Half-filled shell effect

Other cases of approximately monatomic chromophores occur in 4f-+5d transitions now known in Sm11, Eu11, Tm11,28 Ybn, Cera, Prm, and Tbra.16 (The half-filled shell effect expressed by Eq. (3) is very conspicuous in this distribution of known species.) 5transitions are known in UIU, Np111, Puin, Paiy, U, Np, and Pu17. 5s-+5p transitions are known in complexes of Snn and Sbm and 6s — 6p in Tl1, Pbn, and Bira. The halide ions in solvents of not too high electron affinity and in crystals of alkali metal halides show absorption bands which to a certain approximation can be described as 3p - 4s(Cl), 4p — -5s(Br), and 5p - -6s(I). 

Deviations from regular smooth variation of properties of lanthanides occur at quarter-, half- and three-quarter filled 4/ configurations which have been attributed to tetrad effect. This effect has been attributed to small changes in Racah parameters when the ligands around the metal change during the reactions. The half-filled shell effect and the quarter-and three-quarter shell effects are caused by changes in El and 3 in the theoretical ionization potential expressions for /" ions [4],... 

In fig. 4 the first to fourth ionization energies of the lanthanides and actinides are plotted for comparison. It is evident that the half-filled shell effect is much less significant for the actinides than for the lanthanides. This diminished effect is caused by the greater radial extension of the 5f orbitals compared to the 4f orbitals and manifests itself in the easier accessibility of 4-1- oxidation states of many actinides. 

Some of the examples of the tetrad effect are shown in Fig. 6. The half-filled shell effect has been joined by the quarter-filled and three-quarter-filled effects. We make no attempt at explanation. 

As reviewed by Fidelis and Mioduski57) the formation constant K of a complex with a given" ligand (or the distribution coefficient for extraction in another solvent, or an ion-exchange resin) shows a ratio (in the case of two consecutive lanthanides) which provides perceptible variations (from a constant) not only at the half-filled shell (q = 7) Gd(III) but also at the plateaux q = 3 and 4, as well as 10 and 11. These quarter-shell effects can be rationalized 217,218) by the refined spin-pairing energy theory. If D of Eq. (3) is decreased 1 % (65 cm 1) by the nephelauxetic effect in a... 

Figure 1. Experimental variations of 2p-core ionization energies (in eV) for atoms from A1(Z = 13) to Ba(Z = 56). Upper left. 2p /2 and 2p3/2 energies lower left, their weighted-average second-order discrete derivative, as functions of Z upper right spin-orbit splitting between the 2pi/2 and 2p3/2 levels lower right, its second derivative, as functions of Z. On the derivative diagrams shell effects appear about fully filled and half-filled shells and near filling irregularities of the transition elements.

At the moment the number of true four-component molecular EFG calculations is still rather limited due to the considerable computational effort especially in the post-DHF steps. Just five years ago Pj kko expressed the need for fully relativistic benchmark calculations in order to abandon perturbative corrections for considerable relativistic effects and to establish reference results. Furthermore spin-orbit effects can cause an EFG e.g. in atoms with Z > 0 and half-filled shells where according to nonrelativistic theory the EFG should vanish. This is the case for e.g. a system leading to a Pij2P f2 spin-orbit-split configuration. Also in closed-shell molecules with heavy halogen nuclei the spin-orbit effect is not completely quenched [88]. 

Possibly this effect is associated with the particular stability of the half-filled shell, but it seems evident that the criterion of the comparability of the group overlap integrals relating to the metal eg and tiig orbitals (which the authors have used when speculating that the two B values should be about equal) is too approximate to be of any validity. 

In this chapter, we have learned about the photoelectric effect and its impact on the formulation of light as photons. We have also seen that some anomalous electron configurations of the elements are particularly favorable if each atom has one or more half-filled shell, such as the case for the Cr atom with its [Ar]4s 3d electron configuration. Let s suppose it is hypothesized that it requires more energy to remove an electron from a metal that has atoms with one or more half-filled shells than from those that do not (a) Design a series of experiments involving the photoelectric effect that would test the hypothesis, (b) What experimental apparatus would be needed to test the hypothesis It s not necessary that you name actual equipment but rather that you imagine how the apparatus would work—think in terms of the types of measurements that would be needed, and what capability you would need in your apparatus, (c) Describe the type of data you would collect and how you would analyze the data to see whether the hypothesis were correct, (d) Could your experiments be extended to test the hypothesis for other parts of the periodic table, such as the lanthanide or actinide elements ... 

For a half filled shell the reduced matrix elements of with even k satisfy the selection rule Av = 2 therefore the triple product (1.148) also satisfies the selection rule Av = 2 (whereas the electrostatic energy matrices satisfy the selection rule Av = 0, 4). Hence, all diagonal elements of Hi vanish, and all second-order effects are well represented by two-electron effective interactions. 

Hence the diradical states are exceptional in that the epikernel principle cannot be based on the usual first order JT section rule of Eq. (1) The reason is that the E state is essentially based on a half-filled shell configuration, with two electrons in a doubly degenerate e" orbital. As we have shown elsewhere such half-filled shell states are subject to a hole electron exchange symmetry, which counteracts the first order JT distorting forces [42], Moreover, in these highly reactive molecules the absence of a strong first order activity coincides with a pronounced second order effect, due to suitable low lying excited states. This limits the applicability of the epikernel principle in the case of diradicals. 

For the transition metals it is often impossible to reach a noble gas structure except in covalent compounds (see effective atomic number rule) and it is found that relative stability is given by having the sub-shells (d or f) filled, half-filled or empty. 

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