Charged point dipoles

The values of the ion shifts were estimated in the point charges point dipoles approximation of the EFGs calculation both in the PSN and PMN. 

By a simple generalization, one can define nonspherical hard particles for which (1.71) is fulfilled. Other systems for which the pairwise additivity assumption is presumed to hold are systems of idealized point charges, point dipoles, point quadrupoles, etc. 

It should be remembered that hard spheres are not real particles, and (1.7.5) is valid by virtue of definitions (1.7.2) and (1.7.3). Therefore, the pairwise additivity assumption must be viewed as being a built-in feature of the definition of a system of hard spheres. By simple generalization, one can define nonspherical hard particles for which (1.7.1) is fulfilled. Other systems for which the pairwise additivity assumption is presumed to hold are systems of idealized point charges, point dipoles, point quadruples, and the like. A system of real particles such as argon atoms is believed to obey relation (1.7.1) approximately. Although it is now well known that even the simplest molecules do not obey (1.7.1) exactly, it is still considered a useful approximation without which little progress in the theory of liquids, if any, could have been achieved. 

The relaxation of the quadrupolar Xe nucleus is predominantly due to the interaction between the nuclear electric quadrupole moment and the fluctuating EFG at the nuclear site. The origin of the EFG contributing in a solution is, however, still partly an open question. Various models, both electrostatic and electronic, have been developed. The electrostatic models assume the EFG to be due to solvent molecules represented by point charges, point dipoles or quadrupoles, or a dielectric continuum. In the electronic approach, EFG is considered to be a consequence of the deformation of the spherical electron distribution of Xe. The deformation arises from the collisions between xenon and solvent molecules. It is obvious (evidence is provided, for example, by i Xe NMR experiments in liquid-crystal solutions, and by first principles calculations) that neither of these approaches alone is sufficient. In typical isotropic solvents, the Xe ranges from 4 ms to -40 ms. 

At distances far from the dipole, the length d becomes unimportant and the dipole appears as a point dipole. The potential energy for a point dipole in the held produced by a charge (Eq. VI-3) is... 

Derive the expression for the electric field around a point dipole, Eq. VI-5, by treating the dipole as two charges separated by a distance d, then moving to distances X d. 

We will describe integral equation approximations for the two-particle correlation fiinctions. There is no single approximation that is equally good for all interatomic potentials in the 3D world, but the solutions for a few important models can be obtained analytically. These include the Percus-Yevick (PY) approximation [27, 28] for hard spheres and the mean spherical (MS) approximation for charged hard spheres, for hard spheres with point dipoles and for atoms interacting with a Yukawa potential. Numerical solutions for other approximations, such as the hypemetted chain (EfNC) approximation for charged systems, are readily obtained by fast Fourier transfonn methods... 

Instead of using point charges one may also approximate the mteraction Hamiltonian in temis of solute electrons and nuclei interacting with solvent point dipoles... 

The quality of the results that can be obtained with point charge or dipole models depends critically on the input solvation shell structure. In view of the computer power available today, taking the most rigorous route... 

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). 

One method for treating polarizability is the assignment of both partial atomic charges and induced dipoles on the atoms in a molecule. In its most common implementation in biomolecular simulations, inducible point dipoles are added to some or all atomic sites in the molecule [22-25]. An alternative methodology proposed by Allinger and co-workers is the use of bond dipoles [26],... 

Because this method avoids iterative calculations to attain the SCF condition, the extended Lagrangian method is a more efficient way of calculating the dipoles at every time step. However, polarizable point dipole methods are still more computationally intensive than nonpolarizable simulations. Evaluating the dipole-dipole interactions in Eqs. (9-7) and (9-20) is several times more expensive than evaluating the Coulombic interactions between point charges in Eq. (9-1). In addition, the requirement for a shorter integration timestep as compared to an additive model increases the computational cost. 

Figure 1 3. Contour plot of the electron density of CO, showing the magnitudes and directions of atomic and charge transfer dipoles (arrow length is proportional to magnitude). Arrow heads point to the negative end. The molecular dipole moment is given by the vector sum of charge transfer terms (p.c.t.) and the atomic polarizations ( ra p). Values were obtained at the DFT level using the B3LYP functional and the 6-31 1+G(3df) basis set. The SCF molecular dipole = 0.096 D the computed molecular dipole ( Jtc.t.[0] + Aa.p.[0] + Hc.JC] + Aa.p.[C]) = 0.038 au = 0.096 D, close to the experimental value of 0.1 10 D (15).

The MM3(2000) force field is the basis of this chapter. The program includes an induced dipole calculation that allows for the treatment of induction.69 This improvement in the electrostatics yields better predicted dipole moments than in previous versions of MM3. It should be pointed out that most other force fields use point charges whereas the MM series of programs is based on point dipoles. 

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. 

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