Bent's rule
Encyclopedia
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 chemistry. Bent based his rule on the perturbation theory
, and suggests that isovalent orbital 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 because 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.
group. In the molecule Me2XCl2, (X=main group element
s 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 hybridized 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.
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 form 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.
VSEPR theory
Valence shell electron pair repulsion theory is a model in chemistry used to predict the shape of individual molecules based upon the extent of electron-pair electrostatic repulsion. It is also named Gillespie–Nyholm theory after its two main developers...
. 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 chemistry. Bent based his rule on the perturbation theory
Perturbation theory
Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem...
, and suggests that isovalent orbital 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
Ligand
In coordination chemistry, a ligand is an ion or molecule that binds to a central metal atom to form a coordination complex. The bonding between metal and ligand generally involves formal donation of one or more of the ligand's electron pairs. The nature of metal-ligand bonding can range from...
orbitals tend to be rich in p character because of higher electronegativity
Electronegativity
Electronegativity, symbol χ , is a chemical property that describes the tendency of an atom or a functional group to attract electrons towards itself. An atom's electronegativity is affected by both its atomic number and the distance that its valence electrons reside from the charged nucleus...
, with s character concentrated on the central metal. However, in cases where the metal has a lone pair
Lone pair
In chemistry, a lone pair is a valence electron pair without bonding or sharing with other atoms. They are found in the outermost electron shell of an atom, so lone pairs are a subset of a molecule's valence electrons...
, the lone pair orbital is high in s character. This is because s orbitals are closer to the nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
, 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 substituentSubstituent
In organic chemistry and biochemistry, a substituent is an atom or group of atoms substituted in place of a hydrogen atom on the parent chain of a hydrocarbon...
group. In the molecule Me2XCl2, (X=main group element
Main group element
In chemistry and atomic physics, main group elements are elements in groups whose lightest members are represented by helium, lithium,...
s C, Si, Ge, Sn, Pb), the bond angle Cl-X-Cl is smaller than C-X-C bond angle. With the highly electronegative halogen
Halogen
The halogens or halogen elements are a series of nonmetal elements from Group 17 IUPAC Style of the periodic table, comprising fluorine , chlorine , bromine , iodine , and astatine...
substituent, Cl, more p character
Orbital hybridisation
In chemistry, hybridisation is the concept of mixing atomic orbitals to form new hybrid orbitals suitable for the qualitative description of atomic bonding properties. Hybridised orbitals are very useful in the explanation of the shape of molecular orbitals for molecules. It is an integral part...
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 hybridized bond on axial position. This molecule follows the Bent’s rule based on the difference in electronegativity
Electronegativity
Electronegativity, symbol χ , is a chemical property that describes the tendency of an atom or a functional group to attract electrons towards itself. An atom's electronegativity is affected by both its atomic number and the distance that its valence electrons reside from the charged nucleus...
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
VSEPR theory
Valence shell electron pair repulsion theory is a model in chemistry used to predict the shape of individual molecules based upon the extent of electron-pair electrostatic repulsion. It is also named Gillespie–Nyholm theory after its two main developers...
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
Transition metal
The term transition metal has two possible meanings:*The IUPAC definition states that a transition metal is "an element whose atom has an incomplete d sub-shell, or which can give rise to cations with an incomplete d sub-shell." Group 12 elements are not transition metals in this definition.*Some...
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 form 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.
See also
- Coordination complex
- Molecular geometryMolecular geometryMolecular geometry or molecular structure is the three-dimensional arrangement of the atoms that constitute a molecule. It determines several properties of a substance including its reactivity, polarity, phase of matter, color, magnetism, and biological activity.- Molecular geometry determination...
- Molecular orbital theoryMolecular orbital theoryIn chemistry, molecular orbital theory is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule...