Free energy calculations definition

The solvation free energy calculated by considering only the bulk electrostatics is somewhat arbitrary because the boundary between the dielectric medium and the solute is not well defined, and in fact the treatment of the solvent as a homogeneous, isotropic, linear medium right up to a definite boundary is not valid. To obtain an accurate solvation... 

Free energy calculations for the uptake of HO2 and of its conjugated basis, the superoxide anion O2, made possible an estimation of the pK and redox potentials at the air-water interface [27]. The QM/MM calculations for the interface pK of HO2 yield 6.3 0.5 (experimental value is 4.8 in bulk water), whereas estimation of the redox potential of the O2/O2 couple at the interface yields —0.65 eV (experimental value is -0.33 eV in bulk water). Obviously, the precise definition of these quantities at the interface is not straightforward since it implicates a system characterized by large fluctuations and non-equilibrium phenomena (see below) indeed, some usual chemical concepts in bulk solution may need to be revisited when handling with liquid interfaces. 

Again, if we consider the initial substances in the state of liquids or solids, these will have a definite vapour pressure, and the free energy changes, i.e., the maximum work of an isothermal reaction between the condensed forms, may be calculated by supposing the requisite amounts drawn off in the form of saturated vapours, these expanded or compressed to the concentrations in the equilibrium box, passed into the latter, and the products then abstracted from the box, expanded to the concentrations of the saturated vapours, and finally condensed on the solids or liquids. Since the changes of volume of the condensed phases are negligibly small, the maximum work is again ... 

Despite many papers over many years, there is still a serious shortage of information that allows linear free energy relation treatment of these reactions. The available linear free energy relations, some of them calculated for this chapter, are collected in Tables 1.4 and 1.5. There are definite indications that p is... 

As equation 2.4.8 indicates, the equilibrium constant for a reaction is determined by the temperature and the standard Gibbs free energy change (AG°) for the process. The latter quantity in turn depends on temperature, the definitions of the standard states of the various components, and the stoichiometric coefficients of these species. Consequently, in assigning a numerical value to an equilibrium constant, one must be careful to specify the three parameters mentioned above in order to give meaning to this value. Once one has thus specified the point of reference, this value may be used to calculate the equilibrium composition of the mixture in the manner described in Sections 2.6 to 2.9. 

As we pointed out earlier, calculating the derivative of the free energy appears to require a full set of generalized coordinates. However, this may seem quite surprising. Assume that we want to define the PMF as a function of the distance between two molecules. This force is clearly independent of the particular choice of generalized coordinates made to calculate it. In fact, we are now going to prove that an equation can be derived which does not require an explicit definition of generalized coordinates other than . 

The tools for calculating the equilibrium point of a chemical reaction arise from the definition of the chemical potential. If temperature and pressure are fixed, the equilibrium point of a reaction is the point at which the Gibbs free energy function G is at its minimum (Fig. 3.1). As with any convex-upward function, finding the minimum G is a matter of determining the point at which its derivative vanishes. 

In both solvents, the variational transition state (associated with the free energy maximum) corresponds, within the numerical errors, to the dividing surface located at rc = 0. It has to be underlined that this fact is not a previous hypothesis (which would rather correspond to the Conventional Transition State Theory), but it arises, in this particular case, from the Umbrella Sampling calculations. However, there is no information about which is the location of the actual transition state structure in solution. Anyway, the definition of this saddle point has no relevance at all, because the Monte Carlo simulation provides directly the free energy barrier, the determination of the transition state structure requiring additional work and being unnecessary and unuseful. 

If the heat capacity of a chemically complex melt can be obtained by a linear summation of the specific heat of the dissolved oxide constituents at all T (i.e., Stebbins-Carmichael model), the melt is by definition ideal. The addition of excess Gibbs free energy terms thus implies that the Stebbins-Carmichael model calculates only the ideal contribution to the Gibbs free energy of mixing. 

It is not possible at present to evaluate this function theoretically. The system is too complicated. The complexity of theoretical calculations can best be explained by considering the definition of AGg and processes involved in the activation process. AGf is defined in Figure 6.1. Free energy of activation for the forward reaction is the free-energy difference between the free energy of the activated state, G, and the free energy of the initial state, G ... 

Fig.1 Calculated free energy diagram for hydrogen evolution at a potential U = 0 V relative to the standard hydrogen electrode at pH = 0. The free energy of H+ + e is by definition the same as that of j - i at standard conditions. The free energy of H atoms bound to different catalysts is then found by calculating the free energy with respect to molecular hydrogen including zero-point energies and entropy terms (reprinted from Ref 83 with permission).

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