Electronics shells

Cl.1.3.1 SIMPLE METAL CLUSTERS AND THE ELECTRON SHELL MODEL... 

Figure Cl. 1.2. (a) Mass spectmm of sodium clusters (Na ), N= 4-75. The inset corresponds to A = 75-100. Note tire more abundant clusters at A = 8, 20, 40, 58, and 92. (b) Calculated relative electronic stability, A(A + 1) - A(A0 versus N using tire spherical electron shell model. The closed shell orbitals are labelled, which correspond to tire more abundant clusters observed in tire mass spectmm. Knight W D, Clemenger K, de Heer W A, Saunders W A, Chou M Y and Cohen ML 1984 Phys. Rev. Lett. 52 2141, figure 1.

The spherical shell model can only account for tire major shell closings. For open shell clusters, ellipsoidal distortions occur [47], leading to subshell closings which account for the fine stmctures in figure C1.1.2(a ). The electron shell model is one of tire most successful models emerging from cluster physics. The electron shell effects are observed in many physical properties of tire simple metal clusters, including tlieir ionization potentials, electron affinities, polarizabilities and collective excitations [34]. 

Martin T P, Bergmann T, Gohlich H and Lange T 1990 Observation of electronic shells and shells of atoms in large Na clusters Chem. Phys. Lett. 172 209... 

Knight W D, Clemenger K, de Heer W A, Saunders W A, Chou M Y and Cohen M L 1984 Electron shell structure and abundances of sodium clusters Phys. Rev. Lett. 52 2141... 

The electron configuration is the orbital description of the locations of the electrons in an unexcited atom. Using principles of physics, chemists can predict how atoms will react based upon the electron configuration. They can predict properties such as stability, boiling point, and conductivity. Typically, only the outermost electron shells matter in chemistry, so we truncate the inner electron shell notation by replacing the long-hand orbital description with the symbol for a noble gas in brackets. This method of notation vastly simplifies the description for large molecules. 

Table 11 illustrates the known closed proton and neutron shells and the predicted closed nuclear shells (shown in parentheses) that might be important in stabilising the superheavy elements. Included by way of analogy are the long-known closed electron shells observed in the buildup of the electronic stmcture of atoms. These correspond to the noble gases, and the extra stabiUty of these closed shells is reflected in the relatively small chemical reactivity of these elements. The predicted (in parentheses) closed electronic stmctures occur at Z = 118 and Z = 168. 

Neutral or charged PMD radicals that have open electron shells are derived by chemically or polarographicaHy reducing or oxidising the corresponding dyes having closed electron shells. Pyrylocyanine radicals and their heteroanalogues, represented by (10), where X = O or S, and n = 0, 1, or 2 (19,20), are examples. 

In PMD radicals, the bond orders are the same as those in the polymethines with the closed electron shell, insofar as the single occupied MO with its modes near atoms does not contribute to the bond orders. Also, an unpaired electron leads the electron density distribution to equalize. PMD radicals are characterized by a considerable alternation of spin density, which is confirmed by epr spectroscopy data (3,19,20). 

PMD color or the nature of the electron transitions produces the widest appHcation for PMDs. Depending on the polymethine chain length, the end-group topology, and the electron shell occupation, polymethines can absorb light in uv, visible, and near-ir spectral regions. 

When the hole in the /th shell is filled by an electron from theyth shell, there is a hole in the latter shell that will in turn be filled by an electron from a higher kth shell. This may result in the emission of a second x-ray, such that one hole in an inner electron shell can result in a cascade of several x-rays having ever-decreasing energies. 

Naiiow-line uv—vis spectia of free atoms, corresponding to transitions ia the outer electron shells, have long been employed for elemental analysis usiag both atomic absorption (AAS) and emission (AES) spectroscopy (159,160). Atomic spectroscopy is sensitive but destmctive, requiring vaporization and decomposition of the sample iato its constituent elements. Some of these techniques are compared, together with mass spectrometry, ia Table 4 (161,162). 

Atoms and free radicals are highly reactive intermediates in the reaction mechanism and therefore play active roles. They are highly reactive because of their incomplete electron shells and are often able to react with stable molecules at ordinary temperatures. They produce new atoms and radicals that result in other reactions. As a consequence of their high reactivity, atoms and free radicals are present in reaction systems only at very low concentrations. They are often involved in reactions known as chain reactions. The reaction mechanisms involving the conversion of reactants to products can be a sequence of elementary steps. The intermediate steps disappear and only stable product molecules remain once these sequences are completed. These types of reactions are refeiTcd to as open sequence reactions because an active center is not reproduced in any other step of the sequence. There are no closed reaction cycles where a product of one elementary reaction is fed back to react with another species. Reversible reactions of the type A -i- B C -i- D are known as open sequence mechanisms. The chain reactions are classified as a closed sequence in which an active center is reproduced so that a cyclic reaction pattern is set up. In chain reaction mechanisms, one of the reaction intermediates is regenerated during one step of the reaction. This is then fed back to an earlier stage to react with other species so that a closed loop or... 

Such a simple model, without the barrier due to the Qo at the center, has been used to calculate the electronic shell structure of pure alkali metal clusters[9]. 

Table 1. Comparison of experimentally observed electronic shell closings with model calculations ...

See text. The first two columns give the numbers of metal atoms at which electronic shell closings have been observed in experiment for Cs-covered C o and for pure alkali metal clusters, respectively. The columns on the right list the number of electrons required for shell closings in an infinitely deep potential well with and without a central barrier. The numbers in the different columns are mainly arranged in a manner to show correlations. 

Fig. 13. Mass spectra of C qCs. clusters ionized at different photon energies near the ionization threshold the values of x corresponding to the closing of electronic shells are indicated.

A contraction resulting from the filling of the 4f electron shell is of course not exceptional. Similar contractions occur in each row of the periodic table and, in the d block for instance, the ionic radii decrease by 20.5 pm from Sc to Cu , and by 15 pm from Y to Ag . The importance of the lanthanide contraction arises from its consequences ... 

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