Electron count rationalization

The remainder of this article is largely concerned with describing how some of the above observations can be rationalized using Stone s Tensor Surface Harmonic theory, and with the further imphcations of this model for dynamical processes such as cluster rearrangements. The number of example systems and electron count rationalizations will be kept relatively small in favor of explaining the theoretical foundations that underhe the method. Tables of examples and more detailed analyses of the various cases may be found elsewhere. ... 

While sharing of electrons, i.e., covalent bonding, is the major component of the cohesive force in intermetallics, rationalization of their structure formation based on such chemical bonding is not trivial, because of the failure of the common electron counting rules that chemists have developed over the years from the studies of covalent compounds. The origin of the problem is the well-delo-... 

The many higher boranes such as B5H9 and BgH 2 are similarly electron deficient and cannot be described by a single Lewis structure. They can often be described in terms of a combination of two- and three-center bonds. Alternatively, their structures can be rationalized by electron-counting schemes such as those proposed by Wade. Analysis of the electron density of these molecules by the AIM method shows that there are bond paths between all adjacent pairs of atoms. So from the point of view of the AIM theory there are bonds between each adjacent pair of atoms, but these cannot all be regarded as Lewis two-center, two-electron bonds as is the case in B2H6. 

Whereas the main object of this survey is to explore how the shapes of various substances reflect the number of electron pairs holding them together, it is worth considering also how their sizes can be rationalized using the electron-counting approach already outlined (203). 

Clearly, in view of a diversity in the types of heterocyclic compounds, one may hardly expect that all the manifestations of their aromaticity (antiaromaticity) could be rationalized in terms of some simple regularities. We shall therefore attempt to trace certain characteristic trends in the dependence of the aromaticity on the type of heteroatoms, their number and positions in the molecular structure. Our reasoning will be based on the nature of the aromaticity criteria and of the electron count rules. Then turning to individual compounds, we shall add details to the picture. 

Of the clusters with more than six metal atoms, the structures [75] of Os2(CO)2j (757, 284) and Rh2(CO)igj2 (79) can be rationalized in terms of skeletal electron-pair counting. For the clusters with six 38), nine (57), and eleven (59) gold atoms the rules have to be modified in order to agree with the observed structures, the main assumption being that one orbital per gold atom remains empty (55). For clusters of 8 to 15 metal atoms there is no correlation between structures and electron counts yet. 

Historically, a scheme of skeletal electron-counting was developed to rationalize the structures of boranes and their derivatives, to which the following Wade s rules are applicable. 

A simplified model may be used to rationalize the bonding in the heteroatomic species [Zn ZnsBi4 Bi7]5. According to the electron counting theory proposed by Wade, the formation of a closo deltahedra of 12 vertices is stabilized by 13 skeletal electron pairs. The total of 26 electrons required for skeletal bonding may be considered to be provided as follows 2 from the interstitial Zn atom, (8x0 + 4x3 = 12) from the ZngBi4 icosahedral unit (each vertex atom carries an exo lone pair or bond pair), 7 from the capping Bi atoms, and 5 from... 

The relationships between the various structures of the ruthenium, cobalt, and rhodium dicarbido clusters have been discussed in terms of their electron counts and the accommodation of some electrons in MM antibonding orbitals. Such treatments have rationalized the paramagnetism of some clusters via partial occupation of such orbitals leading to swelling of the intra-cluster cavity to a point where the C2 fragment can be accommodated. 

The X-ray crystal structure of Os02(NBu )2 again shows the expected tetrahedral structure with 0s=0 at 1.744(6) A however, one of the imido groups is essentially linear (Os—N = 1.710(8) A, Os—N—C = 178.9(9)°) and the other substantially bent (Os—N = 1.719(8) A, Os—N— C = 155.1(8) A.301 The presence of one linear and one bent imido group in the complex has been partly rationalized on electron-counting procedures and MO considerations,292,301 although both IR and HNMR data indicate that both the imido groups are equivalent in solution.302... 

Let s address the question now as it equally applies to the 8- and 18-electron rules. Compounds that follow the rules are classified as normal and define the electronic accounting favored when no other factors are of overriding importance. The rules give the experimental chemist a simple method to rationalize and predict compound stoichiometry and connectivity. The rules permit logical categorization of the myriad of compounds via similarities in an electron count. Both facilitate more rapid development of a field such as cluster chemistry where both structure and composition can seem intimidating in the absence of an organizing principle. 

It should be clear that extension of these models for octahedral clusters to all early metal clusters with tt-donor ligands is not possible. However, when one deals with a single metal and shape then the cluster electron count followed can be a useful tool. For example, it provides a ready rationalization of stoichiometry as well as... 

Here, we deal with clusters such as prismane, CeHe, and cubane CgHg, which can simply be described in terms of edge-localized two-center, two-electron bonds. Why, then, is it necessary to devote any space to such molecules The answer is that it was not initially clear how TSH theory can rationalize the electron counts of these molecules. Of course, this is not entirely surprising, as the Hybridization patterns used in the TSH model are not well adapted to cover this situation. However, the correct answer can be obtained without abandoning the framework developed in the preceding sections. 

The compositions and ligand geometries of most mononuclear T-metal hydride complexes can be rationalized in terms of conventional electron counts based on full charge... 

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