Hyperbonding

The NBO donor acceptor picture of hypervalency hyperbonds Let us re-examine the 3c/4e MO description from the localized NBO perspective. NBO analysis of the MO wavefunction (3.193) may lead to the Lewis structure A + B—C, with NBOs... 

The cu-prebonds cua bc and cuAb c might alternatively be denoted by pre-scripted symbols such as w (Tab, tu7tAB, etc., to specify further their shape and relationship to conventional 2c/2e bonds as well as the implied modification due to hyperbonding. In what follows, we shall generally adopt the more generic symbols (3.199) for the cu prebonds of a given cuabc hyperbond. 

The distinguishing characteristics of cuabc hyperbonds include the following ... 

Let us describe the general form of the hyperbonding functions in further detail. For the symmetric A>—B -hC case in which atoms A and C are of equivalent electronegativity, we can rewrite the antibond NBOs in (3.194) as... 

With this replacement the two hyperbond functions are finally... 

The electronic configuration (cuAB c)2(a)A Bc)2 of the Ai-B-iC hyperbonded unit may equivalently be expressed in terms of any orthogonal linear combination of the two occupied orbitals coAb c and coA Bc, such as... 

Exercise Determine the formal MO bond orders WM0), bc(M0), and b c AO) for the general (cuAB C)2(cuA BC)2 hyperbonded electron configuration. 

Let us summarize the distinguishing characteristics of to-bonding from the prototype examples of Tables 3.28-3.30. The first eight species exhibit strong to-bonding that may be contrasted with HLiH- (a borderline species) and H3- (non-hyperbonded). 

It is noteworthy that Rydberg orbital occupancies on the central atom (rY, final column of Table 3.29) are relatively negligible (0.01-0.03e), showing that d-orbital participation or other expansion of the valence shell is a relatively insignificant feature of hyperbonded species. However, the case of HLiH- is somewhat paradoxical in this respect. The cationic central Li is found to use conventional sp linear hybrids to form the hydride bonds, and thus seems to represent a genuine case of expansion of the valence shell (i.e., to the 2p subshell) to form two bonding hybrids. However, the two hydride bonds are both so strongly polarized toward H (93%) as to have practically no contribution from Li orbitals, so the actual occupancy of extra-valent 2pu orbitals ( 0.03< ) remains quite small in this case. 

Although HLiH- exhibits certain structural signatures of hyperbonding, it appears more to exemplify normal hybridized bonding (with extra-valent 2pu character) and the limit of complete ionic H- Li+ H- character, rather than true tu-bonding. 

We conclude that the first eight triatomic anions of Table 3.28 exhibit the properties (HB-l)-(HB-5) expected of hyperbonding and can be described by modified Lewis-structural formulas employing 3c/4e to bonds of the form... 

Beyond sigma bonding transition-metal hyperbonding and pi back/frontbonding... 

Common coordination motifs of hyperbonded complexes and the trans influence ... 

Because trans dispositions commonly result from co-bonding (the near-linear alignment of the hyperbonding 3c/4e X—M- L triad), it is not surprising that the origin of the trans influence can be traced to the resonance nature of co-bonding. When H is placed trans to a halide or PH3, the dominant resonance structure will be that with a 2c/2e M—H bond and a donor pair of electrons on the halide or phosphine ligand, as depicted on the left in (4.93) ... 

From Fig. 4.49(d) and the last row of Table 4.32 one can see that the quadruply hyperbonded [PtFg]2- dianion is indeed a (meta)stable local equilibrium species, formally of 20e count at the metal atom. Owing to highly unfavorable anion-anion repulsion, the binding of F to [PtF ]- is endothermic, but this species is nevertheless atrue local equilibrium structure (Rptp = 2.04 A, all positive frequencies) of Oh... 

Figure 4.50 Interacting ri. —hPL—nF NHOs of a Fi-Pt-iF hyperbonded triad in [PtF8 2. ...

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... 

Whereas d8 Ni selects the rectangular di-allylic hyperbonding pattern in (4.121), d6 Fe of ferrocene offers an additional vacant d orbital and hence opens up new geometrical possibilities of an additional cu bond. In concert with the three cu bonds and nominal sd2 (90°) hybridization (Table 4.52), the two Cp ligands are naturally expected to coordinate in r 5 (L2X) fashion to occupy the six octahedrally arrayed coordination sites of the metal. Visualization of this coordination mode is aided by considering the possible patterns of L-type (filled circles 7tcc) and X-type (half-filled circles radical) sites of L2X Cp... 

Localized versus delocalized descriptions of transition-metal bonding and hyperbonding... 

The NBO-based VB-like description of localized transition-metal bonding and hyperbonding (as espoused throughout this chapter) differs significantly from more familiar descriptions of transition-metal complexes in delocalized MO terms. In this... 

Figure 5.56 illustrates the variation of NRT bond orders bef for reactant and product C—F bonds along the reaction coordinate, and Fig. 5.57 illustrates the corresponding variations of natural atomic charge on the two F atoms. Despite the numerical scatter, one can see in Fig. 5.56 that the reactant (6a0 and product (6cp) bond orders respectively diminish and increase while preserving approximately constant total bond order in the shifting toF Cp hyperbond,... 

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