Solution basicity computation

W. J. Irwin, Kinetics of Drug Decomposition, Basic Computer Solutions, Elsevier Science, Amsterdam, 1990. 

This simplified calculation is used to illustrate basic computational techniques. It assumes that all of the Fe(OH)3(aq) is a true solute. The quality of this assumption is a matter of debate as at pH 8, Fe(OH)3(aq), tends to form colloids. Thus, laboratory measurements of ferrihydrite solubility yield results highly dependent on the method by which [Fe(lll)]jQ(gj is isolated. Ultrafiltration techniques that exclude colloids from the [Fe(lll)]jQjgj pool produce very low equilibrium solubility concentrations, on the order of 0.01 nM. This is an important issue because a significant fraction of the iron in seawater is likely colloidal, some of which is inorganic and some organic. In oxic... 

Pranata, J., Relative basicities of carboxylate lone pairs in aqueous solution, J. Comput. Chem. 14,685-690(1993). 

It would be difficult to find more comprehensive or more detailed studies on the physical chemistry of seawater than those done at the University of Miami (Millero, 2001). Several programs were developed for calculation of activity coefficients and speciation of both major ions and trace elements in seawater. The activity coefficient models have been influenced strongly by the Pitzer method but are best described as hybrid because of the need to use ion-pair formation constants (Millero and Schreiber, 1982). The current model is based on Quick Basic computes activity coefficients for 12 major cations and anions, 7 neutral solutes, and more than 36 minor or trace ions. At 25 °C the ionic strength range is 0-6 m. For major components, the temperature range has been extended to 0-50 °C, and in many cases the temperature dependence is reasonably estimated to 75 °C. Details of the model and the parameters and their sources can be found in Millero and Roy (1997) and Millero and Pierrot (1998). Comparison of some individual-ion activity coefficients and some speciation for seawater computed with the Miami model is shown in Section 5.02.8.6 on model reliability. 

Due to the complex weave pattern for LAD screens, it is difficult to derive an exact solution for the flow through a LAD screen. An empirical solution from Armour and Cannon (1968) has been proposed, as well as basic computational fluid dynamics simulations from Zhang et al. (2009) for the flow through a LAD screen. Using the logic from Armour and Cannon (1968), the approximate solution is formulated as the sum of the pressure drop due to viscous (laminar) and inertial (turbulent) resistance. 

The question now is In spite of significant solvent effects, are the solution Lewis basicity scales closely related to the intrinsic gas-phase Lewis basicity scales This is an important question for computational chemists who need to identify the computational methods that yield reliable basicities. A relative comparison of gas-phase computed basicities with solution experimental basicities would avoid the difficult and approximate modelling of the solvent effect [105]. However, this comparison requires that experimental gas-phase and solution basicities (affinities) be strongly correlated. This correlation appears to exist for BF3 affinities and hydrogen-bond basicities. Equation 1.96... 

Ultimately, the affinity or the basicity scales themselves might be computed. This has been done successfully for the methanol affinity in the gas phase [41]. However, the MP2/aug-cc-pVTZ//B3LYP/6-3H-G(d,p) costly level required to obtain good agreement with experimental affinities has limited the scale to a few small Lewis bases. Proton and cation affinities and basicities in the gas phase are now computed on a routine basis (see Chapter 6). Nevertheless, the size of Lewis bases and cations and the number of bases studied are inversely proportional to the level of theory, that is, to the agreement with experimental data. As far as extended solution basicity scales towards usual Lewis acids... 

It can be said that these three main strategies have been applied equally and very often in combination. Basically, the first approach implies the use of a faster computer or a parallel architecture. To some extent it sounds like a brute force approach but the exponential increase of the computer power observed since 1970 has made the hardware solution one of the most popular approaches. The Chemical Abstracts Service (CAS) [10] was among first to use the hardware solution by distributing the CAS database onto several machines. 

Three basic approaches have been used to solve the equations of motion. For relatively simple configurations, direct solution is possible. For complex configurations, numerical methods can be employed. For many practical situations, particularly three-dimensional or one-of-a-kind configurations, scale modeling is employed and the results are interpreted in terms of dimensionless groups. This section outlines the procedures employed and the limitations of these approaches (see Computer-aided engineering (CAE)). 

Method of Continuity (Homotopy) In the case of n equations in n unknowns, when n is large, determining the approximate solution may involve considerable eftoid. In such a case the method of continuity is admirably suited for use on digital computers. It consists basically of the introduction of an extra variable into the n equations... 

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. 

Although GA are undeniably powerful computational tools and have been successfully applied to an impressive variety of problems (see below), they certainly do not represent a cure-all solution to all types of problems. One finds that, in practice, certain problems arc more amenable to this kind of solution scheme than others, and that it is not always obvious why that is so. Much foundational work still remains to be done in developing a complete theory of GA behaviors and capabilities. Figure 11.10 illustrates the basic steps involved in applying a GA. 

An important step toward the understanding and theoretical description of microwave conductivity was made between 1989 and 1993, during the doctoral work of G. Schlichthorl, who used silicon wafers in contact with solutions containing different concentrations of ammonium fluoride.9 The analytical formula obtained for potential-dependent, photoin-duced microwave conductivity (PMC) could explain the experimental results. The still puzzling and controversial observation of dammed-up charge carriers in semiconductor surfaces motivated the collaboration with a researcher (L. Elstner) on silicon devices. A sophisticated computation program was used to calculate microwave conductivity from basic transport equations for a Schottky barrier. The experimental curves could be matched and it was confirmed for silicon interfaces that the analytically derived formulas for potential-dependent microwave conductivity were identical with the numerically derived nonsimplified functions within 10%.10... 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

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