Potentials and Free Energy

Recall that free energy is related to the maximum possible amount of work that can he done hy the system. In the case of a galvanic cell, the work done is electrical work, so we can state the relationship between fi-ee energy and the cell potential as 

Suppose that we wish to study the possible galvanic corrosion between zinc and chromium, so we set up the following cell  

What is the chemical reaction that takes place, and what is the standard free energy change for that reaction  

To calculate the free energy change, we must know two things the cell potential and the number of electrons transferred in the reaction. Then we can simply use these values in Equation 13.5 to obtain the free energy change. 

First we need the balanced chemical equation, which in this case can be written immediately because two electrons are transferred in each half-reaction ( = 2)  

---

The chemical potentials and free energies of the 2-isoxazolines have also been studied and the electron impact and chemical ionization mass spectra determined (77MI41614). Fragmentation pathways and retrocycloadditions of various derivatives were discussed in these reports. 

Before dealing with various important applications of the electrochemical series with some practical examples, a break is given here to present a more detailed elaboration on the hydrogen electrode, reference electrodes, and some of the theoretical and general aspects pertaining to electrode potentials and free energy changes involved with cell reactions. 

This chapter reviewed some of our group s contributions to the development and application of QM/MM methods specifically as applied to enzymatic reactions, including the use of sequential MD/QM methods, the use of effective fragment potentials for reaction mechanisms, the development of the new QM/MM interface in Amber, as well as the implementation and optimization of the SCC-DFTB method in the Amber program. This last implementation allows the application of advanced MD and sampling techniques available in Amber to QM/MM problems, as exemplified by the potential and free energy surface surfaces for the reaction catalyzed by the Tripanosoma cruzi enzyme /ram-sialidasc shown here. 

Table 3-1 shows the comparison between our previous calculations and the present results for the potential and free energy differences for selected structures. Overall the results are in agreement. However, it is important to note that the present results are lower than the previous ones in all cases. 

Table 3-1. Calculated potential and free energy differences for path B (in kcal/mol) between the determined structure and the reactant (ES complex), where Ait is the total HF potential energy difference, A Eqm refers to the QM energy difference between two QM subsystems. A 1 qm/MM is the free energy change in the QM/MM interaction, and A F = AEqm + A I qm/MM- Numbers without parentheses correspond to the present work and numbers in parentheses correspond to our previous determinations (path D) [33]...

Table 3-2. Potential and free energy differences (in kcal/mol) for the TS and intermediate points of all four paths. All energies are relative to the respective reactant structure...

The calculated potential and free energies for the first step of the four paths is presented in Table 3-2. As can be seen, the paths calculated with the combined procedure present activation energies of 17.77 and 16.85 kcal/mol for paths A and B respectively. On the other hand, the calculated potential activation energies are 20.37 kcal/mol for path C and 22.02 for path D. This is in contrast to the calculated... 

In the case of the intermediates, the calculated potential and free energies for the first three paths follow the same trend as for the TS. However, a big difference is observed with respect to path D. This energy difference is due to the fact that in the case of the first three paths, the MM environment of the intermediate structure was more relaxed for the calculations than that of path D. This relaxation in the environment resulted in the big energy differences for both the potential and free energy barriers of path D with respect to the other paths. 

We have compared the potential and free energies from four different calculated paths for the first step of the isomerization of 2o4hex catalyzed by 40T. Two of these paths were determined with a combined chain-of-states method. The remaining two paths were obtained with the coordinate driving method. 

Cations in general should be reactive toward eh, but considerations of redox potential and free energy change are important. Thus, the alkali metal cations, having higher redox potentials, are unreactive toward eh. Another example is... 

These conventions are arbitrary, but you must use them if you wish to use tabulated values of equilibrium constants, standard reduction potentials, and free energies. 

Cell Potentials and Free-Energy Changes for Cell Reactions... 

Figure 1. Relationships between charge densities, potentials, and free energies in James—Healy and VSC-VSP models...

Table 5. Redox potentials and free energy changes for electron transfer between the ground state of selected group of amines and the excited states of anthraquinone and dicyanoanthracene. ...

The Coulombic term in Eq. 6 becomes negligible in polar solvents owing to shielding of the electrostatic interaction between the radical ions generated. Table 5 lists representative redox potentials and free energies for photo-mediated electron transfer between a selected group of amines and photosensitizers such as anthraquinone (AQ) and dicyanoanthracene (DCA). 

Similarly to the RPM case the pressure, the chemical potentials and free energy contain three different contributions the hard-sphere contributions (HS), the contributions from the mass action law (MAL) and electrostatic contribution (EL). 

Galvanic Cells, Cell Potentials, Standard Reduction Potentials, and Free Energy... 

The characteristic model distance des is taken to be zero at coincidence of the Stern surfaces, implying that the actual virus-to-solid separation distance would be approximately I nm on the basis of Smith s work (29). This is quite reasonable, and all solid-virus interaction potentials and free energy differences are matched with a single model distance. 

Table 3. Reduction potentials and free energies of possible reactions between the copper centers of polyporous laccase and some species of reduced oxygen...

---