Preview:

We shall begin by explaining Kössel-Lewis’ approach to chemical bonding which was based on the stable electronic configuration of inert gases attributed to their completely filled orbitals. Consequently, we shall study the Octet Rule which states that, “atoms can combine either by transfer of valence electrons from one atom to another (gaining or losing) or by sharing of valence electrons in order to have an octet in their valence shells”.

Next, we shall learn about Covalent bond formation, its types, factors that favour its formation and so on. In the next section, we will learn how to represent Lewis dot structures by considering only the valence electrons in the atom.

Then we will define Formal Charge in a polyatomic molecule or ion as the difference between the number of valence electrons of that atom in an isolated or free-state and the number of electrons assigned to that atom in the Lewis structure. Subsequently, we shall learn about formation of an ions and the ionic bond.

We shall then define Lattice Enthalpy of an ionic solid as the energy required to completely separate one mole of a solid ionic compound into gaseous constituent ions.

You will then be learning about some important bond parameters like — Bond length, Bond angle, Bond order and Bond enthalpy.

The phenomenon of resonance shall then be discussed. Resonance is the method by which a molecule can accurately be described through different structural diagrams, called canonical structures which can account for the properties of the molecule completely. We shall then learn about dipoles and dipole moments.

Molecules of the type X-Y having two polar ends with partial positive and negative charges are called, dipoles and Dipole moment is the product of the magnitude of the charge and the distance between the centres of positive and negative charge.

Then, an interesting theory called, The Valence Shell Electron Pair Repulsion (VSEPR) Theory will be discussed— which was proposed to explain the geometry of molecules. Consequently, Valence Bond theory was put forward to explain the formation of covalent bonds. We shall then discuss the rules that govern the overlap of atomic orbitals and types of overlapping.

Next, we shall discuss an important phenomenon, Hybridisation as the phenomenon 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. We will also look at the various types of hybridization.

Then, we shall discuss, Molecular Orbital Theory which explains the formation of molecular orbitals like we have studied atomic orbitals by Linear combination of atomic orbitals. In the next section, we shall study the filling up of molecular orbitals like the filling up of atomic orbitals. We shall then study its applications.

Then we will define Hydrogen bond as the attractive force which binds hydrogen atom of one molecule with the electronegative atom (F, O or N) of another molecule. With the discussion of its types and cause we shall end the chapter.

4.0 Introduction:

Atoms of all elements (except those of noble gases) do not have independent existence. Instead, the atoms combine together and exist as stable molecules.

The attractive force which holds the atoms together in molecule is called a chemical bond.

To explain the combination of atoms to form molecules, different theories have been proposed:

a) Kossel-Lewis Approach

b) Valence shell electron pair repulsion theory (VSEPR)

c) Valence bond theory (VBT)

d) Molecular orbital theory (MOT)

Questions from the section:

1. What is a chemical bond?

4.1 Kössel-Lewis Approach to Chemical Bonding

Kössel and Lewis’ theory of chemical bond formation was based on the explanation of valency exhibited by inert gases. They explained that, the stability of inert gases could be attributed to their completely filled outermost shell (or valence shell) which has the general electronic configuration: $ns^2np^6$. This is called an octet configuration.  

• G.N. Lewis considered the atom in terms of a positively charged ‘Kernel’ (the nucleus plus the inner electrons) and the outer shell that could accommodate a maximum of eight electrons.
• He further assumed that, these eight electrons occupy the corners of a cube which surround the Kernel.
• For example, the single outer shell electron of sodium would occupy one corner of the cube, while in the case of a noble gas all the eight corners would be occupied.
• This octet of electrons represents a particularly stable electronic arrangement.
• Lewis postulated that, atoms achieve the stable octet arrangement when they are linked by chemical bonds.
• In the case of sodium and chlorine, this happens by the transfer of an electron from sodium to chlorine thereby giving the $Na^+$ and $Cl^–$ ions. In case of other molecules like, $Cl_2, H_2, F_2$, the bond is formed by the sharing of a pair of electrons between the atoms. In both these processes, each atom attains a stable outer octet of electrons.

Lewis Symbols:

Lewis introduced simple notations to represent valence electrons in an atom. These notations are called Lewis symbols. For example, the Lewis symbols for the elements of second period are as under.

Significance of Lewis Symbols:

• In the formation of a molecule, only the outer shell electrons or valence electrons take part in chemical combination. The inner shell electrons are well protected and are generally not involved in the combination process. Thus, the number of dots around the symbol represents the number of valence electrons.
• Knowing the number of valence electrons helps to calculate the common or group valence of the element.
• The group valence of the elements is generally either equal to the number of dots in Lewis symbols or 8 minus the number of dots or valence electrons.

Definition box: Valency is the number of electrons lost or gained or shared by an atom while combining with other atoms to reach a stable octet configuration of noble gas.

Kössel’s postulates with relation to chemical bonding:

1. In the periodic table, the highly electronegative halogens and the highly electropositive alkali metals are separated by the noble gases.
2. The formation of a negative ion from a halogen atom and a positive ion from an alkali metal atom is associated with the gain and loss of an electron by the respective atoms;
3. The negative and positive ions thus formed attain stable noble gas electronic configurations. The noble gases (with the exception of helium which has a duplet of electrons) have a particularly stable outer shell configuration of eight (octet) electrons, $ns^2np^6$.
4. The negative and positive ions are stabilized by electrostatic attraction. For example, the formation of NaCl from sodium and chlorine, according to the above scheme, can be explained as:

           $$ Na → Na^+ + e^–$$

[Ne] $3s^1$    [Ne]

$$Cl + e^– → Cl^–$$

$$[Ne] 3s^2 3p^5  \hspace{10mm}      [Ne] 3s^2 3p^6 \space or \space   [Ar]$$

$$Na^+ + Cl^– → NaCl \space or \space Na^+Cl^–$$

Similarly, the formation of $CaF_2$ may be

shown as:

$$Ca → Ca^{2+} + 2e^– $$

$$[Ar]4s^2 \hspace{10mm} [Ar]$$

$$ F + e^– → F^–$$

$$[He] 2s^2 2p^5 \hspace{10mm}[He] 2s^2 2p^6 \space or \space [Ne]$$

$$Ca^{2+} + 2F^– → CaF_2 \space or \space Ca^{2+}(F^–)_2$$

The bond formed, as a result of the electrostatic attraction between the positive and negative ions was termed as the electrovalent bond. The electrovalence is thus equal to the number of unit charge(s) on the ion. For instance, calcium is assigned a positive electrovalence of two, while chlorine a negative electrovalence of one.

According to Kössel and Lewis’s approach, atoms of elements combine with each other in different ways based on their nature to form different types of chemical bonds.

4.1.1 Octet Rule

Kössel and Lewis in 1916 developed an important theory of chemical combination between atoms known as Electronic theory of chemical bonding.

According to this, “atoms can combine either by transfer of valence electrons from one atom to another (gaining or losing) or by sharing of valence electrons in order to have an octet in their valence shells”. This is known as octet rule.

Types of chemical bonds:

• Ionic bond or electrovalent bond
• Covalent bond
• Coordinate bond
• Hydrogen bond

4.1.2 Covalent Bond

Langmuir introduced the term covalent bond.

The Lewis-Langmuir theory:

It can be understood by considering the formation of the chlorine molecule, $Cl_2$:

• The Cl atom with electronic configuration, [Ne] $3s^23p^5$, is one electron short of the argon (the nearest noble gas) configuration.
• The $Cl_2$ molecule is formed by the sharing of a pair of electrons between the two chlorine atoms, each chlorine atom contributing one electron to the shared pair.

• In the process, both chlorine atoms attain the outer shell octet of the nearest noble gas (that is, argon).
• The dots represent electrons. Such structures are referred to as Lewis dot structures.

Rules followed by Lewis’ dot structures, common to all molecules (formed by similar or dissimilar atoms):

1. Each bond is formed as a result of sharing of an electron pair between the atoms.
2. Each combining atom contributes at least one electron to the shared pair.
3. The combining atoms attain the outer-shell noble gas configurations as a result of the sharing of electrons. For example, in water and carbon tetrachloride molecules, formation of covalent bonds can be represented as:

d. Thus, when two atoms share one electron pair they are said to be joined by a single covalent bond.

e. If two atoms share two pairs of electrons, the covalent bond between them is called a double bond. For example, in carbon dioxide molecule, we have two double bonds between the carbon and oxygen atoms. Similarly, in ethane molecule the two carbon atoms are joined by a double bond.

f. In many compounds we have multiple bonds between atoms. The formation of multiple bonds conveys the sharing of more than one electron pair between two atoms.

g) When combining atoms share three electron pairs as in the case of two nitrogen atoms in the $N_2$ molecule and the two carbon atoms in the ethyne molecule, a triple bond is formed.

Note box: 1. The number of electrons of an atom, shared by it with other atoms is called its covalency. 2. Electron pairs involved in bonding are bonded pair of electrons (bp). 3. Pairs of valence electrons which are not involved in bonding are known as lone pair of electrons.

Properties of covalent compounds:

• Many covalent compounds are insoluble in water but are soluble in non-polar solvents.
• When dissolved in water, covalent compounds don’t conduct electricity.
• Covalent compounds exist as solids, liquids and gases.
• They undergo reactions slowly.

Factors favouring covalent bond:

1. Electron Affinity: A covalent bond is generally favoured between the two atoms if both the atoms have high electron affinity.

2. Ionisation Energy: Ionisation energy of both the atoms participating in bonding should be high.

3. Atomic Size: Atomic size of the atoms forming covalent bond should be smaller. Smaller the atomic radii of atoms, stronger will be the covalent bond. For example, H-H bond is stronger than Cl-Cl bond which in turn is stronger than Br-Br bond.

4. Electronegativity: The electronegativities of both the atoms should be high. The difference of electronegativities between the two atoms should be minimum.

5. High nuclear charge and small inter-nuclear distance favour the formation of covalent bond.

6. Atoms should have 4, 5, 6 or 7 electrons in their valence shell.

4.1.3 Lewis Representation of Simple Molecules (the Lewis Structures)

The Lewis dot structures can be written by adopting the following steps:

• The total number of electrons required for writing the structures is obtained by adding the valence electrons of the combining atoms. For example, in the $CH_4$ molecule there are a total of eight valence electrons available for bonding (4 from carbon and 4 from the four hydrogen atoms).
• For anions, one negative charge would mean addition of one electron. For a cation, one positive charge would result in subtraction of one electron from the total number of valence electrons. For example, for the $CO_3^{2–}$ ion, the two negative charges indicate that two electrons have been added to the neutral atoms. For $NH_4^+$ ion, one positive charge indicates the loss of one electron from the group of neutral atoms.
• Knowing the chemical symbols of the combining atoms and having knowledge of the skeletal structure of the compound (known or guessed intelligently), it is easy to distribute the total number of electrons as bonding shared pairs between the atoms in proportion to the total bonds.
• In general, the least electronegative atom occupies the central position in the molecules or ion. For example, in the $NF_3$ and $CO_3^{ 2–}$, nitrogen and carbon are the central atoms whereas, fluorine and oxygen occupy the terminal positions.
• After accounting for the shared pairs of electrons for single bonds, the remaining electron pairs are either utilized for multiple bonding or remain as the lone pairs. The basic requirement being that, each atom involved in bonding has an octet of electrons.

Lewis representations of a few molecules and ions are given in Table 4.1:

Example 4.1 Write the Lewis dot structure of CO molecule.

Solution:

Step 1. Count the total number of valence electrons of carbon and oxygen atoms. The outer (valence) shell configurations of carbon and oxygen atoms are: $2s^2$ $2p^2$ and $2s^2$ $2p^4$ , respectively. The valence electrons available are 4 + 6 =10.

Step 2. The skeletal structure of CO is written as: C O

Step 3. Draw a single bond (one shared electron pair) between C and O and complete the octet on O, the remaining two electrons are the lone pair on C.

This does not complete the octet on carbon and hence we have to resort to multiple bonding (in this case a triple bond) between C and O atoms. This satisfies the octet rule condition for both atoms.

Example 4.2 Write the Lewis structure of the nitrite ion, $NO_2^-$ .

Solution:

Step 1. Count the total number of valence electrons of the nitrogen atom, the oxygen atoms and the additional one negative charge (equal to one electron).

$$ N(2s^2 2p^3), O (2s^2 2p^4)$$

$$ 5  + ( 2 \times 6)+1 = 18 \space electrons$$

Step 2. The skeletal structure of $NO_2^-$  is written as: O N O

Step 3. Draw a single bond (one shared electron pair) between the nitrogen and each of the oxygen atoms completing the octets on oxygen atoms. This, however, does not complete the octet on nitrogen if the remaining two electrons constitute lone pair on it.

Hence, we have to resort to multiple bonding between nitrogen and one of the oxygen atoms (in this case a double bond). This leads to the following Lewis dot structures.

4.1.4 Formal Charge

Lewis dot structures, in general, do not represent the actual shape of the molecules. In case of polyatomic ions, the net charge is possessed by the ion as a whole and not by a particular atom. However, a formal charge on each atom can be assigned.

Counting of formal charge on an atom is based on the assumption that, the atom in the molecule owns one electron of each shared pair and both the electrons of a lone pair. Let us consider the ozone molecule ($O_3$), the Lewis structure of $O_3$ may be drawn as:

The atoms have been numbered as 1, 2 and 3.

The formal charge on:

• The central O atom marked 1:

Hence, we represent $O_3$ along with the formal charges as follows:

Significance of formal charges:

• Formal charges do not indicate real charge separation within the molecule. Indicating the charges on the atoms in the Lewis structure only helps in keeping track of the valence electrons in the molecule.
• Formal charges help in the selection of the lowest energy structure from a number of possible Lewis structures for a given species. Generally, the lowest energy structure is the one with the smallest formal charge on the atoms.
• The formal charge represents covalent bonding in which, electron pairs are shared equally by bonded atoms.

4.1.5 Limitations of the Octet Rule

The octet rule is not universal. Although, it is quite useful for understanding the structures of most of the organic compounds, it applies mainly to the second period elements of the periodic table.

There are three types of exceptions to the octet rule:

1. The incomplete octet of the central atom:

This rule cannot be applied to those compounds in which the number of electrons surrounding the central atom is less than eight—usually, less than four valence electrons. Examples are: LiCl, $BeH_2$ and $BCl_3$.

2. Odd-electron molecules

The octet rule is not satisfied for all atoms in a molecule having an odd number of electrons. For example, NO and NO₂ do not satisfy the octet rule.

3. The expanded octet

The octet rule cannot be applied to the elements in and beyond the third period of the periodic table. The elements present in these periods have more than eight valence electrons around the central atom. This is termed as the expanded octet. Hence, the octet rule does not apply in such cases.

Some of the examples of such compounds are: $PF_5, SF_6, H_2SO_4$ and a number of coordination compounds.

Other drawbacks of the octet theory:

• Octet rule is based on the chemical inertness of noble gases. However, some noble gases (like, xenon and krypton) also combine with oxygen and fluorine to form a number of compounds like $XeF_2, KrF_2, XeOF_2$.
• This theory does not account for the shape of molecules.
• It does not explain the relative stability of the molecules.

Questions from section 4.1:

1. Explain the term: Octet configuration.

2. Write a note on significance of Lewis’ symbol.

3. List Kossel’s postulates with regard to chemical bonding.

4. State the Octet rule.

5. Explain Lewis’ dot structure by illustrating the formation of chlorine molecule.

6. Explain the formation of single, double and triple covalent bonds.

7. List the properties of covalent compounds.

8. Explain the factors that favour the formation of covalent bond.

9. What are the steps to be followed while writing Lewis’ dot structures?

10. Define: Formal charge. List its significance.

11. Explain the drawbacks of the Octet rule.

4.2 Ionic or Electrovalent Bond

Concept box: 1. The electron gain enthalpy, $Δ_{eg}H$, is the enthalpy change, when an atom (in gas phase) in its ground state, gains an electron while, Electron affinity is the negative of the energy change that occurs during this electron gain process. 2. Ionization is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons to form ions. 3. The electron gain process may be exothermic or endothermic. Ionization, on the other hand, is always endothermic.

An ionic bond is formed by the transfer of one or more electrons from one atom to another.

The formation of ionic bonds thus depends upon:

a) the ease with which neutral atoms can lose or gain electrons and;

b) the lattice energy of the compound formed.

Formation of the ions:

• The formation of a positive ion involves removal of electron(s) from the neutral atom and formation of the negative ion involves the addition of electron(s) to the neutral atom as illustrated:

• Most ionic compounds have cations derived from metallic elements and anions from non-metallic elements. However, the ammonium ion, $NH_4^+$ is an exception. It usually forms a cation of ionic compounds despite being made of non-metallic elements.

Ionic compounds in crystalline state:

• Ionic compounds in the crystalline state consist of three-dimensional arrangement of cations and anions held together by coulombic interaction energies.
• The ionic compounds form different types of crystal structures depending on the size of the ions and their packing arrangement. The crystal structure of sodium chloride, NaCl (rock salt), for example is shown below:

• In these ionic crystal solids, the sum of the electron gain enthalpy and the ionization enthalpy may be positive but still, the crystal structure gets stabilized due to the energy released in the formation of the crystal lattice.
  For example: The ionization enthalpy for $Na^+$(g) formation from Na(g) is 495.8 kJ $mol^{–1}$ ; while the electron gain enthalpy for the change Cl(g) + $e^–→ Cl^–$ (g) is, – 348.7 kJ $mol^{–1}$ only. The sum of the two, 147.1 kJ $mol^{-1}$ is more than the enthalpy of lattice formation of NaCl(s) (which is, –788 kJ $mol^{–1}$).
• Therefore, the energy released in the processes is more than the energy absorbed.
• Thus, a qualitative measure of the stability of an ionic compound is provided by its enthalpy of lattice formation and not simply by achieving octet of electrons around the ionic species in gaseous state.

Favourable factors for ionic bond formation are as follows:

(i) Low ionization enthalpy of metal atom.

(ii) High electron gain enthalpy ($Δ_{eg}H)$ of a non-metal atom.

(iii) High lattice energy of the compound formed.

4.2.1 Lattice Enthalpy

Definition box: The Lattice Enthalpy of an ionic solid is defined as the energy required to completely separate one mole of a solid ionic compound into gaseous constituent ions.

For example, the lattice enthalpy of NaCl is 788 kJ $mol^{–1}$. This means that 788 kJ of energy is required to separate one mole of solid NaCl into one mole of $Na^+$ (g) and one mole of $Cl^–$ (g) to an infinite distance.

This process requires both, the attractive forces between ions of opposite charges and the repulsive forces between ions of like charge.

4.3 Bond Parameters

4.3.1 Bond Length

Definition box: Bond length is defined as the equilibrium distance between the nuclei of two bonded atoms in a molecule.

Note box: Bond lengths are measured by spectroscopic, X-ray diffraction and electron-diffraction techniques.

Some important radii:

1. Covalent radius: The covalent radius is half of the distance between two similar atoms joined by a covalent bond in the same molecule.

2. Ionic radius: It is half the distance between two ions that are barely touching each other in an ionic compound.

3. Vander Waal’s radius: The van der Waals radius is half of the distance between two similar atoms in separate molecules in a solid.

Figure 4.3 Covalent and van der Waals radii in a chlorine molecule .The inner circles correspond to the size of the chlorine atom ($r_{vdw}$ and $r_c$ are van der Waals and covalent radii respectively).

Measuring bond length:

In an ionic compound, the bond length is the sum of the ionic radii of the constituting atoms (d = r₊ + r_­­-).

In a covalent compound, bond length is the sum of their covalent radii (d = $r_A + r_B$).

The values cited are for single bonds, except where otherwise indicated in parenthesis. (See also Unit 3 for periodic trends).

4.3.2 Bond Angle

Definition box: Bond angle is defined as the angle between the orbitals containing bonding electron pairs around the central atom in a molecule or a complex ion.

4.3.3 Bond Enthalpy

Definition box: Bond Enthalpy is defined as the amount of energy required to break one mole of bonds of a particular type between two atoms in a gaseous state.

The unit of bond enthalpy is kJ $mol^{–1}$.

Example box: 1. The H – H bond enthalpy in hydrogen molecule is: 435.8 kJ $mol^{–1}$. $$ H_2(g) → H(g) + H(g); \Delta_a H^{\ominus}= 435.8 \space kJ \space mol^{–1} $$ (refer page 114, ncert) 2. Similarly, the bond enthalpy for molecules containing multiple bonds like in, $O_2$ and $N_2$ will be: $$ O_2 (O = O) (g) → O(g) + O(g);\Delta_aH^{\ominus}= 498 \space kJ \space mol^{–1} $$ $$ N_2 (N ≡ N) (g) → N(g) + N(g);\Delta_aH^{\ominus}= 946.0 \space kJ \space mol^{–1}$$ 3. For a heteronuclear-diatomic-molecules like HCl, $$ HCl (g) → H(g) + Cl (g); \Delta_aH^{\ominus} = 431.0 \space kJ \space mol^{–1} $$ 4. For polyatomic molecules, the measurement of bond strength is more complicated. For example, in case of $H_2O$ molecule, the enthalpy needed to break the two O – H bonds is not the same. $$ H_2O(g) → H(g) + OH(g); \Delta_aH_1^{\ominus}= 502 \space kJ \space mol^{–1} $$ $$ OH(g) → H(g) + O(g); \Delta_aH_2^{\ominus} = 427 \space kJ \space mol^{–1}$$ The difference in the $ \Delta_a H^{\ominus}$ value shows that, the second O – H bond undergoes further change because of changed chemical environment. For the same reason, there is some difference in energy of the same O – H bond in different molecules like $C_2H_5OH$ (ethanol) and water. Therefore, in polyatomic molecules, the term, “mean” or “average bond enthalpy” is used.

Average bond enthalpy is obtained by dividing total bond dissociation enthalpy by the number of bonds broken. For example, in case of water molecule,

$$ Average \space bond \space enthalpy = \frac {502+427}{2}$$

$$=464.5 \space kJ \space mol^{-1}$$

Factors favouring bond enthalpy:

• Greater the size of the atom, lesser is the bond enthalpy.
• Bond enthalpy increases with increase in the bond order.
• Bond enthalpy decreases with increase in number of lone pair of electrons in the molecule.

4.3.4 Bond Order

Definition box: The Bond Order is given by the number of bonds between the two atoms in a molecule.

Example box: The bond order, in $H_2$ (with a single shared electron pair), in $O_2$ (with two shared electron pairs) and in $N_2$ (with three shared electron pairs) is 1,2,3 respectively. Similarly, in CO (three shared electron pairs between C and O) the bond order is 3. For $N_2$, bond order is 3 and its  $ \Delta_a H^{\ominus}$ is 946 kJ $mol^{–1}$; being one of the highest for a diatomic molecule.

Note box: 1. With increase in bond order, bond enthalpy increases and bond length decreases. 2. Isoelectronic molecules and ions have identical bond orders; for example, $F_2$ and $O_2^{2–}$ have bond order: 1 and; $N_2$, CO and $NO^+$ have bond order: 3.

4.3.5 Resonance Structures

It is often observed that a single Lewis structure cannot explain all properties of a molecule. The molecule will then be expressed as many structures, each of which can explain most of the properties, but none can explain all the properties.

Canonical structures: The different individual structures with similar energy, positions of nuclei, bonding and non-bonding pairs of electrons are taken known as the canonical structures of the hybrid which describes the molecule accurately.

Resonance hybrid: The actual structure in between all these contributing structures is called, Resonance hybrid.

Resonance: When a molecule can be expressed in various canonical forms, it is said to exhibit resonance.

Example 4.3: Explain the structure of $CO_3 ^{2–}$ ion in terms of resonance.

Solution:

The single Lewis structure based on the presence of two single bonds and one double bond between carbon and oxygen atoms is inadequate to represent the molecule accurately as it represents unequal bonds. According to the experimental findings, all carbon to oxygen bonds in CO3 2– are equivalent. Therefore the carbonate ion is best described as a resonance hybrid of the canonical forms I, II, and III shown below

Example 4.4: Explain the structure of CO2 molecule.

Solution:

The experimentally determined carbon to oxygen bond length in CO2 is 115 pm. The lengths of a normal carbon to oxygen double bond (C=O) and carbon to oxygen triple bond (C≡O) are 121 pm and 110 pm respectively. The carbon-oxygen bond lengths in CO2 (115 pm) lie between the values for C=O and C≡O. Obviously, a single Lewis structure cannot depict this position and it becomes necessary to write more than one Lewis structures and to consider that the structure of CO2 is best described as a hybrid of the canonical or resonance forms I, II and III.

Note box: Resonance stabilizes the molecule as the energy of the resonance hybrid is less than the energy of any single canonical structure. Resonance averages the bond characteristics as a whole. Concept of resonance is useful in explaining the behaviour of unsaturated compounds.

Many misconceptions are associated with resonance hybrid. The actual facts are:

• Resonance structures are arbitrary and imaginary.
• The molecule does not exist for a certain fraction of time in one cannonical form and for other fractions of time in other canonical forms.
• There is no such equilibrium between the cannonical forms as there is in, tautomeric forms (keto and enol) in tautomerism.
• The molecule has a single structure which is the resonance hybrid. The cannonical forms are those structures which cannot as such be depicted by a single Lewis structure.

4.3.6 Polarity of Bonds

Non-polar bond: When a covalent bond is formed between two similar atoms, the shared pair of electrons is equally attracted by the two atoms and the bond is said to be non-polar.

For example, in $H_2, O_2, Cl_2, N_2 or F_2$, the bond between two H-atoms or two Cl-atoms or two N-atoms is non-polar.

Note box: The electron pair is situated exactly between the two identical nuclei in non-polar type of bond.

Polar covalent bond:

When a covalent bond is formed between dissimilar atoms, X-Y (with difference in their electronegativities), the bond pair will be pulled closer to the atoms with higher electronegativity (say, Y). As a result, Y will acquire a partial negative charge $(δ^+)$ and the other atom X will acquire a partial positive charge $(δ^+)$.

For example, in case of a heteronuclear molecule like HF, the shared electron pair between the two atoms gets displaced more towards fluorine since the electronegativity of fluorine is far greater than that of hydrogen. This results in a polar covalent bond.

Dipole moment:

Definition box: Dipole: Molecules of the type X-Y having two polar ends with partial positive and negative charges are called, dipoles. Dipole moment: Dipole moment is defined as the product of the magnitude of the charge and the distance between the centres of positive and negative charge. It is usually designated by a Greek letter ‘μ’. Mathematically, it is expressed as follows: Dipole moment (μ) = charge (Q) × distance of separation (r)

• Dipole moment is usually expressed in Debye units (D). The conversion factor is:
  1 D = 3.33564 × $10^{–30}$ C m
  Where, C is coulomb and m is meter.
• Dipole moment is a vector quantity.
• Dipole moment is represented by the crossed arrow:

Lewis structure of the molecule. The cross is on positive end and arrow head is on negative end. This arrow symbolises the direction of the shift of electron density in the molecule.

Note box:   The direction of crossed arrow is opposite to the conventional direction of dipole moment vector.

Illustrations of dipole moments exhibited by various species:

• The dipole moment of HF may be represented as:

In case of polyatomic molecules, the dipole moment not only depends upon the individual dipole moments of bonds known as bond dipoles but also on the spatial arrangement of various bonds in the molecule. In such a case, the dipole moment of a molecule is the vector sum of the dipole moments of various bonds. For example, in $H_2O$ molecule, which has a bent structure, the two O–H bonds are oriented at an angle of $104.5^0$. Net dipole moment of 6.17 × $10^{–30}$ C m (1D = 3.33564 × $10^{–30}$ C m) is the resultant of the dipole moments of two O–H bonds.

Net Dipole moment, $\mu = 1.85 \, D$

$$ = 1.85 \times 3.33564 \times 10^{-30} \space C \space m = 6.17 \times 10^{-30} \space C \space m $$

• The dipole moment in case of $BeF_2$ is zero. This is because the two equal bond dipoles point in opposite directions and cancel the effect of each other.

• In tetra-atomic molecule, for example in $BF_3$, the dipole moment is zero although the B – F bonds are oriented at an angle of 120^o to one another, the three bond moments give a net sum of zero as the resultant of any two is equal and opposite to the third.

• In case of $NH_3$ and $NF_3$ molecules, both the molecules have pyramidal shape with a lone pair of electrons on nitrogen atom. Although fluorine is more electronegative than nitrogen, the resultant dipole moment of $NH_3$ (4.90 × $10^{–30}$ C m) is greater than that of $NF_3$ (0.8 × $10^{–30}$ C m). This is because in case of $NH_3$, the orbital dipole due to lone pair is in the same direction as the resultant dipole moment of the N – H bonds, whereas in $NF_3$ the orbital dipole is in the direction opposite to the resultant dipole moment of the three N–F bonds. The orbital dipole because of lone pair decreases the effect of the resultant N – F bond moments, which results in the low dipole moment of $NF_3$ as represented below:

Story box: Peter Debye, the Dutch chemist received Nobel Prize for his work on X-ray diffraction and dipole moments. The magnitude of the dipole moment is given in Debye units in order to honour him.

Dipole moments of some molecules are shown in Table 4.5.

Applications of dipole moment:

• Measurement of dipole moment is helpful in predicting the geometry of the molecule as indicated in the following examples:

a) Zero dipole moment of $CO_2$ indicates linear structure.

b) Zero dipole moment for $BF_3, C_6H_6 $and $CH_4$ represents their symmetric structure.

c) Finite values of dipole moments for $H_2O$ and $SO_2$ rule out the possibility of linear structure.

• Further, it is helpful in predicting the ionic character of a molecule.
• It also helps in distinguishing between polar and non-polar molecules.

Just as all the covalent bonds have some partial ionic character, the ionic bonds also have partial covalent character. The partial covalent character of ionic bonds was discussed by Fajans in terms of the following rules:

• The smaller the size of the cation and the larger the size of the anion, the greater the covalent character of an ionic bond.
• The greater the charge on the cation, the greater the covalent character of the ionic bond.
• For cations of the same size and charge, the one, with electronic configuration (n-1) dⁿ ns^o (typical of transition metals), is more polarising than the one with a noble gas configuration, $ns^2 np^6$ (typical of alkali and alkaline earth metal cations).

The cation polarises the anion by pulling the electronic charge toward itself and thereby increasing the electronic charge between the two.

This is precisely what happens in a covalent bond, that is, buildup of electron charge density between the nuclei. The polarising power of the cation, the polarisability of the anion and the extent of distortion (that is, polarisation) of anion are the factors, which determine the per cent covalent character of the ionic bond.

Questions from sections 4.2 and 4.3:

1. When is an ionic bond established?

2. What are the factors that affect the ionic bond formation?

3. Explain briefly, the formation of a positive ion and a negative ion.

4. Explain the factors that favour ionic bond formation.

5. Define the term, Lattice enthalpy. Explain with an example.

6. Define bond length. How is it measured?

7. Define:

a) Bond angle

b) Bond enthalpy

8. Describe:

a) Canonical structures

b) Resonance hybrid

c) Resonance

9. What is a non-polar bond?

10. Define:

a) Dipole

b) Dipole moment

11. List the applications of dipole moment.

12. List Fajan’s rules explaining the partial covalent character of the ionic bonds.

4.4 The Valence Shell Electron Pair Repulsion (VSEPR) Theory

Since Lewis-Langmuir concept was unable to explain the geometry of molecules, Sidgwick and Powell proposed a simple theory based on the repulsive interactions of the electron pairs in the valence shell of the atoms called, Valence Shell Electron Pair Repulsion Theory. The main postulates of VSEPR theory are as follows:

• The central atom in polyatomic molecules is surrounded by two types of electron pairs:

a) Bonding pair b_p (shared pair)

b) Lone pair l_p (non-bonding or unshared pair)

• Pairs of electrons in the valence shell repel one another since their electron clouds are negatively charged.
• These pairs of electrons tend to occupy such positions in space that minimise repulsion and thus maximise distance between them.
• The valence shell is considered as a sphere with the electron pairs situated on the spherical surface at maximum distance from one another.
• A multiple bond is considered as if it is a single electron pair by treating the sharing of two or three electron pairs of the multiple bond as single super pair.
• The VSEPR model is applicable even where two or more resonance structures represent a molecule. The repulsive interaction of electron pairs decrease in the order:

Lone  pair (lp) – Lone pair (lp) > Lone pair (lp) – Bond pair (bp) > Bond pair (bp) – Bond pair (bp)

Nyholm and Gillespie refined the VSEPR model by explaining the important difference between the lone pairs and bonding pairs of electrons as follows:

• While the lone pairs are localised on the central atom, each bonded pair is shared between two atoms. As a result, the lone pair electrons in a molecule occupy more space as compared to the bonding pairs of electrons. This results in greater repulsion between lone pairs of electrons as compared to the “lone pair – bond pair” and “bond pair – bond pair” repulsions. These repulsion effects result in deviations from idealised shapes thus altering bond angles in molecules.
• For the prediction of geometrical shapes of molecules with the help of VSEPR theory, it is convenient to divide molecules into two categories as:

(i) molecules in which the central atom has no lone pair and

(ii) molecules in which the central atom has one or more lone pairs.

Merits of the VSEPR theory:

• The VSEPR Theory is able to predict geometry of a large number of molecules, especially the compounds of p-block elements accurately.
• It is also quite successful in determining the geometry quite-accurately even when the energy difference between possible structures is very small.

Limitation:

The theoretical basis of the VSEPR theory regarding the effects of electron pair repulsions on molecular shapes is not very clear.

Table 4.6 shows the arrangement of electron pairs about a central atom A (without any lone pairs) and geometries of some molecules and ions of the type AB. Table 4.7 shows shapes of some simple molecules and ions in which the central atom has one or more lone pairs. Table 4.8 (page 112) explains the reasons for the distortions in the geometry of the molecule.

As depicted in Table 4.6, in the compounds of AB₂, AB₃, AB₄, AB₅ and AB₆, the arrangement of electron pairs and the B atoms around the central atom A are: linear, trigonal planar, tetrahedral, trigonal-bipyramidal and octahedral, respectively. Such arrangement can be seen in the molecules like BF₃ (AB₃), CH₄ (AB₄) and PCl₅ (AB₅) as depicted below by their ball and stick models.

Questions from section 4.4:

1. State the postulates of VSEPR theory. List its merits and demerits.

4.5 Valence Bond Theory

Valence bond theory was introduced by Heitler, London and developed further by Pauling. According to valence bond theory,

• A covalent bond forms between the two atoms by the overlap of half-filled valence atomic orbitals of each atom, each containing one unpaired electron.
• The new orbital formed due to the overlapping of the two orbitals is called, a bond orbital which will be common to both atoms.
• The strength of bond depends upon the extent of overlapping of the atomic orbitals. Greater the degree of overlap, stronger will be the bond.
• The two electrons involved in bond formation must have opposite spins.
• Covalent bond is directional in nature and lies in the direction of maximum overlap of atomic orbitals.

Formation of Hydrogen molecule:

Consider two hydrogen atoms A and B approaching each other having nuclei: $N__A$ and $N__B$ and electrons: $e__A$ and $e__B$. When the two atoms are at large distance from each other, there is no interaction between them. As these two atoms approach each other, new attractive and repulsive forces begin to operate.

Attractive forces arise between,

(i) nucleus of one atom and its own electron that is $N__A – e__A$ and $N__B– e__B$.

(ii) nucleus of one atom and electron of other atom i.e., $N__A– e__B, N__B– e__A$.

Similarly, repulsive forces arise between:

(i) electrons of two atoms like $e__A – e__B$,

(ii) nuclei of two atoms $N__A – N__B$.

• Attractive forces tend to bring the two atoms close to each other whereas, repulsive forces tend to push them apart (Figure 4.6).

• Experimentally, it has been found that, the magnitude of new attractive force is more than the new repulsive forces. As a result, two atoms approach each other and potential energy decreases. Ultimately a stage is reached where the net force of attraction balances the force of repulsion and system acquires minimum energy. At this stage, two hydrogen atoms are said to be bonded together to form a stable molecule having the bond length of 74 pm.
• Since the energy gets released when the bond is formed between two hydrogen atoms, the hydrogen molecule is more stable than that of isolated hydrogen atoms. The energy so released is called as bond enthalpy, which is corresponding to minimum in the curve depicted in Figure 4.7.

Figure 4.7 The potential energy curve for the formation of $H_2$. molecule as a function of inter-nuclear distance of the H atoms. The minimum in the curve corresponds to the most stable state of $H_2$.

• Conversely, 435.8 kJ of energy is required to dissociate one mole of $H_2$ molecule.
  $$ H_2(g) + 435.8 \space kJ \space  mol^{–1} → H(g) + H(g) $$

4.5.1 Orbital Overlap Concept

In the formation of hydrogen molecule, there is a minimum energy state when two hydrogen atoms are so near that their atomic orbitals undergo partial interpenetration.

This type of partial merging of atomic orbitals is called overlapping of atomic orbitals which results in the pairing of electrons.

4.5.2 Directional Properties of Bonds

The valence bond theory explains the shape, the formation and directional properties of bonds in polyatomic molecules like $CH_4, NH_3$ and $H_2O$ in terms of overlap and hybridisation of atomic orbitals.

4.5.3 Overlapping of Atomic Orbitals

Rules for overlap:

• When orbitals of two atoms come close to form a bond, their overlap may be positive, negative or zero depending upon the sign (phase) and direction of orientation of amplitude of orbital wave function in space (Figure 4.8).

• Positive and negative sign on boundary surface diagrams (as shown in the Figure 4.8) represent the sign (phase) of orbital wave function and are not related to charge.
• Orbitals forming bond should have same sign (phase) and orientation in space. This is called positive overlap. Various overlaps of s and p orbitals are depicted in Figure 4.8.
• The criteria of overlap, remains same for formation of covalent bonds in homonuclear and heteronuclear; diatomic and polyatomic molecules.

Note box Similarly, it can be seen that, in the case of $NH_3$ and $H_2O$ molecules, the HNH and HOH angles should be 90°. This is in disagreement with the actual bond angles of 107° and 104.5° in the NH3 and H2O molecules respectively.

4.5.4 Types of Overlapping and Nature of Covalent Bonds

The covalent bond may be classified into two types depending upon the type of overlapping: (i) Sigma (σ) bond and; (ii) pi (π) bond

(a) Sigma(σ) bond:

This type of covalent bond is formed by the end to end (head-on) overlap of bonding orbitals along the inter-nuclear axis. This is called as head on overlap or axial overlap.

This can be formed by any one of the following types of combinations of atomic orbitals:

1. s-s overlapping: In this case, there is overlap of two half-filled s-orbitals along the inter-nuclear axis as shown below,

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

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

(b) Pi (π) bond: In the formation of π bond, the atomic orbitals overlap in such a way that, their axes remain parallel to each other and perpendicular to the inter-nuclear axis. The orbitals formed due to sideways overlapping show two saucer type charged clouds above and below the plane of the participating atoms.

4.5.5 Differences between σ and π bonds

	Bonding molecular orbitals	Anti-bonding molecular orbitals
1	These are formed by the addition of wave functions of atomic orbitals (symmetric combination).	These are formed by the subtraction of wave functions of atomic orbitals (asymmetric combination).
2	Energy of bonding molecular orbitals is less than corresponding atomic orbitals.	Energy of anti-bonding molecular orbitals is more than the corresponding atomic orbitals.
3	Electrons in the bonding molecular orbitals increase force of attraction between the atoms and contribute to bond formation.	Electrons in the anti-bonding molecular orbitals contribute to decrease the force of attraction between the atoms and do not contribute to bond formation.
4	They are represented as σ, π.	They are represented as σ* and π*.

Questions from section 4.5:

1. Explain valence bond theory.

2. What does overlapping of atomic orbitals mean?

3. State the rules for orbital overlap.

4. Explain “positive overlap”.

5. Explain the formation of sigma bonds and pi bonds. Explain the types of sigma bonds formed.

6. State the differences between sigma bond and pi bond.

7. Define hybridization and explain its salient features.

8. What are the conditions for hybridization to occur?

4.6 Hybridisation

In order to explain the characteristic geometrical shapes of polyatomic molecules like CH₄, NH₃ and H₂O, Pauling introduced the concept of hybridisation according to which, the atomic orbitals combine to form new set of equivalent orbitals known as hybrid orbitals. Unlike pure orbitals, the hybrid orbitals are involved in bond formation.

Definition box: Hybridisation: The phenomenon of hybridisation can be defined as 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:

1. The number of hybrid orbitals is equal to the number of the atomic orbitals that are involved in hybridisation.

2. All the hybridised orbitals so formed are always equivalent in energy and shape.

3. The hybrid orbitals are more effective in forming stable bonds than the pure atomic orbitals.

4. These hybrid orbitals are oriented in space such that, there is minimum repulsion between electron pairs and thus, a stable arrangement.

5. Therefore, the type of hybridisation indicates the geometry of the molecules.

Important conditions for hybridisation:

(i) The orbitals present in the valence shell of the atom undergo hybridisation.

(ii) The orbitals undergoing hybridisation should have almost equal energy.

(iii) Excitation of electron is not an essential condition prior to hybridisation.

(iv) It is not only the half-filled orbitals that participate in hybridisation; even filled orbitals of valence shell may take part in hybridisation.

4.6.1 Types of Hybridisation

There are various types of hybridisation involving s, p and d orbitals. The different types of hybridisation are as under:

(1) sp hybridisation:

• This type of hybridisation involves the mixing of one s and one p orbital resulting in the formation of two equivalent sp hybrid orbitals. The suitable orbitals for sp hybridisation are s and p_z, if the hybrid orbitals are to lie along the z-axis.
• Each sp hybrid orbitals have 50% s-character and 50% p-character.
• Such a molecule in which the central atom is sp-hybridised and linked directly to two other central atoms possesses linear geometry (In other words, they are oriented linearly along one direction). This type of hybridisation is also known as diagonal hybridisation.
• The two sp hybrids so formed point in the opposite direction along the z-axis with projecting positive lobes and very small negative lobes. This type of orientation thus provides more effective overlapping, resulting in the formation of stronger bonds.

Example of molecule having sp hybridisation:

$BeCl_2$:

• The ground state electronic configuration of Be is: $1s^22s^2$.
• In the excited state, one of the 2s-electrons is promoted to vacant 2p orbital.
• One 2s and one 2p-orbital get hybridised to form two sp hybridised orbitals.
• These two sp hybrid orbitals are oriented in opposite direction forming an angle of 180°.
• Further, each of the sp hybridised orbital overlaps with the 2p-orbital of chlorine axially and form two Be-Cl sigma bonds (as shown in Figure 4.10 below).

(2) $sp^2$ hybridisation:

This type of hybridisation takes place between one s and two p-orbitals in order to form three equivalent sp² hybridised orbitals.

Example of molecule having $sp^2$ hybridisation:

• In $BCl_3$ molecule, the ground state electronic configuration of central boron atom is $1s^22s^22p^1$. In the excited state, one of the 2s electrons is promoted to vacant 2p orbital. As a result, boron has three unpaired electrons.
• These three orbitals (one 2s and two 2p) of Boron hybridise to form three sp² hybrid orbitals.
• The three hybrid orbitals so formed are oriented in a trigonal planar arrangement and overlap with 2p orbitals of chlorine to form three B-Cl bonds.
• Therefore, in $BCl_3$ (Figure 4.11), the geometry is trigonal planar with Cl-BCl bond angle of 120°.

(3) $sp^3$ hybridisation:

• Mixing of one s-orbital and three p-orbitals of an atom to form four identical $sp^3$ hybridised orbitals is called, $sp^3$ hybridisation.
• There is 25% s-character and 75% p-character in each $sp^3$ hybrid orbital.

Example of molecule having $sp^3$hybridisation:

$CH_4$molecule:

• In $CH_4$molecule, there is mixing of one s-orbital and three p-orbitals of the valence shell to form four $sp^3$  hybrid orbital of equivalent energies and shape.
• The four $sp^3$ hybrid orbitals so formed are directed towards the four corners of the tetrahedron. The angle between $sp^3$  hybrid orbitals is $109.5^°$ as shown in Figure 4.12.

Structure of $NH_3$:

• The nitrogen molecule in ammonia is $sp^3$ hybridised. The expected shape would thus be, a tetrahedral (in the absence of other considerations).
• However, there is one lone pair of electrons on nitrogen atom.
• Therefore, the two types of valence shell electron pair repulsions will exist.
• Among them, “lone pair – bond pair” repulsion will be stronger than “bond pair – bond pair” repulsion because of which, the bond angle is reduced to $107^0$ from expected tetrahedral angle value of $109.5^0$.

Structure of $H_2O$:

• The oxygen atom in a molecule of water is $sp^3$ hybridised.
• The shape should have been a tetrahedral in the absence of other considerations. However, there is one lone pair of electrons on the oxygen atom.
• Therefore, all three types of valence shell electron pair repulsions will exist.
• Among them, “lone pair – lone pair” repulsion will be stronger than, “lone pair – bond pair” repulsion which is in turn stronger than, “bond pair – bond pair” repulsion.
• Due to this, the bond angle is reduced to $104.5^0$from expected tetrahedral angle value of $109.5^0$.

4.6.2 Other Examples of $sp^3, sp^2$ and sp hybridisation

$sp^3$ Hybridisation in $C_2H_6$ molecule:

• In ethane molecule, both the carbon atoms assume $sp^3$ hybrid state.
• One of the four $sp^3$ hybrid orbitals of carbon atom overlaps axially with similar orbitals of other atom to form $sp^3 – sp^3$ sigma bond while the other three hybrid orbitals of each carbon atom are used in forming $sp^3 – s$ sigma bonds with hydrogen atoms.
• Therefore, in ethane C – C bond length is 154 pm and each C – H bond length is 109 pm.

$sp^2$ Hybridisation in $C_2H_4$:

• An electron is promoted from the 2s to the empty 2p to give 4 unpaired electrons. The carbon atom is now said to be in an excited state.

• When the carbon atoms hybridise their outer orbitals before forming bonds, in case of ethene, only hybridise three of the orbitals rather than all four. They use the 2s electron and two of the 2p electrons, but leave the other 2p electron unchanged.
• The new orbitals formed are thus, $sp^2$ hybrids, because they are made by an s orbital and two p orbitals reorganising themselves. One of the $sp^2$ hybrid orbitals of carbon atom overlaps axially with $sp^2$ hybrid orbital of another carbon atom to form C – C sigma bond while the other two $sp^2$ hybrid orbitals of carbon atoms are used for making $sp^2 – s$ sigma bonds with two hydrogen atoms. The unhybridised orbital ($2p_x$ or $2p_y$) of one carbon atom overlaps sidewise with the similar orbital of the other carbon atom to form a weak $\pi$ bond, which consists of two equal electron clouds distributed above and below the plane of carbon and hydrogen atoms.
• The three $sp^2$ hybrid orbitals arrange themselves as far apart as possible – which is at $121^o$ to each other in a plane. The remaining p orbital is at right angles to them.
• Thus, in ethene molecule, the carbon-carbon bond consists of one $sp^2 – sp2$ sigma bond and one pi (π) bond between p orbitals which are not used in the hybridisation and are perpendicular to the plane of molecule; with bond length, 134 pm. The C–H bond is $sp^2 – s$ sigma with bond length, 108 pm. The H–C–H bond angle is $117.6^o$ while the H–C–C angle is $121^o$. The formation of sigma and pi bonds in ethene is shown in Figure 4.15.

sp Hybridisation in $C_2H_2$:

• In the formation of ethyne molecule, both the carbon atoms undergo sp-hybridisation having two unhybridised orbitals, $2p_y$ and $2p_x$.
• One sp hybrid orbital of one carbon atom overlaps axially with sp hybrid orbital of the other carbon atom to form C–C sigma bond, while the other hybridised orbital of each carbon atom overlaps axially with the half-filled s orbital of hydrogen atoms forming σ bonds.
• Each of the two unhybridised p orbitals of both the carbon atoms overlaps sidewise to form two π bonds between the carbon atoms.
• So the triple bond between the two carbon atoms is made up of one sigma and two pi bonds as shown in Figure 4.16.

4.6.3 Hybridisation of Elements involving d-Orbitals

• The elements present in the third period contain d orbitals in addition to s and p orbitals.
• The energy of the 3d orbitals are comparable to the energy of the 3s and 3p orbitals.
• The energy of 3d orbitals are also comparable to those of 4s and 4p orbitals.
• As a consequence, the hybridisation involving either “3s, 3p and 3d” or “3d, 4s and 4p” is possible.
• However, since the difference in energies of 3p and 4s orbitals is significant, hybridisation involving 3p, 3d and 4s orbitals is not possible.

The important hybridisation schemes involving s, p and d orbitals are summarised below:

(i) Formation of $PCl_5$ ($sp^3d$ hybridisation):

• The ground state and the excited state outer electronic configurations of phosphorus (Z = 15) are represented below.

$sp^3d$ hybrid orbitals filled by electron pairs donated by five Cl atoms.

• Now, the five orbitals (one-s, three-p and one-d orbitals) are available for hybridisation to yield five $sp^3d$ hybrid orbitals which are directed towards the five corners of a trigonal bipyramidal as depicted in the Figure 4.17.

• In $PCl_5$, the five $sp^3d$ orbitals of phosphorus overlap with the singly occupied p orbitals of chlorine atoms to form five P–Cl sigma bonds. Three P–Cl bonds lie in one plane and make an angle of $120^o$ with each other; these bonds are termed as equatorial bonds. The remaining two P–Cl bonds–one lying above and the other lying below the equatorial plane, make an angle of $90^o$ with the plane. These bonds are called axial bonds.
• As the axial bond pairs suffers more repulsive interaction from the equatorial bond pairs, axial bonds have been found to be slightly longer and hence slightly weaker than the equatorial bonds; thus making $PCl_5$ molecule more reactive.

(ii) Formation of $SF_6$ ($sp^3d^2$ hybridisation):

• In $SF_6$, the central sulphur atom has the ground state outer electronic configuration: $3s^23p^4$.
• In the exited state, the available six orbitals, one s, three p and two d are singly occupied by electrons as shown:

• These orbitals hybridise to form six new $sp^³d^^2$ hybrid orbitals, which are projected towards the six corners of a regular octahedron in $SF_6$.
• These six $sp^3d^2$ hybrid orbitals overlap with singly occupied orbitals of fluorine atoms to form six S–F sigma bonds.
• Thus, $SF_6$ molecule has a regular octahedral geometry as shown in Figure 4.18.

Note box: All the bond angles in trigonal bipyramidal geometry are not equivalent.

Questions from section 4.6:

1. Explain $sp$ hybridization with an example.

2. Explain $sp^2$hybridization with an example.

3. Explain $sp^3$hybridization with an example.

4. Explain the formation of $PCl_5$by $sp^3d$ hybridisation.

5. Explain the formation of $SF_6$ by $sp^3d^2$ hybridisation.

4.7 Molecular Orbital Theory

Molecular orbital (MO) theory was developed by F. Hund and R.S. Mulliken in 1932.

The salient features of this theory are:

(i) Electrons in molecular orbitals: The electrons in a molecule are present in the various molecular orbitals, just as the electrons of atoms are present in the various atomic orbitals.

(ii) Formation of molecular orbitals: The atomic orbitals of comparable energies and proper symmetry combine to form molecular orbitals.

(iii) Polycentric nature: While an electron in an atomic orbital is influenced by one nucleus, in a molecular orbital, an electron is influenced by two or more nuclei depending upon the number of atoms in the molecule. Such a molecular orbital is said to be polycentric while, an atomic orbital is considered, monocentric.

(iv) Number of molecular orbitals: The number of molecular orbitals formed is equal to the number of combining atomic orbitals. For instance, when two atomic orbitals combine, two molecular orbitals are formed. One is known as bonding molecular orbital while the other is called, anti-bonding molecular orbital.

(v) Energy: The bonding molecular orbital has lower energy and hence greater stability than the corresponding anti-bonding molecular orbital.

(vi) Electron Probability Distribution: Just as the electron probability distribution around a nucleus in an atom is given by an atomic orbital, the electron probability distribution around a group of nuclei in a molecule is given by a molecular orbital.

(vii) Filling up of electrons: The molecular orbitals like atomic orbitals are filled in accordance with the aufbau principle. They also obey the Pauli’s exclusion principle and the Hund’s rule.

Atomic orbitals	Molecular orbitals
Atomic orbitals are monocentric	Molecular orbitals are polycentric
They are less stable	They are more stable
Shapes of atomic orbitals are simple	Shapes of molecular orbitals are complex
Different atomic orbitals are represented as s, p, d and f orbitals	Different molecular orbitals are designated as: (i) Sigma bonding and antibonding molecular orbitals are represented as σ and σ* respectively (ii) Pi bonding and antibonding molecular orbitals are represented as π and π* respectively

4.7.1 Formation of Molecular Orbitals: Linear Combination of Atomic Orbitals (LCAO)

• The amplitude of the electron waves is represented by wave function (ψ) obtained from Schrödinger wave equation. However, it cannot be solved for any system containing more than one electron as is the case for molecular orbitals. To overcome this problem, an approximate method known as linear combination of atomic orbitals (LCAO) has been adopted.
• Molecular orbitals are formed by linear combination of atomic orbitals in two ways:

a) Symmetric combination: Molecular orbital formed by addition of wave function of atomic orbitals is called, Symmetric combination.

b)  Asymmetric combination: Molecular orbital formed by subtraction of wave function of atomic orbitals is called, Symmetric combination.

• Mathematically, the formation of molecular orbitals by the linear combination of atomic orbitals (ψA and ψB) is represented as:

$$ ψ_{MO} = ψ_A \pm ψ_B $$

Therefore, the two molecular orbitals σ and σ* are formed as :

$$ σ = ψ_A + ψ_B$$

$$ σ* = ψ_A – ψ_B$$

• The molecular orbital, “σ” formed by the addition of atomic orbitals is called the bonding molecular orbital while, the molecular orbital, σ*formed by the subtraction of atomic orbital is called antibonding molecular orbital as depicted in Figure 4.19.

Fig.4.19 Formation of bonding (σ) and antibonding (σ*) molecular orbitals by the linear combination of atomic orbitals $ψ_A$ and $ψ_B$ centered on two atoms A and B respectively.

Note box: Addition of atomic orbitals refers to constructive interference of electron waves (or) two electron waves in-phase (or) superimposable. Addition of atomic orbitals increases the attractive force between the combining atoms and subtraction of atomic orbitals decreases the attractive force between the combining atoms.

	Bonding molecular orbitals	Anti-bonding molecular orbitals
1	These are formed by the addition of wave functions of atomic orbitals (symmetric combination).	These are formed by the subtraction of wave functions of atomic orbitals (asymmetric combination).
2	Energy of bonding molecular orbitals is less than corresponding atomic orbitals.	Energy of anti-bonding molecular orbitals is more than the corresponding atomic orbitals.
3	Electrons in the bonding molecular orbitals increase force of attraction between the atoms and contribute to bond formation.	Electrons in the anti-bonding molecular orbitals contribute to decrease the force of attraction between the atoms and do not contribute to bond formation.
4	They are represented as σ, π.	They are represented as σ* and π*.

4.7.2 Conditions for formation of molecular orbitals:

• Combining orbitals must have same energy.
• Combining orbitals must have same symmetry about the molecular axis.
• Atomic orbitals must overlap to the maximum extent.

4.7.3 Types of molecular orbitals:

σ – Molecular Orbitals: Molecular orbitals formed by head-on overlap of atomic orbitals are called, σ – molecular orbitals. Addition of wave functions of atomic orbitals along the molecular axis result in sigma bonding molecular orbitals (σ) whereas, molecular orbitals formed by the subtraction of wave functions of atomic orbitals along the molecular form sigma anti-bonding molecular orbitals (σ*). 

π – Molecular Orbitals: Molecular orbitals formed by the lateral overlap of atomic orbitals are pi (π) molecular orbitals. Addition of wave functions of atomic orbitals laterally, results in pi bonding molecular orbitals. Subtraction of wave functions of atomic orbitals laterally, results in pi anti-bonding molecular orbitals.

	σ – Molecular orbital	π – Molecular orbital
1	These are formed by the overlap of atomic orbitals along the internuclear axis	These are formed by the lateral overlap of atomic orbitals
2	Overlapping of atomic orbitals is maximum	Overlapping of atomic orbitals is partial

4.7.4 Energy level diagram of molecular orbitals

The order of increasing energy of various bonding and anti-bonding molecular orbitals formed by 1s, 2s and 2p atomic orbitals of homonuclear diatomic molecules of elements of second period is as shown in the energy level diagram:

• The increasing order of energies of various molecular orbitals for $O_2$ and $F_2$ is given below:
  $$\sigma_{1s} < \sigma_{1s}^* < \sigma_{2s} < \sigma_{2s}^* < \sigma_{2p_z} < \left[ \pi_{2p_x} = \pi_{2p_y} \right] < \left[ \pi_{2p_x}^* = \pi_{2p_y}^* \right] < \sigma_{2p_z}^*$$ 
• The increasing order of energies of various molecular orbitals for H₂, He₂, Li₂, Be₂, B₂, C₂ and N₂ is given below:
  $$\sigma_{1s} < \sigma_{1s}^* < \sigma_{2s} < \sigma_{2s}^* < \left[ \pi_{2p_x} = \pi_{2p_y} \right] < \sigma_{2p_z} < \left[ \pi_{2p_x}^* = \pi_{2p_y}^* \right] < \sigma_{2p_z}^*$$

Note box: In case of homonuclear diatomic molecules like, N2, B2, the energy of σ2pz, molecular orbital is higher than that of π2px and π2py molecular orbitals. This is due to the small difference between 2s and σpz orbitals which results in greater repulsive force between electrons of σ*2s and σ2pz orbitals. In case of O2 and F2, the energy difference between σ*2s and σ2pz orbitals is large and the interaction between them is thus least. Hence, energy of 2pz orbitals is less than that of π 2px and π2py orbitals.

4.7.5 Electronic Configuration and Molecular Behaviour

Definition box: Electronic configuration of a molecule: The distribution of electrons among various molecular orbitals is called the electronic configuration of the molecule.

From the electronic configuration of the molecule, it is possible to predict the following parameters about the molecule:

1. Stability of Molecules: If number of electrons in bonding molecular orbital is greater than the number of electrons in anti-bonding molecular orbitals, then, the molecule is stable.

2. Bond order: Bond order (b.o.) is defined as, “one half the difference between the number of electrons present in the bonding and the antibonding orbitals”.

Bond order (b.o.) = $\frac{1}{2}(N_b – N_a)$

3. Nature of the bond: Integral bond order values of 1, 2 or 3correspond to single, double or triple bondsrespectively.

4. Bond-length: The bond order between two atoms in amolecule may be taken as an approximate measure of the bond length. The bond length decreases as bond order increases as:

Bond length of single bonded molecule > Bond length of double bonded molecule > Bond length of triple bonded molecule

5. Magnetic nature: If all the molecular orbitals in a molecule are doubly occupied, the substance is diamagnetic (repelled by magnetic field). However, if one or more molecular orbitals are singly occupied it is paramagnetic (attracted by magnetic field).

Note box: Paramagnetic character of a molecule depends on magnetic moment and number of unpaired electrons. Greater the magnetic moment, greater is the Paramagnetic character. Magnetic moment $= \space \sqrt{n(n + 2)}$  B.M. (Bohr-Magneton). Where, n is number of unpaired electrons.

Questions from section 4.7:

1. Explain the salient features of molecular orbital theory.

2. Explain the formation of molecular orbitals by Linear combination of atomic orbitals, thus explaining ways in which orbitals combine.

3. List the conditions for formation of molecular orbitals.

4. Explain the two types of molecular orbitals formed.

5. Describe the terms:

a) Electronic configuration of a molecule

b) Bond order

6. When is a substance considered: (a) Diamagnetic and (b) Paramagnetic?

4.8 Bonding in some Homonuclear Diatomic Molecules

The bonding order, stability and magnetic character of molecules of first and second period elements in the periodic table can be determined from the electronic configuration and molecular orbital energy level diagrams.

1. Hydrogen molecule ($H_2$):

• It is formed by the combination of two hydrogen atoms. Each hydrogen atom has one electron in 1s orbital. Therefore, in a molecule of hydrogen, there are two electrons which are present in σ1s molecular orbital. So, electronic configuration of hydrogen molecule is:
  H₂: [σ1s]²
• Bond order of $H_2$ molecule can be calculated as given below:

$$ Bond \space order = \frac {N_b-N_a}{2} = \frac {2-0}{2} = 1$$

• This means that, the two hydrogen atoms are bonded together by a single covalent bond.
• The bond dissociation energy of hydrogen molecule has been found to be 438 kJ mol^–1and bond length equal to 74 pm.
• The molecule is stable and is diamagnetic since all electrons are paired.

2. Helium molecule ($He_2$):

• The electronic configuration of helium atom is $1s^2$. Each helium atom contains 2 electrons, therefore, in $He_2$ molecule there would be 4 electrons.
• These electrons will be accommodated in σ1s and σ*1s molecular orbitals leading to electronic configuration:
  He₂: (σ1s)²(σ*1s)²
• Bond order of $He_2$ is $\frac{1}{2}(2 – 2) = 0$. This means that, $He_2$ molecule is unstable and does not exist. Similarly, it can be shown that $Be_2$  Molecule (σ1s)²(σ*1s)²(σ2s)²(σ*2s)² also does not exist.

3. Lithium molecule ($Li_2$):

• The electronic configuration of lithium is $1s^2, 2s^1$.
• There are six electrons in $Li_2$. The electronic configuration of $Li_2$ molecule, therefore, is $Li_2$: (σ1s)²(σ*1s)²(σ2s)².
  [The above configuration is also written as KK(σ2s)² where, “KK” represents the closed K shell structure: (σ1s)² (σ*1s)²].
• From the electronic configuration of $Li_2$ molecule, it is clear that, there are four electrons present in bonding molecular orbitals and two electrons present in anti-bonding molecular orbitals.
• Its bond order, therefore, is $\frac{1}{2}(4 – 2) = 1$. This means that $Li_2$molecule is stable and since it has no unpaired electrons it should be diamagnetic.
• Diamagnetic $Li_2$ molecules are known to exist in the vapour phase.

4. Carbon molecule ($C_2$):

• The electronic configuration of carbon is: $1s^22s^22p^2$.
• There are twelve electrons in $C_2$. The electronic configuration of $C_2$ molecule, therefore, is:

• The bond order of $C_2$is $\frac{1}{2}(8 – 4) = 2$. Thus, $C_2$should be diamagnetic.
• Diamagnetic $C_2$molecules have been detected in vapour phase.

Note box: It is important to note that double bond in $C_2$ consists of both pi bonds because of the presence of four electrons in two pi molecular orbitals. In most of the other molecules, a double bond is made up of a sigma bond and a pi bond.

5. Oxygen molecule ($O_2$):

– The electronic configuration of oxygen atom is: $1s^2 2s^2 2p^4$.

Each oxygen atom has 8 electrons. Hence, in $O_2$ molecule there are 16 electrons. The electronic configuration of $O_2$ molecule, therefore, is:

• From the electronic configuration of $O_2$  molecule, it is clear that, ten electrons are present in bonding molecular orbitals and six electrons are present in antibonding molecular orbitals. Its bond order, therefore, is,

$$ \Bond \space order = \frac {1}{2} [N_b – N_a] = \frac {1}{2} [10-6] = 2$$

• So in oxygen molecule, atoms are held by a double bond.
• Moreover, it may be noted that, it contains two unpaired electrons: one in π*2p_x and another in π*2p_y molecular orbitals, therefore, $O_2$  molecule should be paramagnetic.

In figure 4.22 are given, the molecular orbital occupancy and molecular properties for B₂ through Ne₂.

Questions from section 4.8:

1. Determine the bond order for $H_2$molecule. Comment on its properties. Give the molecular orbital diagram of hydrogen.

2. Determine the bond order for $H_2$ molecule. Comment on its properties. Give the molecular orbital diagram of helium.

3. Determine the bond order for $C_2$ molecule. Comment on its properties.

4. Determine the bond order for $O_2$molecule. Comment on its properties.

4.9 Hydrogen Bonding

• When the hydrogen bond is attached to a highly electronegative element, it imparts a partial positive charge due to shifting of electrons (forming the covalent bond) towards the more electronegative element (like, F, O and N). This partially positively charged hydrogen atom forms a bond with another more electronegative atom. This bond is known as hydrogen bond and is weaker than the covalent bond. For example, in HF molecule, the hydrogen bond exists between hydrogen atom of one molecule and fluorine atom of another molecule as depicted below:

• Here, hydrogen bond acts as a bridge between two atoms which holds one atom by covalent bond and the other by hydrogen bond. Hydrogen bond is represented by a dotted line (– – –) while a covalent bond is represented by a solid line.
• We shall now define a hydrogen bond.

Definition box:   Hydrogen bond can be defined as the attractive force which binds hydrogen atom of one molecule with the electronegative atom (F, O or N) of another molecule.

4.9.1 Cause of Formation of Hydrogen Bond

• When hydrogen is bonded to strongly electronegative element ‘X’, the electron pair shared between the two atoms moves far away from hydrogen atom. As a result, the hydrogen atom becomes highly electropositive with respect to the other atom ‘X’.
• Since there is displacement of electrons towards the more electronegative element, X, the hydrogen acquires fractional positive charge (δ⁺) while ‘X’ attains fractional negative charge (δ^–). This results in the formation of a polar molecule having electrostatic force of attraction which can be represented as:

• The magnitude of H-bonding depends on the physical state of the compound. It is maximum in the solid state and minimum in the gaseous state.

4.9.2 Types of H-Bonds

There are two types of H-bonds:

(i) Intermolecular hydrogen bond

(ii) Intramolecular hydrogen bond

(1) Intermolecular hydrogen bond: It is formed between two different molecules of the same or different compounds. For example, H-bond in case of HF molecule, alcohol or water molecules are intermolecular hydrogen bonds.

(2) Intramolecular hydrogen bond: It is formed when hydrogen atom is in between two highly electronegative (F, O, N) atoms present within the same molecule. For example, in o-nitrophenol the hydrogen is in between the two oxygen atoms.

Questions from section 4.9:

1. Define Hydrogen bond and explain the cause of formation of hydrogen bond.

Note box:   Anomalous properties of water:   Water exhibits the following anomalous properties due to hydrogen bonding:   1. Water has an unusually high boiling point than $H_2S$— In water, a large number of water molecules are associated due to hydrogen bonding. Energy is required to break the strong hydrogen bond. Hence the high boiling point of water.   2. Density of ice is less than that of water — In ice, each oxygen atom is tetrahedrally surrounded by four hydrogen atoms. Two of the hydrogen atoms are linked to oxygen through normal covalent bonds and the remaining two hydrogen atoms through hydrogen bonds. This results in a cage or honeycomb-like structure. As a result, the volume occupied by water molecules increases due to which, the density decreases.   3. Density of water is maximum at $4^oC$— When the temperature of ice is increased beyond $0^oC$, a number of hydrogen bonds are broken down. This enables the water molecules to come closer to one another. The volume occupied thus decreases and results in increase in density. Above $4^oC$, due to greater heat energy, water molecules move away from each other predominantly due to the change of hydrogen bonds. As a result, the volume increases and density decreases. This phenomenon is called anomalous expansion of water.