Bent Rule and Energetics of Hybridization

Bent Rule and Energetics of Hybridization

Bent Rule and Energetics of Hybridization

Bent Rule and Energetics of Hybridization

Hybridisation describes that atomic orbitals combine and redistribute their energies to form new orbitals which are known as hybrid orbitals. These are identical with respect to energy and shape. Shapes of the hybrid orbital depends upon contribution of s, p orbitals and its affect the energy of hybridisation.

Bent rule provides a qualitative estimation of construction of hybridized orbitals. It states that in a molecule, the central atom bonded to multiple groups will hybridize in such a way that the orbitals having more s- character are directed towards electropositive groups, while the orbitals having more p- character will be directed towards groups that are more electronegative. Bent rule can also be applied to d-block elements, for this the orbitals having more s character are covalently bonded with ligands. Similarly the orbitals having more d character are directed towards groups that form bonds of greater ionic character.

Bent Proposed the following rules to explain the non-equivalent nature of hybrid orbitals-
1. The more electronegative atom demands greater electron density from the central atom.
2. Greater is the p-character of a hybrid orbital, lesser is its electronegativity.
3. Central atom directs greater p and lesser s-character and less p and greater s- character into its hybrid orbitals directed towards more ans less electronegative substituent respectively.

Bent rule is based on the fact that the energy of s orbitals is lower than that of p orbitals. The bond distribution between two elements having different electronegativity is in such a way that the electron density of bond will shift towards the more electronegative element and the bond become polar.
Let us take an example of molecule of fluoromethane,
Bent Rule

The carbon being more electronegative than hydrogen has electron density of C-H bond shifted towards it. In the bond formation the contribution of hybrid orbitals will determine the energy of electrons. The increase in s character of hybrid orbitals will decrease the energy of electrons as the energy of s orbitals is lower than that of p orbitals. Similarly, as fluorine is more electronegative than carbon, the electron density is shifted towards fluorine in the C-F bond. Also, the electron density of hybrid orbital of carbon is less in C-F bond as compared to C-H bond. Hence the energy of that bond will not depend upon the hybridization of carbon. The shifting of s character towards the C-H bond will stabilize it because of increase in the electron density near the carbon atom. Opposite is the case with C-F bond. Therefore as suggested by bent rule the atomic s character on the carbon atom is directed towards hydrogen which is less electronegative than carbon and away from fluorine as it is more electronegative. Although fluoromethane is a special case but the statement is true for any structure having a central atom and substituents two or more in number.

sp3d Hybridisation in PCl3F2

In sp3d Hybridisation one s, three p and one d-orbitals form five sp3d hybridised orbital. All these five hybrid orbitals are not of the same type so they can be divided into two nonequivalent sets. The first set is known as equatorial set of orbitals. It is formed from one s, one px and one py orbitals. The second set is known as axial set. It is formed from one pz and one d orbitals. It is experimentally observed that the more electronegative substituent 'F' occupies the axial position (as it has less s character) and less electronegative substituent's 'Cl' occupies equatorial position.
Bent Rule

Application of Bent Rule

The Bent's rule can be used to rationalize many aspects of structure, bonding, spectra and the physical and chemical properties of a wide range of compounds. Some of the important applications of Bent's rule are given below-
1. Bong angles
2. Bong Length
3. Coupling constant
4. Inductive effect

Bond Angle

Bonds with greater p-character have smaller bond angles than those with s-character because s-orbitals are closer to the nucleus and hence exert larger inter-electronic repulsion producing higher bond angles.
Bond Angel ∝ % s-character
Example: Alkanes, Alkenes and Alkynes
Alkanes: sp3 Hybridization
In sp3, s-character is 25% and p-character is 75%
Alkenes: sp2 Hybridization
In sp2, s-character is 33.3% and p-character is 66.6%
Alkynes: sp Hybridization
In sp, s-character is 50% and p-character is 50%
Bond angle: 109.5°, 120° and 180° respectively.

In SF4, the bond angle of axial F–S–F bond is 173° (ideally 180°) and the equatorial F–S–F bond angle is 101° (ideally 120°). The axial, as well as equatorial bond angles, are decreased slightly due to increased s-character of the lone pair and more p-character in bond pairs. Furthermore, thionyl tetrafluoride shows the same trend but the slightly higher bond angle between equatorial fluorines than that of sulfur tetrafluoride. This anomaly can be explained in terms of comparatively larger s-character in equatorial fluorines as the lone pair has been replaced by a more electronegative oxygen atom.
Bent Rule

According to Bent rule, as the electronegativity of the substituent increases, orbitals having greater p- character will be directed towards those groups and hence the bond angle decreases. It suggests that the hybrid orbitals having more s- character should be directed towards the lone pairs and those with more p- character directed towards the hydrogen.
Electrinegativity of the substituents Increases, Bond Angel decreases as p-character increases.
Bent Rule

Bond Length

Bond length also depends upon the hybridization of the atom. Let us take an example of fluoromethane, difluoromethane, trifluoromethane and tetrafluoromethane having average Cl-F bond length 1.388Å, 1.331Å, 1.329Å and 1.323Å respectively. As the electronegativity of fluorine atom is very high than hydrogen therefore, in fluoromethane the carbon will direct a hybrid orbital high in p- character towards fluorine. On the other hand, orbitals having high s- character direct towards the hydrogen. Now in difluoromethane the p- character of orbital is shared by both the fluorine atoms results in decrease of p- character as compared to fluoromethane and hence the increased s character in the C-F bonds decreases the bond lengths.
Bond Length ∝ % p-character
Bent Rule

Coupling Constant

It is predicted that the coupling constant of bonds having more s- character is relatively high. For example the coupling constant for methane, acetaldehyde, 1,1,1-trichloroethane, methanol and fluoromethane is 125 Hz, 127 Hz, 134 Hz, 141Hz and 149 Hz respectively. The amount of p- character directed towards the substituent increases as the electronegativity of the substituent increases. This results in increase of s- character in the bonds and hence the coupling constants.
Bent Rule

Inductive effect

Bent rule can explain the inductive effect as it provides a mechanism to relate it with hybridization of the atom. Inductive effect is nothing but the charge transmission via covalent bond. Taking an example of t- butyl and methyl, chloromethyl, dichloromethyl and trichloromethyl having polar substituent constant -0.30, 0, 1.05, 1.94 and 2.65 respectively.

Bent Rule
It shows that as the electronegative atom is attached to the central atom, it will become more electron-withdrawing.
According to bent rule as the electronegativity of the group increases, more p- character is diverted towards the group and results in increase of s- character in C-R bond. As the electron density of s-orbitals is more than that of p- orbitals near nucleus, the electron density in C-R bond will shift towards the carbon atom. Thus, the electron-withdrawing ability of the substituents has been transferred to the adjacent carbon.

Exceptions of Bent's Rule

The general statement of Bent's rule, atomic s-character concentrates in orbitals directed towards electropositive substituents, is true only for main group compounds. However, transition metal complexes show quite strange behavior. It has been observed that the group four transition metals Ti–Hf do not accurately follow Bent's rule. With these complexes, the more electronegative substituents have larger bond angles indicating greater s-character. This can be explained by the fact that the d-orbitals in transition metals are generally lower in energy than s-orbital. Thus, more electronegative substituents will be attracted to the high lying s-orbitals. Transition metal orbitals are sd3 hybridized with very little contribution from p-orbitals.

Exceptions of Bent’s Rule
The broad form of Bent's rule can be stated as follows, The energetically low-lying valence orbital concentrates in bonds directed towards electropositive substituents. This satisfies both the main group and transition metal complexes.


1. What is Bent's rule?

2. How does Bent's rule affect the s and p character of the atomic orbitals?

3. How Bent's rule used to determine shape and bond angle in an compound?

4. Why does more elctronegative atom takes more p character leaving behind s character on central atom?

5. How s character affect the Coupling constant?