Orbital (Modern) Concept of Covalent Bond

Orbital (Modern) Concept of Covalent Bond

The Lewis Concept of Covalent Bonding failed to explain the geometry and magnetic properties of molecules.

In 1927, Heitler and London put forward Valence Bond Theory (VBT). In 1930, Hund, Huckle and Mullikan put forward Molecular Orbital Theory (MOT). Both theories account for bond energies, bond length and shape of covalent molecules. According to both theories:

A Covalent Bond is formed by the overlapping or interpenetrating (fusion) of two atomic orbitals, each containing a single electron.

Valence Bond Theory (VBT)/ Atomic Orbital Theory (AOT) of Covalent Bond

(Heitler-London’s Theory/ Pauling-Slater’s theory)

Introduction

Valence Bond Theory (VBT) or atomic orbital theory was first proposed in 1927 by Heitler and London and was modified in 1931 by Pauling and Slater that accounts for the formation and directional characteristics of covalent bond. Thus Pauling-Slater’s theory is the modified form of Heitler-London’s theory.

Statement

Covalent Bond is formed by the overlapping or interpenetrating (fusion) of two atomic orbitals of the valence shell each containing an unpaired electron. OR A covalent bond between two atoms results by the overlap of half-filled atomic orbitals (AOs) belonging to their outermost shell giving rise to a single bond orbital occupied by both the electrons with opposite spins.

According to VBT, the bonding electrons occupy the atomic orbitals of the bonded atoms, and the shared electron is influenced by one nucleus (monocentric).

According to VBT, atomic orbitals which are involved in the bond formation maintain their individual nature and identities.

In VBT, some of the valence electrons are indicated as unshared and uninvolved in the formation of molecule.

Molecular Orbital Theory (MOT)/ Hund- Mulliken Theory/ LCAO-MO Theory

Introduction

Molecular orbital theory (MOT) was mainly developed in 1930 (1932) by Hund, Huckle and Mulliken. This theory is also sometimes called Hund-Mulliken’s Theory. This theory is based on the Linear Combination of Atomic Orbitals (LCAO) of the atoms constituting the molecule or ion and hence is also called LCAO-MO Theory.

Statement

A covalent bond between two atoms results by the overlap of half-filled atomic orbitals (AOs) belonging to their outermost shells which get mixed up to give an equivalent number new molecular orbitals containing the two bonding electrons with opposite spin and are influenced by two or more nuclei (i.e. they are polycentric).  OR  A covalent bond is formed by the overlapping or interpenetrating (fusion) of two half-filled atomic orbitals and the bonding (shared) electrons occupy the molecular orbitals which are polycentric and influenced by more than one nucleus.

According to MOT, the bonding electrons occupy the molecular orbital and the shared electron is influenced by more than one nucleus (polycentric).

According to MOT, atomic orbitals which form molecular orbitals do not retain their individual nature. In MOT, all of the valence electrons take part in the bonding of molecules.

Explanation

Internuclear axis/Bond Axis

The line joining the nuclei of atomic orbitals of both the atoms is called internuclear axis (INA) or bond axis or molecular axis. It is an imaginary line joining the two nuclei of atomic orbitals.

Overlapping

The interpenetration or fusion of half-filled atomic orbitals (or hybrid orbitals) is called Overlapping. The overlapping of atomic orbitals takes place if they have similar signs on their lobes. + and  - signs of the lobes of atomic orbitals are only geometric signs of the atomic orbital wave function and should not be confused with + and - charges. The wave functions either have + and - sign. The + sign shows that these orbitals are spherically symmetrical and electron cloud is concentrated in that orbital (or lobe) while - sign indicates that electron cloud is less concentrated in that orbital or lobe.

Types of Overlapping according to internuclear axis        

There are two types of overlapping:       

(a)       Head-on (i.e. End to end) overlapping (results in (σ-bond).

(b)       Side-ways (i.e. lateral) overlapping (results in (p-bond).

       

(a)    Head-on OR End to End Overlapping

The overlapping of two half-filled atomic orbitals along the internuclear (molecular) axis giving sigma molecular orbitals resulting in sigma bond is called Head-to-Head or Head-on or End-on or Linear or Axial or Linear-axis overlapping. The various types of linear axis overlapping to form sigma bond are given below:

Atomic-atomic orbitals overlapping

1.         s-s orbitals overlap

2.         s-p_x orbitals overlap

3.         p_x-p_x orbitals overlap

Atomic-hybridized orbitals overlapping

4.         s-sp³ (hybrid) orbital overlap

5.         s-sp² (hybrid) orbital overlap

6.         s-sp (hybrid) orbital overlap

7.         p_x -sp³ (hybrid) orbital overlap

8.         p_x -sp³ (hybrid) orbital overlap

9.         p_x -sp³ (hybrid) orbital overlap

Hybridized-hybridized orbitals overlapping

10.       sp³-sp³ (hybrid)orbital

11.       sp²-sp² (hybrid)orbital

12.       sp-sp (hybrid)orbital

       

(b)    Side-Wise OR Side to Side Overlapping

The overlapping of two half-filled p-atomic orbitals along a line perpendicular to the internuclear (molecular) axis giving pi molecular orbitals resulting in pi bond is called sideways or sidewise or side-to-side or lateral or parallel overlapping. The lateral overlapping takes place only between two p_y or p_z atomic orbitals.

Types of Overlapping according to LCAO Method             

According to MOT, the linear combination of atomic orbitals (LCAO) gives rise to two types of overlapping:

(a)       Additive overlap/ Positive overlap/ ++ overlap

(b)       Subtractive overlap/ Negative overlap/+ -  overlap

(a)    Additive overlap/ Positive overlap/ ++ overlap

The linear additive overlap (also called positive overlap or ++ overlap) involves the overlapping of the positive lobe of an atomic orbital with the positive lobe of another atomic orbital to form a molecular orbital having a lower energy than each of the combining atomic orbitals exerting attraction between the two nuclei by concentrating the electron density between them. This attraction between the two nuclei and occupation of this molecular orbital by two electrons with opposite spins results in the bond formation. Hence this molecular orbital is called bonding molecular orbital (BMO).

(b)    Subtractive overlap/ Negative overlap/+ - overlap

The linear subtractive overlap (also called Negative overlap/+ -  overlap) involves the overlapping of the positive lobe of an atomic orbital with the negative lobe of another atomic orbital to form a molecular orbital having a higher energy than each of the combining atomic orbitals exerting repulsion between the two nuclei by concentrating the electron density away from the region between the two nuclei so that nuclei are exposed and face each other. This repulsion opposes bond formation and this molecular orbital is unoccupied with electrons. Hence this molecular orbital is called antibonding molecular orbital (AMO).

Difference between Atomic Orbital and Molecular Orbital

1. An atomic orbital is defined as the region of space round the nucleus in an atom in which there is maximum probability of finding the electron  A molecular orbital is defined as the region of space round the two or more nuclei in a molecule.

2. An atomic orbital belongs to one nucleus only and hence is monocentric. A molecular orbital belongs to two or more nuclei and hence is polycentric.

3.  An atomic orbital may contain one or two electrons. A molecular orbital always contain two electrons or no electrons at all.

4.Atomic orbital may be pure or hybridized. Molecular orbital may be bonding or antibonding.

5. Pure atomic orbitals are designated by s, p, d, and f-orbitals and hybrid atomic orbitals are    designated by sp³, sp², sp etc. Molecular orbitals are designated as (s and p-orbitals).

6. Atomic orbitals have a simple shape like sphere, dumb-bell, double dumb-bell etc. Molecular  orbitals have complicated shapes.

     Types of Molecular Orbitals according to LCAO Method

According to MOT, the Linear Combination of Atomic Orbitals (LCAO) by additive overlap (or positive overlap or ++ overlap) and subtractive overlap (or negative overlap /+ - overlap) gives rise to two types of molecular orbitals, one of lower energy and the other of higher energy than the average energy of the two isolated overlapping atomic orbitals:

(a)       Bonding Molecular Orbital (BMO)

(b)       Antibonding Molecular Orbital (AMO)

(a)    Bonding Molecular Orbital

The molecular orbital in which there is a maximum electronic cloud density between the centers of two nuclei and which has lower energy than the total energy of the atomic orbitals from which it is derived is called a Bonding Molecular Orbital (BMO).

If the two electrons of the atomic orbitals, occupy the lower energy molecular orbital, the electron density is concentrated in the region between the two nuclei, exerting attraction on both the nuclei.

Therefore, occupation of this orbital by two electrons results in the bond formation. Hence, this molecular orbital is called Bonding Molecular Orbital.

(b)  Antibonding Molecular Orbital

The molecular orbital in which there is a minimum electron cloud density between the centers of two nuclei and which has higher energy than the energy of the separate atomic orbitals from which it is derived is called Antibonding Molecular Orbital (AMO).

If the two electrons of the atomic orbitals, occupy the higher energy molecular orbital, the electron density is away from region between the two nuclei, so that nuclei are exposed and face each other, resulting in strong repulsion between them.

This opposes bond formation. Hence this molecular orbital is called Antibonding Molecular Orbital.

Energy diagram of Bonding and Antibonding Molecular Orbitals

1.   An energy diagram for the molecular orbitals (for hydrogen) is shown below in which two atomic orbitals approach each other to form two molecular orbitals.

2.   The molecular orbital with less energy than its parent atomic orbitals is more stable and      occupied with two electrons of opposite spin and is called Bonding Molecular Orbital. This is   the Lowest Electronic Energy State or Ground State of (Hydrogen) Molecule.

3. The molecular orbital with high energy than its parent atomic orbitals is less stable and      unoccupied with electrons and is called Antibonding Molecular Orbital (AMO).An electron may occupy AMO in excited state. This state is achieved when electrons in ground state absorbs a   photon of light of proper energy.

Types of Molecular Orbitals

There are two types of molecular orbitals:

1.        Sigma Molecular Orbital      (σ-MO)            [which has sigma (σ) bond].

2.        Pi-Molecular Orbital             (p--MO)           [which has sigma (p) bond].

Sigma Bond/σ-Bond

Definition of Sigma Bond

A covalent bond which is formed by the head on overlapping of half-filled atomic orbitals (or hybrid orbitals) along a internuclear axis giving rise to sigma bonding and sigma antibonding (σ*) molecular orbitals is called a sigma (σ) bond and the electrons that occupy sigma orbital (bond) are called sigma electrons. In other words, a sigma bond is a (bonding) molecular orbital which is symmetrical about a line joining the two nuclei (internuclear axis). Sigma bond is produced (assuming x-axis to be the molecular axis) by s-s-overlap (as in H₂), s-p_x overlap (as in HF, HCl, HBr, HI, H₂O, NH₃ etc) and p_x-p_x overlap (as in F₂, Cl₂, Br₂, and I₂). A sigma bond is also produced when a hybrid orbital overlaps with atomic orbital or two hybrid orbitals overlap together along the internuclear axis.

Various Combinations of Linear overlapping giving sigma bonds

The linear axis overlapping of different orbitals leading to sigma bond formation is given below:

Atomic-atomic orbitals overlapping

1.         s-s orbitals overlap

2.         s-px orbitals overlap

3.         px-px orbitals overlap

Atomic-hybridized orbitals overlapping

4.         s-sp³ (hybrid) orbital overlap

5.         s-sp² (hybrid) orbital overlap

6.         s-sp (hybrid) orbital overlap

7.         p_x -sp³ (hybrid) orbital overlap

8.         p_x -sp³ (hybrid) orbital overlap

9.         p_x -sp³ (hybrid) orbital overlap

Hybridized-hybridized orbitals overlapping

10.       sp³-sp³ (hybrid)orbital

11.       sp²-sp² (hybrid)orbital

12.       sp-sp (hybrid)orbital

Example of Sigma Bond Formation

(1).   Formation of Sigma Bond in Hydrogen (H₂) Molecule

Each hydrogen atom has one half-filled 1s-orbital. In the formation of H₂ molecule, 1s-orbitals of both hydrogen atoms containing an unpaired electron overlap with each other along internuclear axis (s-s- overlap) to form a H – H sigma bond (which constitutes a single covalent bond in H₂ molecule). The antibonding orbital remains vacant. 

 (2).   Formation of Sigma Bond in Fluorine (F₂) Molecule

Each fluorine atom has one half-filled 2p-orbital. In the formation of F₂ molecule, 2p_x-orbitals of both fluorine atoms containing an unpaired electron overlap with each other along internuclear axis (p_x-p_x- overlap) to form a F – F sigma bond (which constitutes a single covalent bond in F₂ molecule). The antibonding orbital remains vacant.

(3).   Formation of Sigma Bond in Hydrogen fluoride (HF) Molecule

Hydrogen atom has one half-filled 1s-orbital and fluorine atom has one half-filled 2p-orbital. In the formation of HF molecule, 1s-orbital of hydrogen atom and 2p_x-orbital of fluorine atom containing an unpaired electron overlap with each other along internuclear axis (s-p_x-overlap) to form a H – F sigma bond (which constitutes a single covalent bond in H–F molecule). The antibonding orbital remains vacant.

Characteristics of Sigma Bond

1.       A sigma bond results from end to end overlap of atomic orbitals giving two types of molecular orbitals (as when atomic orbitals combine an equivalent number of new molecular orbitals is formed), one of lower energy and other of higher energy than the combining atomic orbitals called sigma-bonding (s^b_MO OR s-orbital) and sigma-antibonding (s*_MO or s*-orbital) molecular orbitals respectively. Sigma bonding molecular orbital denoted as (s^b_MO OR s-orbital) is obtained when the + lope of one atomic orbital overlaps with the + lope of another atomic orbital having a single region of electron density in between the two nuclei of atomic orbitals, and thus s-bonding orbital is occupied with two electrons of opposite spin. Sigma antibonding molecular orbital denoted as s*_MO or s*-orbital is obtained when the + lobe of one atomic orbital overlaps with the - lobe of another atomic orbital having negligible electron density in between the two nuclei of atomic orbitals and hence the nuclei fly apart and so s*orbital is unoccupied with electrons. The electrons may occupy s*orbital in excited state.

2.  s^b-orbital and s*-orbitals both have cylindrical symmetry around the internuclear axis. It is for  this reason that these molecular orbitals are called sigma molecular orbitals.

3.        s-orbital has no node while s*-orbital has one node.

               

4. There is free rotation of s-orbital about the bond axis. Thus if an atomic orbital (which forms s-orbital) is rotated on the internuclear axis, the extent of overlap region does not change i.e. electronic distribution and bond length do not change in case of sigma bonds. Thus s-bond (or s-orbital) decides the direction of the bond and the bond length.

5. The s-orbitals as well as p-orbitals can overlap in linear axis or along internuclear axis to form sigma bond. The hybrid orbitals can also form sigma bond by linear overlap along internuclear axis.

6. The extent of overlapping in sigma bond is sufficient (due to end to end overlap of atomic      orbitals) resulting in a strong bond between two atoms (i.e. less reactive and more stable) with   higher bond energy.

7. The relative strength of sigma is related to the extent of overlap of atomic orbitals. This is    known as the Principle of Maximum Overlap. The relative strength of the sigma bonds      obtained by various overlapping of atomic orbitals is as s s < sp < pp (i.e. the relative bond   strength is p  p > s  p > s  s). Thus sigma bond formed by s-s overlap is relatively weak since s-orbitals have spherical distribution of electron density. On the other hand, sigma bond formed by p-p or p-s overlap is relatively stronger since p-orbitals are concentrated in a  particular direction and their lobes are longer than the radius of the corresponding s-orbital.

8.  Sigma bond is formed independently because atoms always combine first with a sigma bond.

9.        Only one sigma bond exists between two atoms.

10.    A sigma bond is equivalent to a single bond.

11.   Sigma electrons in a sigma bond are localized i.e. confined to only two atoms.

12. In sigma bond formation, one lobe of p-orbital stretches while the other lobe reduces in size.

Pi (p) Bond

Definition

A covalent bond which is formed by the side-ways overlapping of two half-filled p-atomic orbitals (belonging to the same atom) whose axes are common along a line perpendicular to the internuclear axis giving rise to pi-bonding and pi-antibonding (p*) molecular orbitals is called a pi (p) bond and the electrons that occupy pi-orbital (bond) are called pi-electrons.

Explanation

1.        A pi bond results from lateral overlap of two p-atomic orbitals at the two sides of the lobe giving two types of molecular orbitals (as when atomic orbitals combine an equivalent number of new molecular orbitals is formed), one of lower energy and other of higher energy than the combining atomic orbitals called pi-bonding (p^b_MO) and pi-antibonding (p* or p*_MO) molecular orbitals respectively. pi bonding molecular orbital denoted as (p^b_MO) or (p-orbital is obtained when the + lope of one p-atomic orbital overlaps with the + lope of another p-atomic orbital having two regions of electron density above and below the nodal plane (i.e. place where two orbitals coincide), and thus (p-bonding orbital is occupied with two electrons of opposite spin. pi antibonding molecular orbital denoted as (p*_MOor p*-orbital is obtained when the + lobe of one p-atomic orbital overlaps with the - lobe of another p-atomic orbital having negligible electron density in between the two nuclei of atomic orbitals and hence the nuclei fly apart and so p*-orbital is unoccupied with electrons. The electrons may occupy p*orbital in excited state.

2.  p^b_MO orbital and p*orbitals both have unsymmetrical electronic distribution around the             internuclear axis.

3.        p^b_MO orbital has one node while p*orbital has two nodes.

               

4. There is restriction of free rotation of p^b_MO orbital about the bond axis. Thus if an atomic orbital (which forms p^b_MO -orbital) is rotated on the internuclear axis, the extent of overlap region decreases (further rotation leads to cease the overlapping of two orbitals) i.e. electronic distribution and bond length changes incase ofp-bond. This increases the potential energy of the molecule and hence its reactivity is increased. Thus it does not decide the direction of bond but shortens the bond length. The formation of two pi-bonds (as in a triple bond) shortens the bond length to a greater extent than the formation of one pi-bond (as in a double bond).

5. The s-orbitals cannot take part in pi-bond formation. Only p-orbitals can form pi-bond by p_y-p_y  or p_z-p_z overlaps.

6. The extent of overlapping in pi bond is less i.e. it has less extent of overlapping (due to parallel overlap of atomic orbitals in which electron density is maximum above and below the line joining the nuclei.) resulting in a weak bond between two atoms (i.e. more reactive and less stable) with lower bond energy.

7.Pi-bond is not formed independently because a p-bond is only formed when the two different overlapping p-orbitals are on two atoms which are already bonded by sigma bond.

8. One or two pi-bonds can be formed between two sigma-bonded atoms [as in O₂ (one (p-bond) and in N₂ (two p-bonds)].

9. A pi bond is equivalent to a double bond and two pi-bonds are equivalent to a triple bond.

10.Pi electrons in a pi bond may be localized (i.e. confined to only two atoms) or delocalized.

11.Both lobes of p-orbitals take part in pi-bond formation. They retain their shape i.e. (p-bonding orbital has a shape similar to that of p-orbital (dumbbell shape).

Difference between Sigma and Pi Bond

1.   It is formed by the head on overlapping of two half filled pure atomic orbitals or hybrid orbitals along the internuclear axis. It is formed by the side-wise overlapping of two half-filled pure atomic orbitals in the form of p-orbitals along a line perpendicular to internuclear axis.

2. It is stronger bond (i.e. more stable and less reactive) due to greater or maximum overlapping of orbitals. It is a weaker bond (i.e. less stable and more reactive) due to lesser overlapping of orbitals.

3. It has only one region of electron cloud density around the bond axis. It has two regions of electron cloud density, one above and one below the sigma-bond axis.

4. It has symmetrical electron cloud density around the bond axis. It has unsymmetrical electron cloud density around the bond axis.

5.   Sigma bond can form between s-orbitals (s-s overlap) as well as s and p-orbitals (s-p_x and p_x and p_x-p_x overlap). s-orbitals cannot take part in making pi bond. Only p-orbitals can form pi bond p_y-p_y or p_z-p_z overlaps.

6. One lobe of p-orbital taking part in sigma bond formation, stretches while the other lobe reduces in size. Both lobes of p-orbitals take part in pi-bond formation. They retain their shape.

7. It is formed alone and independently as atoms always combine first with a sigma bond. It is always formed only between two atoms which are already bonded by a sigma bond.

8. Only one sigma bond exists between two atoms. One or two pi bonds can be formed between two sigma-bonded atoms.

9. All single bonds are sigma bonds. A double bond consists of one sigma and a pi bond, a triple bond consists of one sigma and two pi bonds.

10. It determines the direction of bond and bond length. It does not decide the direction of bond but shortens the bond length. The formation of two pi bonds (as in a triple bond) shortens the bond length to a greater extent than the formation of one pi bond (as in a double bond).

11. Sigma electrons in a sigma bond are localized. Pi electrons in a pi bond may be localized or delocalized.