Potential calculation

Methfessel M, Rodriguez C O and Andersen O K 1989 Fast full-potential calculations with a converged basis of atom-centered linear muffIn-tIn orbitals structural and dynamic properties of silicon Phys. Rev. B 40 2009-12... 

Hockney R W 1970. The Potential Calculation and Some Applications. Methods in Computational Physi 9 136-211. 

The results of electrostatic potential calculations can be used to predict initial attack positions of protons (or other ions) during a reaction. You can use the Contour Plot dialog box to request a plot of the contour map of the electrostatic potential of a molecular system after you done a semi-empirical or ab initio calculation. By definition, the electrostatic potential is calculated using the following expression ... 

We have performed full-potential calculations on TisSia in its proposed stable crystal structure. The enthalpy of formation obtained from these calculations agrees well with the value deduced from experiment. Due to the low crystal symmetry, the possibility of a more complex bonding character arises. The charge density in this phase differs considerably from that in the hypothetical unstable structure, so two-electron bonds can be excluded in this phase. We have also showed that the opening of a quasigap in the Si DOS has its origin in the Ti-Si interaction. 

Table I. Electrostatic potentials calculated from pKobs values for A — x (3) with various charge densities [42]...

Figure 4 shows the electrostatic potential calculated as a function of E, at distances 5, 10, and 15 A from the cylinder axis by using the data given in Fig. 1. Experimental points come fairly close to the calculated values at 10 A, when > 1.

Fig. 4. Relationship between the electrostatic potential calculated from the PB equation and the charge density parameter at distances 5,10, and 15 A from the axis of a cylinder with 3 A radius. Points indicate experimental data listed in Table 1 [42]...

To evaluate Ks, Blackburn assumed In Ks = As + Bs/T, where T is the absolute temperature, and Ag and Bs are constants characteristic of Pu02 x(s) which were found from an examination of available oxygen potential data [Alexander (22), Atlas and Schlehman (j5), Markin and Mclver (23), Woodley (24), Javed (25), Tetenbaum (26-27), and Blackburn (28) ]. This evaluation gave Bs = -101600 and As =20.8. We have compared the oxygen potentials calculated using Eq. (14) and these parameter values with more recent unpublished data of Tetenbaum (27) and have found reasonable agreement. 

Until now, applications of semiempirical all-valence-electron methods have been rare, although the experimental data for a series of alkyl radicals are available (108,109). In Figure 9, we present the theoretical values of ionization potentials calculated (68) for formyl radical by the CNDO version of Del Bene and Jaffe (110), which is superior to the standard CNDO/2 method in estimation of ionization potentials of closed-shell systems (111). The first ionization potential is seen, in Figure 9, to agree fairly well with the experimental value. Similarly, good results were also obtained (113) with some other radicals (Table VII). 

The theoretical potential calculated on the basis of the ceU model shows that PGA is not suitable for testing a purely electrostatic theory since in this case significant specific binding of counterions to the polyion was detected. For an ion like (C Hg) N, this is offset to some extent by the four longer alkyl groups that protect the positive charge of the rigid sphere [15]. 

At zero concentration of the potential-determining substances, the values of electrode potential calculated with Eq. (3.26) or (3.30) tend toward °°, which is physically meaningless. This implies that these equations cannot be used below a certain concentration. 

Several methods exist that can be used to measure changes of ESE for solid electrodes as a function of potential or other factors, but the accuracy of such measurements is much lower than that for Uquid electrodes. A plot of ESE vs. potential is called the electrocapillaty cutye (ECC). Typical ECCs measured at a mercury electrode in NaF solutions of different concentration are shown in Fig. 10.6. Also shown in this figure is a plot of values vs. potential calculated via Eq. (10.27). This plot almost coincides with that obtained from capacitance measurements (Fig. lO.lfc). This is evidence for the mutual compatibility of results obtained by these two methods of measurement. 

Membrane permeability for the Cl ions is not in contrast to the conclusion that a simple membrane equilibrium such as that described in Section 5.4.1 is established at the membrane. In fact, the membrane potential calculated for the example above with Eq. (5.26) from the Cl ion concentration ratio is exactly -90mV (i.e., the d ions in the two solutions are in equilibrium, and there is no unidirectional flux of these ions). 

A more sophisticated approach takes into account the fact that the presence of the reacting ion at a given point in the solution distorts the distribution of other ions of the electrolyte and thereby distorts the potential distribution. This phenomenon is called the effect of the micropotential. The average /i potential is then replaced by another average potential, calculated in the presence of the reacting ion at a given point. 

Suspension Model of Interaction of Asphaltene and Oil This model is based upon the concept that asphaltenes exist as particles suspended in oil. Their suspension is assisted by resins (heavy and mostly aromatic molecules) adsorbed to the surface of asphaltenes and keeping them afloat because of the repulsive forces between resin molecules in the solution and the adsorbed resins on the asphaltene surface (see Figure 4). Stability of such a suspension is considered to be a function of the concentration of resins in solution, the fraction of asphaltene surface sites occupied by resin molecules, and the equilibrium conditions between the resins in solution and on the asphaltene surface. Utilization of this model requires the following (12) 1. Resin chemical potential calculation based on the statistical mechanical theory of polymer solutions. 2. Studies regarding resin adsorption on asphaltene particle surface and... 

The structural similarity of Al22Br2o 12(THF) 6 to (3-rhombohedral boron with the familiar B84 unit raises the question whether another, more covalent, form of aluminum in addition to the metallic a-form exists, similar to the geometry of the Al atoms in the Al12 icosahedra of 6. The mild conditions applied for the synthesis of Al22Br20 might also favor the formation of such a modification. In order to support this hypothesis, we investigated the structural competition between the fee and ff-B type for Al by means of ab initio full-potential calculations, with the results shown in Fig. 15.52... 

Fig. 15. Structural competition between the fee and fif-B type of aluminum during expansion (ab initio full potential calculation).

Standard States for Chemical Potential Calculations (for Use in Studies of Chemical Reaction Equilibria)... 

Espinosa, E., C. Lecomte, N. E. Ghermani, J. Devemy, M. M. Rohmer, M. Benard, and E. Molins. 1996. Hydrogen Bonds First Quantitative Agreement between Electrostatic Potential Calculations from Experimental X-(X+N) and Theoretical Ab Initio SCF Models. J. Am Chem. Soc. 118, 2501. 

Li, G.H. Zhang, X.D. Cui, Q., Free energy perturbation calculations with combined QM/MM. Potential complications, simplifications, and applications to redox potential calculations, J. Phys. Chem. B 2003,107, 8643-8653. 

The electrostatic potential calculations have shown that the minor groove of AT rich B-DNA sequence has the lowest negative potential.15 This led to the implication that the cationic drugs will exhibit binding specificity to the minor groove regions of AT rich sequences. The crystal structure of a DNA distamycin complex showed that there is only one molecule bound to the minor groove of an AATT DNA site.2 However, experimental studies... 

Equilibrium potentials calculated at 37°C from the Nernst equation. Calculated assuming a —90 mV resting potential for the muscle membrane and assuming that chloride ions are at equilibrium at rest. 

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