Paper 3: (Stereochemistry, Metal-Ligand Equilibria and Reaction Mechanism of Transition Metal Complexes)

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Scarlett Norman
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1 Subject Paper No and Title Module No and Title Module Tag 4, Bent rule and energetics of hybridisation CHE_P3_M4

2 TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction 2.1 Bent rule and energetics of hybridization 3. Application of bent rule 3.1 Bond angle 3.2 Bond length 3.3 Coupling constant 3.4 Inductive effect 3.5 Molecular structure 4. Berry pseudorotation 5. Summary

3 1. Learning Outcomes After studying this module, you shall be able to know about: Bent rule and energetics of hybridisation. Application of bent rule Berry psedorotation mechanism in trigonal bipyramidal and square pyramidal structure 2. Introduction 2.1 Bent rule and energetics of hybridization In hybridization, atomic orbitals linearly combine to give hybrid orbitals and the energy of that hybrid orbital is sum of energies of all atomic orbitals. This energy of hybridization depends upon the magnitude of bond energies and helps in determining the structure of the molecules. In hybridization combining of atomic orbitals takes place in which their energy is redistributed to form hybrid orbitals that are identical in shape and energy. The energy of hybridization and shape of hybrid orbitals depends upon the contribution of s and p orbitals during hybridization. Bent rule defines the relation of electronegativity of the ligand and geometry of central metal atom. It is stated by Henry Bent as "Atomic s character concentrates in orbitals directed toward electropositive substituents". It relates the hybridization of orbitals of central atoms and electronegativity of the substituents. The reactivity of a molecule is an important factor in determining its chemical structure. According to valence bond theory, covalent bonds are responsible for the formation of molecular structures by overlapping of hybridized atomic orbitals. p-block elements hybridized as sp n, where n is 1, 2,3. 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 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 s 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, 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

4 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. 3. Application of bent rule 3.1 Bong angles Bent rule can explain the difference in the bond angles of molecules from ideality. The relation between the hybridization of central metal atom and bond angle can be explain by taking example of methane, ethylene and acetylene. In the given molecules the hybridization of carbon is sp 3, sp 2, and sp respectively. And the bond angles between substituents are 109.5, ~120, and 180 respectively. 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.. Table 1 shows the variation in bond angle with respect to the substituent attached to oxygen atom. Table.1 Variation in bond angle with respect to the substituent attached to oxygen atom. Molecule Dimethyl ether Bond angle between substituents 111 Methanol water 104.5

5 Oxygen difluoride Bond length Bond length also depends upon the hybridization of the atom. Let s take an example of fluoromethane, difluoromethane, trifluoromethane and tetrafluoromethane having average Cl-F bond length 1.388Å, 1.358Å, 1.329Å and 1.323Å respectively as shown in the table2. Table.2 Bond length and hybridization Molecule Average C-Cl bond length Chloromethane Å Å Dichloromethane Å Trichloromethane Å Tetrachlorometha ne 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

6 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. 3.3 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 as shown in the table 3. Table 3 Coupling constant and s character Molecule Coupling constant 125 Hz Methane Acetyldehyde 127 Hz 134 Hz 1,1,1- trichloroethane 141 Hz Methanol

7 149 Hz Fluoromethane 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. 3.4 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 are shown in the table 4. Table.4 Substituent Polar substituent constant t-butyl 0.00 Methyl 1.05 Chloromethyl 1.94 Dichloromethyl

8 2.65 Trichloromethyl 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. 3.5 Molecular structure Bent rule provides an accuracy to valance bond theory. As according to valance bond theory the covalent bond between two atoms is a two electron bond. In VBT, atoms do not result in a pure hydrogen like structure. But if this is so, the structure of methane i.e. tetrahedral is only possible if the 2s and 2p orbitals of carbon have the same geometry. This results in the introduction of orbital hybridization. In this the atomic orbitals are mixed to form equivalent hybrid orbitals. The number of hybrid orbitals would be same as that of starting atomic orbitals which are mixed. With the help of orbital hybridization, the valance bond theory successfully explains the properties and geometry of number of molecules. As per the traditional hybridized theory is concerned, all the hybrid orbitals are equivalent. For example when the s and p orbitals are combined to give four sp i 3 =!! (s + 3 p i), three sp i 2 =!! (s + 2 p i) and two sp i =!! (s + p i) orbitals. For p i orbitals the total contribution of s and p orbitals before and after hybridization must be equivalent and the hybrid orbitals so formed must be orthogonal to each other. If this is not so, it defines that they would have non-zero orbital overlap and the orbital electrons would interact and if any of the orbital involve in covalent bonding the other orbital also interact with that bond. This will violate the two electrons per bond rule of VBT. Construction of s and p orbitals: Let the first hybrid orbital be given as: s + λ I p i Where, p i is bonding group and λ i is amount of p character in hybrid orbitals And the second hybrid orbital is given as: s + λ j p j

9 Where, p j is bonding group and λ j is amount of p character in second hybrid orbital For normalization of resulting orbitals, the value of λ j and p j must be determined. And the resulting orbital is orthogonal to the first hybrid orbital. As it is the sum of two normalized wavefunction, it is also normalized. For the involvement of two hybrid orbitals in the separate covalent bond the orthogonality of the wavefunction must be established. Now, The inner product of orthogonal orbitals must be zero. Now, the s orbital is normalized so the inner product <s/s> = 1 Also, the s orbital is orthogonal to p i and p j orbitals. As a result of which <s/p i > and <s/p j > is equals to zero. Now the p i and p j orbitals are at an angle of ω ij to each other. Therefore, By rearranging, This is Coulson s theorem. Now, the Bent rule is easily applicable as an increase in the coefficient of λ j will increase the p character of the s + λ I p i hybrid orbital. If a central atom is bonded to X and Y groups, and Y is more electronegative group than X then λ X < λ Y for the hybrid orbital. Thus, bent rule explains the molecular structure excellently. 4. Berry Pseudorotation Berry pseudorotation is the conversion of molecule s geometry by changing the axial ligands with equatorial ligands. Trigonal bipyramidal molecules mostly undergo this type of isomerization. For example in PF 5, but it can also occur in molecules having square pyramidal geometry. This mechanism is first discovered by R. Stephen Berry in 1960.

4.1 Berry pseudorotation mechanism in trigonal bipyramidal In trigonal pyramidal structures the two axial ligands interfere with the two equatorial ligands closely like a pair of scissors.

10 4.1 Berry pseudorotation mechanism in trigonal bipyramidal In trigonal pyramidal structures the two axial ligands interfere with the two equatorial ligands closely like a pair of scissors. As a result of which both axial and equatorial ligands starts moving with same speed, which results in the increase of angle between the other axial and equatorial ligands. The transition state is square based pyramid in which the four interchanging ligands are the base. After this the equatorial ligands become the axial one. In the PF 5 molecule, this mechanism of interchanging of ligands requires energy of about 3.6 kcal/mole. The berry psedorotation in trigonal bipyramidal structure is shown in the diagram below. Here, the geometry of transition state is square planar therefore, the hybridization of the transition state is sp 3 d x 2 - y Berry pseudorotation mechanism in square pyramidal structure In the square pyramidal molecules for example IF 5, the mechanism for the berry psedoration is opposite to that of trigonal bipyramidal molecules. In this mechanism, when molecule vibrates back and forth, movement of one pair of fluorine scissors with the third fluorine in the transition state. The ligands which are active in this scissors motion are still participating in pseudorotation kcal/mol of energy is required in this interchanging of ligands.

11 5. Summary Bent rule 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 be used to relate: 1. Bond angle 2. Bond length 3. Coupling constant 4. Inductive effect 5. Molecular structure Berry pseudorotation is intra isomerization of molecule s geometry by changing the axial ligands with equatorial ligands

Paper 3: INORGANIC CHEMISTRY I (Stereochemistry, Metal-Ligand Equilibria and Reaction Mechanism of Transition Metal Complexes) Module 3: dπ-pπ bonding

Paper 3: INORGANIC CHEMISTRY I (Stereochemistry, Metal-Ligand Equilibria and Reaction Mechanism of Transition Metal Complexes) Module 3: dπ-pπ bonding Subject Paper No and Title Module No and Title Module Tag 3, INORGANIC CHEMISTRY I (Stereochemistry, Metal- Ligand Equilibria and Reaction Mechanism of Transition Metal Complexes) 3, dπ-pπ bonding CHE_P3_M3