Notes on Chemical Bonding for BSc Honours and Generic elective

Notes on Chemical Bonding

Chemical bonding is a fundamental concept in chemistry that explains how atoms combine to form molecules and compounds. There are several types of chemical bonds, each with its own characteristics and properties.

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Types of Chemical Bonds:

Ionic Bonds:

An ionic bond is a type of chemical bond that forms between two atoms with significantly different electronegativities. It is formed considerably between metals and nonmetals. Such bonds are formed when one or more electrons are transferred from one atom to the other.

Examples:

Common examples of compounds held together by ionic bonds include sodium chloride (table salt), potassium chloride (used in some salt substitutes), calcium carbonate (found in chalk and shells), and magnesium oxide. The figure below explains how sodium ion looses one electron which is accepted by chlorine atom. Thus sodium becomes a cation and chlorine becomes an anion. An electrostatic force of attraction between these two ions is called the ionic bond.

Here are the key characteristics and properties of ionic bonds:

1.Electronegativity Difference:

Ionic bonds typically form when there is a large difference in electronegativity (the tendency of an atom to attract electrons) between two atoms. One atom, usually a metal with low electronegativity, donates electrons to another atom, typically a nonmetal with high electronegativity.

2.Formation of Ions:

The atom that loses electrons becomes positively charged and forms a cation. The atom that gains electrons becomes negatively charged and forms an anion.

3.Attraction of Opposite Charges: The electrostatic attraction between the positively charged cations and negatively charged anions is what holds the ions together. This attraction creates a strong bond.

4.Physical Properties:

a.Ionic compounds tend to have high melting and boiling points because the electrostatic forces between ions require a lot of energy to overcome.

b.They are typically solid at room temperature.

c.Ionic compounds are often brittle because when pressure is applied, like charges align and repel each other, causing the crystal lattice to break.

5.Solubility:

Ionic compounds are often soluble in polar solvents like water because the polar water molecules can surround and stabilize the ions, allowing them to separate and disperse.

6.Electrical Conductivity:

In the solid state, ionic compounds do not conduct electricity because the ions are held in a fixed lattice structure. However, when melted or dissolved in water (forming an electrolyte solution), they can conduct electricity because the ions are free to move and carry electrical charge.

7.Crystal Lattice Structure: Ionic compounds typically have a three-dimensional crystal lattice structure in which ions are arranged in a repeating pattern.

8.Transfer of Electrons:

In an ionic bond, electrons are essentially transferred from one atom to another. The atom that donates electrons becomes a cation, while the one that accepts electrons becomes an anion.

 Lattice energy: The amount of energy released when one mole of an ionic compound is formed from its constituent ions is called the lattice energy of the compound.

Higher is the lattice energy of a compound higher is its stability.

Lattice energy depends on the following two factors:

a.Size of ions: The strength and stability of ionic bond is inversely proportional to the size of ions. If the size of ions is small, the inter-ionic attraction increases and more energy is released in the formation of the comp[ound. The ionic bond becomes stronger and stable.

For example the size of Na⁺ and K⁺ ions are 0.95A⁰ and 1.33A⁰ respectively. This is why the ionic bond in NaCl is stronger than that in KCl.

b.Charege on ions: Greater is the charge on ions greater will be the inter-ionic attraction. Greater energy is released in the formation of compound. The ionic bond becomes stronger and stable.

Calculation of Lattice energy using Born-Haber Cycle: The Born-Haber cycle is a way to calculate the lattice energy of an ionic compound using a series of steps and Hess's law. It's a theoretical framework that helps us understand the relationship between the energy changes involved in various processes such as ionization, sublimation, dissociation, and formation of ions and compounds. The cycle is named after two scientists, Max Born and Fritz Haber, who made significant contributions to its development.

Calculation of Lattice energy of NaCl: This involves the following steps:

Applications of Born Haber Cycle: This can be used to determine any of the value expressed in the above equation if all other values are known. Additionally Born Haber cycle can be used to determine Proton affinity of a base.

Lattice energy can also be calculated using Born Lande equation:

Fajan’s Rule: This rule helps in understanding the partial covalent character in ionic compounds or covalent character in ionic bonds.

Purely ionic compounds like NaCl or KCl are almost insoluble in organic solvents. Lithium iodide is expected to be purely ionic as there is large difference in electeronegativities between Li and Cl. But its solubility in organic solvents indicates its partial covalent character. This can be explained using Fajan’s rule.

Fajan’s Rule is based on polarizing power of a cation and polarisability of an anion.

The power of an ion to distort the electron cloud of another ion is called the polarizing power. Similarly, The tendency of an ion to get polarized is its polarisability. The figure below indicates how a cation distorts  (polarises) the electron cloud of an anion.

When the cation and anion come close together, the nucleus of the cation attracts the electron cloud of anion and repels its nucleus. As a result the anion gets distorted and the electron cloud is tilted towards the cation. In other words we can say the electrons are now partially shared between the two nuclei and covalent character is developed in the ionic bond.

Factors affecting partial covalent character in ionic bond:

Smaller size of cations and larger size of anions: Smaller size of cations tends to form more covalent character, as they can polarize the anion easily. For example BeCl_2, MgCl₂, and CaCl₂ have melting points 678, 986 and 1045⁰c. This indicates that BeCl₂ is most covalent due to smallest size in the group compared to other two.

Larger the size of anions, less tightly the electrons will be held by the nucleus. These are easily polarized and large covalent character is induced in corresponding compounds. We may consider CaCl₂ and CaI₂. The size of iodide ion is greater than chloride. Thus CaI₂ should be more polarized than CaCl₂. This is reflected from the melting point of CaI₂ (less m.p 848 K) compared to CaCl₂ (higher m.p of 1045 K).

 The number of charges: A cation with high charge (e.g., Mg²⁺, Al³⁺) has greater polarizing power which can induce large covalent character. Thus corresponding m.p of the compound should be lower.

It's important to note that Fajan's rules are more of qualitative guidelines and do not provide precise quantitative predictions. Real chemical compounds often exhibit a combination of ionic and covalent characteristics, and the degree of each character can vary.

These rules are commonly used to explain and predict the behavior of ionic compounds, particularly in the context of solubility, melting points, and other properties. A compound in which high polarization is expected according to the above points is expected to be more covalent and less soluble in polar solvent like water and should posses less melting point.

Covalent Bond:

A covalent bond is a type of chemical bond where two atoms share one or more pairs of electrons. This sharing allows each atom to achieve a stable electron configuration, usually resembling the electron configuration of the nearest noble gas. Covalent bonds are essential in the formation of molecules, which are groups of atoms held together by these shared electrons.

Example:

A classic example of a covalent bond is the bond between two hydrogen atoms to form a hydrogen molecule (H₂).

Formation of H₂:

Each hydrogen atom has one electron in its outer shell.

To achieve a stable electron configuration (similar to the noble gas helium), each hydrogen atom shares its electron with another hydrogen atom.

This sharing creates a covalent bond, resulting in a stable H₂ molecule.

Characteristics of Covalent Bonds:

1.Electron Sharing:

In a covalent bond, atoms share one or more pairs of electrons to achieve a full outer shell.

This sharing can occur between atoms of the same element (e.g., H₂, O₂) or different elements (e.g., H₂O, CO₂).

2.Molecule Formation:

Covalent bonds lead to the formation of molecules, which are groups of atoms bonded together.

3.Bond Strength:

Covalent bonds are generally strong, requiring significant energy to break.

4.Bond Length:

The distance between the nuclei of the bonded atoms, known as bond length, is specific to the type of bond and the atoms involved.

5.Polarity:

Covalent bonds can be polar or nonpolar:

Nonpolar Covalent Bond: Equal sharing of electrons (e.g., H₂, O₂).

Polar Covalent Bond: Unequal sharing of electrons due to differences in electronegativity (e.g., H₂O).

6.Type of covalent bonds based on the number of electron shared:

Single Bond: Involves the sharing of one pair of electrons (e.g., H₂).

Double Bond: Involves the sharing of two pairs of electrons (e.g., O₂).

Triple Bond: Involves the sharing of three pairs of electrons (e.g., N₂).

7.Low Melting and Boiling Points:

Substances with covalent bonds typically have lower melting and boiling points compared to ionic compounds.

8.Electrical Conductivity:

Covalent compounds do not conduct electricity in the solid or liquid state because they do not have free ions or electrons.

9.Solubility:

Covalent compounds are often soluble in nonpolar solvents but may not dissolve well in water, especially if they are nonpolar.

10.Common in Organic Compounds:

Covalent bonds are the most common type of bond in organic molecules, such as carbohydrates, proteins, and nucleic acids.

Covalent bonds are fundamental in chemistry, playing a crucial role in the structure and function of many biological molecules, such as DNA, proteins, and carbohydrates.

Valence bond theory:

Valence Bond Theory (VBT) is a fundamental concept in chemistry that explains the formation of covalent bonds based on the interaction of atomic orbitals when atoms combine to create molecules.

Key Concepts of Valence Bond Theory:

1. Atomic Orbitals Overlap:

According to VBT, a covalent bond forms when the atomic orbitals of two atoms overlap.

The overlapping takes place between those atomic orbitals which belong to the valence shell of combining atoms and contain unpaired electrons with opposite spins.

Due to opposite spin of the shared electrons the neutralisation of spin magnetic moment occurs which contribute to the total binding force between the two atoms.

This overlap allows the atoms to share electrons, creating a region of increased electron density between the nuclei.

2.Bond Formation and Energy:

When atomic orbitals overlap, the energy of the system decreases, making the bond formation energetically favorable. The extent of overlap determines the strength of the bond—the greater the overlap, the stronger the bond. The relative strength of covalent bonds formed by the overlap of orbitals is p-p > p-s > s-s.

3.Types of Overlapping:

Sigma (σ) Bonds: Formed by the head-on overlap of orbitals along the axis connecting the two nuclei (bond axis). Sigma bonds are the strongest type of covalent bond and can involve s-s, s-p, or p-p orbital overlaps.

Pi (π) Bonds: Formed by the side-to-side overlap of p orbitals. Pi bonds are generally weaker than sigma bonds and exist in double and triple bonds alongside sigma bonds.

4.VBT leads to further theories which explains the structure and properties of molecules with more details:

VBT leads to the concept of hybridization, Molecular orbital and resonance..

Limitations of Valence Bond Theory:

Does Not Explain Molecular Shapes Fully: VBT, while effective in explaining bonding, does not fully account for the geometry of molecules, which is better explained by Valence Shell Electron Pair Repulsion (VSEPR) theory and Molecular Orbital Theory (MOT).

Localized Electrons: VBT treats electrons as localized between atoms, which does not account for the delocalization observed in resonance structures or in molecules like benzene.

VSEPR theory:

Valence Shell Electron Pair Repulsion Theory:

Sidgwick and Powel suggested that the shape of a molecule can be explained by the repulsion between the electron pairs present in the valence shell of the central atom.

The main postulates of this theory are:

1. The unpaired electrons in the valence shell of the central atom and unpaired electrons of the surrounding atoms form bond pairs around the central atom.

2. The paired electrons of the central atom remain as lone pair in the molecule.

3. The bond pairs and lone pairs repeal one another.

4. Electron pairs around the central atom remain at maximum distance apart to avoid repulsion and this brings symmetry and stability to the molecule.

5. The force of repulsion among the bond pairs and lone pairs are not the same. This is because lone pairs remain under the influence of a single nucleus and bond pairs are under the influence of double nuclei. For this reason lone pairs occupy large volume compared to bond pairs.

6. The order of repulsion among bond and lone pairs is:

L.P – L.P > L.P – B.P > B.P – B.P

7. A molecule with only bond pairs around the central atom will have a regular geometry, whereas a molecule with both bond and lone pairs will get a deviation from regular geometry.

Let us look into the following molecules which have regular geometry. A molecule will be represented according to its number of bond pairs and lone pairs. For example AX₂E₀ represents a molecule with central atom A has two bond pairs and no lone pairs. Similarly AX₃E represents a molecule with central atom A has three bond pairs and one lone pair. We will proceed one by one systematically.

Type of molecule	Shape	Geometry	Example
AX2E0	Linear		BeF2 HgCl2
AX3E0	Trigonal planar		BF3
AX4E0	Tetrahedral		CH4 NiCl42-
AX5E0	1.Trigonal bipyramidal		PCl5 Fe(CO)5
	2. Square pyramidal
			MnCl52-
AX6E0	Octahedral		SF6 WCl6
AX7E0	Pentagonal bipyramidal		IF7

 Now let us move further to the molecules with both bond and lone pairs. and let us see how they have irregular geometry.

Steric number (Bond + Lone pair)	Molecular geometry (0 lone pairs)	Molecular geometry  (1 lone pair)	Molecular geometry (2 lone pairs)	Molecular geometry (3 lone pairs)
2	Linear
3	Trigonal planar	Bent
4	Tetrahedral	Trigonal pyramidal	Bent
5	Trigonal bipyramidal	Seesaw	T-shaped	Linear
6	Octahedral	Square pyramidal	Square planar
7	Pentagonal bipyramidal	Pentagonal pyramidal	Pentagonal planar

Hybridisation:

The process of mixing of two or more atomic orbitals of the same atom having similar energies to get hybrid orbitals of equivalent energies, maximum stability and fixed orientation is called the hybridization.

This can be considered as the extension of valence bond theory. Hybridization can explain molecular shapes, formation of bonds and their length and strength.

Note that hybridisation always takes place at the central atom(s) of a molecule and the number of hybrid orbitals formed is equal to the number of orbitals intermix for hybridisation. Based on the type of atomic orbitals involved in the mixing, hybridization can be classified into various types as discussed below.

Types of Hybridization:

sp³ Hybridization:

Orbitals Involved: One s and three p orbitals of the central atom of a molecule intermix to give four sp³  hybrid orbitals.

Let us discuss the formation of methane molecule by the process of hybridisation.

Step 1: Electronic Configuration of Carbon

Carbon (C) has an atomic number of 6, and its ground-state electronic configuration is: 
1s² 2s² 2p_x¹ 2p_y¹ 2p_z⁰
The valence shell (2nd shell) contains 2s² 2p², meaning carbon has two unpaired electrons in the p-orbitals.

Step 2: Excitation of Carbon

To form four bonds with hydrogen, carbon promotes one electron from the 2s orbital to the empty 2p orbital, resulting in:
1s² 2s¹ 2p_x¹ 2p_y¹ 2p_z¹
Now, carbon has four unpaired electrons.

Step 3: Hybridization (sp³ Formation)

The one 2s orbital and the three 2p orbitals mix to form four equivalent sp³ hybrid orbitals. Each of these orbitals has 25% s-character and 75% p-character.

These 4 hybrid orbitals of the central carbon atom direct towards the four corners of a regular tetrahedron.

Step 4: Bond Formation in Methane

Each of the four sp³ hybrid orbitals overlaps with the 1s orbital of a hydrogen atom, forming four sigma (σ) bonds. The result is a tetrahedral structure with bond angles of 109.5°.

Geometry: Tetrahedral (109.5° bond angle)

Other Example: CH₄ (methane), NH₃ (ammonia), H₂O (water)

sp² Hybridization:

Consider the formation of BF₃ molecule.

B₅ = 1s² 2s² 2p_x¹ 2p_y⁰ 2p_z⁰ (Ground state)

B₅ = 1s² 2s¹ 2p_x¹ 2p_y¹ 2p_z⁰ (Excited state)

Orbitals Involved: One s and two p orbitals intermix to form 3 hybrid orbitals which direct towards the corners of a triangle.

Geometry: Trigonal planar (120° bond angle)

Now three unpaired p orbitals of 3 F atoms overlap with the hybrid orbitals to make 3 sigma bonds.

Example: BF₃, C₂H₄ (ethene), SO₃

sp Hybridization:

Consider the formation of BeCl₂ molecule.

Be₄ = 1s² 2s² 2p_x⁰ 2p_y⁰ 2p_z⁰ (Ground state)

Be₄ = 1s² 2s¹ 2p_x¹ 2p_y⁰ 2p_z⁰ (Excited state)

Orbitals Involved: One s and one p orbital of the central Be atom form 2 hybrid orbitals which are rearranged linearly to each other.

Geometry: Linear (180° bond angle)

Now two unpaired p orbitals of 2 Cl atoms overlap with the hybrid orbitals to make 2 sigma bonds.

Example: BeCl₂, CO₂, C₂H₂ (ethyne)

sp³d Hybridization:

Orbitals Involved: One s, three p, and one d orbital

Geometry: Trigonal bipyramidal (90°, 120° bond angles)

Example: PCl₅, SF₄

sp³d² Hybridization:

Orbitals Involved: One s, three p, and two d orbitals

Geometry: Octahedral (90° bond angle)

Example: SF₆, [CrF₆]³⁻

Molecular Orbital Theory

Molecular Orbital Theory (MOT) is a fundamental theory in chemistry that describes the behavior of electrons in a molecule using molecular orbitals, which are formed by the combination of atomic orbitals.

Key Concepts of Molecular Orbital Theory

Formation of Molecular Orbitals:

Atomic orbitals combine to form molecular orbitals when atoms bond and the number of molecular orbitals formed equals the number of atomic orbitals combined.

Types of Molecular Orbitals:

Bonding Molecular Orbital (BMO): Lower energy, leads to stability (e.g., σ and π orbitals).

Antibonding Molecular Orbital (ABMO): Higher energy, decreases stability (e.g., σ* and π* orbitals).

Bond Order Calculation:

Bond Order = (Number of electrons in BMO−Number of electrons in ABMO)/2

A higher bond order means a stronger bond.

Filling of Molecular Orbitals (Aufbau Principle):

Orbitals fill in increasing energy order.

Hund’s rule and Pauli’s exclusion principle apply.

Molecular Orbital Energy Diagram:

For diatomic molecules (e.g., O₂, N₂), molecular orbitals are arranged in a specific order based on energy levels.

The energy order differs for molecules with atomic numbers Z ≤ 7 (e.g., B₂, C₂, N₂) and Z > 7 (e.g., O₂, F₂, Ne₂).

The molecular electronic configuration for a total electrons upto 14 (such as N2) is: (σ1s) (σ1s*) (σ2s) (σ2s*) (π2px) = (π2py) (σ2pz) (π2px*) (π2py*)

The molecular electronic configuration for a total electrons greater than 14 (such as O2) is: (σ1s) (σ1s*) (σ2s) (σ2s*) (σ2pz)  (π2px) = (π2py) (π2px*) (π2py*)

MO Diagram for homonuclear diatomic molecules:

Helium molecule:

https://en.m.wikipedia.org/wiki/File:Molecular_orbital_diagram_of_He2.png

Bond Order = (Number of electrons in BMO−Number of electrons in ABMO)/2

Thus BO = (2-2)/2 = 0

It means helium molecule does not exist as the bond order is 0. We can say 0 bod order means no bond between two helium atoms.

Nitrogen molecule:

Molecular electronic configuration of N2 = (σ1s)² (σ1s*)² (σ2s)² (σ2s*)² (π2px)² (π2py)² (σ2pz)² (π2px*)(π2py*)

Bond Order = (Number of electrons in BMO−Number of electrons in ABMO)/2

Thus BO = (10-4)/2 = 3

Thus nitrogen molecule has a triple bond between two nitrogen atoms. This is because nitrogen is almost inert to chemical reaction.

Nitrogen is diamagnetic by nature as it has all paired electrons.

Oxygen Molecule:

Molecular electronic configuration of O2 = (σ1s)² (σ1s*)² (σ2s)² (σ2s*)² (σ2pz)² (π2px)² (π2py)² (π2px*)¹ (π2py*)¹

Bond Order = (Number of electrons in BMO−Number of electrons in ABMO)/2

Thus BO = (10-6)/2 = 2

Thus oxygen molecule has a double bond between two oxygen atoms.

Oxygen molecule is paramagnetic by nature as it has  unpaired electrons.

MO Diagram for heteronuclear diatomic molecules:

CO Molecule:

In the diagram, the energy of corresponding atomic orbitals are different. The electronegativity of O atom is more than carbon so it attracts electrons more towards its nucleus. Thus an O atom should have 2s more close to its nucleus compared to C atom. In the diagram 2s atomic orbital of O atom is placed lower level compared to C atom.

BO = (10-4)/2 = 3

A tripple bond is indicated between C and O of CO molecule which is true and the molecule is diamagnetic as no unpaired electrons present.

Delocalization of Electrons:

Unlike Valence Bond Theory, MOT explains electron delocalization in molecules like benzene.

Applications of Molecular Orbital Theory

*Explains bonding in diatomic molecules (e.g., O₂, N₂, F₂).

*Justifies magnetic properties (why O₂ is paramagnetic).

*Used in spectroscopy, quantum chemistry, and understanding delocalized π-bonding in molecules like benzene.

fig: sigma and pi bond: 

https://creativecommons.org/licenses/by-sa/3.0/deed.en https://commons.wikimedia.org/wiki/File:Sigma-pi_bonding.png https://upload.wikimedia.org/wikipedia/commons/7/7b/Sigma-pi_bonding.png

Attribution: Tem5psu, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons

To be Continued ....