Energy curves profiles

Fig. 13 Energy profiles for C C, Cl in DMF. Curve a potential energy in the gas phase. Curve b potential energy in the solvent (D p = 62 meV). Curve c variation of the solvation free energy. Curve d solvent reorganization energy.

If one now sets the potential of the working electrode more positive than that of equilibrium, the oxidation process is facilitated (as seen in Figure 5). Thus, the profile of the free energy curves becomes that illustrated in Figure 12, in which the energy barrier for the oxidation is lower than that of reduction. 

Figure 3. Computed potential energy curves for the diabatic and adiabatic state in the [HsN-H-NH ] system in the gas phase using 6-31G(d) basis set. The HF and MOVE energy profiles are overlapping.

A fascinating category of experiments can be found in Table IV. These are the use of lasers to determine thermodynamic parameters. These include calorimetry (43), enthalpies of vaporization and vaporization rates (44, 45), and heat capacities (46). Other laser experiments that can be found in Table IV include the use of CW laser spectroscopy to determine the iodine binding-energy curve (47), the study of vibrational line profiles to determine intermolecular interactions (48), two photon ionization spectrometry (49), a study of optical activity and optical rotatory dispersion (50) and the development of several experiments using blue diode lasers (57). 

Figure 15.1 Effect of /3-phase particle size on the concentration, Xeq, of component B in the a phase in equilibrium with a /3-phase particle in a binary system at the temperature T. assuming that, 6 is pure B. (a) Schematic free-energy curves for a phase and three /3-phase particles of different radii, R > R2 > Rs. The free energies (per mole) of the particles increase with decreasing radius due to the contributions of the interfacial energy, which increase as the ratio of interfacial area to volume increases, (b) Corresponding phase diagram. The concentration of B in the a phase in equilibrium with the /0-phase particles, as determined by the common-tangent construction in (a), increases as R decreases, as shown in an exaggerated fashion for clarity, (c) Schematic concentration profiles in the a matrix between the three /3-phase particles.

Figure 7 Qualitative depiction of the energy profile along the reaction co-ordinate for the Sn2 reaction Cl ICII3CI >CICn3 I Cl, which involves nucleophilic substitution of the chloride of methylchloride by a chloride ion. The potential energy curves drop as the two reactants approach until a loose complex is formed. Then the energy rises rapidly to the transition state, which has two equal C-Cl interatomic distances (zero on the abscissa). The energy profile looks quite different in the gas and solution phases. Compared to the reactants (or products), the loose complex and the TS are poorly solvated, so the energies for these are much higher in solution than in a vacuum.

Quantum mechanical calculations in the gas phase and DMSO solution at different temperatures can highlight the hazards of standard 0 K gas-phase calculations.259 For the Wittig reaction, a small barrier in the potential energy curve is transformed into a significant entropic barrier in the free energy profile, and the formally neutral oxaphosphetane intermediate is displaced in favour of the zwitterionic betaine in the presence of DMSO. 

The effects of the solvent and finite temperature (entropy) on the Wittig reaction have been studied by using DFT in combination with molecular dynamics and a continuum solvation model.62 The free energy profile has been found to have a significant entropic barrier to the addition step of the reaction where only a small barrier was present in the potential energy curve. 

Everett and Powl (1976) applied both the 9-3 and the 10-4 expressions in their theoretical treatment of potential energy profiles for the adsorption of small molecules in slit-like and cylindrical micropores. As one would expect, the two corresponding potential energy curves were of a similar shape, but the differences between them became greater as the pore size was reduced. Strictly, the replacement of the summation by integration is dependent on the distance between the molecule and the surface plane, becoming more accurate as the distance is increased (Steele, 1974). 

Figure 11.9 shows an S parameter and o-Ps intensity (I3) vs energy curve for a typical polyurethane (PU) and a polyurethane topcoat paint (PTG) containing a Ti02 pigment. A distinct difference in the depth profile is observed. 

The problem of deciding on the mechanism is especially challenging because it has many of the problems inherent in a discussion of a reaction pathway which may be either concerted or proceed via a biradical intermediate. To illustrate the type of problems involved, consider the reaction coordinate and bond order profile shown in Figure 5. On a free-energy curve, one can imagine that a totally... 

---