Bent s rule

Nearly four decades ago, American chemist Henry Bent40 formulated a remarkable principle that relates atomic hybridization to substituent electronegativity. This principle, now called Bent s rule, was originally expressed in the following words ... 

A somewhat different way of rationalizing Bent s rule can be given as follows. Fet us initially assume idealized equivalent sp -1 hybrids for a given AL species of n ligands. If we now formally replace one F by a highly electronegative X, we can represent the resulting species as a resonance hybrid of neutral and ionic forms... 

According to Eq. (3.74) /P(AX) increases with /ax, and therefore with the electronegativity of X, in accordance with Bent s rule. Note that Eq. (3.74) makes no direct reference to Asp and requires only the hybridizations of idealized neutral and ionic structures. Thus, analogous resonance-type reasoning might be used to generalize Bent s rule for more general spd hybridization (Section 4.6). 

Let us now attempt to express Bent s rule in more quantitative form. The dependence of hybrid p character fp on ligand electronegativity xl is illustrated in Fig. 3.20 for a series of 40 mono-substituted ALH hydrides, where L is chosen from the substituent series of first- and second-row ligands... 

As seen in Fig. 3.20, the general trends along each series of substituents L are consistent with Bent s rule. Thus, with increasing xl along a row of the periodic table,... 

Equations (3.75a)-(3.75j) constitute a more quantitative formulation of the relationship between hybrid p character and substituent electronegativity, generalizing Bent s rule. The accuracy of these approximations is generally of the order of a few percent, sufficient to determine hybrid angles within 1-2° as illustrated in the following examples. 

As examples of the previous section have shown, bond hybrids are sometimes misaligned with respect to the line of centers between nuclei, a condition described as bond bending. Such bending may be considered to represent the influence of factors other than Bent s rule. In this section we examine the origin and characteristics of bond bending. 

In accord with Bent s rule (Section 3.2.6), FAa is therefore expected to grow with increasing electropositivity of the central atom A or increasing electronegativity of either X or Y. 

The cu-bonding model provides a more complete and fundamental description of hypervalent molecules that are often interpreted in terms of the VSEPR model.144 In the present section we examine some MX species that are commonly used to illustrate VSEPR principles, comparing and contrasting the VSEPR mnemonic with general Bent s rule, hybridization, and donor-acceptor concepts for rationalizing molecular geometry. Tables 3.32 and 3.33 summarize geometrical and NBO/NRT descriptors for a variety of normal-valent and hypervalent second-row fluorides to be discussed below, and Fig. 3.87 shows optimized structures of the hypervalent MF species (M = P, S, Cl n = 3-6). 

The average sigma-hybridization is sp2, but the hybrid toward B is considerably richer in s character ( spL1) than are those toward H, in accordance with Bent s rule. 

Metal halides, oxides, and nitrides Bent s rule for transition metals... 

A robust generalization of Bent s rule for d-block compounds can be based on the following simple argument (cf. Section 3.2.6) increased electronegativity of ligand X in an MH X compound may be considered equivalent to a higher admixture of... 

Bent s rule for d-block elements. Increased metal s character tends to go to the M—L bonds of higher covalent character, and increased d character to the bonds of higher ionic character. 

Note that the association of higher d character with higher bond ionicity extends to polarity of either sign, a subtle but important difference with respect to corresponding Bent s rule statements for p-block elements.29... 

Geometrical consequences of Bent s rule. Relative to idealized ML, angles, increased d character (increased bond polarity) tends to decrease acute angles and increase obtuse angles for n > 4, but has little effect for n < 3 (near-perpendicular bond angles). 

We can estimate the numerical trends more directly from the statement of Bent s rule based on (4.58). Noting that the Os—H bond of OsH4 is almost perfectly covalent (i.e., 49.6% polarization to Os, Qw — 0 in OsH4), we can expect for a substituted OsH3X compound that the charge Qx of a general monovalent X will vary from Qx = — 1 in the pure ionic case to Qx = 0 in the pure covalent case. As a crude measure of the fractional weightings /ion and /cov of ionic and covalent forms in (4.58), we can therefore write... 

Problem Compare the OsH3X hybridizations and bond angles predicted by the simple Bent s rule estimates (4.59) and (4.60) with the actual values of Table 4.17. 

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