Bents Rule

Martin, J. P. Fran9ois, and R. Gijbels, Theor. Chim. Acta, 1989, 76, 195-209 B. H. Wells, and S. Wilson, Chem. Phys. Lett., 19S3, 101, 429-434 V. Parasuk, J. Almlof, and B. DeLeeuw, Chem. Phys. Lett., 1991, 176, 1-6. 

Taylor, in Lecture Notes in Quantum Chemistry, Lecture Notes in Chemistry 58 , ed. B. O. Roos, Springer, Berlin, 1992, pp. 325-412. 

Papousek and M. R. Aliev, Molecular Vibrational Rotational Spectra , 1981, Elsevier, Amsterdam. 

Branching of the minimum energy reaction path into two different paths at a certain point (bifurcation point) on the potential energy surface. 

The difference between the total energy of a molecular system and the sum of the energies of its isolated components. 

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Fig. 22. A scheme presenting the action of the Walsh-Bent rule on sp -hybridized orbitals at the substituted carbon atom in a benzene ring X is a strongly electronegative substituent.

Apply the bent-bond model to the preferred conformations of acetaldehyde and propene. Do bent-bonds maintain or remove eclipsing interactions in the equilibrium structures of the two molecules Formulate a simple rule based on the bent-bond model for predicting conformational preferences in systems containing trigonal atoms. 

ABSTRACT This article concerns various foundational aspects of the periodic system of the elements. These issues include the dual nature of the concept of an "element" to include element as a "basic substance" and as a "simple substance." We will discuss the question of whether there is an optimal form of the periodic table, including whether the left-step table fulfils this role. We will also discuss the derivation or explanation of the [n + , n] or Madelung rule for electron-shell filling and whether indeed it is important to attempt to derive this rule from first principles. In particular, we examine the views of two chemists, Henry Bent and Eugen Schwarz, who have independently addressed many of these issues. 2008 Wiley Periodicals, Inc. Int J Quantum Chem 109 959-971, 2009... 

One of the main benefits of the paper by Bent and Weinhold is a plausible explanation for the n + i rule which does not, at first sight, seem to suffer from the drawbacks of the explanations of Allen and Knight as well as Ostrovsky. However, the recent explanation by Bent and Weinhold comes at a certain cost as will be explained. 

It should also be said that the reason why Bent and Weinhold devote such attention to the n + ( rule is that, as mentioned earlier, the rule is clearly represented on the left-step table, the form of the periodic table that they favor. In addition, as was mentioned, the authors believe that the best representation of the periodic system should be based on the electronic structure of the neutral atoms of all the elements and not on their macroscopic properties. 

Their reasoning is based on the difference in energy between a bent secondary vinyl cation such as 84 and a linear secondary vinyl cation such as 85. The authors, based on a third of the difference in ground-state ionization potentials for a carbon 2s and 2p orbital, estimate this difference to be 77 kcal/mole in favor of the linear ion 85 yet despite this large difference, there are significant amounts of 6-membered cyclic products, which, in the authors opinion, rule out distinct bent and linear vinyl cations such as 84 and 85 (82). 

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). 

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