Embedding point charges

This approximation is known as the mean spherical approximation (MSA). For the case of a hard-sphere fluid for which u r) = 0, the MSA is equivalent to the PY approximation. For the case that the hard spheres have embedded point charges, the function u(r) is simply Coulomb s law. Although the MSA provides the least detailed expression for c(r), it is popular because the OZ equation can often be solved using this approximation to yield an analytical expression for g(r). The equation for g(r) within a hard sphere is... 

Another crucial point is the convergence of the electrostatic potential as a function of the size and shape of the embedding point charge field. Special summation techniques have to be used in order to achieve a fast and correct convergence [44]. Many authors use the method of fractional charges for this purpose, which has been originally proposed by Evjen [45] and was later extended by Piela and coworkers [46,47]. 

Fig. 4a,b Clusters used to investigate the adsorption of CO on the polar surfaces of ZnO a free cluster with twofold and threefold coordinated Zn and O atoms b embedded hydroxylated ZnijO, cluster with part of the embedding point charge field... 

Since the adsorption is a local process, the cluster approach seems to be the most natural way to treat adsorption phenomena. Indeed, it can yield rehable results provided that the quantum cluster and its embedding are designed properly and are carefully tested. The size and form of the quantum cluster as well as of the embedding point charge field depend strongly on the crystal structure of the oxide substrate and on the property one wants to caloilate. Cluster and periodic calculations do yield similar results if both of them are performed properly. 

The rough electrode near a non primitive electrolyte. This is a case relevant to computer simulations of realistic solvent models near a model of a metallic surface such as the silver( 111) surface, for which experiments have recently been reported [61]. Most models of water employed in the computer simulations consist of neutral molecules with embedded point charges. 

Carnie and Chan and Blum and Henderson have calculated the capacitance for an idealized model of an electrified interface using the mean spherical approximation (MSA). The interface is considered to consist of a solution of charged hard spheres in a solvent of hard spheres with embedded point dipoles, while the electrode is considered to be a uniformly charged hard wall whose dielectric constant is equal to that of the electrolyte (so that image forces need not be considered). 

Cisneros GA, Na-Im Tholander S, Elking D, Darden TA, Parisel O, Piquemal J-P (2008) Simple formulas for improved point-charge electrostatics in classical force fields and hybrid Quantum Me-chanical/Molecular Mechanical embedding. Int J Quant Chem 108 1905... 

In addition to the described above methods, there are computational QM-MM (quantum mechanics-classic mechanics) methods in progress of development. They allow prediction and understanding of solvatochromism and fluorescence characteristics of dyes that are situated in various molecular structures changing electrical properties on nanoscale. Their electronic transitions and according microscopic structures are calculated using QM coupled to the point charges with Coulombic potentials. It is very important that in typical QM-MM simulations, no dielectric constant is involved Orientational dielectric effects come naturally from reorientation and translation of the elements of the system on the pathway of attaining the equilibrium. Dynamics of such complex systems as proteins embedded in natural environment may be revealed with femtosecond time resolution. In more detail, this topic is analyzed in this volume [76]. 

The first term in Eq. 4.26 represents Van der Waals forces between atoms of the microscopic environment and the embedded molecule, this term is not involved in the construction of the Fock matrix. The second one represents Coulomb interactions between the embedded electron density and the electric charge distribution in the environment which is approximated by point charges. 

Consider now two point charges q and -q which are separated by a distance d (Fig. 5.4). This configuration of charges is called a dipole with dipole moment p = pez, where p = qd. If the charges are embedded in a uniform unbounded medium with permittivity em, the potential of the dipole at any point P is... 

Analysis of ion atmospheres around highly charged macromolecules has traditionally been performed using numerical solutions to the nonlinear Poisson-Boltzmann (P-B) equation (Anderson and Record, 1980 Bai et al, 2007 Baker, 2004), in which the macromolecule is approximated as a collection of point charges embedded in a low dielectric cavity surrounded by a high-dielectric solvent. This approach utilizes the precise three-dimensional structure of the macromolecule (albeit in a static sense). We would not expect such a framework to capture subtleties, which are dependent on the partial dehydration of ions. 

The divergence is less severe either when the charge is described by a volumetric density (as the electronic density) or when point charges (pointwise nuclei) are embedded in a cavity and thus are prevented from approaching the surface too closely. 

The electrostatic embedding approach appears reasonable in cases of weak interactions, with negligible intermolecular charge transfer, provided that the interactions can be described as some average electric perturbation. By properly modifying the disposition of the point charges more realistic embedding schemes could also be introduced. 

Kliiner et al. [19] has analyzed the bimodal velocity distributions observed in NO desorption from NiO(0 01) shown in Fig. 24 by calculating a full ab initio potential energy surface (PES) for an excited state in addition to the PES for the ground state. Calculation of the electronically excited state uses a NiOj cluster embedded in a semi-infinite Madelung potential of point charges 2. The excited state relevant for laser-induced desorption is an NO -like intermediate, where one electron is transferred from the cluster to the NO molecule. 

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