Point-charge density

The point-charge density increases monotonically with decreasing d until it reaches a maximum at the critical ratio of d/r = r. At this point e = 0.5513 and... 

Table 1.16. Bond Critical Points, Charge Density, and Methanes Bond Angles for Substituted...

The mathematics is completed by one additional theorem relating the divergence of the gradient of the electrical potential at a given point to the charge density at that point through Poisson s equation... 

Another way of calculating the electrostatic component of solvation uses the Poisson-Boltzmann equations [22, 23]. This formalism, which is also frequently applied to biological macromolecules, treats the solvent as a high-dielectric continuum, whereas the solute is considered as an array of point charges in a constant, low-dielectric medium. Changes of the potential within a medium with the dielectric constant e can be related to the charge density p according to the Poisson equation (Eq. (41)). 

The electrostatic potential at a point r, 0(r), is defined as the work done to bring unit positive charge from infinity to the point. The electrostatic interaction energy between a point charge q located at r and the molecule equals The electrostatic potential has contributions from both the nuclei and from the electrons, unlike the electron density, which only reflects the electronic distribution. The electrostatic potential due to the M nuclei is ... 

Ire boundary element method of Kashin is similar in spirit to the polarisable continuum model, lut the surface of the cavity is taken to be the molecular surface of the solute [Kashin and lamboodiri 1987 Kashin 1990]. This cavity surface is divided into small boimdary elements, he solute is modelled as a set of atoms with point polarisabilities. The electric field induces 1 dipole proportional to its polarisability. The electric field at an atom has contributions from lipoles on other atoms in the molecule, from polarisation charges on the boundary, and where appropriate) from the charges of electrolytes in the solution. The charge density is issumed to be constant within each boundary element but is not reduced to a single )oint as in the PCM model. A set of linear equations can be set up to describe the electrostatic nteractions within the system. The solutions to these equations give the boundary element harge distribution and the induced dipoles, from which thermodynamic quantities can be letermined. 

The charge density is simply the distribution of charge throughout the system and has 1 units of Cm . The Poisson equation is thus a second-order differential equation (V the usual abbreviation for (d /dr ) + (f /dx/) + (d /dz )). For a set of point charges in constant dielectric the Poisson equation reduces to Coulomb s law. However, if the dielectr... 

A cubic lattice is superimposed onto the solute(s) and the surrounding solvent. Values of the electrostatic potential, charge density, dielectric constant and ionic strength are assigned to each grid point. The atomic charges do not usually coincide with a grid point and so the... 

A number of types of calculations can be performed. These include optimization of geometry, transition structure optimization, frequency calculation, and IRC calculation. It is also possible to compute electronic excited states using the TDDFT method. Solvation effects can be included using the COSMO method. Electric fields and point charges may be included in the calculation. Relativistic density functional calculations can be run using the ZORA method or the Pauli Hamiltonian. The program authors recommend using the ZORA method. 

The electron density distributions are approximated by a series of point charges. There are four possible types of contributions, i.e. 

Fig. 5. A representation of ranitidine displaying four layers of the Connolly solvent-accessible dot surface normally color-coded in this process to correspond with the energies of electrostatic potential (color not shown here). Thus, the highest charge density would be indicated by red dots representing points where the attraction to an atom is strongest, and conversely, purple points would signify regions of maximal positive charge.

Isothiazole-4,5-dicarboxylic acid, 3-phenyl-dimethyl ester synthesis, S, 150 Isothiazole-5-glyoxylic acid ethyl ester reduction, 6, 156 Isothiazole-4-mercurioacetate reactions, 6, 164 Isothiazole-5-mercurioacetate reactions, 6, 164 Isothiazoles, 6, I3I-I75 acidity, 6, 141 alkylation, 6, 148 aromaticity, S, 32 6, 144-145 basicity, 6, I4I biological activity, 6, 175 boiling points, 6, I43-I44, 144 bond fixation, 6, 145 bond orders, 6, I32-I34 calculated, 6, 133 bromination, S, 58 6, 147 charge densities, 6, 132-134 cycloaddition reactions, 6, 152 desulfurization, S, 75 6, 152 deuteration, S, 70... 

Figure 4 (a) Density pi, the sum of point charges represented by vertical lines, plus Gaussian... 

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