Self-consistent held calculation

As often happens in self-consistent Held calculations (e.g., in the Har-tree theory of atoms) the two errors (i) and (ii) cancel each other to a large extent. Many post-Flory attempts, which tried to improve on one term, (i) or (ii), leaving the other unaltered, led to results that were power than eq. (1.39). 

Fig. 3.7. (a) Ab initio self-consistent Held calculated electron deformation density distribution of trans [(it -CjHslFelCOljlj in the plane containing the iron-iron axis and the bridging carbonyl ligand. The contour interval is -200e/nm and the dashed contours correspond to negative deformation and the solid contours correspond to zero and positive deformation density (b) experimental electron deformation density distribution derived from X-N calculations. The contour interval is — lOOe/nm . (From Bbnard, 1982.)... 

A number of types of calculations begin with a HF calculation and then correct for correlation. Some of these methods are Moller-Plesset perturbation theory (MPn, where n is the order of correction), the generalized valence bond (GVB) method, multi-conhgurational self-consistent held (MCSCF), conhgu-ration interaction (Cl), and coupled cluster theory (CC). As a group, these methods are referred to as correlated calculations. 

An MCSCF calculation in which all combinations of the active space orbitals are included is called a complete active space self-consistent held (CASSCF) calculation. This type of calculation is popular because it gives the maximum correlation in the valence region. The smallest MCSCF calculations are two-conhguration SCF (TCSCF) calculations. The generalized valence bond (GVB) method is a small MCSCF including a pair of orbitals for each molecular bond. 

The self-consistent reaction held (SCRF) method is an adaptation of the Poisson method for ah initio calculations. There are quite a number of variations on this method. One point of difference is the shape of the solvent cavity. Various models use spherical cavities, spheres for each atom, or an isosurface... 

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). 

Because of the small number of ions involved in typical simulations, it is difficult to calculate the self diffusion coefficient reliably. However, the differences in mobility between different ions and the trends, when the ion approaches the metal surface, can be qualitatively assessed by a scatter plot like that in Fig. 29. The figure shows the area parallel to the surface probed by I", F , and Li+ ions. Each ion is dissolved in a film of adsorbed water on a mercury surface consisting of 150 water molecules and held fixed at the indicated distance from the surface. Trajectories are shown over 60 picoseconds. Both in the bulk (left panels) and closer to the surface (right panels) the mobility decreases in the sequence large anion (I ) > small anion (F ) > small cation (Li+). The mobility close to the surface is reduced quite substantially, especially for Li+ and F . 

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