Bond order clusters

Table 2. Heats offormation, H (kcal), magnitude of electron density, Q (Of), displace from the cluster to adsorbed oxygen molecules, equilibrium interatomic distances R (A-B) and bond orders P (A-B), corresponding to them, in PANI-O2 adsorption complexes.

In order to study the possible reasons and mechanisms of the catalytic activity of conducting polymers (CP), the electronic structure of some molecular CPs clusters and its adsorption complexes with oxygen were modeled [6], In the CP-O2 complex, the CP surface is an electron density donor. For example, in the case of PANI, the bond orders in adsorbed O2 molecules decrease by about 30%, and the bond lengths L increase by about 24%. Thus, the adsorbed O2 molecules have a fairly high degree of activation and can readily interact with the protons. 

Other electron-poor clusters include the 44-electron Pt3(CO)3(PPh3)4 and the 42-electron species Pd3(CO)3(PPh3)3 and [Re3Cl12p. For the 44-electron system, the 18-electron rule predicts two double bonds within the M3 triangle and for the 42-electron complexes, three double bonds. The structures of the platinum and palladium complexes are unknown, but the Re-Re distances of 2.47-2.49 A in the anion [Re l ]3- are regarded (20) as short and consistent with a formal bond order of two. 

Here, as in other branches of inorganic chemistry, interatomic distances show a considerable variation and, although some correlation with bond order is possible, attempts to do so should be regarded with caution.For metals with close-packed structures, the coordination number of any atom is 12 for cubic or hexagonal structures, and 14 (8 plus 6 more neighbors at about 15% further away) for body-centered cubic structures. In general, this number exceeds the number of electrons per atom available for metal-metal bond formation and precludes the formation of localized, two-electron bonds between metal atoms. Bond orders of less than 1 are therefore commonly recorded. For metal clusters, it is necessary to consider the variety of ways in which valence electrons may be utilized in chemical bonding within the Mm... 

Information about internuclear distances in organic compounds has led to the view that the effective radius of an atom varies directly with bond order. This is understandable for elements like carbon, with a limited range of hybridized states, but less so for metallic (cluster) systems. The problem is threefold ... 

In a formal (E.A.N. rule) sense, the Os-Os bond order in each of the three clusters corresponds to 1, and yet it is clear that a variety of different Os- Os bond types exist since each of the different metal centers (A) — (D) will utilize a different basis set of hybrid (or frontier) orbitals. 

Compounds with metal-metal bonding occur frequently throughout the Periodic Table. The trivial but necessary condition for covalent M-M bonding is a low oxidation state which leaves valence electrons with the metal atom. This condition, however, is not sufficient. Compounds need to be metal-rich to allow for sufficiently close contacts between metal atoms, and the extension of the valence electron orbitals in space must be large in order to provide good overlap. Hence, it is no surprise that M-M bonding and cluster formation dominates with the heavier elements in the Periodic Table, involving s, p, d, and even f electrons. 

The main characteristic of cluster-type indices is that all bonds are connected to the common, central atom (star-type structure). The third-order cluster molecular connectivity index (3yc) is the first, simplest member of the cluster-type indices where three bonds are joined to the common central atom [102-104, 111-113,152-154,166,167,269]. The simplest chemical structure it refers to is the non-hydrogen part of ferf-butane. This index is then calculated using Eq. (43) ... 

The method of moments of coupled-cluster equations (MMCC) is extended to potential energy surfaces involving multiple bond breaking by developing the quasi-variational (QV) and quadratic (Q) variants of the MMCC theory. The QVMMCC and QMMCC methods are related to the extended CC (ECC) theory, in which products involving cluster operators and their deexcitation counterparts mimic the effects of higher-order clusters. The test calculations for N2 show that the QMMCC and ECC methods can provide spectacular improvements in the description of multiple bond breaking by the standard CC approaches. 

Figure 4.8 shows that the individual bonds in four-atom s-valent clusters are unsaturated, taking bond orders that are much less than unity. The two end bonds of the linear chain provide the only exception. This reduction in bond order compared to the isolated dimer is, of course, due to a given spherically symmetric s orbital forming bonds with all its neighbours. However, we will see later in Chapter 7 that the angular character of hybrid orbitals allows some sp-valent solids to exhibit saturated bond behaviour. Thus, the concept of the bond order is important because it not only... 

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