Free-energy selectivity parameter

The preceding approach, in principle, also enables the effect of the valency and the activity coefficients of different displacer salts to be considered in the evaluation of the Zc or the corresponding z values for any HP-IEX system. For example, if the retention results for a series of polypeptides and/or proteins chromatographed with the same HP-IEX sorbent, column, flow rate, elution conditions, buffer composition, pH, and at the same temperature, but with NaCl or CaCl2 as the displacing salt are compared, then the relative differences between these two salt systems can be evaluated in terms of a free energy selectivity parameter r such that... 

Linear free energy relationship parameters as a measure of selectivity... 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

While alkane metathesis is noteworthy, it affords lower homologues and especially methane, which cannot be used easily as a building block for basic chemicals. The reverse reaction, however, which would incorporate methane, would be much more valuable. Nonetheless, the free energy of this reaction is positive, and it is 8.2 kj/mol at 150 °C, which corresponds to an equihbrium conversion of 13%. On the other hand, thermodynamic calculation predicts that the conversion can be increased to 98% for a methane/propane ratio of 1250. The temperature and the contact time are also important parameters (kinetic), and optimal experimental conditions for a reaction carried in a continuous flow tubiflar reactor are as follows 300 mg of [(= SiO)2Ta - H], 1250/1 methane/propane mixture. Flow =1.5 mL/min, P = 50 bars and T = 250 °C [105]. After 1000 min, the steady state is reached, and 1.88 moles of ethane are produced per mole of propane consmned, which corresponds to a selectivity of 96% selectivity in the cross-metathesis reaction (Fig. 4). The overall reaction provides a route to the direct transformation of methane into more valuable hydrocarbon materials. 

Measurements of the dissolution behavior of polymorphic forms of relatively insoluble drugs are a convenient way of measuring thermodynamic parameters which, in turn, provide a rational approach to selection of the more energetic polymorphic forms of these drugs for absorption. Large differences in free energy... 

In common with similar approaches that relate solvent accessible surface to cavity free energy90-93, the simple SMI model required careful parameterization, and assumed that atoms interacted with solvent in a manner independent of their immediate molecular environment and their hybridization76. In more recent implementations of the SMx approach, ak parameters are selected for particular atoms based on properties determined from the SCF wavefunction that is evaluated during calculation of the solute and solvent polarization energies27. On the other hand, the inclusion of more parameters in the solvation model requires access to substantial amounts of experimental data for the solvation free energies of molecules in the training set94 95. 

Fig. 2.5. Possible applications of a coupling parameter, A, in free energy calculations, (a) and (b) correspond, respectively, to simple and coupled modifications of torsional degrees of freedom, involved in the study of conformational equilibria (c) represents an intramolecular, end-to-end reaction coordinate that may be used, for instance, to model the folding of a short peptide (d) symbolizes the alteration of selected nonbonded interactions to estimate relative free energies, in the spirit of site-directed mutagenesis experiments (e) is a simple distance separating chemical species that can be employed in potential of mean force (PMF) calculations and (f) corresponds to the annihilation of selected nonbonded interactions for the estimation of e.g., free energies of solvation. In the examples (a), (b), and (e), the coupling parameter, A, is not independent of the Cartesian coordinates, x. Appropriate metric tensor correction should be considered through a relevant transformation into generalized coordinates...

Fig. 2. Selected geometric parameters (A) of the optimized structures of the key species for oxidative coupling for the catalytically active generic [Ni0(r(2-butadiene)2PH3] species la and the [Ni°(ri2-butadiene)3] species Fb of the C8- and Ci2-product channel, respectively, via the most feasible pathway for p2-/rans/r 2-ds-butadiene coupling (of opposite enantiofaces) along la -> 2a and Fb -> 2b. Free energies (AG, AG 5 in kcalmol-1) are given relative to the favorable stereoisomer of the respective bis(r 2-/rans-butadiene) and tris(r 2-/r

A considerable amount of work has been done on the development of water-ion potential energy functions." " Most of these functions are of the standard Lennard-Jones plus Coulomb form, with parameters selected to give the experimental free energy or enthalpy of solvation. ... 

It is a heavy oversimplification to compare the activity of an enzyme in a membrane with its capability to bind a substrate in a bulk system. A more relevant parameter is the free energy of transfer for a substrate molecule to pass from an aqueous phase into the membrane phase and the binding sites of an enzyme. As an example, the ion selectivity of some ionophores changes drastically when comparing the selectivity of a carrier-modified membrane with the selectivity of the same carrier in bulk systems such as water. 

---