Self-consistent effects

Here jb/if(r) is the density of bound/free ions, n0i/oe is the ion/electron density at infinity r) is the self-consistent effective potential e is the absolute value of the electron charge Tj/e is the ion/electron temperature S /e =... 

The shape of the curves in Fig. 16 suggests that the electronic states in the B2 and the B32 structures play an important role for the B2-B32 phase transition in the system LiCdi xTlx (cf. Fig. 3). To study the influence of the electronic structure on the position of the phase transition as a function of x quantitatively, however, other mechanisms, such as self-consistency effects and the influence of the non-stoichiometry, have to be known. 

Table 1 shows the spin-orbit splittings of the neutral mercury atom from ZORA calculations. Different potentials have been used to construct the ZORA kinetic energy operator. In the column labelled ZORA/NUC, only the nuclear potential has been used while the column ZORA/FULL reports results from fully self-consistent ZORA calculations, in which the ZORA Hamiltonian is reconstructed in each SCF iteration using the full effective potential including the Hartree and exchange-correlation term. Note that these results are identical to a model potential calculation since for a neutral atom, the model potential is just the full self-consistent effective potential. The entries in the column labelled ZORA/COUL have been calculated using only the Coulombic parts of the model potential, i. e. the nuclear and Hartree potentials. 

The spherical jellium model has been applied to alkali metal clusters by many authors (see Ref. [6]). Fig. (1) shows the self-consistent effective potential for a sodium cluster with twenty atoms. The degenerate levels are filled up to electron number = 20. In a spherical cluster with 21 electrons, the last electron will have to occupy the If level above (dashed line). This electron is less... 

Fig. 1. Self-consistent effective potential for Na2o in the spherical jellium model. The occupied electronic shells are indicated, as well as the lowest unoccupied shell.

Kohn W and Sham L J 1965 Self-consistent equations including exchange and correlation effects Phys. Rev A 140 1133-8... 

Most TB approaches are not charge self-consistent. This means that they do not ensure that the charge derived from the wavefiinctions yields the effective potential assumed in their calculation. Some methods have been developed which yield charge densities consistent with the electronic potential [14, H and 16]. 

The result of this approximation is that each mode is subject to an effective average potential created by all the expectation values of the other modes. Usually the modes are propagated self-consistently. The effective potentials governing die evolution of the mean-field modes will change in time as the system evolves. The advantage of this method is that a multi-dimensional problem is reduced to several one-dimensional problems. 

For the case of nonzero temperatures the vacuum averages in Eq.(7) should be replaced by thermal averages over phonon populations. Using (7) and (5) we obtain that the scattering of an exciton in the effective medium by the perturbation fi — v z)) is described by the following self-consistent condition... 

Kohn W and L J Sham 1965. Self-consistent Equations Including Exchange and Correlation Effects. Physical Review A140 1133-1138. 

Constanciel R and R Contreras 1984. Self-Consistent Field Theory of Solvent Effects Representation by Continuum Models - Introduction of Desolvation Contribution. Theoretica Chimica Acta 65 1-11. 

SCRF (self-consistent reaction field) method for including solvation effects in ah initio calculations... 

Ab initio calculations can be performed at the Hartree-Fock level of approximation, equivalent to a self-consistent-field (SCF) calculation, or at a post Hartree-Fock level which includes the effects of correlation — defined to be everything that the Hartree-Fock level of approximation leaves out of a non-relativistic solution to the Schrodinger equation (within the clamped-nuclei Born-Oppenhe-imer approximation). 

One of the most efficient ways to treat this problem is to combine the ab initio MO method and the RISM theory, and this has been achieved by a slight modification of the original RISM-SCF method. Effective atomic charges in liquid water are determined such that the electronic structure and the liquid properties become self-consistent, and along the route of convergence the polarization effect can be naturally incorporated. 

Self-Consistent Equations Including Exchange and Correlation Effects W. Kohn and L. J. Sham Physical Review 140 (1965) All33... 

This is not an SCRF model, as the dipole moment and stabilization are not calculated in a self-consistent way. When the back-polarization of the medium is taken into account, the dipole moment changes, depending on how polarizable the molecule is. Taking only the first-order effect into account, the stabilization becomes (a is the molecular polarizability, the first-order change in the dipole moment with respect to an electric field, Section 10.1.1). 

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