Filled subshell

T dtc) and the d Zn(rffc)2, indicate a relatively great stabiUty for electronic states with symmetrical orbital functions. It parallels the maxima in ionisation potentials of the elements with half and completely filled subshells. 

L = 0 and S = 0 always hold for a fully occupied subshell. Therefore, the core electrons of an atom do not contribute to magnetism. L = 0 and g = 2 hold for half-filled subshells, resulting in a pure spin paramagnetism according to equation (19.6). 

It turns out that fully filled or half-filled subshells have added stability compared with subshells having some other numbers of electrons. One effect of this added stability is the fact that some elements do not follow the n +1 rule exactly. For example, copper would be expected to have a configuration... 

Paramagnetism indicates unpaired electrons, which in turn are often associated with partially filled subshells. First we write the electron configurations of the elements, and then those of the ions. From those electron configurations, we determine whether the species is paramagnetic or diamagnetic. 

True/False. The ionization energy is higher than expected for filled and half-filled subshells. 

Nonmetals follow the general trends of atomic radii, ionization energy, and electron affinity. Radii increase to the left in any row and down any column on the periodic table. Ionization energies and electron affinities increase up any column and towards the right in any row on the periodic table. The noble gases do not have electron affinity values. Ionization energies are not very important for the nonmetals because they normally form anions. Variations appear whenever the nonmetal has a half-filled or filled subshell of electrons. The electronegativity... 

The even higher value of Be (greater than B) is due to the increased stability of the electron configuration of Be. Beryllium has a filled s-subshell. Filled subshells have an increased stability, and additional energy is required to pull an electron away. Give yourself 1 point for the filled subshell discussion. 

This can be explained in terms of the relative stability of different electronic configurations and thus provides evidence for these electronic configurations. To help you understand this, you have to appreciate that there is a special stability associated with a filled subshell or a half-filled subshell - for example, the p subshell when it contains three or six electrons. Likewise, the d subshell is most stable when it contains five or ten electrons. The more stable the electronic configuration, then the more difficult it is to remove an electron and therefore the ionisation energy is higher. 

The terms arising from a configuration with more than one electron in a given partly filled subshell are not so easily found, since the Pauli principle must be taken into account. We omit discussion. 

Let us notice that even while calculating these matrices for the partially filled shells lN we face the necessity to use in jj coupling the CFP of both partially and almost filled subshells. Therefore, in calculations of this sort it is very important to have a universal system of relations connecting complementary shells. The calculations show that this method gives the... 

Relationships between coefficients gk for different degrees of occupation of the subshells (the cases of almost and completely filled subshells) are described by equalities (20.35), (20.36) and (20.38). Therefore, for magnetic interactions one has additionally to consider such conditions only in the case of coefficient dk. Bearing in mind that k acquires only odd values and that the submatrix elements of operator Tk are diagonal with respect to seniority quantum number v, we find... 

The incompletely filled (/-subshell is responsible for the wide range of colors shown by compounds of the (/-block elements. Furthermore, many (/-metal compounds are paramagnetic (Box 3.2). Indeed, one of the challenges we face in this chapter is to build a model of bonding that accounts for color and magnetism in a unified way. 

Expected JL t t t n n n ft ft ft atom can attain half-filled or completely filled subshells. 

Cu(I) d10 It is instructive to first consider a reduced Cu site that has a filled subshell d10 electron configuration. This cannot be studied by most of the spectroscopic methods used in inorganic and bioinorganic chemistry (the alternative approach is photoelectron spectroscopy (PES) that is presented in Ref. 45). The edge for a Cu(I) complex is at 8990 eV and corresponds to the threshold energy for... 

Another factor is that the configuration 3dw4s has a spherically symmetrical distribution of electron density, a stabilizing arrangement characteristic of all filled or half-filled subshells. On the other hand, the configuration 3d 4s2 has a hole (a missing electron) in the 3d subshell, destroying the symmetry and any extra stabilization. 

Ans. Cr [Ar] 3d5 4s1. Aufbau would give 3d44s2, so an s shifts to d to gain the stability of the half-filled subshell. Note that the actual configuration has complete spherical symmetry. 

Ans. A value of about 9.2eV for P would be halfway between the values for Si and S, but because of the stability of the half-filled subshell, a significantly high energy might be required to remove an electron from P, perhaps higher than for S observed value is 10.9 eV. 

The second output for HF was calculated using VBSCF/STO-3G, with the program XMVB (7), and is displayed in Output 2.2. The relevant output information begins again with the symbolic representation of the structures, which are written in the same manner as before, 4 5 , 4 4 , and 5 5 , and represent the HL and ionic structures of the H—F bond, as sketched in Scheme 2.1. The number labels of the orbitals are 4 for the bond hybrid of F, and 5 for the AO of H. The rest of the valence electrons are kept in doubly occupied orbitals on fluorine, and the filled subshell is labeled as 1 1 2 2 3 3 . This subshell accompanies all the structures. The core electrons are not mentioned specifically, although they are included in the calculations. 

Note that there are two anomalies in the first transition series [Ar]3d54s1 (instead of [Ar]3d44s2) for Cr and [Ar]3d104s1 (instead of [Ar]3d94s2) for Cu. These two configurations arise from the extra stability of a half-filled or completely filled subshell. Such stability comes from the spherically symmetric electron density around the nucleus for these configurations. Take the simpler case of p3 as an example. The angular portion of the density function is proportional to... 

An example often used in texts is the 1 s22s22p2 configuration of carbon. Since all filled subshells lead to L = 0 and S = 0, we only need to be concerned with p2 here. There are 15 microstates for this configuration ... 

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