Bent Rule in Chemistry - Football
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Bent Rule in Chemistry

In the early 1930s, shortly after much of the initial development of quantum mechanics, these theories were applied to molecular structure by Pauling,[6] Slater,[7] Coulson,[8] and others. In particular, Pauling introduced the concept of hybridization, in which the atomic orbitals s and p are combined to obtain hybrid orbitals sp, sp2 and sp3. Hybrid orbitals have been shown to be powerful in explaining the molecular geometries of simple molecules such as methane (tetrahedron with a sp3 carbon). In the 1940s, however, there were slight deviations from these ideal geometries. [9] A particularly well-known example is water, where the angle between hydrogens is 104.5°, well below the expected 109.5°. To explain these discrepancies, it has been suggested that hybridization can lead to orbitals with unequal s and p characters. J.-C. Walsh described in 1947[9] a relationship between the electronegativity of carbon-related groups and the hybridization of that carbon. Finally, in 1961, Bent published a comprehensive review of the literature relating to molecular structure, hybridization of central atoms, and substitution of electronegativity [2], and for this work, Bent`s rule takes its name. Bent`s rule is the answer to all of the above questions. The ruler is useful for explaining bond lengths, bond angles, the position of substituents in a molecule, and the structure of many molecules.

In our next article, we will apply this rule to different molecules and examine their consequences. Until then, instead of directing equivalent sp3 orbitals to the four substituents, moving the character to the C-H bonds will significantly stabilize these bonds due to the increase in electron density near the carbon, while moving the character away from the C-F bond will increase their energy by a smaller amount because the electron density of this bond is farther from carbon. The atomic character of the carbon atom was directed towards the more electropositive hydrogen substitutes and away from electronegative fluorine, which is exactly what Bent`s rule suggests. As one descends into the table, the substituents become more electronegative and the angle of bond between them decreases. According to Bent`s rule, as the surrogate electronegativity increases, orbitals with a larger p-character are directed to these groups. Thanks to the discussion above, this will reduce the connection angle. This is consistent with the experimental results. Comparing this explanation with the VSEPR theory, VSEPR cannot explain why the angle in dimethyl ether is greater than 109.5°. Let`s explore how Bent`s rule could be applied to your example of methyl fluoride.

In the $ce{C-F}$ bond, the carbon hybrid orbital is directed to the electronegative fluorine. Bent`s rule suggests that this hybrid carbon orbital will be richer in p-characters than we would otherwise have suspected. Instead of the carbon hybrid orbital $ce{sp^3}$ used in this bond being hybridized, it will tend to have more p-signs and therefore move towards hybridization $ce{sp^4}$. The chemical structure of a molecule is closely related to its properties and reactivity. The theory of valence bonds suggests that molecular structures are due to covalent bonds between atoms and that each bond consists of two overlapping atomic orbitals that are usually hybridized. Traditionally, it is thought that the elements of the p-block in molecules hybridize strictly like spn, where n is either 1, 2 or 3. In addition, hybrid orbitals are all assumed to be equivalent (i.e. orbitals n +1 spn have the same character p). The results of this approach are generally good, but they can be improved by allowing isovalent hybridization, in which hybridized orbitals can have a non-integer and uneven p character.

Bent`s rule provides a qualitative estimate of how these hybridized orbitals should be constructed. [3] Bent`s rule is that in a molecule, a central atom bound to several groups hybridizes so that orbitals with more s-characters are directed to electropositive groups, while orbitals with more p-characters are directed to more electronegative groups. By removing the assumption that all hybrid orbitals are equivalent spn orbitals, it is possible to obtain better predictions and explanations of properties such as molecular geometry and binding force. [4] Bent`s rule has been proposed as an alternative to VSEPR theory as an elementary explanation of the observed molecular geometries of simple molecules, with the advantage that they are more easily compatible with modern binding theories and have stronger experimental support. Bentsche`s rule provides an alternative explanation for why certain connecting angles differ from the ideal geometry. First, a trend between the hybridization of central atoms and the bond angle can be determined using the model compounds methane, ethylene and acetylene. In order, the carbon atoms align the sp3, sp2 and sp orbitals with the hydrogen substituents. The bonding angles between the substituents are ~109.5°, ~120° and 180°.

This simple system shows that atomic orbitals hybridized with a higher p-sign have a smaller angle between them. This result can be done rigorously and quantitatively like Coulson`s theorem (see the formal theory section below). The same trend applies to nitrogen compounds. Contrary to the expectations of the VSEPR theory, but according to Bent`s rule, the bonding angles of ammonia (NH3) and nitrogen trifluoride (NF3) are 107° and 102° respectively. What for? S orbitals are lower in energy than p orbitals. Therefore, electrons are more stable (lower energy) when they are in orbitals with more s-characters. The two electrons in the $ce{C-F}$ bond spend more time on electronegative fluorine and less time on carbon. If this is the case (and it is), why are you “wasting” a valuable, low-energy orbital character in a carbon hybrid orbital that doesn`t have much electron density to stabilize? Instead, save the s sign for use in hybrid carbon orbitals that have more electron density around carbon (such as $ce{C-H}$ bonds). Thus, as a result of Bent`s rule, we would expect more p-characters in the carbon hybrid orbital used to form the $ce{C-F}$ bond, and more s-characters in the carbon hybrid orbitals used to form the $ce{C-H}$ bonds. Bent`s rule speaks of the hybridization of the central atom ($ce{A}$) in the molecule $ce{X-A-Y}$. In this article, we will learn a relatively new rule proposed by Henry Bent. Henry Bent (1926-2015) was an American physical chemist who was a well-known professor at North Carolina State University and the University of Pittsburgh.

The rule was recently established in 1961 and mainly talks about how different atoms/ligands are aligned after hybridization in space. Although fluoromethane is a special case, the above argument can be applied to any structure with a central atom and 2 or more substituents. The key is that the concentration of atomic character in the orbitals directed to the electropositive substituents leads to a general reduction in the energy of the system by exhaustion in the orbitals directed to the electronegative substituents. This stabilizing compromise is responsible for Bent`s rule. Now that the link between hybridization and connecting angles has been established, Bent`s rule can be applied to specific examples. The following elements were used in Bent`s original work, which considers that the electronegativity of the methyl group is lower than that of the hydrogen atom, because methyl substitution reduces the acid dissociation constants of formic acid and acetic acid. [2] The inductive effect can be explained by Bent`s rule. [13] The inductive effect is charge transfer by covalent bonds, and Ben`s rule provides a mechanism for such results on hybridization differences. In the following table[14], central carbon, measured by the polar substituent constant, becomes more electronegative as the groups bound to central carbon become electron negative. Polar substituent constants are in principle similar to the σ values of Hammett`s equation, because an increasing value corresponds to a greater electron elimination capacity. Bent`s rule suggests that as the electronegativity of the groups increases, more p-character is redirected to these groups, leaving more s-characters in the bond between the central carbon and the R group. Since s orbitals have a greater electron density closer to the nucleus than p orbitals, the electron density in the C−R bond moves more strongly towards carbon with an increasing s character.

This will result in a stronger withdrawal of central carbon into group R. [9] Thus, the electron deprivation capacity of substituents has been transferred to neighboring carbon, exactly what the inductive effect predicts. Bent`s rule that central atoms direct orbitals with a larger p character to larger electronegative substituents is easily applicable to the above by noting that an increase in the coefficient λi increases the p character of the hybrid orbital s + √λipi. So if a central atom A is bound to two groups X and Y and Y is more electronegative than X, then A will hybridize so that λX < λY. More sophisticated theoretical and computational techniques beyond Bent`s rule are needed to accurately predict molecular geometries from first principles, but Bent`s rule provides an excellent heuristic for explaining molecular structures. The above cases seem to show that the size of chlorine is less important than its electronegativity. A prediction based solely on sterics would lead to the opposite trend, as large chlorine substituents would be cheaper from each other.

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