Electrostatic potential variability

Many physical properties such as the electrostatic potential, the dipole moment and so on, do not depend on electron spin and so we can ask a slightly different question what is the chance that we will find the electron in a certain region of space dr irrespective of spin To find the answer, we integrate over the spin variable, and to use the example 5.2 above... 

Keffer DJ, Mintmire JW (2000) Efficient parallel algorithms for molecular dynamics simulations using variable charge transfer electrostatic potentials. Int J Quant Chem 80(4-5) 733-742... 

The macroscopic property of interest, e.g., heat of vaporization, is represented in terms of some subset of the computed quantities on the right side of Eq. (3.7). The latter are measures of various aspects of a molecule s interactive behavior, with all but surface area being defined in terms of the electrostatic potential computed on the molecular surface. Vs max and Fs min, the most positive and most negative values of V(r) on the surface, are site-specific they indicate the tendencies and most favorable locations for nucleophilic and electrophilic interactions. In contrast, II, a ot and v are statistically-based global quantities, which are defined in terms of the entire molecular surface. II is a measure of local polarity, °fot indicates the degree of variability of the potential on the surface, and v is a measure of the electrostatic balance between the positive and negative regions of V(r) (Murray et al. 1994 Murray and Politzer 1994). 

In the Bom like approaches to solvation energy, the electrostatic potential of the ion appears as the basic variable of the theory. From Eq (1), it may be seen that if we have accurate electron densities at hand, the electrostatic potential strongly depends on the ionic radius r. The choice of suitable ionic radii usually introduces some arbitrariness in the calculation of AESolv there is no a physical criterium to justify the use of empirical rA values coming from different sources [15-16],... 

Physically meaningful ionic radii may be obtained from Poisson equation for anions, and from electrostatic potentials defined in the the context of DFT for cations [17,18], However, there remains the problem of being forced to use different mathematical criteria in both cases, because the electrostatic potential of anions and cations display a different functional behaviour with respect to the radial variable. 

The use of electrostatic potentials, defined in the context of DFT, for the calculation of ion solvation energies has been reviewed. It has been shown that physically meaningful ionic radii may be obtained from this methodology. In spite of the fact that the electrostatic potentials for cations and anions display a quite different functional dependence with the radial variable, we have shown that it is still possible in both cases to build up a procedure consistent with the Bom model of ion solvation. 

The variances indicate the variabilities, or ranges, of the positive, the negative and the overall electrostatic potentials on the molecular surfaces. They are particularly sensitive to the extrema, Vs,max and Vs,min, due to the terms being squared. This also means that they may be much... 

Significant efforts have been made to assemble teratogenic data basses with peer-reviewed evaluations (ref. 1). New avenues for the SAR studies have been opened, such as quantitative methods for structural superposition of molecules and for superposition of their reactivity characteristics (ref. 2). Emphasis has been placed on the electrostatic properties of the molecules, such as the molecular electrostatic potential, the electric fields, and the polarizability terms calculated from perturbation expansions (ref. 2). Computer-assisted multivariate SAR which deals with many variables simultaneously has been advanced (ref. 3). 

The variable used to describe the differences in escaping tendency of charged particles from charged phases is the electrostatic potential, . The electrostatic potential at a point, a, is defined as the work per unit charge required to bring a positive test charge reversibly from infinity to the point,... 

As one can see, the electrostatic potential is independent of the variable p (Fig. 4), i.e., the problem under assumptions made becomes essentially one-dimensional. We have also written the two first terms only in the iteration scheme. 

Our experience has been that the computed electrostatic potentials Vs(r) on the surfaces of all-carbon tubes are generally weakly positive and rather bland, with little variability. Vs(r) is usually less than lOkcal/mole. Slightly negative regions are most likely to be found on the outer surfaces of the caps. The total variance, ofot, tends to be less than 20(kcal/mole)2 this is typical of alkane and aromatic hydrocarbons, but much less than most other organic molecules, for which <72t is normally 10CF300 (kcal/mole)2.46,47... 

Extinction, which is the failure of the kinematic scattering theory (Ihki hki) is only a minor problem in X-ray diffraction. In neutron diffraction, extinction is serious and pervasive throughout the whole data, as shown by the examples in Thble 3.2. The best methods available for extinction correction require careful measurement of crystal dimensions. Although somewhat empirical, it has proved to be very effective [184, 185]. At least one, and sometimes six, additional extinction parameters, gis0 or gij, have to be added to the variable parameters. Uncertainty in the validity of these extinction parameters appears to have very little effect on atomic positional coordinates, but may influence the absolute values of the atomic temperature factors. This is important in charge density or electrostatic potential... 

Parallel Algorithms for Molecular Dynamics Simulations Using Variable Charge Transfer Electrostatic Potentials. 

Early MEP-based parameters considered included surface area (A), If, and v. Flere II is a measure of local polarity, and is a measure of electrostatic interaction tendency. Larger values imply larger charge separation leading to greater electrostatic interaction. Electrostatic interactions are also described by v, which is a measure of electrostatic balance. The three charge related variables are defined in terms of the surface electrostatic potential difference, 8U at the ith point, Eq. [33],... 

All the necessary information relating to electrokinetic phenomena is contained in the phenomenological equations (6.7.13) and (6.7.14) or in the equivalent set (6.7.18a) and (6.7.18b). The former set is especially useful if one inquires about state conditions under which either Jy or /+ is held fixed. The latter set is useful to characterize operating conditions at constant pressure or constant electrostatic potential. The preceding discussion illustrates the flexibility of phenomenological equations that permit either fluxes or forces to be used as dependent variables. 

In all cases, the variability for the PDQC charges in Table 2 is highest for the central carbon atom. As Woods et al. note, the exposure of the van der Waals surface of the methanol carbon atom is quite limited. As a result, the electrostatic potential will be more sparsely sampled in this region and perhaps therefore will not be as well described by the final parameters. Classical electrostatics is likely playing a role here as well. Classically, all the charge on a charged object is found on the surface of the object. Because class III charge... 

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