Orbitals inner -shell shielding

The electron density i/ (0)p at the nucleus primarily originates from the ability of s-electrons to penetrate the nucleus. The core-shell Is and 2s electrons make by far the major contributions. Valence orbitals of p-, d-, or/-character, in contrast, have nodes at r = 0 and cannot contribute to iA(0)p except for minor relativistic contributions of p-electrons. Nevertheless, the isomer shift is found to depend on various chemical parameters, of which the oxidation state as given by the number of valence electrons in p-, or d-, or /-orbitals of the Mossbauer atom is most important. In general, the effect is explained by the contraction of inner 5-orbitals due to shielding of the nuclear potential by the electron charge in the valence shell. In addition to this indirect effect, a direct contribution to the isomer shift arises from valence 5-orbitals due to their participation in the formation of molecular orbitals (MOs). It will be shown in Chap. 5 that the latter issue plays a decisive role. In the following section, an overview of experimental observations will be presented. 

As a result of the presence of one or more maxima near the nucleus, s orbitals are very penetrating and are somewhat less shielded by inner-shell electrons than are orbitals with larger values of L In turn, (hey tend to shield somewliat better than other orbitals. Orbitals with high l values, such as A and f orbitals, arc much less penetrating and are far poorer at shielding. 

The nuclear charge experienced by the outermost electrons of an atom the actual nuclear charge minus the effects of shielding due to inner-shell electrons. Example Set of dx2-y2 and dz2 orbitals those d orbitals within a set with lobes directed along the x-, y-, and z-axes. 

The valence orbital (2s and 2p) energy levels of the fluorine atom are stabilized remarkably well by a large positive charge of the nucleus and the absence of shielding eifects by inner-shell electrons. The orbital energy level of the 2p lies at —18.6 eV. This is 5 eV lower than that of the proton s ls-orbital [6]. 

Numerical ab initio calculations for selected examples with polarized basis sets and Cl of reasonably size confirmed that the size of the matrix elements within the active space matrix is negligible. In contrast, the elements of that involve both the active and inner shells are large, since is primeuily due to the shielding of nuclei by inner-shell electrons [11]. It is therefore common practice in many semiquantitative applications, to account for the effect of the fixed-core electrons by replacing the factor gPgZ r in by the empirical value of the atomic spin-orbit coupling constant valence p orbitals on... 

The wavefunction described with the optimum a,y corresponds well with a somewhat perturbed lslj 2s configuration. Two of the electrons depend on the electron-nuclear distance with a values (screening parameters) that correspond to a partially screened interaction with the - -3-charged Li nucleus in a split-shell electron distribution. The third electron (that with pre-multiplying r) has an a value somewhat larger than for a hydrogenic 2s orbital, indicative of the fact that the inner-shell electrons do not completely shield the Li nucleus. The electron-electron a values all reflect the existence of electron-electron repulsion, with the effect most pronounced for the Is-ls interaction. All these observations are consistent with the notion that the exponentially correlated wavefunction gives an excellent zero-order description of the electronic structure of Li. 

If the nucleus were large, then orbitals of different / would have different orbital energies. This explains the energy differences for the s,p,d,... levels, because the outer shell electrons move in the field of the nucleus shielded by the inner shell electrons (thus, in a field of something that can be seen as a large pseudo-nucleus). 

The early calculations by Dickinson [168] of the diamagnetic shielding in atoms using Hartree or Hartree-Fock SCF atomic orbitals made it clear that the major contribution to is due to inner shell electrons and that the relative contribution of the outer electrons decreases markedly with atomic number Z. As a consequence of this are the values for atoms rather insensitive to the effective atomic... 

The 4/ electrons, responsible for the magnetic behavior of the rare earth metals and ions, are localized within the inner shell (4/), and the atomic or ionic moment is due to both spin and orbital angular momenta. The radial portion of the 4/ wave function as a function of distance is shown in Figure 2 to illustrate that the 4/ shell is shielded by the 5d and 6s shells. Because of this shielding, the / orbitals are relatively insensitive to the symmetry of the crystal field in which they are placed. Table 2 illustrates the agreement between observed and calculated values of p when the orbital moment is included. 

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