Counting electrons, 18-electron rule

Because the electron-counting paradigm incorporates the 18-electron rule when appHed to transition-metal complexes, exceptions can be expected as found for classical coordination complexes. Relatively minor exceptions are found in (Tj -C H )2Fe2C2BgHg [54854-86-3] (52) and [Ni(B2QH22)2] A [11141-32-5] (53). The former Q,n electrons) is noticeably distorted from an idealized stmcture, and the latter is reminiscent of the and complexes discussed above. An extremely deficient electron count is obtained for complexes such as P7036-06-9] which have essentially undistorted... 

The pattern of orbital energies in Figure 11.13 provides a convincing explanation for why benzene is aromatic while square cyclobutadiene and planar- cyclooctatetraene are not. We start by counting tt electrons cyclobutadiene has four, benzene six, and cyclooctatetraene has eight. These tt electrons are assigned to MOs in accordance with the usual rules—lowest energy orbitals first, a maximum of two electrons per orbital. 

Perhaps the most notable difference between S-N and N-O compounds is the existence of a wide range of cyclic compounds for the former. As indicated by the examples illustrated below, these range from four- to ten-membered ring systems and include cations and anions as well as neutral systems (1.14-1.18) (Sections 5.2-5.4). Interestingly, the most stable systems conform to the well known Htickel (4n -1- 2) r-electron rule. By using a simple electron-counting procedure (each S atom contributes two electrons and each N atom provides one electron to the r-system in these planar rings) it can be seen that stable entities include species with n = 1, 2 and 3. 

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. 

Identify the ligands and the geometiy of the coordination complex, construct the crystal field energy level diagram, count d electrons from the metal and place them according to the Pauli principle and Hund s rule. 

From the examples shown in Fig. 4.43, we may conclude that the 18e triply hyperbonded complexes are often the stable end-products of successive ligand cu-additions to normal-valent parent species, which is consistent with the well-known 18-electron rule. However, incompletely hyperbonded complexes of 12e, 14e, or 16e count are certainly stable as isolated equilibrium species, and in favorable cases the sequence of cu-additions may also achieve equilibrium configurations exceeding the 18e count, as the example of [PtF8]2 has demonstrated.44... 

As a simple example of non-d coordination, let us consider the hexaammine-zinc(II) cation [Zn(NH3)6]2+, whose optimized structure is shown in Fig. 4.51. Each ammine ligand serves as a formal two-electron sigma donor, and the total electron count atZn therefore corresponds to a 22e system, again violating the 18-electron rule. Each ammine ligand is bound to the Zn2+ cation by about 60.7 kcal mol-1, which is in part attributable to classical electrostatic interactions of ion-dipole type. 

Electron counting in these supraicosahedral gallium clusters consisits of ambiguities since it is not clear which of the bare vertex atoms of the core polyhedra provide the usual three internal orbitals and which vertex atoms provide four internal orbitals. Typically the Wade-Mingos [16-18] or the Jemmis [32, 33] skeletal electron rule is obeyed if about half of the bare vertex gallium atoms use all four orbitals of their sp3 manifolds as internal orbitals, and thus are donors of three skeletal electrons, and the other half of the bare vertex gallium atoms use only three orbitals of their sp3 manifolds and thus are donors of only a single skeletal electron each. 

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). 

It should also be noted that a six-electron rule affords conformity with the electron counting procedures of Rudolph (13)... 

Ralph Rudolph made major contributions to our understanding of the structure and bonding of polyhedral cluster compounds and he had an abiding interest in developing a rationale which would enable the structure of individual compounds to be systematized and related to each other. He independently arrived at a method of counting skeletal electrons which is now generally referred to as Wade s Rules, and this has had a decisive influence on our general perceptions of polyhedral cluster compounds. Related to this was his preoccupation with the problem of heteroatoms such as sulfur, and the number of electrons which such atoms contribute to the heteroborane clusters. 

With metal clusters it is even harder than in other fields of inorganic chemistry to substantiate theoretical results by energy measurements. Only two such measurements have come to the attention of the author — the photoelectron spectrum of [CpFe(C0)]4 370) andbond energy determinations in 03(00)9CX-compounds 187). However, a considerable number of papers deal with metal-metal bonding in, and the symmetry properties of, clusters as related to their stoichiometry and their electron count. These studies have confirmed the wide apphcability of the simple 18-electron rule in predicting metal-metal bonds and structures, but they have also led to an understanding of the limits of this rule for clusters with more than four metal atoms. 

Clusters with up to four metal atoms generally obey the 18-electron rule for each metal atom. This is no longer the case for six-atom clusters. For instance, in an octahedral cluster a total of 84 electrons (provided by the metal atoms and the ligands) would be predicted for a stable configuration, counting each edge of the octahedron as a metal-metal bond. The 84-electron count for an octahedral cluster is realized in only one known case, namely [HCufPPhj)] 42, 92), and almost aU other cases, as listed in ref. 20), have 86 electrons. 

Its electron count, by either method, shows that the complex adheres to the 16-electron rule ... 

The highly covalent nature of transition metal carbonyls and their derivatives leads to the 18-electron rule being closely followed. The mononuclear species Ni(CO)4, Fe(CO)5, Ru(CO)5, Os(CO)5, Cr(CO)6, Mo(CO)6 and W(CO)6 obey this well and, if the formalized rules of electron counting are applied, so do the metal—metal bonded and carbonyl bridged species. Such compounds are therefore coordinately saturated and the normal (but by no means unique) mode of substitution is dissociative (a 16-electron valence shell being less difficult to achieve than one with 20 electrons).94... 

---