Isopotential contour

Fig. 3-2. Molecular electrostatic potential with 6-31G //3-21G basis set in the molecular plane of (ii)-nitrous acid. Black dots refer to four different protonation sites in potential minima. For values of isopotential contours see Nguyen and Hegarty, 1984.

Anodes and cathodes need not be separate electrodes but can be areas on the same piece of metal. O Halloran et al. [4] have developed a technique in which isopotential contours on the corroding electrode may be mapped (see Fig. 1). As the technique involves gathering a large number of data points, a microprocessor is used. A small reference electrode is passed across a corroding specimen close to its surface and the potential differences relative to another fixed reference electrode are recorded. The potential profile reflects the ion current density in the vicinity of the corroding surface and... 

Figure 2.3. Electrostatic potential dendrogram constructed from an electrostatic potential distance matrix for a set of 42 WW domains showing four clusters. WW domains are colored according to their peptide ligand binding preferences. FourWWdomains representative of the clusters are shown with positive (blue) and negative (red) electrostatic isopotential contours. In the cluster of...

Figure 12 Mounding of the leachate-groundwater table below Grindsted Landfill (DK) shown as isopotential contours for the landfill and surrounding area at four different seasons during 1993 (after Kjeldsen et al, 1998b).

Parr and Berk [309] have found that the isopotential contours of the nuclear potential V (r) of simple molecules show a remarkable similarity to the actual isodensity contours of the electronic ground states of these molecules. 

Isopotential contours of the composite nuclear potentials (NUPCO s, see Chapter 4), provide an inexpensive, approximate shape representation that can be computed easily even for very large molecules. Although NUPCO s only approximate the MIDCO s of molecules, the family of NUPCO s of a molecule describes an important molecular property that has a major effect on the actual molecular shape. Consequently, NUPCO s can be used for direct comparisons between molecules, and similar NUPCO s are likely to be associated with similar molecular shapes. All the shape analysis techniques originally developed for MIDCO s are equally applicable to NUPCO s. The shape groups, the (a,b) parameter maps [where a is the nuclear potential threshold of a NUPCO G(a)], the shape matrices, shape codes, and the shape globe invariance maps of NUPCO s of molecules can serve as inexpensive methods for the detection and evaluation of a particular aspect of molecular similarity. 

Isopotential contours of the composite nuclear potentials (NUPCO s), provide an inexpensive approximate shape representation that can be computed easily even for very large molecules. 

An important fact has been pointed out by Parr and Berk the bare nuclear potential Vn(r) shows many similarities with the electronic density function p(r). The computed isopotential contours of the composite nuclearpotential VnC lwere remarkably similar to some of the molecular isodensity contours (MIDCOs) of the electronic ground states in several simple molecules. One may regard the composite nuclear potential as the harbinger of electronic density, and isopotential contours of the composite nuclear potential V (r) can serve as surprisingly good approximations of MIDCOs. The nuclear potential contours (NUPCOs) are suitable for an inexpensive, approximate shape representation of molecules. 

The electrostatic potential of a molecule can be displayed in various ways. Originally, it was often presented as isopotential contours on planes through the molecule [20-22,24], A more recent practice is to show three-dimensional plots of just a single positive value and a single negative value of V(r). However, this necessarily gives an incomplete picture since other values may also be important. 

FIGURE 1.12 Contour lines (isopotential lines) for around a positively charged sphere with yg — l at xa — 1. Arbitrary scale. 

This observation of Parr and Berk provides the basis for a simple approach to molecular shape analysis and molecular similarity analysis, described below. Although the molecular shapes, as defined by the electronic density, differ somewhat from the shapes of the nuclear potentials, their similarity can be exploited the nuclear potential contour surfaces provide a simple approximation of the shape of molecules. We shall refer to the isopotential surfaces of the nuclear potential contours as NUPCO surfaces. These surfaces have a major advantage the computation of NUPCO s is a trivially simple task as compared to the calculation of electronic densities. Furthermore, nuclear potential is a useful molecular property in its own right, without any reference to electronic density a comparison of NUPCO s of various molecules can provide a valid tool for evaluating molecular similarity. The superposition of potentials of different sets of nuclei can result in similar composite potentials, consequently, the comparison of NUPCO s is better... 

FIGURE 18.9 Electric field and concentration gradients for an electrochemical reaction at a catalyst surface the contours indicate the isopotential surfaces in the electrolyte and the arrow marks indicate the flux of the species generated at the catalyst surface (i.e., Y = 1). The scale indicates the conversion. Parameters correspond to the case shown in Figure 18.8b. 

Figure 1. MNDOC-CI results for carbene (a) state energies including contour map for Tj and isopotential line for Egj = 0 (b) SOC values.

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