Solution-phase energies

Solvation can have an influence on the relative stability of different surface intermediates. Solution-phase energies are more challenging to calculate than vacuum ones the solution phase involves many more species and the (free) energy... 

Much of chemistry occurs in the condensed phase solution phase ET reactions have been a major focus for theory and experiment for the last 50 years. Experiments, and quantitative theories, have probed how reaction-free energy, solvent polarity, donor-acceptor distance, bridging stmctures, solvent relaxation, and vibronic coupling influence ET kinetics. Important connections have also been drawn between optical charge transfer transitions and thennal ET. 

Procedures to compute acidities are essentially similar to those for the basicities discussed in the previous section. The acidities in the gas phase and in solution can be calculated as the free energy changes AG and AG" upon proton release of the isolated and solvated molecules, respectively. To discuss the relative strengths of acidity in the gas and aqueous solution phases, we only need the magnitude of —AG and — AG" for haloacetic acids relative to those for acetic acids. Thus the free energy calculations for acetic acid, haloacetic acids, and each conjugate base are carried out in the gas phase and in aqueous solution. 

There is an excellent correlation between these data and the gas-phase data, in terms both of the stability order and the energy differences between carbocations. A plot of the gas-phase hydride affinity versus the ionization enthalpy gives a line of slope 1.63 with a correlation coefficient of 0.973. This result is in agreement with the expectation that the gas-phase stability would be somewhat more sensitive to structure than the solution-phase stability. The energy gap between tertiary and secondary ions is about 17kcal/mol in the gas phase and about 9.5 kcal/mole in the SO2CIF solution. 

In contrast to apportioning the standard free energy between different groups in the solute molecule, the standard free energy can also be dispensed between the different types of forces involved in the solute/phase-phase distribution. This approach has been elegantly developed by Martire et al. [13]. In a simplified form, the standard free energy can be divided into portions that result from the different types of interaction, e.g.,... 

It seems justified to supplement the authors conclusions by adding that in the case of samples pretreated with hydrogen their higher energy of activation (12.3 kcal/mole) may result from the presence of a certain content of the /8-hydride phase in the a-solution phase. 

The basic scheme for the numerical solution is the same as that used for the 1 -D model, except that in this case the solid temperature field used to solve the DAE system for each monolith channel must be calculated from the three-dimensional solid-phase energy balance equation. The three-dimensional energy balance equation can be solved by a nonlinear finite element solver (such as ABAQUS) for the solid-phase temperature field while a nonlinear finite difference solver for the DAE system calculates the gas-phase temperature and... 

The solution phase is modeled explicitly by the sequential addition of solution molecules in order to completely fill the vacuum region that separates repeated metal slabs (Fig. 4.2a) up to the known density of the solution. The inclusion of explicit solvent molecules allow us to directly follow the influence of specific intermolecular interactions (e.g., hydrogen bonding in aqueous systems or electron polarization of the metal surface) that influence the binding energies of different intermediates and the reaction energies and activation barriers for specific elementary steps. 

Furthermore, the changes in the binding energy that result upon changes in the potential can result in dissociation and/or substitution by other solution-phase species. These last two topics will be explored in further detail later in this chapter. 

Relatively few investigations involving palladium carbonyl clusters have been carried out, partly because palladium per se does not form stable, discrete homometallic carbonyl clusters at room temperature in either solid or solution states.114,917-922 Nevertheless, solution-phase palladium carbonyl complexes have been synthesized with other stabilizing ligands (e.g., phosphines),105,923 and carbon monoxide readily absorbs on palladium surfaces.924 Moreover, gas-phase [Pd3(CO)n]-anions (n = 1-6) have been generated and their binding energies determined via the collision-induced dissociation method.925... 

Where AG is free energy, R is gas constant (1.987 cal/deg K mole-1), T is degrees Kelvin, and AS is entropy. Kd is the distribution constant of the herbicide between the solution phase and the adsorbed phase (equation 4). Thus, least squares linear regression analysis of ln(Kd) vs. 1/T yielded values for heats of adsorption (AH) for the herbicides in Keeton soil. 

When the gas-phase reactions, such as the relative acidities or basicities were compared with their counterparts in solution (in a solvent such as water) it was generally found16,17 that the energetics in the solvent were strongly affected by solvation effects and particularly the solvation of the ionic reactants. Relationships between the gas-phase and solution-phase reactions and the solvation energies of the reactants are generally obtained through thermodynamic cycles. From the cycle,... 

The time resolved spectra produced on excimer laser photolysis of Mn2(CO)io are shown in figure 6. Note that as in the case of iron pentacarbonyl and chromium hexacarbonyl photolysis, there is a distinct increase in the amplitude of the lower frequency absorption bands as the photolysis energy increases. By comparison with the frequency of matrix isolated and solution phase Mn(C0)5, the band at -1996 cm l is assigned to the gas phase Mn(C0)5 radical [33]. This... 

So far we have not touched on the fact that the important topic of solvation energy is not yet taken into account. The extent to which solvation influences gas-phase energy values can be considerable. As an example, gas-phase data for fundamental enolisation reactions are included in Table 1. Related aqueous solution phase data can be derived from equilibrium constants 31). The gas-phase heats of enolisation for acetone and propionaldehyde are 19.5 and 13 keal/mol, respectively. The corresponding free energies of enolisation in solution are 9.9 and 5.4 kcal/mol. (Whether the difference between gas and solution derives from enthalpy or entropy effects is irrelevant at this stage.) Despite this, our experience with gas-phase enthalpies calculated by the methods described in this chapter leads us to believe that even the current approach is most valuable for evaluation of reactivity. 

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