase SCF calculations. 

Fig. 2.5. Possible applications of a coupling parameter, A, in free energy calculations, (a) and (b) correspond, respectively, to simple and coupled modifications of torsional degrees of freedom, involved in the study of conformational equilibria (c) represents an intramolecular, end-to-end reaction coordinate that may be used, for instance, to model the folding of a short peptide (d) symbolizes the alteration of selected nonbonded interactions to estimate relative free energies, in the spirit of site-directed mutagenesis experiments (e) is a simple distance separating chemical species that can be employed in potential of mean force (PMF) calculations and (f) corresponds to the annihilation of selected nonbonded interactions for the estimation of e.g., free energies of solvation. In the examples (a), (b), and (e), the coupling parameter, A, is not independent of the Cartesian coordinates, x. Appropriate metric tensor correction should be considered through a relevant transformation into generalized coordinates...

An alternative approach to calculating the free energy of solvation is to carry out simulations corresponding to the two vertical arrows in the thermodynamic cycle in Fig. 2.6. The transformation to nothing should not be taken literally -this means that the perturbed Hamiltonian contains not only terms responsible for solute-solvent interactions - viz. for the right vertical arrow - but also all the terms that involve intramolecular interactions in the solute. If they vanish, the solvent is reduced to a collection of noninteracting atoms. In this sense, it disappears or is annihilated from both the solution and the gas phase. For this reason, the corresponding computational scheme is called double annihilation. Calculations of... 

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