Potentials electrostatic

The electrostatic potential within a phase, that is, l/e times the electrical work of bringing unit charge from vacuum at infinity into the phase, is called the Galvani, or inner, potential Similarly, the electrostatic potential difference 

The electrostatic potential generated by a molecule A at a distant point B can be expanded m inverse powers of the distance r between B and the centre of mass (CM) of A. This series is called the multipole expansion because the coefficients can be expressed in temis of the multipole moments of the molecule. With this expansion in hand, it is 

Heyes, D.M. Electrostatic potentials arid fields in infinite point charge lattices. J. Chem. Phys. 74 (1981) 1924-1929. 

J.S. Munay, P. Politzer, Electrostatic potential, in Encyclopedia of Gjmpu-tational Chemistry, Vol.2, P. von Rague-Schleyer, N.L. Allinger, T. Clark, J. Gasteiger, P.A. Kollman, H.F. Schaefer III, P.R. Schreiner (Eds.) John Wiley Sons, Chichester. UK, 1998, pp. 912-920. 

Vector field gradient of the electrostatic potential, i.e., force 

The model used is the RPM. The average electrostatic potential ifr) at a distance r away from an ion / is related to tire charge density p.(r) by Poisson s equation 

Gilson, M. K., Sharp, K. A., Honig, B. H. Calculating the electrostatic potential of molecules in solution Method and error assessment. J. Comp. Chem. 9 (1988) 327-335. 

Besides molecular orbitals, other molecular properties, such as electrostatic potentials or spin density, can be represented by isovalue surfaces. Normally, these scalar properties are mapped onto different surfaces see above). This type of high-dimensional visualization permits fast and easy identification of the relevant molecular regions. 

Task 1 Calculate the first non-vanishing multipole moment of the electrostatic potential of composed objects (i.e., structural units and clusters). 

Momany F A 1978 Determination of partial atomic charges from ab initio molecular electrostatic potentials. Application to formamide, methanol and formic acid J. Phys. Chem. 82 592 

Molecular surfaces can express various chemical and physical properties, such as electrostatic potential, atomic charges or hydrophobicity, using colored mapping. 

If there are ions in the solution, they will try to change their location according to the electrostatic potential in the system. Their distribution can be described according to Boltzmarm. Including these effects and applying some mathematics leads to the final linearized Poisson-Boltzmann equation (Eq. (43)). 

These properties arc also relevant if molecular interactions arc considered. In contrast to electrostatic potentials, they only take effect at small distances between interacting molecular regions, 

The representation of molecules by molecular surface properties was introduced in Section 2.10. Different properties such as the electrostatic potential, hydrogen bonding potential, or hydrophobicity potential can be mapped to this surface and seiwe for shape analysis [44] or the calculation of surface autocorrelation vectors (refer to Section 8.4.2). 

Knowledge of the spatial dimensions of a molecule is insufficient to imderstand the details of complex molecular interactions. In fact, molecular properties such as electrostatic potential, hydrophilic/lipophilic properties, and hydrogen bonding ability should be taken into account. These properties can be classified as scalar isosurfaces), vector field, and volumetric properties. 

The calculation of autocorrelation vectors of surface properties [25] is similar (Eq. (21), with the distance d XiXj) between two points and Xj on the molecular surface within the interval between d[ and d a certain property p, e.g., the electrostatic potential (ESP) at a point on the molecular surface and the number of distance intervals 1). 

Experimental investigations of the model system of dye molecules adsorbed onto surfaces of polystyrene spheres have finuly established the sensitivity and surface specificity of the SHG method even for particles of micrometre size [117]. The surface sensitivity of die SHG process has been exploited for probing molecular transport across the bilayer in liposomes [118], for measurement of electrostatic potentials at the surface of small particles [119] and for imaging 

To display properties on molecular surfaces, two different approaches are applied. One method assigns color codes to each grid point of the surface. The grid points are connected to lines chicken-wire) or to surfaces (solid sphere) and then the color values are interpolated onto a color gradient [200]. The second method projects colored textures onto the surface [202, 203] and is mostly used to display such properties as electrostatic potentials, polarizability, hydrophobidty, and spin density. 

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