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The attractive force which holds various constituents (atoms, ions, etc.) together in different chemical
species is called a chemical bond.
Formation of chemical compounds takes place as a result of combination of atoms of various elements in different ways,

Q. Why do atoms combine? Why are only certain combinations possible? Why do some atoms combine while certain others do not? Why do molecules possess definite shapes?
To answer such questions we study different theories and concepts---
(a) Kössel-Lewis approach
 (b) Valence Bond (VB) Theory
(C) Valence Shell Electron Pair Repulsion (VSEPR) Theory, and 
 (d) Molecular Orbital (MO) Theory.

Lewis postulated that atoms achieve the stable octet when they are linked by chemical bonds.
It can be done by two ways---
i) Electrovalent bond --By complete transference of electrons i.e. by give and take of electrons. Elements having only one or two electrons in their valence orbit i.e. metals loos their valence electrons and change in to positive ions on other hand elements with six or seven electrons i.e. non-metals in their valence shell receive electrons and change in to negative ions then these oppositely charged ions join together by electrostatic force of attraction and forming bond is known as electrovalent bond and participating electrons decide the electrovalency of the element.
Note—Generally this type of bond form between the elements having big difference in their electronegativity.
e.g. In the case of sodium and chlorine, an electron transfers from sodium to chlorine thereby giving the Na+ and Clions.
ii) Covalent bond—This bond form by sharing of electrons. Atoms share their electrons to complete their octate. Sharing may be of one sided or both sided. In one sided sharing, forming bond is known as co-ordinate bond and shared electron pair is given by one of the bonded atoms and that is known as donor and another atom is known as accepter e.g. bond between ammonia and boron triflouride NH3--BF3 OR NH3 -- BF3
And may be sharing of both sided then a covalent bond will form. And shared electron pair in valence orbit is known as bond pair and non bonding electron pairs are known as lone pairs of electrons.
Note—This type of bond generally form between the atoms of same electronegativity (i.e. atoms of same element) or atoms of slightly different electronegativity.
e.g. In the case of molecules like Cl2, H2, F2, etc., the bond is formed by the sharing of a pair of electrons
between the atoms. In the process each atom attains a stable outer octet of electrons.
Formation of co valent bond between the chlorine atoms.

Lewis Symbols: In the formation of a molecule, only the outer shell electrons take part in chemical combination and they are known as valence electrons. The inner shell are generally not involved in the combination process.
G.N. Lewis, introduced dot symbol for valence electrons in an atom. These notations are called Lewis symbols. E.g., the Lewis symbols for the elements of second period are as under:
Significance of Lewis Symbols:
1. The number of dots around the symbol represents the number of valence electrons.
2.This number of valence electrons helps to calculate the common or 
group valence ( Valency means power of combination) of the element.
3.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.

Kössel, in relation to chemical bonding, drew attention to the following facts:

 In the periodic table, the highly electronegative halogens and the highly electropositive alkali metals are separated by the noble gases;

• 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;

• 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, ns2 np6.
• The negative and positive ions are stabilized by electrostatic attraction.
For example, the formation of CaF2 from Ca and F, according to the above scheme, can be explained as:
Applications of Kössel’s postulationsThey provide the basis for the modern concepts regarding ion-formation by electron transfer and the formation of ionic crystalline compounds.
--They have great value in the understanding and systematisation of the ionic compounds.

Drawbacks of Kössel’sTheory-- A large number of compounds did not fit into these concepts.
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.
Covalent Bond
Langmuir (1919) refined the Lewis postulations by introducing the term covalent bond. The Lewis-Langmuir theory can be understood by considering the formation of the chlorine molecule,Cl2. The Cl atom with electronic configuration, [Ne]3s2 3p5, is one electron short of the argon configuration.
The formation of the Cl2molecule can be understood in terms of 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 or Cl – Cl
Covalent bond between two Cl atoms
atoms attain the outer shell octet of the nearest noble gas (i.e., argon).
The dots represent electrons. Such structures are referred to as Lewis dot structures.
Some other molecules may represented as---
Thus, when two atoms share one electron pair they are said to be joined by a single covalent bond.
If two atoms share two pairs of electrons, the covalent bond between them is called a double bond. E.g.
carbon dioxide molecule.
Double bonds in CO2molecule
When combining atoms share threeelectron pairs as in the case of two nitrogen atoms in the N2 molecule and the two carbon atoms in the ethyne molecule, a triple bond is formed.
Application of Lewis structures ( Lewis Representation of Simple Molecules ) of the molecules--The Lewis dot structures provide a picture of bonding in molecules and ions in terms of the shared pairs of electrons and the octet rule.
Draw backs of Lewis theoryIt cannot explain the bonding and behaviour of a molecule completely.
( It helps in understanding the formation and properties of a molecule to a large extent.)
The Lewis dot structures can be written by adopting the following steps:

1) The total number of electrons required for writing the structures are obtained by adding the valence electrons of the combining atoms. e.g. in the CHmolecule there are eight valence electrons available for bonding (4 from carbon and 4 from the four hydrogen atoms).

2. For anions, each negative charge would mean addition of one electron.

3. For cations, each positive charge would result in subtraction of one electron from the total number of valence electrons. E.g.(1) For the CO3 2–ion, the two negative charges indicate that there are two additional electrons than those provided by the neutral atoms. (2) For NH4+ ion, one positive charge indicates the loss of one electron from the group of neutral atoms.

4. Knowing the chemical symbols of the combining atoms and having knowledge of the skeletal structure of the compound then distribute the total number of electrons as bonding shared pairs between the atoms in proportion to the total bonds.

5. In general the least electronegative atom occupies the central position in the molecule/ion.e.g. in the NF3 and CO32–, nitrogen and carbon are the central atoms whereas fluorine and oxygen occupy the terminal positions.

6. 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 bonded atom gets an octet of electrons.

 Each H atom attains the configuration of helium (a duplet of electrons)
Formal Charge
Lewis dot structures, in general, do not represent the actual shapes of the molecules.
The formal charge of an atom in a polyatomic molecule or ion may be defined 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.
It is expressed as :
Formal charge (F.C.) on an atom in a Lewis structure = total number of valence electrons in the free atom —
bonding (lone pair) electrons — (1/2) total number of
bonding(shared) electrons.
(The counting 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 (O3). The Lewis structure of O3 may be drawn as---- And we represent O3 along with the formal charges as follows:
Note--We must understand that 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.
Significance of the formal charge--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 charges on the atoms. The formal charge is a factor based on a pure covalent view of bonding in which electron pairs are shared equally by neighbouring atoms.

Limitations of the Octet Rule. There are three types of exceptions to the octet rule.
1. The incomplete octet of the central atom
In some compounds, the number of electrons surrounding the central atom is less than eight. This is especially the case with elements having less than four valence electrons. Examples are LiCl, BeH2 and BCl3.
Li, Be and B have 1,2 and 3 valence electrons only. Some other such compounds are AlCl3 and BF3.
2. Odd-electron molecules
In molecules with an odd number of electrons like nitric oxide, NO and nitrogen dioxide, NO2, the octet rule is not satisfied for all the Atoms

3. The expanded octet
Elements in and beyond the third period of the periodic table have, apart from 3s and 3porbitals, 3d orbitals also available for bonding. In a number of compounds of these elements there are more than eight valence electrons around the central atom. This is termed as the expanded octet. Examples of such compounds are: PF5, SF6, H2SO4 and a number of coordination compounds.
Note-Ssulphur also forms many compounds in which the octet rule is obeyed. Ex. sulphur dichloride,
Other drawbacks of the octet theory
4. Octet rule is based upon the chemical inertness of noble gases. However, some noble gases (for example
xenon and krypton) also combine with oxygen and fluorine to form a number of compounds like XeF2, KrF2, XeOF2 etc.,
5. This theory does not account for the shape of molecules.
6. It does not explain the relative stability of the molecules being totally silent about the energy of a molecule.

From the Kössel and Lewis, formation of ionic compounds would depend upon:

1. The ease of formation of the positive and negative ions from the respective neutral atoms;

2. The arrangement of the positive and negative ions in the solid, that is, the lattice of the crystalline compound.
The formation of a positive ion involves ionization, i.e., removal of electron(s) from the neutral atom and that of the negative ion involves the addition of electron(s) to the neutral atom.
M(g) -- M+(g) + e ; Ionization enthalpy
X(g) + e --- X (g) ; Electron gain enthalpy
M+(g) + X (g) -- MX(s)
(The electron gain process may be exothermic or endothermic. The ionization, on the other hand, is always endothermic.).
Hence ionic bonds will be formed more easily between elements with comparatively low ionization enthalpies and elements with comparatively high negative value of electron gain enthalpy.
Most ionic compounds have cations derived from metallic elements and anions from non-metallic elements. The ammonium ion, NH4+ (made up of two nonmetallic elements) is an exception..

These compounds crystallise in different crystal structures determined by the size of the ions, their packing arrangements and other factors. The crystal structure of sodium chloride, NaCl (rock salt), for example is shown below.

In ionic 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.
e.g. 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 compensated for by the enthalpy of lattice formation of NaCl(s) (–788 kJ mol–1).
Therefore, the energy released in the processes is more than the energy absorbed.
Lattice enthalpy plays a key role in the formation of ionic compounds

Lattice Enthalpy--
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. E.g., 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.


Bond Length

Bond length is defined as the equilibrium distance between the nuclei of two bonded atoms in a molecule. Bond lengths are measured by spectroscopic, X-ray diffraction and electron-diffraction techniques.
Each atom of the bonded pair contributes to the bond length . In the case of a covalent bond, the contribution from each atom is called the covalent radius of that atom.

The covalent radius is measured approximately as the radius of an atom’s core which is in contact with the core of an adjacent atom in a bonded situation.
The covalent radius is half of the distance between two similar atoms joined by covalent bond in the same molecule
. The bond length in a covalent molecule AB.
R = rA + rB (R is the bond length and rA and rB are the covalent radii of atoms A and B respectively)
. The van der Waals radius represents the overall size of the atom which includes its valence shell in a nonbonded situation.

Further, the van der Waals radius is half of the distance between two similar atoms in separate molecules in a solid. .The inner circlescorrespond to the size of the chlorine atom (rvdw and rc are van der Waals and covalent radii respectively).

Bond Angle
It is defined as the angle between the orbitals containing bonding electron pairs around the central atom in a molecule/complex ion. Bond angle is expressed in degree which can be experimentally determined by spectroscopic methods. It gives some idea regarding the distribution of orbitals around the central atom in a molecule/complex ion and hence it helps us in determining its shape. For example H–O–H bond angle in water can be represented as under :
Bond Enthalpy

It 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. For example, the H – H bond enthalpy in hydrogen molecule is 435.8 kJ mol–1.
H2(g) -- H(g) + H(g); ΔaH = 435.8 kJ mol–1
Similarly the bond enthalpy for molecules containing multiple bonds, for example O2 and N2will be as under :
O2 (O = O) (g) --- O(g) + O(g); ΔaH = 498 kJ mol–1
N2 (N ≡ N) (g) -- N(g) + N(g); ΔaH= 946.0 kJ mol–1
 It is important that larger the bond dissociation enthalpy, stronger will be the bond in the molecule. For a heteronuclear diatomic molecules like HCl, we have
HCl (g) ---- H(g) + Cl (g); ΔaH= 431.0 kJ mol–1
In case of polyatomic molecules, the measurement of bond strength is more complicated. For example in case of H2O molecule, the enthalpy needed to break the two O – H bonds is not the same.
H2O(g) ----H(g) + OH(g); ΔaH1 = 502 kJ mol–1
OH(g) --H(g) + O(g); ΔaH2 = 427 kJ mol–1
The difference in the ΔaH value shows that the second O – H bond undergoes some change because of changed chemical environment. This is the reason for some difference in energy of the same O – H bond in different molecules like C2H5OH (ethanol) and water. Therefore in polyatomic molecules the term mean or average bond enthalpy is used. It is obtained by dividing total bond dissociation enthalpy by the number of bonds broken as explained below in case of water molecule,
Average bond enthalpy = 502 + 427 = 464.5 kJ mol–1
Bond OrderAccording to Lewis description of covalent bond, the Bond Order is given by the number
Of bonds between the two atoms in a molecule.
The bond order, for example in H2 (with a single shared electron pair), in O2 (with two shared electron pairs) and in N2 (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 N2, bond order is 3 and its  Δ a H is 946 kJ mol–1; being one of the highest for a diatomic molecule.

Isoelectronic molecules and ions have identical bond orders; for example, F2 and O2 2– have bond order 1. N2, CO and NO+ have bond order 3.
A general correlation useful for understanding the stablities of molecules is that: with increase in bond order, bond enthalpy increases and bond length decreases.
Resonance Structures
It is often observed that a single Lewis structure is unable to the represent experimentally determined parameters of a molecule.
For example, the ozone, O3 molecule can be equally represented by the structures I and II shown below:
Fig. Resonance in the O3 molecule(structures I and II represent the two canonical forms while the structure III is the resonance hybrid)
In both structures we have a O–O single bond and a O=O double bond. The normal O–O and O=O bond lengths are 148 pm and 121 pm respectively. Experimentally determined oxygen-oxygen bond lengths in the O3 molecule are same (128 pm). Thus the oxygen-oxygen bonds in the O3 molecule are intermediate between a double and a single bond. Obviously, this cannot be represented by either of the two Lewis structures shown
The concept of resonance was introduced to deal with the type of difficulty experienced in the depiction of accurate structures of molecules like O3.
According to the conceptof resonance, whenever a single Lewis structure cannot describe a molecule accurately, a number of structures withsimilar energy, positions of nuclei, bonding and non-bonding pairs of electrons are taken as the canonical structures of the hybrid which describes the molecule accurately.
Thus for O3, the two structures shown above constitute the canonical structures or resonance structures and their hybrid i.e., the III structure represents the structure of O3 more accurately. This is also called resonance
hybrid. Resonance is represented by a double headed arrow (). Some of the other examples of resonance
structures are provided by the carbonate ion and the carbon dioxide molecule. In general, it may be stated that
1. Resonance stabilizes the molecule as the energy of the resonance hybrid is less than the energy of any single canonical structure; and,
2. Resonance averages the bond characteristics as a whole. Thus the energy of the O3resonance hybrid is lower than either of the two cannonical froms I and II
Note---Many misconceptions are associated with resonance and the same need to be dispelled. You should remember that :
1. The cannonical forms have no real existence.
2. 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.
3. There is no such equilibrium between the cannonical forms as we have between tautomeric forms (keto and
enol) in tautomerism.
4. The molecule as such has a single structure which is the resonance hybrid of the cannonical forms and
which cannot as such be depicted by a single Lewis structure.
Polarity of Bonds
The existence of a hundred percent ionic or covalent bond represents an ideal situation.
In reality no bond or a compound is either completely covalent or ionic. Even in case of covalent bond between two hydrogen atoms, there is some ionic character. When covalent bond is formed between two similar atoms, for example in H2, O2, Cl2, N2 or F2, the shared pair of electrons is equally attracted by the two atoms. As a result electron pair is situated exactly between the two identical nuclei. The bond so formed is called nonpolar covalent bond.
Contrary to this 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. The resultant covalent bond is a polar covalent bond.
As a result of polarisation, the molecule possesses the dipole moment, It can be 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.
Further dipole moment is a vector quantity and is depicted by a small arrow (-) with tail on the positive centre and head pointing towards the negative centre. For example the dipole moment of HF may be represented as :
The shift in electron density is symbolized by crossed arrow (+-- ) above the Lewis structure to indicate the direction of the shift.
In case of polyatomic molecules the dipole moment not only depend 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 case, the dipole moment of a molecule is the vector sum of the dipole moments of various bonds.
For example in H2O molecule, which has a bent structure, the two O–H bonds are oriented at an angle of 104.50. Net dipole moment of 6.17 × 10–30C m (1D = 3.33564 × 10–30 C m) is the resultant of the dipole
moments of two O–H bonds.
Net Dipole moment, = 1.85 D = 1.85 × 3.33564 × 10–30 C m = 6.17 ×10–30 C m
The dipole moment in case of BeF2is 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 BF3, the dipole moment is zero although the B – F bonds are oriented at an angle of 120° to one another, the three bond moments give a net vector sum of zero as the resultant of any two is equal and opposite to the third.
In case of NH3and NF3 molecule. 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 NH3 ( 4.90 × 10–30 C m) is greater than that of NF3 (0.8 × 10–30 C m).
This is because, in case of NH3 the orbital dipole due to lone pair is in the same direction as the resultant dipole moment of the N – H bonds, whereas in NF3 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 NF3 as represented below :
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:
1. The smaller the size of the cation and the larger the size of the anion, the greater the covalent character of an ionic bond. E.g. HCl
2. The greater the charge on the cation, the greater the covalent character of the ionic bond.
3. For cations of the same size and charge, the one, with electronic configuration (n-1)dnnso, typical of transition metals, is more polarising than the one with a noble gas configuration, ns2 np6, typical of alkali and alkaline earth metal cations. The cation polarises the anion, pulling the electronic charge toward itself and thereby increasing the electronic charge between the two. This is precisely what happens in a covalent bond, i.e., buildup of electron charge density between the nuclei. The polarising power of the cation, the polarisability of the anion and the extent of distortion (polarisation) of anion are the factors, which determine the per cent
covalent character of the ionic bond.
As already explained, Lewis concept is unable to explain the shapes of molecules
. This theory provides a simple procedure to predict the shapes of covalent molecules. Sidgwick and Powell in 1940, proposed a simple theory based on the repulsive interactions of the electron pairs in the valence shell of the atoms. It was further developed and redefined by Nyholm and Gillespie (1957).
The main postulates of VSEPR theory are as follows:
1. The shape of a molecule depends upon the number of valence shell electron pairs(bonded or nonbonded) around the central atom.
2. Pairs of electrons in the valence shell repel one another since their electron clouds are negatively charged
3. These pairs of electrons tend to occupy such positions in space that minimize repulsion and thus maximise distance between them.
4. The valence shell is taken as a sphere with the electron pairs localising on the spherical surface at maximum distance from one another.
5. A multiple bond is treated as if it is a single electron pair and the two or three electron pairs of a multiple bond are treated as a single super pair. (i.e. more then one pair of electrons are shared between two bonding atoms.)
6. Where two or more resonance structures can represent a molecule, the VSEPR model is applicable to any
such structure. (all canonical forms show same structure.)
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)
Difference between the lone pairs and bonding pairs of electrons. Nyholm and Gillespie (1957) defined it.
The lone pairs are localised on the central atom but 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 and
alterations in bond angles in molecules.
For the prediction of geometrical shapes of molecules with the help of VSEPR theory, We divide molecules into two categories as (i) molecules in which thecentral atom has no lone pair and
(ii) molecules in which the central atom has one or more lone pairs.

Table (above) shows the arrangement of electron pairs about a central atom A (without any lone pairs) Table shows shapes of some simple molecules and ions in which the central atom has one or more lone pairs.

No. of
No. of
Reason for the shape acquired
AB2E 4 1 Bent Theoretically the shape should have been triangular planar but actually it is found to be bent or v-shaped. The reason being the lone pairbond pair repulsion is much more as compared to the bond pair bond pair repulsion. So the angle is reduced to 119.5° from 120°.
AB3E 3 1
Had there been a bp in place of lp the shape would have been tetrahedral but one lone pair is present and due to the repulsion between lp-bp (which is more than bp-bp repulsion) the angle
between bond pairs is reduced to 107° from 109.5°.
AB2E2 2 2 Bent The shape should have been tetrahedral if there were all bp but two lp are present so the shape is distorted tetrahedral or angular. The reason is lp-lp repulsion is more than lp-bp repulsion which is more than bp-bp repulsion. Thus, the angle is reduced to 104.5° from 109.5°.
AB4E 4 1 See-Saw In (a) the lp is present at axial position so there are three lp—bp repulsions at 90°. In(b) the lp is in an equatorial position, and there are two lp—bp repulsions. Hence, arrangement (b) is more stable. The shape shown in (b) is described as a distorted tetrahedron, a folded square or a see-saw.
AB3E2 3 2 T-shape In (a) the lp are at equatorial position so there are less lp-bp repulsions as compared to others in which the lp are at axial positions. So structure (a) is most stable. (T-shaped).
Advantages of VSEPR theory--
The VSEPR Theory is able to predict geometry of a large number of molecules.

,theoretical basis of the VSEPR theory regarding the effects of electron pair repulsions on molecular shapes is not clear.
Drawbacks of lewis theory---1. It fails to explain the formation of chemical bond.
2. It does not give any reason for the difference in bond dissociation enthalpies and bond lengths in molecules like H2 (435.8 kJ mol-1, 74 pm) and F2 (150.6 kJ mol-1, 42 pm), although in both the cases a single covalent
bond is formed by the sharing of an electron pair between the respective atoms.
3. It gives no idea about the shapes of polyatomic molecules.
To overcome these limitations the two important theories based on quantum mechanical principles are introduced. These are valence bond (VB) theory and molecular orbital (MO) theory.
Valence bond theory was introduced by Heitler and London (1927) and developed further by Pauling and others.
This valence bond theory is based on the knowledge of atomic orbitals, electronic configurations of elements, the overlap criteria of atomic orbitals, the hybridization of atomic orbitals and the principles of variation and superposition. Here valence bond theory has been discussed in terms of qualitative and non-mathematical treatment only.
Consider two hydrogen atoms A and B approaching each other having nuclei NA and NB and electrons present in them are represented by eA and eB. 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 NA – eA and NB– eB.
(ii) nucleus of one atom and electron of other atom i.e., NA– eB, NB– eA.
Similarly repulsive forces arise between (i) electrons of two atoms like eA – eB,
(ii) nuclei of two atoms NA – NB.
Attractive forces tend to bring the two atoms close to each other whereas repulsive forces tend to push them apart (Fig.).
Fig. 4.7 Forces of attraction and repulsion during the formation of H2molecule.
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 
The potential energy curve for the formation of H2molecule as a function of internuclear distance of the H atoms. The minimum in the curve corresponds to the most stable state of H2.
Conversely, 435.8 kJ of energy is required to dissociate one mole of H2 molecule.
H2(g) + 435.8 kJ mol–1-- H(g) + H(g)
Orbital Overlap Concept
As above, in the formation of hydrogen molecule, when two hydrogen atoms come close to each other, they attain a minimum energy state that their atomic orbitals undergo partial interpenetration. This partial merging of atomic orbitals is called overlapping of atomic orbitals which results in the pairing of electrons. The extent of
overlap decides the strength of a covalent bond. In general, greater the overlap the stronger is the bond formed between two atoms. Therefore, according to orbital overlap concept, the formation of a covalent bond
between two atoms results by pairing of electrons present in the valence shell having opposite spins.
Directional Properties of Bonds
We know the formation of covalent bond depends on the overlapping of atomic orbitals. E.g. The molecule of hydrogen is formed due to the overlap of 1s-orbitals of two H atoms, when they combine with each other.
In case of polyatomic molecules like CH4, NH3 and H2O, the geometry of the molecules is also important in addition to the bond formation. For example
Q.Why is it so that CH4 molecule has tetrahedral shape and HCH bond angles are 109.5°?
Q. Why is the shape of NH3molecule pyramidal ?
The valence bond theory explains the formation and directional properties of bonds in polyatomic molecules like CH4, NH3 and H2O, etc. in terms of overlap and hybridization of atomic orbitals.
Overlapping of Atomic Orbitals
When two atoms come close to each other, there is overlapping of atomic orbitals. This overlap may be positive, negative or zero depending upon the properties of overlapping of atomic orbitals. The various arrangements of s and p orbitals resulting in positive, negative and zero overlap are depicted in Fig.
Fig. Positive, negative and zero overlaps of s and p atomic orbitals
Let us first consider the CH4(methane) molecule. The electronic configuration of carbon in its ground state is [He]2s2 2p2 which in the excited state becomes [He] 2s1 2px12py1 2pz1. Here the three p orbitals of carbon are at 90° to one another, the HCH angle for these will also be 90°. The 2s orbital of carbon and the 1s orbital of H are spherically symmetrical and they can overlap in any direction. Therefore the direction of the fourth C-H bond cannot be ascertained. This description does not fit in with the tetrahedral HCH angles of 109.5°.
Clearly, it follows that simple atomic orbital overlap does not account for the directional characteristics of bonds in CH4.
Using similar procedure and arguments, it can be seen that in the case of NH3 and H2O 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.
Types of Overlapping and Nature of Covalent Bonds
The covalent bond may be classified into two types depending upon the types of overlapping:
(i) Sigma(α) bond, and (ii) pi(π) bond
(i) Sigma(α) bond : This type of covalent bond is formed by the end to end (hand-on) overlap of bonding orbitals along the internuclear 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 internuclear axis as shown
below : e.g. H2 or H – H molecule
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. e.g. HF or H – F molecule.
3. p–p overlapping : This type of overlap takes place between half filled p-orbitals of the two approaching atoms. e.g. F2 or F – F molecule
(ii) 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 internuclear axis. The orbitals formed due to sidewise overlapping consists of two saucer type charged clouds above and below the plane of the participating atoms.
Difference between sigma and pi bond--
S.No. sigma bond pi bond
1. Form by head on overlapping i.e. along the axis. Form by sidewise overlapping i.e. perpendicular to the axis.
2. It is an independent bond, so in b/w two atomic sps. always first bond will be sigma bond. It is a dependent bond, so it forms after a sigma bond b/w two atoms.
3. It determines the geometry of molecule. It depends upon sigma bond, and form parallel to sigma bond so it does not play any role in geometry determination of the molecule.
4. In a sigma bond, the overlapping of orbitals takes place to a larger extent. Hence, it is stronger as compared to the pi bond The extent of overlapping occurs to a smaller extent. Hence, it is weaker as compared to the sigma bond.
5. In a single bond, only one sigma bond is there.
In the molecules containing multiple bond (double
or triple bonds), first bond will be sigma and rest bonds will be pi bonds.
In order to explain the characteristic geometrical shapes of polyatomic molecules like CH4, NH3and H2O etc., Pauling introduced the concept of hybridisation. According to him the atomic orbitals combine to form new set of equivalent orbitals known as hybrid orbitals. Unlike pure orbitals, the hybrid orbitals are used in bond formation. The phenomenon is known as hybridization which 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 known as hybrid orbitals.
Salient features of hybridisation: The main features of hybridisation are as under :
1. The number of hybrid orbitals is equal to the number of the atomic orbitals that get hybridised.
2. The hybridised orbitals 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 directed in space in some preferred direction to have minimum repulsion between electron pairs and thus a stable arrangement. Therefore, the type of hybridization indicates the geometry of the molecules.
Important conditions for hybridisation
(i) The orbitals present in the valence shell of the atom are hybridised.
(ii) The orbitals undergoing hybridization should have almost equal energy.
(iii) Promotion of electron is not essential condition prior to hybridisation.(iv) It is not necessary that only half filled orbitals participate in hybridisation. In some cases, even filled orbitals of valence shell take part in
hybridisation.e.g. NH3
Note—Hybridisation is a hypothetical phenomenon.
Types of Hybridisation
There are various types of hybridization involving s, p and d orbitals. The different types of hybridisation are as under:
(I) sp hybridisation:
1. In this type of hybridisation, mixing of one s and one p orbital takes place, resulting in the formation of two
equivalent sp hybrid orbitals. (The suitable orbitals for sp hybridisation are s and pz, if the hybrid orbitals are to lie along the z-axis.)
2. Each sp hybrid orbitals has 50% s-character and 50% p-character.
3. If in a molecule, the central atom is sp-hybridised, it possesses linear geometry. This type of hybridisation is also known as diagonal hybridisation.
4. Bond angle - 1800
Example of molecule having sp hybridisation
BeCl2: *The ground state electronic configuration of Be is 1s22s2.
*In the exited state one of the 2s-electrons is promoted to vacant 2p orbital to account for its divalency.
*One 2s and one 2p-orbitals get hybridised to form two sp hybridised orbitals.
*These two sp hybrid orbitals are oriented in opposite direction forming an angle of 180°.
*Each of the sp hybridised orbital overlaps with the 2p-orbital of chlorine axially and form two Be- Cl sigma bonds. This is shown in Fig.
Fig. (a) Formation of sp hybrids from s and p orbitals; (b) Formation of the linear BeCl2molecule
(II) sp2hybridisation :
1. In this type of hybridisation, mixing of one s and one 2p orbital takes place, resulting in the formation of three
equivalent sp2hybrid orbitals.
2. Each sp2hybrid orbitals has 33.3% s-character and 66.6% p-character.
3. If in a molecule, the central atom is sp2-hybridised, it possesses triangular planer geometry.
4. Bond angle - 1200
Example, in BCl3molecule,
*The ground state electronic configuration of central boron atom is 1s22s22p1.
* In the excited state, one of the 2selectrons is promoted to vacant 2p orbital as a result boron has three unpaired electrons.
*These three orbitals (one 2s and two 2p) 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 BCl3 (Fig.), the geometry is trigonal planar with ClBCl bond angle of 120°.
Fig. Formation of sp2 hybrids and the BCl3 molecule
(III) sp3 hybridisation--
1. In thishybridisation there is mixing of one s-orbital and three p-orbitals of the valence shell to form four sp3 hybrid orbital of equivalent energies and shape.
2. There is 25% s-character and 75% pcharacter in each sp3 hybrid orbital.
3. The four sp3 hybrid orbitals so formed are directed towards the four corners of the tetrahedron.
4. The angle between sp3 hybrid orbital is 109.5° as shown in Fig..
Example of CH4molecule
*The ground state electronic configuration of central carbon atom is 1s22s22p2.
* In the excited state, one of the 2selectrons is promoted to vacant 2p orbital as a result carbon has four unpaired electrons.
*These four orbitals (one 2s and three 2p) hybridise to form four sp3 hybrid orbitals.
*The four hybrid orbitals so formed are oriented in a tetrahedral arrangement in 3-d space and overlap with 1s orbitals of hydrogen to form four C-H bonds.
* Therefore, in CH4 (Fig.), the geometry is regular tetrahedron with H-C-H bond angle of 109° 28’
Other examples—NH3molecule--
*N has three unpaired electrons 2p orbitals and a lone pair of electrons in 2s orbital.
* These orbitals mix together and form four sp3 hybrid orbitals.
*Three sp3 hybrid orbitals having unpaired electrons and a lone pair of electrons is present in the fourth one. *These three hybrid orbitals overlap with 1s orbitals of hydrogen atoms to form three N–H sigma bonds.
*We know that the force of repulsion between a lone pair and a bond pair is more than the force of repulsion between two bond pairs of electrons. The molecule thus gets distorted and the bond angle is reduced to 107° from 109.5°.
* The geometry of such a molecule will be pyramidal as shown in Fig.
Fig. Formation of NH3 molecule Fig. Formation of H2O molecule
In case of H2O molecule, the four oxygen orbitals (one 2s and three 2p) undergo sp3 hybridisation, out of which two contain one electron each and the other two contain a pair of electrons. These four sp3 hybrid orbitals acquire a tetrahedral geometry, with two corners occupied by hydrogen atoms while the other two by the lone pairs. The bond angle in this case is reduced to 104.5° from 109.5° (Fig. as above) and the molecule thus acquires a V-shape or angular geometry or bent structure.
Other Examples of sp3, sp2 and spHybridisation---sp3 Hybridisation in C2H6 molecule: In ethane molecule both the carbon atoms assume sp3hybrid state. One of the four sp3 hybrid orbitals of carbon atom overlaps axially with similar orbitals of other atom to form sp3-sp3 sigma bond while the other three hybrid orbitals of each carbon atom are used in forming sp3s sigma bonds with hydrogen atoms. Therefore in ethane C–C bond length is 154 pm and each C–H bond length is 109 pm.
sp2 Hybridisation in C2H4:In the formation of ethene molecule, one of the sp2hybrid orbitals of carbon atom overlaps axially with sp2hybridised orbital of another carbon atom to form C–C sigma bond. While the other two sp2 hybrid orbitals of each carbon atom are used for making sp2s sigma bond with two hydrogen atoms. The unhybridised orbital (2px or 2py) of one carbon atom overlaps sidewise with the similar orbital of the other carbon atom to form weak pi bond, which consists of two equal electron clouds distributed above and below the plane of carbon and hydrogen atoms. Thus, in ethene molecule, the carbon - carbon bond consists of one sp2sp2sigma bond and one pi (p ) bond between p orbitals which are not used in the hybridisation and are perpendicular to the plane of molecule; the bond length 134 pm. The C–H bond is sp2s sigma with bond length 108 pm. The
H–C–H bond angle is 117.6° while the H–C–C angle is 121°. The formation of sigma and pi bonds in ethene is shown in Fig.Formation of sigma and pi bonds in ethane---
. sp Hybridisation in C2H2: In the formation of ethyne molecule, both the carbon atoms undergo sp-hybridisation having two unhybridised orbital i.e., 2py and 2px. 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 s bonds. Each of the two unhybridised p orbitals of both the carbon atoms overlaps sidewise to form two p 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 Fig.
Fig. Formation of sigma and pi bonds in ethyne
Hybridisation of Elements involvingd Orbitals
The elements present in the third period contain d orbitals in addition to s and porbitals. 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
(However, since the difference in energies of 3p and 4s orbitals is significant, no hybridisation involving 3p, 3d and 4s orbitals is possible.)
IV) sp3d hybridisation
1. In thishybridisation there is mixing of one s-orbital,-orbital and pi bonds three p-orbitals and one d-orbital of the valence shell to form five sp3d hybridorbitals of equivalent energies and shape.
2. There is 20% s-character and 60% p-character and 20% d-chracter in each sp3d hybrid orbital.
3. The five sp3d hybrid orbitals so formed are directed towards the five corners of the trigonal bipyramidal geometry..
4. The angle between sp3d hybrid orbitals are of two types according to their orientation;
i) Along the axis- angles with plane = 90° ii) equatorial angles = 120°
Example -- Formation of PCl5molecule:
The ground state and the excited state outer electronic configurations of phosphorus (Z=15) are represented below.
------sp3d hybrid orbitals filled by electron pairs donated by five Cl atoms.------
Now the five orbitals (i.e., one s, three p and one d orbitals) are available for hybridisation to yield a set of five sp3d hybrid orbitals which are directed towards the five corners of a trigonal bipyramidal as depicted in the Fig.
Trigonal bipyramidal geometry of PCl5molecule
All the bond angles in trigonal bipyramidal geometry are not equivalent. In PCl5the five sp3d orbitals of phosphorus overlap with the singly occupied p orbitals of chlorine atoms to form five P–Cl sigma bonds. Three P–Cl bond lie in one planeand make an angle of 120° 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° with the plane. These bonds are called axial bonds. As the axial bond pairs suffer more repulsive
interaction from the equatorial bond pairs, therefore axial bonds have been found to be slightly longer and hence slightly weaker than the equatorial bonds; which makes PCl5molecule more reactive.
sp3d2 hybridisation---

2. There is 16.6% s-character and 49.8% p-character and 33.2% d-chracter in each sp3d2hybrid orbital.
3. The six sp3d2hybrid orbitals so formed are directed towards the six corners of the regular octahedron..
4. The angle between sp3d2hybrid orbitals are 90°.
Formation of SF6molecule:
In SF6 the central sulphur atom has the ground state outer electronic configuration 3s23p4. In the exited state the available six orbitals i.e., one s, three p and two d are singly occupied by electrons. These orbitals hybridise to form six new sp3d2hybrid orbitals, which are projected towards the six corners of a regular octahedron in SF6. These six sp3d2hybrid orbitals overlap with singly occupied orbitals of fluorine atoms to form six S–F sigma bonds. Thus SF6 molecule has a regular octahedral geometry as shown in Fig.
Fig. Octahedral geometry of SF6 molecule

Molecular orbital (MO) theory was developed by F. Hund and R.S. Mulliken in 1932. The salient features of this theory are :
(i) The electrons in a molecule are present in the various molecular orbitals as the electrons of atoms are present in the various atomic orbitals.
(ii) The atomic orbitals of comparable energies and proper symmetry combine to form molecular orbitals.
(iii) While an electron in an atomic orbital is influenced by one nucleus, in a molecular orbital it is influenced by two or more nuclei depending upon the number of atoms in the molecule. Thus, an atomic orbital is monocentric whilea molecular orbital is polycentric.
(iv) The number of molecular orbital formed is equal to the number of combining atomic orbitals. When two atomic orbitals combine, two molecular orbitals are formed. One is known as bonding molecular orbital while the other is called antibonding molecular orbital.
(v) The bonding molecular orbital has lower energy and hence greater stability than the corresponding antibonding molecular orbital.
(vi) 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) The molecular orbitals like atomic orbitals are filled in accordance with the aufbau principle obeying the Pauli’s exclusion principle and the Hund’s rule.
Formation of Molecular Orbitals
Linear Combination of Atomic Orbitals (LCAO)
According to wave mechanics, the atomic orbitals can be expressed by wave functions (’s) which represent the amplitude of the electron waves. These are obtained from the solution of Schrödinger wave equation. However, since it cannot be solved for any system containing more than one electron, molecular orbitals which are one electron wave functions for molecules are difficult to obtain directly from the solution of Schrödinger wave equation. To overcome this problem, an approximate method known as
linear combination of atomic orbitals (LCAO) has been adopted.
Consider the homonuclear or homoatomic hydrogen molecule consisting of two atoms A and B. Each hydrogen atom in the ground state has one electron in 1s orbital. The atomic orbitals of these atoms may be represented by the wave functionsAand B. Mathematically, the formation of molecular orbitals may be described by the
linear combination of atomic orbitals that can take place by addition and by subtraction of wave functions of individual atomic orbitals as shown below :
MO = A + B
Therefore, the two molecular orbitals
and * are formed as :
A + B
* = A – B
The molecular orbitalformed by the addition of atomic orbitals is called the bonding molecular orbital while the molecular orbital * formed by the subtraction of atomic orbital is called antibonding molecular orbital as depicted in Fig.
Fig. Formation of bonding () and antibonding(*) molecular orbitals by the linear combination of atomic orbitals Aand B centered on two atoms A and B respectively.
The electron density in a bonding molecular orbital is located between the nuclei of the bonded atoms because of which the repulsion between the nuclei is very less while in case of an antibonding molecular orbital, most of the
electron density is located away from the space between the nuclei. Infact, there is a nodal plane (on which the electron density is zero) between the nuclei and hence the repulsion between the nuclei is high.
Electrons placed in a bonding molecular orbital tend to hold the nuclei together and stabilise a molecule. Therefore, a bonding molecular orbital always possesses lower energy than either of the atomic orbitals that
have combined to form it. In contrast, the electrons placed in the antibonding molecular orbital destabilise the molecule. This is because the mutual repulsion of the electrons in this orbital is more than the attraction between the electrons and the nuclei, which causes a net increase in energy.
Note--- The energy of the antibonding orbital is raised above the energy of the parent atomic orbitals that have combined and the energy of the bonding orbital has been lowered than the parent orbitals. The total energy of two molecular orbitals, however, remains the same as that of two original atomic orbitals.
Conditions for the Combination of Atomic Orbitals
The linear combination of atomic orbitals to form molecular orbitals takes place only if the following conditions are satisfied:
1.The combining atomic orbitals must have the same or nearly the same energy.
This means that 1s orbital can combine with another 1s orbital but not with 2s orbital because the energy of 2s orbital is appreciably higher than that of 1s orbital. This is not true if the atoms are very different.
2.The combining atomic orbitals must have the same symmetry about the molecular axis. By convention z-axis is taken as the molecular axis. It is important to note that atomic orbitals having same or nearly the same energy will not combine if they do not have the same symmetry.For example, 2pz orbital of one atom can combine with 2pz orbital of the other atom but not with the 2px or 2py orbitals because of their different symmetries.
3.The combining atomic orbitals must overlap to the maximum extent. Greater the extent of overlap, the greater will be the electron-density between the nuclei of a molecular orbital.
Types of Molecular Orbitals
Molecular orbitals of diatomic molecules are designated as (sigma), (pi), (delta), etc.
In this nomenclature, the sigma() molecular orbitals are symmetrical aroundthe bond-axis while pi() molecular orbitalsare not symmetrical. For example, the linearcombination of 1s orbitals centered on twonuclei produces two molecular orbitals whichare symmetrical around the bond-axis. Suchmolecular orbitals are of thetype and aredesignated as 1s and *1s [Fig(a),
If internuclear axis is taken to be in the z-direction, it can be seen that a linear combination of 2pz- orbitals of two atoms also produces two sigma molecular orbitals designated as 2pz and *2pz. [Fig. 4.20(b)]
Molecular orbitals obtained from 2px and 2py orbitals are not symmetrical around the bond axis because of the presence of positive lobes above and negative lobes below the molecular plane. Such molecular orbitals, are
labelled asand* [Fig(c)].
Abonding MO has larger electron density above and below the inter-nuclear axis. The*antibonding MO has a node between the nuclei.
Energy Level Diagram for Molecular Orbitals
We have seen that 1s atomic orbitals on two atoms form two molecular orbitals designated as1s and *1s. In the same manner, the 2s and 2p atomic orbitals (eight atomic orbitalson two atoms) give rise to the following eight molecular orbitals:
Antibonding MOs*2s *2pz *2px *2py
Bonding MOs2s 2pz 2px 2py
The energy levels of these molecular orbitals have been determined experimentally from spectroscopic data for homonuclear diatomic molecules of second row elements of the periodic table. The increasing order of energies of various molecular orbitals for O2 and F2is given below :
1s < *1s < 2s < *2s <2pz<(2px = 2py) < *2px= *2py)<*2pz
Molecules Li2, Be2, B2, C2, N2 not following this energy sequence of molecular orbitals. Experimentally it is observed that for molecules such as B2, C2, N2 etc. the increasing order of energies of various molecular orbitals is---1s < *1s < 2s < *2s < (2px = 2py) <2pz< *2px= *2py) <*2pz
The important characteristic featureof this order is that the energy of 2pzmolecular orbital is higher than that of 2px and 2py molecular orbitals.
Electronic Configuration and Molecular Behaviour
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 get important information about
the molecule as discussed below.

Stability of Molecules: If Nb is the number of electrons occupying bonding orbitals and Na the number occupying the antibonding orbitals, then
(i) the molecule is stable if Nb is greater than Na, because more bonding orbitals are occupied and so the bonding influence is stronger and a stable molecule results
(ii) the molecule is unstable if Nb is less than Na because, In the antibonding influence is stronger and therefore the molecule is unstable.

Bond order(b.o.)--- is defined as one half the difference between the number of electrons present in the bonding and the antibondingorbitals i.e., Bond order (b.o.) = (Nb–Na)
The rules discussed above regarding the stability of the molecule can be restated in terms of bond order as follows: A positive bond order (i.e., Nb > Na) means a stable molecule while a negative (i.e., Nb<Na) or zero (i.e., Nb = Na) bond order means an unstable molecule.
Nature of the bond
Integral bond order values of 1, 2 or 3 correspond to single, double or triple bonds respectively.
The bond order between two atoms in a molecule may be taken as an approximate measure of the bond length. The bond length decreases as bond order increases.
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), e.g., O2 molecule.


1. Hydrogen molecule (H2): It is formed by the combination of two hydrogen atoms. Each hydrogen atom has one electron in 1s orbital. Therefore, in all there are two electrons in hydrogen molecule which are present in 1smolecular orbital. So electronic configuration of hydrogen molecule is H2 : (1s)2
The bond order of H2molecule can be calculated as given below:
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. Since no
unpaired electron is present in hydrogen molecule, therefore, it is diamagnetic.
2. Helium molecule (He2 ): The electronic configuration of helium atom is 1s2. Each helium atom contains 2 electrons, therefore, in He2molecule there would be 4 electrons. These electrons will be accommodated in 1s
and *1s molecular orbitals leading to electronic configuration:
He2: (1s)2(*1s)2
Bond order of He2 is €(2 – 2) = 0
He2molecule is therefore unstable and does not exist.
Similarly, it can be shown that Be2molecule(1s)2(*1s)2(2s)2(*2s)2also does not exist.
3. Lithium molecule (Li2 ): The electronic configuration of lithium is 1s2, 2s1 . There are six electrons in Li2. The electronic configuration of Li2molecule, therefore, is
Li2: (1s)2(*1s)2(2s)2 OR KK(2s)2
Here KK represents the closed Kshell structure (1s)2(*1s)2.
From the electronic configuration of Li2 molecule it is clear that there are four electrons present in bonding molecular orbitals and two electrons present in antibonding molecular orbitals. Its bond order, therefore, is
€ (4 – 2) = 1. It means that Li2molecule is stable and since it has no unpaired electrons it should be diamagnetic. Indeed diamagnetic Limolecules are known to exist in the vapour phase.

4. Carbon molecule (C2): The electronic configuration of carbon is 1s2 2s2 2p2. There are twelve electrons in C2. The electronic configuration of C2 molecule, therefore, is
The bond order of C2 is € (8 – 4) = 2 and C2 should be diamagnetic. Diamagnetic C2molecules have indeed been detected in vapour phase.

NOTE—The double bond in C2  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.
Q, In a similar fashion discus the bonding in N2 molecule..

5. Oxygen molecule (O2 ): The electronic configuration of oxygen atom is 1s2 2s2 2p4. Each oxygen atom has 8 electrons, hence, in O2 molecule there are 16 electrons. The electronic configuration of O2 molecule, therefore, is
From the electronic configuration of O2molecule 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,
So in oxygen molecule, atoms are held by a double bond. Moreover, it may be noted that it contains two unpaired electrons in *2pxand *2py molecular orbitals, therefore, O2molecule should be paramagnetic, a prediction that corresponds to experimental observation. In this way, the theory successfully explains the paramagnetic nature of oxygen.

Nitrogen, oxygen and fluorine are the higly electronegative elements. When they are attached to a hydrogen atom to form covalent bond, the electrons of the covalent bond are shifted towards the more electronegative atom. This partially positively charged hydrogen atom forms a bond with the other 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 :
 H--FHFH--F
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 solid line represents the covalent
bond. Thus, hydrogen bond can be defined as the electrostatic attractive force which binds hydrogen atom of one molecule with the electronegative atom (F, O or N) of another molecule.

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 X, the hydrogen acquires fractional positive charge (+) while ‘X’ attain fractional negative charge(–). This results in the formation of a polar molecule having electrostatic force of attraction which can be represented as :
The magnitude of H-bondingdepends on the physical state of the compound. It is maximum in the solid state and minimum in the gaseous state. Thus, the hydrogen bonds have strong influence on the structure and properties of the compounds.
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, etc.

(2) Intramolecular hydrogen bond :
It is formed when hydrogen atom is in between the 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.

Chemistry for class 11.....

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