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In chemistry, Bent's rule describes and explains the relationship between the orbital hybridization of central atoms in molecules and the electronegativities of substituents. The rule was stated by Henry A. Bent as follows:

Atomic s character concentrates in orbitals directed toward electropositive substituents.

//The chemical structure of a molecule is intimately related to its properties and reactivity. Valence bond theory proposes that molecular structures are due to covalent bonds between the atoms and that each bond consists of two overlapping and typically hybridised atomic orbitals. Traditionally, p-block elements in molecules are assumed to hybridise strictly as spⁿ, where n is either 1, 2, or 3. In addition, the hybrid orbitals are all assumed to be equivalent (i.e. the n + 1 spⁿ orbitals have the same p character). Predictions using this approach are usually good, but they can be improved by allowing isovalent hybridization, in which the hybridised orbitals may have noninteger and unequal p character.// Remove this chunk of text - not stated in the article anywhere else

Traditionally, hybridized orbitals were considered to be equivalent, which provided a good approximation of molecular structure for a long time. However, experimental results showed that real-world molecules would deviate from this model. Bent's rule explains disparities between ideal geometries and real-world bond angles. Furthermore, Bent's rule provides a qualitative estimate as to how these hybridised orbitals should be constructed. Bent's rule is that in a molecule, a central atom bonded to multiple groups will hybridise so that orbitals with more s character are directed towards electropositive groups, while orbitals with more p character will be directed towards groups that are more electronegative. By removing the assumption that all hybrid orbitals are equivalent spⁿ orbitals, better predictions and explanations of properties such as molecular geometry and bond strength can be obtained.

Bent's rule can be justified through the relative energy levels of s and p orbitals, which can also be illustrated using some real world examples. Bent's rule affects how we predict bond angles and can be used to supplement our understanding of molecular geometries of simple molecules stemming from VSEPR theory. Additionally, Bent's rule can be used to rationalize bond lengths, J_CH coupling constants and observed inductive affects. Finally, Bent's rule can be described formally by molecular orbital computations.

//Bent's rule has been proposed as an alternative to VSEPR theory as an elementary explanation for observed molecular geometries of simple molecules with the advantages of being more easily reconcilable with modern theories of bonding and having stronger experimental support.// Remove this text?

The validity of Bent's rule for 75 bond types between the main group elements was examined recently. For bonds with the larger atoms from the lower periods, trends in orbital hybridization depend strongly on both electronegativity and orbital size.

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VSEPR Theory versus Bent's Rule

Valence shell electron pair repulsion (VSEPR) theory predicts molecule geometry. VSEPR predicts molecular geometry to take the configuration that allows electron pairs to be most spaced out. This electron distance maximization happens because all electrons are negatively charged, and like charges repel each other. The result of VSEPR theory is being able to predict bond angles with accuracy. According to VSEPR theory, the geometry of a molecule can be predicted by counting how many electron pairs and atoms are connected to a central atom. Bent’s rule states “[A]tomic s character concentrates in orbitals directed toward electropositive substituents”.  Bent’s rule implies that real world bond angles will deviate from the bond angle predicted by VSEPR theory; the relative electronegativities of atoms surrounding the central atom will impact the molecule geometry. VSEPR theory suggests a way to accurately predict molecule shape using simple rules. However, VSEPR theory cannot always predict real world molecular bond angles exactly. On the other hand, Bent’s rule seems to hold for many more real world examples. Furthermore, it has been shown that Bent’s rule corroborates quantum mechanical computations when describing molecule  geometry.

Molecule	Bond Angle Between Substituents	3D Images with Bond Angles	Molecular Rotation
Dimethyl ether	111.5° ± 1.5°
Methanol	108.5° ± 2°
Water	104.5°
Oxygen difluoride	104.2°

The table above demonstrates the differences between VSEPR theory predicted bond angles and their real-world angles. According to VSEPR theory, diethyl ether, methanol, water and oxygen difluoride should all have a bond angle of 109.5^o. Using VSEPR theory, all these molecules should have the same bond angle because they have the same “bent” shape. Yet, clearly the bond angles between all these molecules deviate from their ideal geometries in different ways. Bent’s rule can help elucidate these apparent discrepancies. Electronegative substituents will have more p character. Bond angle has a proportional relationship with s character and an inverse relationship with p character. Thus, as substituents become more electronegative, the bond angle of the molecule should decrease. Dimethyl ether, methanol, water and oxygen difluoride follow this trend as expected (as is shown in the table above).  Two methyl groups are the substituents attached to the central oxygen in diethyl ether. Because the two methyl groups are electropositive, greater s character will be observed and the real bond angle is larger than the ideal bond angle of 109.5^o. Methanol has one electropositive methyl substituent and one electronegative hydrogen substituent. Hence, less s character is observed than dimethyl ether. When there are two hydrogen substituent groups, the angle is decreased even further with the increase in electronegativity and p character. Finally, when both hydrogen substituents are replaced with fluorine in oxygen difluoride, there is another decrease in the bond angle. Fluorine is highly electronegative, resulting in this significant decrease in bond angle.

Applications of Bent's Rule

Bent’s rule is able to characterize molecule geometry with accuracy. Bent’s rule provides a reliable and robust framework for predicting the bond angles of molecules. Bent’s rule accuracy and precision in predicting the geometry of real-world molecules continues to demonstrate its credibility. Beyond bond angle prediction, Bent’s rule has some significant applications and is of considerable interest to chemists. Bent’s rule can be applied to analyzing bonding interactions and molecular syntheses.

Bent’s rule can uncover information about the nature of bonding interactions. Grabowski characterized halogen and hydrogen bonds as they are important to chemists and biologists. Grabowski found that Bent’s rule can be used to corroborate his findings.  From this work, it can be seen that Bent’s rule can provide insight into the bonding and anti-bonding behaviours between molecules. Hence, Bent’s rule can be used to predict the behaviour of reactions between molecules.

Bent’s rule can be used to predict which products are favoured in an organic synthesis depending on the starting materials. Wang et. al. studied the equilibria of various silabenzenes. Wang et. al. considered how the substituents affected the silabenzenes’ equilibrium and found that Bent’s rule played a significant role in the results. The study conducted by Wang et. al. demonstrates how Bent’s rule can be used to predict the route of a synthesis and the stability of products. Showing a similar application, Dubois et. al were able to justify some of their findings using Bent’s rule when they found a reaction to be irreversible. Both these studies show how Bent’s rule can be used to aid synthetic chemistry. Knowing how molecular geometry accurately due to Bent’s rule allows synthetic chemists to predict relative product stability. Additionally, Bent’s rule can help chemists chose their starting materials to drive the reaction towards a particular product. Hence, Bent’s rule allows synthetic chemists to exert more control over reactions of interest.

References

(1)        Ball, D. W.; Key, J. A. Molecular Shapes and Polarity. 2014.

(2)        Bent, H. A. An Appraisal of Valence-Bond Structures and Hybridization in Compounds of the First-Row Elements. Chem. Rev. 1961, 61 (3), 275–311. https://doi.org/10.1021/cr60211a005.

(3)        Jonas, V.; Boehme, C.; Frenking, G. Bent’s Rule and the Structure of Transition Metal Compounds. Inorg. Chem. 1996, 35 (7), 2097–2099. https://doi.org/10.1021/ic951397o.

(4)        Gillespie, R. J. Fifty Years of the VSEPR Model. Coord. Chem. Rev. 2008, 252 (12–14), 1315–1327. https://doi.org/10.1016/j.ccr.2007.07.007.

(5)        Esselman, B. J.; Block, S. B. VSEPR-Plus: Correct Molecular and Electronic Structures Can Lead to Better Student Conceptual Models. J. Chem. Educ. 2019, 96 (1), 75–81. https://doi.org/10.1021/acs.jchemed.8b00316.

(6)        Ghosh, D. C.; Bhattacharyya, S. Computation of Quantum Mechanical Hybridization and Dipole Correlation of the Electronic Structure of the F ₃ B–NH ₃ Supermolecule. Int. J. Quantum Chem. 2005, 105 (3), 270–279. https://doi.org/10.1002/qua.20690.

(7)        Wang, X.; Huang, Y.; An, K.; Fan, J.; Zhu, J. Theoretical Study on the Interconversion of Silabenzenes and Their Monocyclic Non-Aromatic Isomers via the [1,3]-Substituent Shift: Interplay of Aromaticity and Bent’s Rule. J. Organomet. Chem. 2014, 770, 146–150. https://doi.org/10.1016/j.jorganchem.2014.08.018.

(8)        Grabowski, S. J. Halogen Bond and Its Counterparts: Bent’s Rule Explains the Formation of Nonbonding Interactions. J. Phys. Chem. A 2011, 115 (44), 12340–12347. https://doi.org/10.1021/jp205019s.

(9)        Dubois, M. A. J.; Rojas, J. J.; Sterling, A. J.; Broderick, H. C.; Smith, M. A.; White, A. J. P.; Miller, P. W.; Choi, C.; Mousseau, J. J.; Duarte, F.; Bull, J. A. Visible Light Photoredox-Catalyzed Decarboxylative Alkylation of 3-Aryl-Oxetanes and Azetidines via Benzylic Tertiary Radicals and Implications of Benzylic Radical Stability. J. Org. Chem. 2023, 88 (10), 6476–6488. https://doi.org/10.1021/acs.joc.3c00083.

(10)          Geometry of Molecules - Chemistry LibreTexts. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Chemical_Bonding/Lewis_Theory_of_Bonding/Geometry_of_Molecules (accessed 2023-12-04).