Diagonal effect

The existence of many ionic structures in MCVB wave functions has often been criticized by some workers as being unphysical. This has been the case particularly when a covalent bond between like atoms is being represented. Nevertheless, we have seen in Chapter 2 that ionic structures contribute to electron delocalization in the H2 molecule and would be expected to do likewise in all cases. Later in this chapter we will see that they can also be interpreted as contributions from ionic states of the constituent atoms. When the bond is between unlike atoms, it is to be expected that ionic stmctures in the wave function will also contribute to various electric moments, the dipole moment being the simplest. The amounts of these ionic structures in the wave functions will be determined by a sort of balancing act in the variation principle between the diagonal effects of the ionic state energies and the off-diagonal effect of the delocalization. 

A conical intersection is expected above 10,000 cm 1 that has not yet been rigorously identified. This conical intersection also creates important anharmonicities in the fully diagonalized effective Hamiltonians of Weigert... 

All metallic properties have been lost in these elements, and so charge-lo-size ratios have little meaning. However, the same effects appear in the electronegativities of these elements, which show a strong diagonal effects... 

In order to remove the driven term in the effective Hamiltonian H of the slow mode given by Eq. (47), without affecting the diagonal effective Hamiltonian H ... 

One of the few periodic trends of the metals not to show a strong diagonal effect is the standard reduction potential. In fact, this trend follows more of a horizontal rule. The standard reduction potential, E°, is defined in Equation (5.21). The standard reduction potential for the normal hydrogen electrode (N.H.E.), or the half-reaction shown in Equation (5.22), is given a value of zero. Metal atoms with E s more n ative than the N.H.E. are easier to oxidize and harder to reduce. Metal atoms with s more positive than the N.H.E. are easier to reduce and harder to oxidize ... 

A rather useful means of discussing the diagonal effect is to appeal to the charge density of the ions of the elements in question, a property that consists of the charge of an ion divided by its volume. The ions of elements that show a diagonal relationship typically have similar charge densities. However, in the case of the boron—sdicon relationship, that option is not even available since these elements do not typically form ions. 

As with most Cl schemes of that period, the construction of the Hamiltonian matrix and its direct diagonalization effectively limited the size of calculations to a few thousand determinants. One possible strategy for extending the capability of this type of calculation is to introduce some sort of selection criterion for the A -particle functions, and to leave out those that do not contribute appreciably. Such methods had been developed within the framework of multireference Cl (MR-CI) calculations, and Hess, Peyerimhoff, and coworkers (Hess et al. 1982) extended this to the case of spin-orbit interactions. Their procedure was based on performing a configuration-selected non-relativistic MR-CI, followed by extrapolation to zero threshold. This technique may be applied in a one-step scheme, where selection criteria are introduced not only for the correlating many-particle states, but also for those that couple to the reference space via spin-orbit interaction. The size of the calculation that has to be performed in the double group may thereby be reduced. The errors introduced by these selection procedures appear to be small. 

Four relevant properties of elements related to the diagonal effect. 

The elements of the diagonal effect. Lithium and magnesium, beryllium and aluminum, and boron and silicon, each pair diagonally located, have similar properties. 

To make sense out of the descriptive chemistry of the representative elements, we have defined and discussed the basis of the first five components of a network of interconnected ideas for understanding the periodic table. These organizing principles are (1) the periodic law, (2) the uniqueness principle, (3) the diagonal effect, (4) the inert-pair effect, and (5) the metal-nonmetal line. The definitions of these components are summarized in Table 9.5. The five components are also summarized in Figure 9.20. A color version of this figure is shown on the inside front cover of the text. 

The Diagonal Effect A diagonal relationship exists between the chemistry of the first member of a group and that of the second member of the next group. Applies only to Groups 1 A, 2A, and 3A. 

Mastering the descriptive chemistry of the main-group or representative elements of the periodic table is a formidable task. In order to bring some order to our study of this topic, we have started to construct a network of interconnected ideas. Five components have been described in this chapter. Three additional components will be defined and described in the next few chapters. The first five components are the periodic law, the uniqueness principle, the diagonal effect, the inert-pair effect, and the metal-nonmetal line. 

Sketch the icon that represents the diagonal effect. Briefly explain how the icon symbolically represents the third component of the interconnected network of ideas for understanding the periodic table. 

Write a concise paragraph explaining what is meant by the diagonal effect and how it can be accounted for. 

Our network of interconnected ideas helps us to account for many expected properties of the alkali metals. The hydrides, oxides, hydroxides, and halides of these elements are ionic. The oxides and hydroxides are basic in character. Lithium, although stiU an alkali metal with much in common with its congeners, is certainly a good example of the uniqueness principle. It has much in common with magnesium, as forecast by the diagonal effect. 

Recall that in Section 9.3 we used beryllium and aluminum to introduce the diagonal effect. We need not repeat that reasoning here. Suffice it to say that these two elements have much in common including (1) beryllium is more easily separated from its congeners than it is from aluminum, (2) both oxides are amphoteric rather than basic, (3) aluminum chloride forms a dimer structurally related to the beryllium halide polymers as shown in Figure 13.5b, and (4) the resistance of both of these metals to attack by acids is due to the presence of a strong oxide film. Lest complacency set in about the ability of our network to explain all these things, it should be noted that beryllium shows almost as many similarities to zinc as it does to aluminum. 

The alkaline-earth metals have many similarities to the alkali metals. In both groups, the lightest element is unique, the second element is intermediate in character, the third, fourth, and fifth elements form a closely allied series, and the sixth element is rare and radioactive. The network helps us account for and predict the properties of both groups. The network components of particular importance are the periodic law, the uniqueness principle, the diagonal effect, and the acid-base character of oxides. The alkaline-earth metals have similar reducing properties, boil and melt at higher temperatures, and are less electropositive and reactive than the alkali metals. 

The Group 3A elements superimposed on the interconnected network of ideas. These include the periodic law, (a) the uniqueness principle, (b) the diagonal effect, (c) the inert-pair effect, (d) the metal-nonmetal line, the acid-base character of the metal (M) and nonmetal (NM) oxides in aqueous solution, and the trends in reduction potentials. 

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