Dynamically screened Coulomb

Similar ladder diagrams describe the dressing of interaction vertex as it shown in Fig. 2b. The dressed vertex can be used to obtain the polarization operator, that defines effective dynamically screened Coulomb interaction... 

Other known methods that have been used in the study of lanthanides include the OP scheme, the LDA + U approach, where U is the on-site Hubbard repulsion, and the DMFT, being the most recent and also the most advanced development. In particular, when combined with LDA + U, the so-called LDA - - DMFT scheme, it has been rather successful for many complex systems. We note here that both DMFT and LDA + U focus mostly on spectroscopies and excited states (quasiparticles), expressed via the spectral DOS. In a recent review article (Held, 2007), the application of the LDA + DMFT to volume collapse in Ce was discussed. Finally, the GW approximation and method, based on an electron self-energy obtained by calculating the lowest order diagram in the dynamically screened Coulomb interaction, aims mainly at an improved description of excitations, and its most successful applications have been for weakly correlated systems. However, recently, there have been applications of the quasi-particle self-consistent GW method to localized 4f systems (Chantis et al., 2007). 

Owing to the long-range character of Coulomb forces, the formulation of kinetic equations for plasmas is more complicated than that for neutral gases. Therefore, the Coulomb systems show a collective behavior, and we observe for example, the dynamical screening of the Coulomb potential. 

Let us now consider the problem of bound states in plasmas. The interaction between the plasma particles is given by the Coulomb force. A characteristic feature of this interaction is its long range. Therefore, Coulomb systems show a collective behavior, so we can observe, for instance, the dynamical screening of the Coulomb potential and plasma oscillations. 

The radial correlation leads to a dynamical screening of the nuclear charge, imposed by one electron on the other. This allows the electrons to start at the inner boundary of the Coulomb zone with rt r2, but to leave the Coulomb zone with > r2 (or r, < r2). 

The LDA-fU theory may be regarded as an approximate GW method [37]. The screened Coulomb and exchange parameters U and J are usually estimated in a supercell approximation [39]. However, there is some arbitrariness in the choice of the localized orbitals when performing the partitioning of the Hamiltonian. A further step in the improvement of LDA-I-U consists in adding dynamical effects — frequency dependence in H r,r u). This may be performed using a DMFT-type approach (DMFT= Dynamical Mean Field Theory) [40] as part of the so-called LDA-b-1- approaches [41]. 

Hassan, S.A., Mehler, E.L., Zhang, D., Weinstein, H. Molecular dynamics simulations of peptides and proteins with a continuum electrostatic model based on screened Coulomb potentials. Proteins 2003, 51(1), 109-25. 

We employ the time-dependent screened HF approximation (TDSHF), which replaces the bare Coulomb interaction v in the HF self- energy (Fig.l) by a dynamically screened interaction (eq.(2.4)) v ... 

Neglect of Hydrodynamic Interactions.—The coupling of hydrodynamic flow exerts a major influence on the dynamics of colloidal dispersions.In certain special cases, however, it has proved reasonable or expedient to neglect the hydrodynamic interactions. One such instance is the very dilute, electrostatically-stabilized dispersion in which particles interact via a screened Coulomb potential, that is, equation (2) with ku 1. 

To investigate the effect of the Debye-Huckel approximation on the solution properties, Stevens and Kremer [152] performed molecular dynamics simulations of salt-free solutions of bead-spring polyelectrolyte chains in which the presence of counterions was treated via a screened Coulomb potential, and compared the results with their simulations with explicit counterions [146,148]. To elucidate the effect of the Debye-Hiickel approximation, the dependence of the mean square end-to-end distance, R ), osmotic pressure, and chain structure factor on polymer concentration was examined. Stevens and Kremer found that (i ) tends to be larger at low densities for DH simulations and is smaller at higher densities. However, the difference in (i ) between DH simulations and simulations with explicit counterions is within 10%. This trend seems to be a generic feature for all N in their simulations. The functional form and density dependence of the chain structure factor are very close in both simulations. The most severe Debye-Huckel approximation affects the dependence of the osmotic pressure on polymer concentration. It appears that in the DH simulations not only is the magnitude of the osmotic pressure incorrect, but also the concentration dependence is wrong. 

---