Coulombic, generally

This leads to the third virial coefficient for hard spheres. In general, the nth virial coefficient of pairwise additive potentials is related to the coefficient7) in the expansion of g(r), except for Coulombic systems for which the virial coefficients diverge and special teclmiques are necessary to resiim the series. 

It is often the case that the solvent acts as a bulk medium, which affects the solute mainly by its dielectric properties. Therefore, as in the case of electrostatic shielding presented above, explicitly defined solvent molecules do not have to be present. In fact, the bulk can be considered as perturbing the molecule in the gas phase , leading to so-called continuum solvent models [14, 15]. To represent the electrostatic contribution to the free energy of solvation, the generalized Bom (GB) method is widely used. Wilhin the GB equation, AG equals the difference between and the vacuum Coulomb energy (Eq. (38)) ... 

The friction force g is unknown in general. The Coulomb law assumes g = a and provides the more general relations as compared with (1.48) (Hlavacek et al., 1988 Duvaut, Lions, 1972 Demkowicz, Oden, 1982 Haslinger, Panagiotopoulos, 1984 Namm, 1995)... 

Metalliding. MetaUiding, a General Electric Company process (9), is a high temperature electrolytic technique in which an anode and a cathode are suspended in a molten fluoride salt bath. As a direct current is passed from the anode to the cathode, the anode material diffuses into the surface of the cathode, which produces a uniform, pore-free alloy rather than the typical plate usually associated with electrolytic processes. The process is called metalliding because it encompasses the interaction, mostly in the soHd state, of many metals and metalloids ranging from beryUium to uranium. It is operated at 500—1200°C in an inert atmosphere and a metal vessel the coulombic yields are usually quantitative, and processing times are short controUed... 

The outer Helmholtz plane (OHP) refers to the distance of closest approach of non specifically adsorbed ions, generally cations. The interactions of the ions of the OHP with the surface are not specific and have the character of longer range coulombic interactions. Cations that populate the outer Helmholtz plane are usually solvated and are generally larger in size than the anions. 

For quantitative evaluation of ERDA energy spectra considerable deviations of recoil cross-sections from the Rutherford cross-section (Eq. 3.51) must be taken into account. Light projectiles with high energy can penetrate the Coulomb barrier of the recoil atom the nuclear interaction generally leads to a cross-section that is larger than ctr, see Eq. (3.51). For example, the H recoil cross-section for MeV He projec-... 

First, there are some general constraints on the global Hamiltonian. Obviously must contain the physics which is assumed to be essential for the problem under consideration. In our case the coulombic interaction and the ideal entropy play this role. Another requirement is that H leads... 

DFT methods compute electron correlation via general functionals of the electron density (see Appendix A for details). DFT functionals partition the electronic energy into several components which are computed separately the kinetic energy, the electron-nuclear interaction, the Coulomb repulsion, and an exchange-correlation term accounting for the remainder of the electron-electron interaction (which is itself... 

The original FMM has been refined by adjusting the accuracy of the multipole expansion as a function of the distance between boxes, producing the very Fast Multipole Moment (vFMM) method. Both of these have been generalized tc continuous charge distributions, as is required for calculating the Coulomb interactioi between electrons in a quantum description. The use of FMM methods in electronic structure calculations enables the Coulomb part of the electron-electron interaction h be calculated with a computational effort which depends linearly on the number of basi functions, once the system becomes sufficiently large. 

Potential (Coulomb) energy operator (general, electron-electron, nuclear-electron, nuclear-nuclear)... 

Some exceptions to this general observation were found halide and nitrite salts have unusually high hydrogen-bond basicities (as would be expected), while penta-cyanopropionide, picrate, triflate, and perfluorobezenesulfonate salts not only had unusually low hydrogen-bond basicities (also as would be expected) but also lower s values, perhaps due to the weakening of the Coulombic interactions by delocalization of the charge on the anions. 

In the more general case of the anodic oxidation or cathodic reduction of a species by change transfer, 7 coulombs will be required for 1 mol where... 

Besides its temperature dependence, hopping transport is also characterized by an electric field-dependent mobility. This dependence becomes measurable at high field (namely, for a field in excess of ca. 10d V/cm). Such a behavior was first reported in 1970 in polyvinylcarbazole (PVK) [48. The phenomenon was explained through a Poole-ITenkel mechanism [49], in which the Coulomb potential near a charged localized level is modified by the applied field in such a way that the tunnel transfer rale between sites increases. The general dependence of the mobility is then given by Eq. (14.69)... 

In Section II.C we gave a general discussion of the Coulomb correlation, and we will now define the correlation error in the independent-particle model in greater detail. It is convenient to study the first- and second-order density matrices and, according to the definitions (Eq. II.9) applied to the symmetryless case, we obtain... 

The general idea of using different orbitals for different spins" seems thus to render an important extension of the entire framework of the independent-particle model. There seem to be essential physical reasons for a comparatively large orbital splitting depending on correlation, since electrons with opposite spins try to avoid each other because of their mutual Coulomb repulsion, and, in systems with unbalanced spins, there may further exist an extra exchange polarization of the type emphasized by Slater. 

In Eq. (15) 2 qB/r is the coulombic part of the mean force potential, and Wjj is the noncoulombic part. The earlier association constants of Fuoss, Prue, and Bjerrum are special cases of this general chemical model [15]. The importance of noncoulombic interactions is proved [ 16] by ... 

A second difficulty which has only been alluded to—or rather neglected—in the present outline is the validity of the assumption that in and out fields exist. The existence of an asymptotic limit might well be rigorously provable for matrix elements of the form <0 r(o ) l particle), but not for more general situations without explicitly removing the Coulomb interaction between the particles. 

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