Electrostatic potentials definition

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 ... 

The actual state, and absolute amount, of intrinsic energy existing in a body, or system of bodies, are things which lie quite outside the range of pure thermodynamics. This indefiniteness has, however, not the slightest influence on the stringency of the definition, since we can proceed as in the definition of electrostatic potential, and choose any convenient standard state of the body, and use the term intrinsic energy with reference to this standard state. 

The outer electrical potential of a phase is the electrostatic potential given by the excess charge of the phase. Thus, if a unit electric charge is brought infinitely slowly from infinity to the surface of the conductor to a distance that is negligible compared with the dimensions of the conductor considered (for a conductor with dimensions of the order of centimetres, this distance equals about 10 4cm), work is done that, by definition, equals the outer electric potential ip. 

Electrochemical interfaces are sometimes referred to as electrified interfaces, meaning that potential differences, charge densities, dipole moments, and electric currents occur. It is obviously important to have a precise definition of the electrostatic potential of a phase. There are two different concepts. The outer or Volta potential ij)a of the phase a is the work required to bring a unit point charge from infinity to a point just outside the surface of the phase. By just outside we mean a position very close to the surface, but so fax away that the image interaction with the phase can be ignored in practice, that means a distance of about 10 5 — 10 3 cm from the surface. Obviously, the outer potential i/ a U a measurable quantity. 

The article is organized as follows in Section 2, a general discussion concerning the definition of electrostatic potentials in the frame of DFT is presented. In Section 3, the solvation energy is reformulated from a model based on isoelectronic processes at nucleus. The variational formulation of the insertion energy naturally leads to an energy functional, which is expressed in terms of the variation of the electron density with respect to... 

The operators for the potential, the electric field, and the electric field gradient have the same symmetry, respectively, as those for the atomic charge, the dipole moment, and the quadrupole moment discussed in chapter 7. In analogy with the moments, only the spherical components on the density give a central contribution to the electrostatic potential, while the dipolar components are the sole central contributors to the electric field, and only quadrupolar components contribute to the electric field gradient in its traceless definition. 

Since /(r) is the electrostatic potential energy per unit charge, the gradient of this parameter with distance must be equal to the force acting on a unit charge - which is the definition of the electric field. Hence it follows that... 

Representation of the density n(r) [or, effectively, the electrostatic potential — 0(r)] near any one of the sinks as an expansion in the monopole and dipole contribution only [as in eqn. (230c)] is generally, unsatisfactory. This is precisely the region where the higher multipole moments make their greatest contribution. However, the situation can be improved considerably. Felderhof and Deutch [25] suggested that the physical size of the sinks and dipoles be reduced from R to effectively zero, but that the magnitude of all the monopoles and dipoles, p/, are maintained, by the definition... 

Electrochemistry deals with charged particles that have both electrical and chemical properties. Since electrochemical interfaces are usually referred as electrified interfaces, it is clear that potential differences, charge densities, dipole moments, and electric currents occur at these interfaces. The electrical properties of systems containing charged species are very important for understanding how they behave at interfaces. Therefore, it is important to have a precise definition of the electrostatic potential of a phase [1-6]. Note that what really matters in electrochemical systems is not the value of the potential but its difference at a given interface, although it is illustrative to discuss its main properties. 

The core of the model is then the definition of the Q matrix, which in the most recent implementations of PCM depends only on the electrostatic potentials, takes into the proper account the part of the solute electron density outside the molecular cavity, and allows the treatment of conventional, isotropic solutions, and anisotropic media such as liquid crystals. Furthermore, analytical first and second derivatives with respect to geometrical, electric, and magnetic parameters have been coded, thus giving access to proper evaluation of structural, thermodynamic, kinetic, and spectroscopic solvent shifts. 

To sum up, there are two potentials which are definite V, the electrostatic potential in empty, or nearly empty, space just outside the phase and fa the thermodynamic electrochemical potential of a charged component i. 

Both of these quantities contain an arbitrary constant, the zero from which the potentials are measured, but differences of either the electrostatic potential or of the electrochemical potential, between two phases, are definite. The thermionic work function, x, the work required to extract electrons from the highest energy level within the phase, to a state of rest just outside the phase, is also definite and the relation between the three definite quantities fa, V, and x is given by (3.1), where is the electrochemical potential of electrons very widely separated from all other charges. The internal electric potential , and other expressions relating to the electrical part of the potential inside a phase containing dense matter, are undefined, and so are the differences of these quantities between two phases of different composition. This indefiniteness arises from the impossibility of separating the electrostatic part of the forces between particles, from the chemical, or more complex interactions between electrons and atomic nuclei, when both types of force are present. 

The process is essentially similar to that of the establishment of the contact potential between two metals in a vacuum the equalization in the two phases of the energy levels (or electrochemical potentials), of the ion passing the phase boundary, establishes a definite difference in the electrostatic potentials of the metal and the electrolyte. The main difference from the case of simple contact potentials is that the energy level of the ion in solution is very largely determined by the energy of hydration. 

A single electrode potential, if defined as the difference in electrostatic potential between the spaces just outside the metal and the solution, is definite, but it cannot be measured by merely connecting up the phases with wires, and adjusting a potentiometer, until no current flows for this connexion introduces more than one phase boundary. Practically all electrolytic cells consist of at least three phase boundaries and the terminals at which the electromotive force of the cell is measured are, finally, of the same metal. There may, of course, be any. greater number of phase boundaries. A simple type of cell consists of two metals, M and M, dipping into a solution 8 containing the ions of each metal. 

Adsorbed films between two immiscible liquids. The question of the meaning of the term pn in the surface layer has been raised by Crax-ford, Gatty, and Teorell,2 without, however, coming to any very clear decision. Danielli s estimate was a very rough one, based on the application of the Donnan equilibrium between the surface layer and the interior, and suffers from the difficulties always attending an attempt to consider concentrations in the surface layer in a similar way to concentrations in a bulk phase the surface layer is not homogeneous. pH is closely related to, and is determined by, the electrochemical potential (see Chap. VIII, pp. 304 ff.), and this depends on the electrostatic potential, which varies rapidly at different levels near to the surface it appears possible that the only satisfactory definition of pa in the surface may be one which varies rapidly at different depths. The question appears one which would repay... 

Over the last years, the basic concepts embedded within the SCRF formalism have undergone some significant improvements, and there are several commonly used variants on this idea. To exemplify the different methods and how their results differ, one recent work from this group [52] considered the sensitivity of results to the particular variant chosen. Due to its dependence upon only the dipole moment of the solute, the older approach is referred to herein as the dipole variant. The dipole method is also crude in the sense that the solute is placed in a spherical cavity within the solute medium, not a very realistic shape in most cases. The polarizable continuum method (PCM) [53,54,55] embeds the solute in a cavity that more accurately mimics the shape of the molecule, created by a series of overlapping spheres. The reaction field is represented by an apparent surface charge approach. The standard PCM approach utilizes an integral equation formulation (IEF) [56,57], A variant of this method is the conductor-polarized continuum model (CPCM) [58] wherein the apparent charges distributed on the cavity surface are such that the total electrostatic potential cancels on the surface. The self-consistent isodensity PCM procedure [59] determines the cavity self-consistently from an isodensity surface. The UAHF (United Atom model for Hartree-Fock/6-31 G ) definition [60] was used for the construction of the solute cavity. 

A similar rationale is behind the polarizable-continuum approaches. Here, the solvent is modeled by a homogeneous continuum, i.e., the individual solvent molecules are not treated, and, therefore, this corresponds to a so called implicit approach. There are two central features of the model that can influence the outcomes of the calculations critically. At first, the solute is supposed to occupy some cavity in the solvent, whereby the precise definition of the size and shape of the cavity is not unique. Second, the continuum is able to respond to the charge distribution of the solute and, thereby, in turn by creating an electrostatic potential in which the solute exists to influence the properties of the solute. Again, the precise description of this response can differ among different approaches. 

---