Class 11- Chemistry: Chapter 4: Chemical Bonding and Molecular Structure by Subhas C Chakra

 

Chemical Bonding and Molecular Structure

 Chemical Bond
The force that holds different atoms in a molecule is called chemical bond.
• Octet Rule
Atoms of different elements take part in chemical combination in order to complete their octet or to attain the noble gas configuration.
• Valence Electrons
It is the outermost shell electron which takes part in chemical combination.
• Facts Stated by Kossel in Relation to Chemical Bonding
— In the periodic table, the highly electronegative halogens and the highly electro-positive alkali metals are separated by noble gases.
— Formation of an anion and cation by the halogens and alkali metals are formed by gain of electron and loss of electron respectively.
— Both the negative and positive ions acquire the noble gas configuration.
— The negative and positive ions are stabilized by electrostatic attraction Example,

• Modes of Chemical Combination
— By the transfer of electrons: The chemical bond which formed by the complete transfer of one or more electrons from one atom to another is termed as electrovalent bond or ionic bond.
— By sharing of electrons: The bond which is formed by the equal sharing of electrons between one or two atoms is called covalent bond. In these bonds electrons are contributed by both.
— Co-ordinate bond: When the electrons are contributed by one atom and shared by both, the bond is formed and it is known as dative bond or co-ordinate bond.

• Ionic or Electrovalent Bond
Ionic or Electrovalent bond is formed by the complete transfer of electrons from one atom to another. Generally, it is formed between metals and non-metals. We can say that it is the electrostatic force of attraction which holds the oppositely charged ions together.
The compounds which is formed by ionic or electrovalent bond is known as electrovalent compounds. For Example, ,
(i) NaCl is an electrovalent compound. Formation of NaCl is given below:

Na+ ion has the configuration of Ne while Cl– ion represents the configuration of [Ar].
(ii) Formation of magnesium oxide from magnesium and oxygen.

Electrovalency :  Electrovalency is the number of electrons lost or gained during the formation of an ionic bond or electrovalent bond.

• Factors Affecting the Formation of Ionic Bond
(i) Ionization enthalpy: As we know that ionization enthalpy of any element is the amount of energy required to remove an electron from outermost shell of an isolated gaseous atom to convert it into cation.
Hence, lesser the ionization enthalpy, easier will be the formation of a cation and have greater chance to form an ionic bond. Due to this reason alkali metals have more tendency to form an ionic bond.
For example, in formation of Na+ ion I.E = 496 kJ/mole
While in case of magnesium, it is 743 kJ/mole. That’s why the formation of positive ion for sodium is easier than that of magnesium.
Therefore, we can conclude that lower the ionization enthalpy, greater the chances of ionic bond formation.
(ii) Electron gain enthalpy (Electron affinities): It is defined as the energy released when an isolated gaseous atom takes up an electron to form anion. Greater the negative electron gain enthalpy, easier will be the formation of anion. Consequently, the probability of formation of ionic bond increases.
For example. Halogens possess high electron affinity. So, the formation of anion is very common in halogens.





(iii) Lattice energy or enthalpy: It is defined as the amount of energy required to separate 1 mole of ionic compound into separate oppositely charged ions.

Lattice energy of an ionic compound depends upon following factors:

(i) Size of the ions: Smaller the size, greater will be the lattice energy.
(ii) Charge on the ions: Greater the magnitude of charge, greater the interionic attraction and hence higher the lattice energy.
• General Characteristics of ionic Compounds
(i) Physical State: They generally exist as crystalline solids, known as crystal lattice. Ionic compounds do not exist as single molecules like other gaseous molecules e.g., H2 , N2 , 02 , Cl2 etc.
(ii) Melting and boiling points: Since ionic compounds contain high interionic force between them, they generally have high melting and boiling points.
(iii) Solubility: They are soluble in polar solvents such as water but do not dissolve in organic solvents like benzene, CCl4etc.
(iv) Electrical conductivity: In solid state they are poor conductors of electricity but in molten state or when dissolved in water, they conduct electricity.
(v) Ionic reactions: Ionic compounds produce ions in the solution which gives very fast reaction with oppositely charged ions.
For example,



• Covalent Bond—Lewis-Langmuir Concept
When the bond is formed between two or more atoms by mutual contribution and sharing of electrons, it is known as covalent bond.
If the combining atoms are same the covalent molecule is known as homoatomic. If they are different, they are known as heteroatomic molecule.
For Example,

• Lewis Representation of Simple Molecules (the Lewis Structures)
The Lewis dot Structure can be written through the following steps:
(i) Calculate the total number of valence electrons of the combining atoms.
(ii) Each anion means addition of one electron and each cation means removal of one electron. This gives the total number of electrons to be distributed.
(iii) By knowing the chemical symbols of the combining atoms.
(iv) After placing shared pairs of electrons for single bond, the remaining electrons may account for either multiple bonds or as lone pairs. It is to be noted that octet of each atom should be completed.


• Formal Charge
In polyatomic ions, the net charge is the charge on the ion as a whole and not by particular atom. However, charges can be assigned to individual atoms or ions. These are called formal charges.
It can be expressed as

Calculation of formal charges can be done as follows :

• Limitations of the Octet Rule

(i) The incomplete octet of the central atoms: In some covalent compounds central atom has less than eight electrons, i.e., it has an incomplete octet.  

  Li, Be and B have 1, 2, and 3 valence electrons only.

 
(ii) Odd-electron molecules: There are certain molecules which have odd number of electrons the octet rule is not applied for all the atoms.

(iii) The expanded Octet: In many compounds there are more than eight valence electrons around the central atom. It is termed as expanded octet. 

 

• Other Drawbacks of Octet Theory
(i) Some noble gases, also combine with oxygen and fluorine to form a number of compounds like XeF2 , XeOF2   , etc.

.

(ii) This theory does not account for the shape of the molecule.
(iii) It does not give any idea about the energy of the molecule and its relative stability.
• Bond Length

It is defined as the equilibrium distance between the centres of the nuclei of the two bonded atoms. It is expressed in terms of A. Experimentally, it can be defined by X-ray diffraction or electron diffraction method.

• Bond Angle

• It is defined as  the angle between the lines representing the orbitals containing the bonding – electrons.
• It helps us in determining the shape. It can be expressed in degree. Bond angle can be experimentally determined by spectroscopic methods.

Relation between Bond length(in pm ) and Bond angles( in degrees) :

• Bond Enthalpy

It is defined as the amount of energy required to break one mole of bonds of a particular type to separate them into gaseous atoms.

Bond Enthalpy is also known as bond dissociation enthalpy or simple bond enthalpy. 

Unit of bond enthalpy = kJ mol-1
Greater the bond enthalpy, stronger is the bond. For e.g., the H—H bond enthalpy in hydrogen is 435.8 kJ mol-1.

The magnitude of bond enthalpy is also related to bond multiplicity. 

Greater the bond multiplicity, more will be the bond enthalpy. 

For example, 

Bond enthalpy of C —C bond is 347 kJ mol-1 while that of C = C bond is 610 kJ mol-1.

Bond Enthalpy Equation :

Calculation of Bond Enthalpy:

The Change in Bond Energy or bond Enthalpy is very simple. The steps involved are as follows :

An example of a numerical problem is given here.

In polyatomic molecules, the term mean or average bond enthalpy is used.

• Bond Order
According to Lewis, in a covalent bond, the bond order is given by the number of bonds between two atoms in a molecule. 

For example,
Bond order of H2 (H —H) =1
Bond order of 02 (O = O) =2
Bond order of N2 (N = N) =3

• Isoelectronic molecules and ions have identical bond orders. 

• For example, F2 and O22- have bond order = 1. N2, CO and NO+ have bond order = 3. 

• With the increase in bond order, bond enthalpy increases and bond length decreases.  

Calculation of Bond Order:

The calculation of bond order is illustrated as follows:

 

Calculation of Bond order for molecules with Resonance structures is illustrated here.

• Resonance Structures
There are many molecules whose behaviour cannot be explained by a single-Lew is structure, Tor example, Lewis structure of Ozone represented as follows:

Thus, according to the concept of resonance, whenever a single Lewis structure cannot explain all the properties of the molecule, the molecule is then supposed to have many structures with similar energy. Positions of nuclei, bonding and nonbonding pairs of electrons are taken as the canonical structure of the hybrid which describes the molecule accurately. For 03, the two structures shown above are canonical structures and the III structure represents the structure of 03 more accurately. This is also called resonance hybrid.
Some resonating structures of some more molecules and ions are shown as follows:

• Polarity of Bonds
Polar and Non-Polar Covalent bonds

• Non-Polar Covalent bonds: 

When the atoms joined by covalent bond are the same like; H2, O2, Cl2, the shared pair of electrons is equally attracted by two atoms and thus the shared electron pair is equidistant to both of them.

Alternatively, we can say that it lies exactly in the centre of the bonding atoms. As a result, no poles are developed and the bond is called as non-polar covalent bond. The corresponding molecules are known as non-polar molecules.
For Example,

Examples :

• Polar bond: 

When covalent bonds formed between different atoms of different electronegativity, shared electron pair between two atoms gets displaced towards highly electronegative atoms.

For Example, in HCl molecule, since electronegativity of chlorine is high as compared to hydrogen thus, electron pair is displaced more towards chlorine atom, thus chlorine will acquire a partial negative charge (δ–) and hydrogen atom have a partial positive charge (δ+) with the magnitude of charge same as on chlorination.

 Such covalent bond is called polar covalent bond.

• Dipole Moment
Due to polarity, polar molecules are also known as dipole molecules and they possess dipole moment. Dipole moment is defined as the product of magnitude of the positive or negative charge and the distance between the charges.

• Applications of Dipole Moment
(i) For determining the polarity of the molecules.
(ii) In finding the shapes of the molecules.
For example, the molecules with zero dipole moment will be linear or symmetrical. Those molecules which have unsymmetrical shapes will be either bent or angular.
(e.g., NH3with μ = 1.47 D).
(iii) In calculating the percentage ionic character of polar bonds.
• The Valence Shell Electron Pair Repulsion (VSEPR) Theory
Sidgwick and Powell in 1940, proposed a simple theory based on repulsive character of electron pairs in the valence shell of the atoms. It was further developed by Nyholm and Gillespie (1957).

Main Postulates  :
(i) The exact shape of molecule depends upon the number of electron pairs (bonded or non bonded) around the central atoms.
(ii) The electron pairs have a tendency to repel each other since they exist around the central atom and the electron clouds are negatively charged.
(iii) Electron pairs try to take such position which can minimize the repulsion between them.
(iv) The valence shell is taken as a sphere with the electron pairs placed at maximum distance.
(v) A multiple bond is treated as if it is a single electron pair and the electron pairs which constitute the bond as single pairs.
• Valence Bond Theory
Valence bond theory was introduced by Heitler and London (1927) and developed by Pauling and others. It is based on the concept of atomic orbitals and the electronic configuration of the atoms.
Let us consider the formation of hydrogen molecule based on valence-bond theory.
Let two hydrogen atoms A and B having their nuclei NA  and NB  and electrons present in them are eA and eB .
As these two atoms come closer new attractive and repulsive forces begin to operate.
(i) The nucleus of one atom is attracted towards its own electron and the electron of the other and vice versa.
(ii) Repulsive forces arise between the electrons of two atoms and nuclei of two atoms. Attractive forces tend to bring the two atoms closer whereas repulsive forces tend to push them apart.
• Orbital Overlap Concept
According to orbital overlap concept, covalent bond formed between atoms results in the overlap of orbitals belonging to the atoms having opposite spins of electrons. Formation of hydrogen molecule as a result of overlap of the two atomic orbitals of hydrogen atoms is shown in the figures that follows:

Stability of a Molecular orbital depends upon the extent of the overlap of the atomic orbitals.
• Types of Orbital Overlap
Depending upon the type of overlapping, the covalent bonds are of two types, known as sigma (σ ) and pi (π) bonds.
(i) Sigma (σ bond): Sigma bond is formed by the end to end (head-on) overlap of bonding orbitals along the internuclear axis.
The axial overlap involving these orbitals is of three types:
• s-s overlapping: In this case, there is overlap of two half-filled s-orbitals along the internuclear axis as shown below:

• s-p overlapping: This type of overlapping occurs between half-filled s-orbitals of one atom and half filled p-orbitals of another atoms.

• p-p overlapping: This type of overlapping takes place between half filled p-orbitals of the two approaching atoms.

(ii) pi (π bond): π bond is formed by the atomic orbitals when they overlap in such a way that their axes remain parallel to each other and perpendicular to the internuclear axis. The orbital formed is due to lateral overlapping or side wise overlapping.

• Strength of Sigma and pf Bonds
Sigma bond (σ bond) is formed by the axial overlapping of the atomic orbitals while the π-bond is formed by side wise overlapping. Since axial overlapping is greater as compared to side wise. Thus, the sigma bond is said to be stronger bond in comparison to a π-bond.
Distinction between sigma and n bonds

• Hybridisation
Hybridisation is the process of intermixing of the orbitals of slightly different energies so as to redistribute their energies resulting in the formation of new set of orbitals of equivalent energies and shape.
Salient Features of Hybridisation:
(i) Orbitals with almost equal energy take part in the hybridisation.
(ii) Number of hybrid orbitals produced is equal to the number of atomic orbitals mixed,
(iii) Geometry of a covalent molecule can be indicated by the type of hybridisation.
(iv) The hybrid orbitals are more effective in forming stable bonds than the pure atomic orbitals.
Conditions necessary for hybridisation:
(i) Orbitals of valence shell take part in the hybridisation.
(ii) Orbitals involved in hybridisation should have almost equal energy.
(iii) Promotion of electron is not necessary condition prior to hybridisation.
(iv) In some cases filled orbitals of valence shell also take part in hybridisation.
Types of Hybridisation:
(i) sp hybridisation: When one s and one p-orbital hybridise to form two equivalent orbitals, the orbital is known as sp hybrid orbital, and the type of hybridisation is called sp hybridisation.
Each of the hybrid orbitals formed has 50% s-character and 50%, p-character. This type of hybridisation is also known as diagonal hybridisation.


(ii) sp2 hybridisation: In this type, one s and two p-orbitals hybridise to form three equivalent sp2 hybridised orbitals.
All the three hybrid orbitals remain in the same plane making an angle of 120°. Example. A few compounds in which sp2 hybridisation takes place are BF3, BH3, BCl3 carbon compounds containing double bond etc.

(iii) sp3 hybridisation: In this type, one s and three p-orbitals in the valence shell of an atom get hybridised to form four equivalent hybrid orbitals. There is 25% s-character and 75% p-character in each sp3 hybrid orbital. The four sp3 orbitals are directed towards four corners of the tetrahedron.

The angle between sp3 hybrid orbitals is 109.5°.
A compound in which sp3 hybridisation occurs is, (CH4). The structures of NH2 and H20 molecules can also be explained with the help of sp3 hybridisation.
• Formation of Molecular Orbitals: Linear Combination of Atomic Orbitals (LCAO)
The formation of molecular orbitals can be explained by the linear combination of atomic orbitals. Combination takes place either by addition or by subtraction of wave function as shown below.



The molecular orbital formed by addition of atomic orbitals is called bonding molecular orbital while molecular orbital formed by subtraction of atomic orbitals is called antibonding molecular orbital.
Conditions for the combination of atomic orbitals:
(1) The combining atomic orbitals must have almost equal energy.
(2) The combining atomic orbitals must have same symmetry about the molecular axis.
(3) The combining atomic orbitals must overlap to the maximum extent.
• Types of Molecular Orbitals
Sigma (σ) Molecular Orbitals: They are symmetrical around the bond-axis.
pi (π) Molecular Orbitals: They are not symmetrical, because of the presence of positive lobes above and negative lobes below the molecular plane.
• Electronic configuration and Molecular Behaviour
The distribution of electrons among various molecular orbitals is called electronic configuration of the molecule.
• Stability of Molecules

• Bond Order
Bond order is defined as half of the difference between the number of electrons present in bonding and antibonding molecular orbitals.
Bond order (B.O.) = 1/2 [Nb-Na]
The bond order may be a whole number, a fraction or even zero.
It may also be positive or negative.
Nature of the bond: Integral bond order value for single double and triple bond will be 1, 2 and 3 respectively.
Bond-Length: Bond order is inversely proportional to bond-length. Thus, greater the bond order, smaller will be the bond-length.
Magnetic Nature: If all the molecular orbitals have paired electrons, the substance is diamagnetic. If one or more molecular orbitals have unpaired electrons, it is paramagnetic e.g., 02 molecule.
• Bonding in Some Homonuclear (Diatomic) Molecules
(1) Hydrogen molecule (H2): It is formed by the combination of two hydrogen atoms. Each hydrogen atom has one electron in Is orbital, so, the electronic configuration of hydrogen molecule is

This indicates that two hydrogen atoms are bonded by a single covalent bond. Bond dissociation energy of hydrogen has been found = 438 kJ/mole. Bond-Length = 74 pm
No unpaired electron is present therefore,, it is diamagnetic.
(2) Helium molecule (He2): Each helium atom contains 2 electrons, thus in He2 molecule there would be 4 electrons.
The electrons will be accommodated in σ1s and σ*1s molecular orbitals:



• Hydrogen Bonding
When highly electronegative elements like nitrogen, oxygen, flourine are attached to hydrogen to form covalent bond, the electrons of the covalent bond are shifted towards the more electronegative atom. Thus, partial positive charge develops on hydrogen atom which forms a bond with the other electronegative atom. This bond is known as hydrogen bond and it is weaker than the covalent bond. For example, in HF molecule, hydrogen bond exists between hydrogen atom of one molecule and fluorine atom of another molecule.
It can be depicted as

• Types of H-Bonds
(i) Intermolecular hydrogen bond (ii) Intramolecular hydrogen bond.
(i) Intermolecular hydrogen bond: It is formed between two different molecules of the same or different compounds. For Example, in HF molecules, water molecules etc.
(ii) Intramolecular hydrogen bond: In this type, hydrogen atom is in between the two highly electronegative F, N, O atoms present within the same molecule. For example, in o-nitrophenol, the hydrogen is in between the two oxygen atoms.

What is Molecular Orbital Theory?

The Molecular Orbital Theory (often abbreviated to MOT) is a theory on chemical bonding developed at the beginning of the twentieth century by F. Hund and R. S. Mulliken to describe the structure and properties of different molecules. The valence-bond theory failed to adequately explain how certain molecules contain two or more equivalent bonds whose bond orders lie between that of a single bond and that of a double bond, such as the bonds in resonance-stabilized molecules. This is where the molecular orbital theory proved to be more powerful than the valence-bond theory (since the orbitals described by the MOT reflect the geometries of the molecules to which it is applied).

The key features of the molecular orbital theory are listed below.

• The total number of molecular orbitals formed will always be equal to the total number of atomic orbitals offered by the bonding species.
• There exist different types of molecular orbitals viz; bonding molecular orbitals, anti-bonding molecular orbitals, and non-bonding molecular orbitals. Of these, anti-bonding molecular orbitals will always have higher energy than the parent orbitals whereas bonding molecular orbitals will always have lower energy than the parent orbitals.
• The electrons are filled into molecular orbitals in the increasing order of orbital energy (from the orbital with the lowest energy to the orbital with the highest energy).
• The most effective combinations of atomic orbitals (for the formation of molecular orbitals) occur when the combining atomic orbitals have similar energies.

In simple terms, the molecular orbital theory states that each atom tends to combine together and form molecular orbitals. As a result of such arrangement, electrons are found in various atomic orbitals and they are usually associated with different nuclei. In short, an electron in a molecule can be present anywhere in the molecule.

One of the main impacts of the molecular orbital theory after its formulation is that it paved a new way to understand the process of bonding. With this theory, the molecular orbitals are basically considered as linear combinations of atomic orbitals. The approximations are further done using the Hartree–Fock (HF) or the density functional theory (DFT) models to the Schrödinger equation.

Table of Content

• Linear Combination of Atomic Orbitals
• Conditions
• Molecular Orbitals
• Types
• Formation of Molecular Orbitals
• Bonding Molecular Orbitals
• Anti-bonding Molecular Orbitals
• Differences
• Features of MOT

Molecular orbital theory approximation of the molecular orbitals as linear combinations of atomic orbitals can be illustrated as follows.

However, to understand the molecular orbital theory more clearly and in-depth, it is important to understand what atomic and molecular orbitals are first.

Conditions for Linear Combination of Atomic Orbitals

The conditions that are required for the linear combination of atomic orbitals are as follows:

Same Energy of Combining Orbitals

 The atomic orbitals combining to form molecular orbitals should have comparable energy. This means that 2p orbital of an atom can combine with another 2p orbital of another atom but 1s and 2p cannot combine together as they have appreciable energy difference.

Same Symmetry about Molecular Axis

The combining atoms should have the same symmetry around the molecular axis for proper combination, otherwise, the electron density will be sparse. For e.g. all the sub-orbitals of 2p have the same energy but still, 2pz orbital of an atom can only combine with a 2pz orbital of another atom but cannot combine with 2px and 2py orbital as they have a different axis of symmetry. In general, the z-axis is considered as the molecular axis of symmetry.

Proper Overlap between Atomic Orbitals

The two atomic orbitals will combine to form molecular orbital if the overlap is proper. Greater the extent of overlap of orbitals, greater will be the nuclear density between the nuclei of the two atoms.

The condition can be understood by two simple requirements. For the formation of proper molecular orbital, proper energy and orientation are required. For proper energy, the two atomic orbitals should have the same energy and for the proper orientation, the atomic orbitals should have proper overlap and the same molecular axis of symmetry.

What are Molecular Orbitals?

The space in a molecule in which the probability of finding an electron is maximum can be calculated using the molecular orbital function. Molecular orbitals are basically mathematical functions that describe the wave nature of electrons in a given molecule.

These orbitals can be constructed via the combination of hybridized orbitals or atomic orbitals from each atom belonging to the specific molecule. Molecular orbitals provide a great model via the molecular orbital theory to demonstrate the bonding of molecules.

Types of Molecular Orbitals

According to the molecular orbital theory, there exist three primary types of molecular orbitals that are formed from the linear combination of atomic orbitals. These orbitals are detailed below.

Anti Bonding Molecular Orbitals

The electron density is concentrated behind the nuclei of the two bonding atoms in anti-bonding molecular orbitals. This results in the nuclei of the two atoms being pulled away from each other. These kinds of orbitals weaken the bond between two atoms.

Non-Bonding Molecular Orbitals

In the case of non-bonding molecular orbitals, due to a complete lack of symmetry in the compatibility of two bonding atomic orbitals, the molecular orbitals formed have no positive or negative interactions with each other. These types of orbitals do not affect the bond between the two atoms.

Formation of Molecular Orbitals

An atomic orbital is an electron wave; the waves of the two atomic orbitals may be in phase or out of phase. Suppose ΨA and ΨB represent the amplitude of the electron wave of the atomic orbitals of the two atoms A and B.

Case 1: When the two waves are in phase so that they add up and amplitude of the wave is Φ= ΨA + ΨB

 

Case 2: when the two waves are out of phase, the waves are subtracted from each other so that the amplitude of the new wave is Φ ´= ΨA – ΨB

Characteristics of Bonding Molecular Orbitals

• The probability of finding the electron in the internuclear region of the bonding molecular orbital is greater than that of combining atomic orbitals.
• The electrons present in the bonding molecular orbital result in the attraction between the two atoms.
• The bonding molecular orbital has lower energy as a result of attraction and hence has greater stability than that of the combining atomic orbitals.
• They are formed by the additive effect of the atomic orbitals so that the amplitude of the new wave is given by Φ= ΨA + ΨB
• They are represented by σ, π, and δ.

Characteristics of Anti-bonding Molecular Orbitals

• The probability of finding the electron in the internuclear region decreases in the anti-bonding molecular orbitals.
•  The electrons present in the anti-bonding molecular orbital result in the repulsion between the two atoms.
• The anti-bonding molecular orbitals have higher energy because of the repulsive forces and lower stability.
• They are formed by the subtractive effect of the atomic orbitals. The amplitude of the new wave is given by Φ ´= ΨA – ΨB
• They are represented by σ∗, π∗, δ∗

Why are Antibonding Orbitals Higher in Energy?

The energy levels of bonding molecular orbitals are always lower than those of anti-bonding molecular orbitals. This is because the electrons in the orbital are attracted by the nuclei in the case of bonding Molecular Orbitals whereas the nuclei repel each other in the case of the anti-bonding Molecular Orbitals.

Difference between Bonding and Antibonding Molecular Orbitals

Molecular Orbital Theory
Bonding Molecular Orbitals	Anti-Bonding Molecular Orbitals
Molecular orbitals formed by the additive effect of the atomic orbitals is called bonding molecular orbitals	Molecular orbitals formed by the subtractive effect of atomic is called anti-bonding molecular orbitals
Probability of finding the electrons is more in the case of bonding molecular orbitals	Probability of finding electrons is less in antibonding molecular orbitals. There is also a node between the anti-bonding molecular orbital between two nuclei where the electron density is zero.
These are formed by the combination of + and + and – with – part of the electron waves	These are formed by the overlap of + with – part.
The electron density, in the bonding molecular orbital in the internuclear region, is high. As a result, the nuclei are shielded from each other and hence the repulsion is very less.	The electron density in the antibonding molecular orbital in the internuclear region is very low and so the nuclei are directly exposed to each other. Therefore the nuclei are less shielded from each other.
The bonding molecular orbitals are represented by σ, π, δ.	The corresponding anti-bonding molecular orbitals are represented by σ∗ , π∗, δ∗.

The lowering of the energy of bonding molecular orbital than the combining atomic orbital is called stabilization energy and similarly increase in energy of the anti-bonding molecular orbitals is called destabilization energy.

Try this: Paramagnetic materials, those with unpaired electrons, are attracted by magnetic fields whereas diamagnetic materials, those with no unpaired electrons, are weakly repelled by such fields. By constructing a molecular orbital picture for each of the following molecules, determine whether it is paramagnetic or diamagnetic.

• B2
• C2
• O2
• NO
• CO

Features of Molecular Orbital Theory

• The atomic orbitals overlap to form new orbitals called molecular orbitals. When two atomic orbitals overlap they lose their identity and form new orbitals called molecular orbitals.
• The electrons in the molecules are filled in the new energy states called the Molecular orbitals similar to the electrons in an atom being filled in an energy state called atomic orbitals.
• The probability of finding the electronic distribution in a molecule around its group of nuclei is given by the molecular orbital.
• The two combining atomic orbitals should possess energies of comparable value and similar orientation. For example, 1s can combine with 1s and not with 2s.
• The number of molecular orbitals formed is equal to the number of atomic orbitals combining.
• The shape of molecular orbitals formed depends upon the shape of the combining atomic orbitals.

According to the Molecular Orbital Theory, the filling of orbitals takes place according to the following rules:

• Aufbau’s principle: Molecular orbitals are filled in the increasing order of energy levels.
• Pauli’s exclusion principle: In an atom or a molecule, no two electrons can have the same set of four quantum numbers.
• Hund’s rule of maximum multiplicity: Pairing of electrons doesn’t take place until all the atomic or molecular orbitals are singly occupied.