Non-Coulombic systems

To describe the simple phenomena mentioned above, we would hke to have only transparent approximations as in the Poisson-Boltzmann theory for ionic systems or in the van der Waals theory for non-coulombic systems [14]. Certainly there are many ways to reach this goal. Here we show that a field-theoretic approach is well suited for that. Its advantage is to focus on some aspects of charged interfaces traditionally paid little attention for instance, the role of symmetry in the effective interaction between ions and the analysis of the profiles in terms of a transformation group, as is done in quantum field theory. 

The casting of the Laplacian as outlined here is general to all many-body problems, including non-Coulombic systems, and is particularly useful for systems with a high degree of symmetry. 

Extending the Topological Analysis and Seeking the Real-Space Subsystems in Non-Coulombic Systems with Homogeneous Potential Energy Functions... 

Keywords Quanmm theory of atoms in molecules Topological analysis Non-Coulombic systems Homogeneous potentials Virial theorem... 

The Topological Analysis of Non-Coulombic Systems The Harmonic Trap Model... 

To conclude this section let us note that already, with this very simple model, we find a variety of behaviors. There is a clear effect of the asymmetry of the ions. We have obtained a simple description of the role of the major constituents of the phenomena—coulombic interaction, ideal entropy, and specific interaction. In the Lie group invariant (78) Coulombic attraction leads to the term -cr /2. Ideal entropy yields a contribution proportional to the kinetic pressure 2 g +g ) and the specific part yields a contribution which retains the bilinear form a g +a g g + a g. At high charge densities the asymptotic behavior is determined by the opposition of the coulombic and specific non-coulombic contributions. At low charge densities the entropic contribution is important and, in the case of a totally symmetric electrolyte, the effect of the specific non-coulombic interaction is cancelled so that the behavior of the system is determined by coulombic and entropic contributions. 

C. Fiolhais, F. Nogueira and M. Marques, Eds., Lecture Notes in Physics, Springer, Berlin, 2003, pp. 1—55. Density Functionals for Non-Relativistic Coulomb Systems in the New Century. 

The DLVO theory, a quantitative theory of colloid fastness based on electrostatic forces, was developed simultaneously by Deryaguin and Landau [75] and Verwey and Overbeek [76], These authors view the adsorptive layer as a charge carrier, caused by adsorption of ions, which establishes the same charge on all particles. The resulting Coulombic repulsion between these equally charged particles thus stabilizes the dispersion. This theory lends itself somewhat less to non-aqueous systems. 

We note that some coexistence curves of ionic systems with pronounced non-Coulombic interactions were also investigated with great care. These include aqueous solutions of tetraalkylammonium salts [77,79] and solutions... 

These three critical points, namely the neglect of non-Coulombic contributions for solute atoms, a fluctuating charge distribution of the QM particles and electrostatic embedding of MM partial charges, lead to the formulation of the quantum mechanical charge field (QMCF) ansatz [54] which has been applied in molecular dynamics studies of various hydrated systems, recently. 

The studies of Al(in) and Zn(II) have served as a methodical proof of the QMCF concept showing improvements of the accuracy resulting from the optimised QM/MM coupling, and at the same time eliminating the requirement of potential parameters (Coulombics and non-Coulombics) for the central species. QMCF simulations of other systems like Mn(II) and Cu(II) have led to the same conclusion [54],... 

Two subsequent simulation studies for low-frequency vibration systems clearly show that the strong and striking dominance of Coulomb force effects found for CH3C1 in water is by no means so clear-cut (or even true) in low-frequency diatomic systems. In the first of these, related to experiments by the Barbara group (24,25), Benjamin and Whitnell (26) found that for the diatomic I2 of frequency 115 cm, with a vibrational relaxation time of about 1 ps, the presence of Coulomb forces accelerated the VET in water by about a factor of 4, a noticeable but somewhat muted effect considering that one is comparing an ion to a neutral (with the same frequency). The authors noted the importance of the fact that the short-range non-Coulomb forces themselves are quite efficient at the low I2 frequency. 

As we have suggested recently [68] the technique involving separation of the CM motion and representation of the wave function in terms of explicitly correlated gaussians is not only limited to non- adiabatic systems with coulombic interactions, but can also also extended to study assembles of particles interacting with different types of two- and multi-body potentials. In particular, with this approach one can calculate the vibration-rotation structure of molecules and clusters. In all these cases the wave function will be expanded as symmetry projected linear combinations of the explicitly correlated fa of eqn.(29) multiplied by an angular term, Y M. 

For very low ionic strength, typical for non-aqueous systems, screening becomes negligible [xa 1) and the expressions acquire the forms for charged spheres without countercharge, that is the Coulomb case ... 

Small exponents. Evidence for Ising criticality can be provided by some properties showing weak divergences, which are absent in the mean-field case. One such case is the specific heat, which diverges with the exponent a. Kaatze and coworkers [112] have indeed shown the presence of such an a anomaly in EtNH3N03 + //-octanol, but as already mentioned, this system shows an anomalous location of the critical point, indicating that non-Coulomb interactions play a considerable role in driving the phase separation. 

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