Counting rules

Electron-counting Rules for Metallocarboranes and Other Heteroboranes... 

Reductions of [PtClg] " in an atmosphere of CO provide a series of clusters, [Pt3(CO)6] ( = 1-6,10) consisting of stacks of Pt3 triangles in slightly twisted columns Pt-Pt = 266 pm in triangles, 303-309 pm between triangular planes (Fig. 27.12). A feature of these and other Pt clusters is that they mostly have electron counts lower than predicted by the usual electron counting rules. In the series just mentioned for instance, = 1 and n — 2 have electron counts of 44 and 86 whereas 48 and 90 would... 

The assignment of oxidation states has more a formal character in the sense of electron counting rules [145]. In this context it should, however, be justified to use at least the term low valent silicon. 

The structure of cluster compounds of transition metals and the limits of applicability of the electron counting rules forpolyhedral molecules. Y. L. Slovokhotov and Y. T. Struchkov, Russ. Chem. Rev. (Engl. Transl), 1985, 54, 323 (150). 

The 8V + 6 valence electron rule has been completely substantiated by the calculated four-membered species in Table 2 [7], Boldyrev, Wang, and their collaborators presented experimental and theoretical evidence of aromaticity in the Al/ [19] Ga/" [20], In " [20] and isoelectronic heterosystems, XAl [21], The Al/" unit (14e) was found to be square planar and to possess two n electrons, thus conforming to the (An + 2)n electron counting rule for aromaticity. The n electron counting rule would be more powerful if we could predict the number of n electrons of metal atomic rings in an unequivocal manner. Our SN+6 electron rule only requires the number of valence electrons in Al/, which is easy to count. 

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-... 

Regardless of their possible metallic properties, metal-rich Zintl system or phases are defined here as cation-rich compounds exhibiting anionic moieties of metal or metalloid elements whose structures can be generally understood by applying the classical or modern electron counting rules for molecules. 

The location of electrons linking more than three atoms cannot be illustrated as easily. The simple, descriptive models must give way to the theoretical treatment by molecular orbital theory. With its aid, however, certain electron counting rules have been deduced for cluster compounds that set up relations between the structure and the number of valence electrons. A bridge between molecular-orbital theory and vividness is offered by the electron-localization function (cf p. 89). 

B8C18 has a dodecahedral Bg c/o.vo-skclclon with 2n = 16 electrons. In this case, the Wade rule neither can be applied, nor can it be interpreted as an electron precise cluster nor as a cluster with 3c2e bonds. B4(BF2)6 has a tetrahedral B4 skeleton with a radially bonded BF2 ligand at each vertex, but it has two more BF2 groups bonded to two tetrahedron edges. In such cases the simple electron counting rules fail. 

Os4Pd6(CO)8(//-CO)8(/x-dppm)2] in low yields, while the reaction of [Os5(/u5-C)(CO)i5] with [Pd2(/u-dppm)2Cl2] afforded [Os5Pd4(/u6-C)(CO)12(/u-CO)3(/u-dppm)2] and [Os5(/X5-C)(CO)13(/r-dppm)] in moderate yields.289 The electron counts found in these osmium-palladium clusters do not always agree with those predicted by skeletal electron counting rules. This may simply be ascribed to the ability of Pd to be satisfied with both 16- and 18-electron counts.289... 

A useful introduction to the structures of cluster molecules and the electron counting rules proposed by Wade and others. 

So far we have restricted ourselves to operators containing quarks in the same patch. For operators with quarks in different patches, one has to be careful, since the loop integration might jeopardize the power-counting rules. Indeed, consistent counting is to sum up all the hard-loops, as shown by Schafer [10]. 

Despite this, proven rules for boron clusters can be applied to the smaller metalloid Al, Ga, and In clusters with certain additional assumptions, as recent DFT calculations have shown [87]. In addition, counting rules for smaller Ga and Al metalloid clusters have been developed [123], which will, however, probably not be transferable to the larger clusters. Therefore the first assignment principle presented here for the larger metalloid clusters incorporates the structures of the elements in the various modifications, which means that the metalloid or elementoid clusters are described as nanostructured element modifications. 

This chapter summarizes recent developments in the expanding field of electron-deficient compounds having from three up to 13 skeletal boron and carbon atoms. In particular, the focus will be on the transition of classical organoboranes into non-classical compounds. Therefore, we first want to briefly review electron counting rules and bonding characteristics of these classes. For a more thorough discussion see Chapter 1 by King and Schleyer. 

Williams [1] has given an excellent review on Early Carboranes and Their Structural Legacy and he defines carboranes as follows Carboranes are mixed hydrides of carbon and boron in which atoms of both elements feature in the electron-deficient polyhedral molecular skeleton . According to the electron counting rules [2] for closo- (2n + 2 SE), nido- (2n + 4 SE) and arachno-clusters (2n + 6 SE SE = skeletal electrons, n = number of framework atoms) and the An + 2 n electron Hiickel rule, small compounds with skeletal carbon and boron atoms may have an electron count for carboranes and for aromatics (see Chapters 1.1.2 and 1.1.3). 

For example, both Hiickel aromatics B and C conform to the Wade-Mingos electron counting rules [2] (see Chapter 1.1.2) and to the structural systematics developed for boranes and heteroboranes [1] the hexagonal bipyramid with the apices removed is in agreement with an arachno electron count of 18 SE for (CH)g [2],... 

REMARKS ON THE CHEMICAL BOND FACTOR AND VALENCE-ELECTRON COUNTING RULES... 

Wade electron counting rules borane-like cluster nomenclature. On initially studying compounds such as boranes (boron hydrides) and carboranes (or carbaboranes boron—carbon hydrides), Wade (1976) proposed a number of rules which have then been extended to several compounds and which relate the number of skeletal electrons with the structure of deltahedral clusters. A polyhedron which has only A-shaped, that is triangular, faces is also called a deltahedron. 

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