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Bent’s rule was formulated in 1961 by American chemist, Henry Bent, to explain deviations in structures predicted from the VSEPR theory. The rule states: “atomic s character tends to concentrate in orbitals that are directed toward electropositive groups and atomic p character tends to concentrate in orbitals that are directed toward electronegative groups”. This rule, which is experimentally observed and supported by molecular orbital calculations, is a useful tool in inorganic and organic chemsitry. Bent based his rule on the perturbation theory, and suggests that isovalent hybridization should transfer more s-character to the more electropositive-bonding orbital to maximize bonding energy. Hybrid orbitals for main group elements consist of one s and three p orbitals, with the s orbital having lower energy. To have more s character, means that the bonding orbital is lower in energy and shaped more like an s orbital rather than a p orbital. In other words, ligand orbitals tend to be rich in p character because of higher electronegativity, with s character concentrated on the central metal. However, in cases where the metal has a lone pair, the lone pair orbital is high in s character. This is due to the fact that s orbitals are closer to the nucleus, allowing for greater stabilization of the lone pair.

Bent’s rule was derived from the systematic comparison of experimentally determined physical properties of molecules, correlated with valence bond structures and bond hybridization. This rule has been used to qualitatively describe molecular geometries and predict the structure of substituted atoms or molecules. While Bent’s rule was originally intended to describe bonding in elements of the first row periodic table, it also experimentally holds true for transition metal complexes.

Examples of Bent's Rule
According to Bent’s rule, molecular geometry can be explained and predicted by changing the substituent group. In the molecule Me2XCl2, (X= main group elements C, Si, Ge, Sn, Pb), the bond angle Cl-X-Cl is smaller than C-X-C bond angle. With the highly electronegative halogen substituent, Cl, more p character is concentrated on central atom in X-Cl than X-C bonds. Subsequently, bonds with greater p character have smaller bond angles than those with greater s character. For example, when X=C, the Cl-C-Cl has 108.3ﾟ bond angle that is smaller than C-C-C bond angle, 113.0ﾟ. In addition, this can be applied to heavier main group elements. When X=Si, Cl-Si-Cl has a bond angle (107.2ﾟ) that is smaller than that of C-Si-C (114.7ﾟ). In another example, Cl can be substituted to form the molecule (CH3)2PbF2. This molecule is distorted following Bent's rule, in which the bond angle of C-Pb-C (134.8ﾟ) is larger than the angle of the F-Pb-F bond (101.4ﾟ).

The molecule ClF5 has a square pyramidal structure, with four identical Cl-F sp hybridized bonds on equatorial position and one Cl-F sp hybridbridized bond on axial position. This molecule follows the Bent’s rule based on the difference in electronegativity between two atoms. Increased s character of the lone pair on the central atom, Cl, leads to reduced s character (greater p-character) on the axial Cl-F bond. Although the overlap of the axial orbital decreases due to the reduced s character of central atom, the central atom, Cl, becomes less electronegative toward F on axial position. Therefore, the bond of Cl-F on axial position becomes shorter and stronger than other equatorial bonds according to the Pauling’s ionic resonance energy and Schomaker-Stevenson equation.

The molecule XSF4 (X = LP, O and CH2) also follows the Bent’s rule. In SF4, the bond angle of the axial F-S-F bond is 173ﾟ (ideally 180ﾟ) and equatorial F-S-F bond angle is 101ﾟ (ideally 120ﾟ). The axial bond angle has changed slightly due to VSEPR effects. Because of the increased s character of lone pair, more p character is concentrated on the equatorial fluorine atomes, leading to a decrease in the F-S-F bond angles. In OSF4, the axial F-S-F has a bond angle of 164ﾟ (ideally 180ﾟ), whereas the equatorial F-S-F has a bond angle of 115ﾟ (ideally 120ﾟ). These smaller than ideal bond angles are due to VSEPR effects arising from the sterics of the lone pair.

Exceptions to Bent's Rule
According to Bent’s rule, “Atomic s character concentrates in orbitals directed towards electropositive substituents”. However, this general statement is only true for main group elements. For the main group elements, atomic p-orbitals are directed towards more electronegative substituents. This can be rationalized by the fact that the decreased angles of bonds with more p-character coincide with the decreased steric demands of more electronegative atoms. Also, electron density can be more easily withdrawn (by electronegative substituents) from higher lying p-orbitals than from s-orbitals.

Transition metal complexes are the exception to Bent’s rule. It has been experimentally determined that the group 4 transition metal compounds of Ti-Hf do not rigorously follow Bent’s rule. With these complexes, the more electronegative substituents have larger bond angles (indicating greater s character), which goes against Bent’s rule. This can explained by the fact that with transition metals, the energy levels of the d-orbitals are generally below the energy of the s-orbitals, thus the more electronegative substituents will be attracted to the higher lying s-orbitals. Transition metal bonds are essentially sd3 hybridized, with very little contribution from the p-orbitals.

A more generalized from of Bent’s rule can be stated as follows: “The energetically lower lying valence orbital concentrates in bonds directed toward electropositive substituents.” This satisfies both main group and transition metal complexes.