Electrostatic correction

A theoretical approach based on the electrical double layer correction has been proposed to explain the observed enhancement of the rate of ion transfer across zwitter-ionic phospholipid monolayers at ITIES [17]. If the orientation of the headgroups is such that the phosphonic group remains closer to the ITIES than the ammonium groups, the local concentration of cations is increased at the ITIES and hence the current observed due to cation transfer is larger than in the absence of phospholipids at the interface. This enhancement is evaluated from the solution of the PB equation, and calculations have been carried out for the conditions of the experiments presented in the literature. The theoretical results turn out to be in good agreement with those experimental studies, thus showing the importance of the electrostatic correction on the rate of ion transfer across an ITIES with adsorbed phospholipids. 

Table 1. Average ligand-surrounding interaction energies, electrostatic corrections and observed binding free energies (kcal/mol) for the eight thrombin inhibitors (from Ref. 46). b...

Equation (96) shows that the effective KS potential may be simply obtained by adding to the standard KS potential of the isolated solute, an electrostatic correction which turns out to be the RE potential Or, and the exchange- correlation correction 8vxc. It is worth mentioning here, that Eq (96) is formally equivalent to the effective Fock operator correction bfteffi defined in the context of the self consistent reaction field (SCRF) theory [2,3,14] within the HF theory, the exchange contribution is exactly self-contained in Or, whereas correlation effects are completely neglected. As a result, within the HF theory 8v = Or, as expected. 

The complete treatment of solvation effects, including the solute selfpolarization contribution was developed in the frame of the DFT-KS formalism. Within this self consistent field like formulation, the fundamental expressions (96) and (97) provide an appropriate scheme for the variational treatment of solvent effects in the context of the KS theory. The effective KS potential naturally appears as a sum of three contributions the effective KS potential of the isolated solute, the electrostatic correction which is identified with the RF potential and an exchange-correlation correction. Simple formulae for these quantities have been presented within the LDA approximation. There is however, another alternative to express the solva-... 

Electrostatic discrete functional group models. The development of charge on the surface of the humic macromolecule decreases the tendency to dissociate protons from the acid functional groups. To overcome this problem an electrostatic correction factor is introduced into the acid dissociation and complexation constants. This is similar to the approach adopted for the SCMs for inorganic surfaces. 

Entry no. 2 presents another problem in that the electrostatic correction term for AG° in the solvent used, acetic acid, is very large, —15.3 kcal mol-1 (see Table 3 Z,Z2 = —2, rn = 7 A). Again, E° = 2.52 V is far too small to give any reasonable fit to the Marcus relation. With E° = 3.08 V, the result is at least consistent with that of entry no. 1. Entries nos. 3 and 4 have been treated with A values for self-exchange reactions of pyridine and acetate equal to 10 and 20 kcal mol-1 respectively fccalc comes out at 1010 M 1 s irrespective of the choice of E° = 2.52 or 3.08 V. For entry no. 5 X (CH3OH) was assumed to be > 20 kcal mol-1 and the quoted value of kcalc is estimated with E° = 3.08 V. It thus represents a maximum value and the reaction is certainly not feasible as an electron-transfer step. 

Based on the Fe(EDTA)2- results, the blue copper center in stellacyanin appears to be much more accessible than that situated in either azurin or plastocyanin. Thus it should be profitable to compare the electron transfer reactivities of these three proteins with a variety of redox agents. Kinetic studies of the oxidation of the three blue proteins by Co(phen)33+ have been made (26), and the results together with those for other redox agents are set out in Table IV. The electrostatic corrections to the predicted kn values are modest both for the large charge on plastocyanin and the small one on azurin, as the protein selfexchange and the cross reaction work terms compensate. The reactivity... 

The electrostatics-corrected self-exchange rate for plastocyanin based on Co(phen)33+ is 2.6 X 103 M 1 sec 1. The kncorr value for plastocyanin based on the cytochrome c cross reaction, 5 X 105 M"1 sec 1, is substantially smaller than the uncorrected value (3 X 107 M 1 sec 1). Taking either value, however, it is apparent that both cytochrome c and Co-(phen)33+ are better electron transfer agents for plastocyanin than is Fe(EDTA)2". 

Fig. 8.2 Measured impact sensitivities (/i50 values) plotted against computed AV for various energetic compounds (a = nitramines, = non-nitramine energetic compounds) (a). Comparison of impact sensitivities predicted on an electrostatically corrected volume-based model [39f,g] (b).

Figure 5.4 Finite-size correction of the probability densities of the electrostatic energies of positively charged imidazolium ion in water. The uncorrected distributions are shown with symbols, together with corresponding Gaussian distributions. In addition to the electrostatic correction, a thermodynamic correction is also applied, but this correction is small in magnitude, see Hummer etal. (1998ft). With the corrections, the distributions collapse and agree closely for all system sizes of 16 < iV < 512 water molecules.

Electrostatic correction computed by the Kirkwood-Westheimer theory. 

The intrinsic constants are thermod3mamic constants written for reactions occurring at a hypothetical isolated site on the surface. Actual activities on the surface cannot be directly determined but Q or apparent stability quotients can be calculated based on measurable bulk concentrations. The intrinsic constants and apparent stability quotients are related by considering the electrostatic correction for an ion in solution near the surface compared to an isolated ion on the surface. In an idealized planar model, is the mean potential at the plane of surface charge created by the ionization of the surface functional groups and the formation of surface complexes and is the mean potential at the plane of adsorbed counter ions at a distance 3 from the surface (17). The electrostatic interaction energies at the surface and at a distance 3 are expressed as exponentials. Therefore ... 

More recently, Westall, et al. (1995) have developed a relatively simple log K spectrum model without inclusion of explicit electrostatic corrections. 

Electrostatic correction was made with the diffuse (Gouy-Chapman) double-layer model. The figure shows the effect of pH on the relative extent of surface complexation. 

Figure 7. The effect of ligands and metal ions on surface protonation of a hydrous oxide is illustrated by two examples (1). Part a Binding of a ligand (pH 7) to hematite, which increases surface protonation. Part h Adsorption of Pb2+ to hematite (pH 4.4), which reduces surface protonation. Part c Surface protonation of hematite alone as a function of pH (for comparison). All data were calculated with the following surface complex formation equilibria (1 = 5 X 10"3 M >. Electrostatic correction was made by diffuse double layer model.

In order to be true constants, surface equilibrium constants must be written in terms of dissolved species concentrations at the oxide surface constants written in terms of bulk solution concentrations require an electrostatic correction for the effects of the electrical double layer... 

In Equation 1.6, the electrostatic correction to AG° vanishes when z — z2 = 1 (e.g., whenzi andz2 are equal, respectively, to 3 and 2,2 and 1,1 and 0, 0 and — 1, —1 and —2, etc.)-2 In these cases, the difference in Gibbs free energy between the successor and precursor complexes is not significantly different from that between the individual (separated) reactants and final (separated) products (Scheme 1.1). 

For the treatment of large polyatomic systems, computational methodologies deal with a compromise between an overall description of the entire system and a more detailed handling of a properly selected part of it. This situation particularly applies to the transition metal structures that have to be drastically minimized for an adequate ob initio, local density functional, or even semiempirical calculation at a good correlation level. In contrast to this simplification of the system, the improvements of the simpler methods, which are capable of handling the system as a whole, have regained acceptability. This is the case of the EHMO method developed by Hoffman [19], which was initially used for a reasonable description of the structural and electronic properties of the systems at a frozen geometry. Improvements of this method are mainly related to the addition of the (two-body electrostatic correction) term as explained above [20,21],... 

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