Conformational free energy, definition

For a monosubstituted oxane, the excess free enthalpy of the conformation with an axial substituent over the conformation with an equatorial substituent is, as we know by definition, the conformational free energy (CFE) of the substituent in oxane at this position. These values, possibly measured indirectly by utilizing intennediate compounds, are shown in Table 2.2. Equatorial conformations correspond to anti conformations in butane and methoxyethane, and the axial conformations (not represented) to gauche conformations. We can observe that the environment of derivative 2.20 is closest to that of the cyclohexane and that the CFE is of the same order. On the other hand, the presence of the cyclic oxygen lowers notably the CFE of derivative 2.19. The important point is the noteworthy increase in the CFE of compound 2.18, where the methyl group is close to the cyclic oxygen and possesses, on one side, an environment similar to that of methoxyethane. Let us look at the equilibrium (2.4) of the dimethylated derivative 2.21. 

However, let note, that the assumption about independence of the osmotic pressure of semi-diluted solutions on the length of a chain is not physically definitely well-founded per se it is equivalent to position that the system of strongly intertwined chains is thermodynamically equivalent to the system of gaped monomeric links of the same concentration. Therefore, both Flory-Huggins method and Scaling method do not take into account the conformation constituent of free energy of polymeric chains. 

Equation 2.16 contains contributions from the translational entropy of the mobile species, the conformational entropy of polymer chains, the free energy associated with the different chemical equilibria in the system, the polymer-polymer and polymer-surface van der Waals (vdW) interaction energies, the electrostatic interaction energies and the repulsive interactions between all the different molecular species. The expressions for each of these terms are shown in Table 2.2, while the definition of the symbols is given in Appendix. Note that in Table 2.2, the densities. 

Conformational isomerism, as already defined (Section 3.b), is a property of stereoisomers separated by a low barrier of energy. The separation of isomers at room temperature requires half-lives of several hours, which correspond approximately to a free energy of activation of AG > 20 kcal/mol [56]. An operational and convenient definition of conformational isomerism is thus to consider as conformers those stereoisomers which are not physically separable under ordinary conditions, in other words, which are separated by an energy barrier lower than 20 kcal/mol. Such a definition is further useful in that it sets no conditions as to the chemical process by which conformer interconversion occurs while bond rotation is the most frequently encountered interconversion process, inversion processes are also important. 

Nonetheless, this raises the question of what is an appropriate definition of the NAC. Mulholland suggests a definition that is much less arbitrary the NAC is the conformation of the substrate bound to the enzyme, and what is critical then is the free energy needed to form this conformation in aqueous solution. MulhoUand estimates this energy as 4-5 kcal mol through a free energy perturbation calculation and MD using AMI and CHARMM. This is half the estimate of Bruice and suggests that formation of the NAC is only partly responsible for the catalytic effect afforded by CM. 

It should be emphasized that A/jls is dependent on rc and Eq.(3.12) differs from the usual definition of the solvation free energy where the conformation of the biomolecule is not fixed. Substituting Eqs. (3.10) and (3.11) into Eq.(3.6) and using Eq.(3.12) yield... 

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