Single cage structures

Each low oxidation state metal cluster cage possesses a characteristic number of valence electrons (ve) as Table 23.5 shows. We shall not describe the MO basis for these numbers, but merely apply them to rationalize observed structures. Look back to Section 23.2 for the numbers of electrons donated by ligands. Any organometallic complex with a triangular M3 framework requires 48 valence electrons, for example  

Similarly, clusters with tetrahedral or octahedral cages require 60 or 86 valence electrons respectively, for example  

The last example is of a cage containing an interstitial atom (see structure 23.12) and contributing all of its valence electrons to cluster bonding. An interstitial C atom contributes 4 electrons, a B atom, 3, an N or P atom, 5, and so on. 

Worked example 23.5 An application of total valence electrons counts 

Suggest what change in cluster structure might accompany the reaction  

This can be applied more widely than for the structures listed in Table 24.5. Thus, the linear arrangement of the Os atoms in Os3(CO)i2l2 can be rationalized in terms of its 50 valence electron count, i.e. formally, the addition of two electrons to a 48-electron triangle  

A difference of two between the valence electron counts in Table 24.5 corresponds to a 2-electron reduction (adding two electrons) or oxidation (removing two electrons). This formally corresponds to breaking or making 

This can be applied more widely than for the structures listed in Table 24.5. Thus, the linear arrangement of the 

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AIN, GaN, and InN are attractive materials for applications such as blue lasers and field emitters single-source precursors for these of formula [R2MNR 2]2 (R = alkyl, R = alkyl or H) have been reported.236 The reaction of alkylamines with group 13 trialkyl metal compounds affords oligomeric or polymeric ring and cage structures of metal amides and imides (see section on nitrides). 

Addition of diethyl bromomalonate in the presence of l,8-diazabicyclo[5.4.0]-undec-7-ene (DBU) to La Cs2 generated only one cycloadduct but four unexpected isomers with singly bonded structures [156, 157]. Single-crystal XRD results of the most abundant isomer show that the addend tends to attack the most positively charged carbon of the Cs2 cage (C23 in Figure 7.12), which is distant from the encapsulated La atom. 

One of the well-studied inclusion compounds is trimethylchroman. 1, commonly known as Dianin s compound. First prepared in 1914 by the Russian chemist A. P. Dianin, this compound has attracted considerable attention due to its ability to tenaciously hold on to certain organic solvents. A cage structure was predicted in the adducts of 1 based on space group, unit cell dimensions and packing considerations and was confirmed by detailed X-ray single crystal structure smdies on the chloroform and ethanol adducts of 1 after 15 years. Irrespective of the guest, the 1... 

The idea of a fixed crystal structure in which single cages contained at most one guest proved irresistible to statistical thermodynamicists. After an initial effort by Powell, Royal Dutch Shell workers van der Waals and Platteeuw generated a method that still stands today as a principal, regular industrial use of statistical thermodynamics. However, the model was not suitable for manual calculations (as were the methods of Katz in item 3 above), but required access to then-scarce computers, which limited its application to large companies or major universities. Widespread adoption of the model awaited the proliferation of personal computers. 

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