4.2 Ionic or Electrovalent Bond other factors. The crystal structure of sodium chloride, NaCl (rock salt), for example isFrom the Kössel and Lewis treatment of the shown below.formation of an ionic bond, it follows that the formation of ionic compounds would primarily depend upon: • The ease of formation of the positive and negative ions from the respective neutral atoms; • 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 Rock salt structure neutral atom. In ionic solids, the sum of the electron gain M(g) → M+(g) + e– ; enthalpy and the ionization enthalpy may be Ionization enthalpy positive but still the crystal structure gets X(g) + e– → X – (g) ; stabilized due to the energy released in the Electron gain enthalpy formation of the crystal lattice. For example: the ionization enthalpy for Na+(g) formation M+(g) + X –(g) → MX(s) from Na(g) is 495.8 kJ mol–1 ; while the electron The electron gain enthalpy, ∆egH, is the gain enthalpy for the change Cl(g) + e–→ enthalpy change (Unit 3), when a gas phase Cl– (g) is, – 348.7 kJ mol–1 only. The sum of the atom in its ground state gains an electron. two, 147.1 kJ mol-1 is more than compensated The electron gain process may be exothermic for by the enthalpy of lattice formation of or endothermic. The ionization, on the other NaCl(s) (–788 kJ mol–1). Therefore, the energy hand, is always endothermic. Electron released in the processes is more than the Reprint 2025-26 Chemical Bonding And Molecular Structure 107 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. Since lattice enthalpy plays a key role in the formation of ionic compounds, it is important that we learn more about it. 4.2.1 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. For example, the lattice enthalpy of NaCl is 788 kJ mol–1. This means that 788 Fig. 4.1 The bond length in a covalent kJ of energy is required to separate one mole molecule AB. of solid NaCl into one mole of Na+ (g) and one R = rA + rB (R is the bond length and rA and rB are mole of Cl– (g) to an infinite distance. the covalent radii of atoms A and B respectively) This process involves both the attractive forces between ions of opposite charges in the same molecule. The van der Waals and the repulsive forces between ions of radius represents the overall size of the like charge. The solid crystal being three- atom which includes its valence shell in a dimensional; it is not possible to calculate nonbonded situation. Further, the van der lattice enthalpy directly from the interaction Waals radius is half of the distance between of forces of attraction and repulsion only. two similar atoms in separate molecules in Factors associated with the crystal geometry a solid. Covalent and van der Waals radii of have to be included. chlorine are depicted in Fig. 4.2.

4.1 KÖssel-Lewis Approach to the number of valence electrons. This number Chemical Bonding of valence electrons helps to calculate the common or group valence of the element.In order to explain the formation of chemical The group valence of the elements is generallybond in terms of electrons, a number of either equal to the number of dots in Lewisattempts were made, but it was only in symbols or 8 minus the number of dots or1916 when Kössel and Lewis succeeded valence electrons.independently in giving a satisfactory explanation. They were the first to provide Kössel, in relation to chemical bonding, some logical explanation of valence which was drew attention to the following facts: based on the inertness of noble gases. • In the periodic table, the highly Lewis pictured the atom in terms of a electronegative halogens and the highly positively charged ‘Kernel’ (the nucleus plus electropositive alkali metals are separated by the noble gases;the inner electrons) and the outer shell that could accommodate a maximum of eight • The formation of a negative ion from a electrons. He, further assumed that these halogen atom and a positive ion from eight electrons occupy the corners of a cube an alkali metal atom is associated with which surround the ‘Kernel’. Thus the single the gain and loss of an electron by the outer shell electron of sodium would occupy respective atoms; one corner of the cube, while in the case of • The negative and positive ions thus a noble gas all the eight corners would be formed attain stable noble gas electronic occupied. This octet of electrons, represents configurations. The noble gases (with the a particularly stable electronic arrangement. exception of helium which has a duplet Lewis postulated that atoms achieve of electrons) have a particularly stable the stable octet when they are linked by outer shell configuration of eight (octet) chemical bonds. In the case of sodium and electrons, ns2np6. chlorine, this can happen by the transfer of • The negative and positive ions are stabilized an electron from sodium to chlorine thereby by electrostatic attraction. giving the Na+ and Cl– ions. In the case of For example, the formation of NaCl fromother molecules like Cl2, H2, F2, etc., the bond sodium and chlorine, according to the aboveis formed by the sharing of a pair of electrons scheme, can be explained as:between the atoms. In the process each atom attains a stable outer octet of electrons. Na → Na+ + e– Lewis Symbols: In the formation of a [Ne] 3s1 [Ne] molecule, only the outer shell electrons take Cl + e– → Cl– part in chemical combination and they are [Ne] 3s2 3p5 [Ne] 3s2 3p6 or [Ar] known as valence electrons. The inner shell Na+ + Cl– → NaCl or Na+Cl– electrons are well protected and are generally Similarly the formation of CaF2 may benot involved in the combination process. shown as:G.N. Lewis, an American chemist introduced simple notations to represent valence electrons Ca → Ca2+ + 2e– in an atom. These notations are called Lewis [Ar]4s2 [Ar] symbols. For example, the Lewis symbols for F + e– → F– the elements of second period are as under: [He] 2s2 2p5 [He] 2s2 2p6 or [Ne] Ca2+ + 2F– → CaF2 or Ca2+(F– )2 The bond formed, as a result of the Significance of Lewis Symbols : The electrostatic attraction between the number of dots around the symbol represents positive and negative ions was termed as Reprint 2025-26 102 chemistry the electrovalent bond. The electrovalence chlorine atoms attain the outer shell octet of is thus equal to the number of unit charge(s) the nearest noble gas (i.e., argon). on the ion. Thus, calcium is assigned a The dots represent electrons. Suchpositive electrovalence of two, while chlorine structures are referred to as Lewis dota negative electrovalence of one. structures. Kössel’s postulations provide the basis for The Lewis dot structures can be written forthe modern concepts regarding ion-formation other molecules also, in which the combiningby electron transfer and the formation of ionic atoms may be identical or different. Thecrystalline compounds. His views have proved important conditions being that:to be of great value in the understanding and • Each bond is formed as a result of sharingsystematisation of the ionic compounds. At of an electron pair between the atoms.the same time he did recognise the fact that • Each combining atom contributes at leasta large number of compounds did not fit into one electron to the shared pair.these concepts. • The combining atoms attain the outer-4.1.1 Octet Rule shell noble gas configurations as a result Kössel and Lewis in 1916 developed an of the sharing of electrons. important theory of chemical combination • Thus in water and carbon tetrachloridebetween atoms known as electronic theory molecules, formation of covalent bondsof chemical bonding. According to this, can be represented as: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. 4.1.2 Covalent Bond Langmuir (1919) refined the Lewis postulations by abandoning the idea of the stationary cubical arrangement of the octet, and by introducing the term covalent Thus, when two atoms share onebond. The Lewis-Langmuir theory can be electron pair they are said to be joined byunderstood by considering the formation of a single covalent bond. In many compoundsthe chlorine molecule, Cl2. The Cl atom with we have multiple bonds between atoms. Theelectronic configuration, [Ne]3s2 3p5, is one formation of multiple bonds envisages sharingelectron short of the argon configuration. of more than one electron pair between twoThe formation of the Cl­2 molecule can be atoms. If two atoms share two pairs ofunderstood in terms of the sharing of a pair electrons, the covalent bond between themof electrons between the two chlorine atoms, is called a double bond. For example, in theeach chlorine atom contributing one electron carbon dioxide molecule, we have two doubleto the shared pair. In the process both bonds between the carbon and oxygen atoms. Similarly in ethene molecule the two carbon atoms are joined by a double bond. or Cl – Cl Double bonds in CO2 molecule Covalent bond between two Cl atoms Reprint 2025-26 Chemical Bonding And Molecular Structure 103 number of valence electrons. For example, for the CO32– ion, the two negative charges indicate that there are two additional electrons than those provided by the neutral atoms. For NH4+ ion, one positive charge indicates the loss of one electron from the group of neutral atoms. C2H4 molecule • Knowing the chemical symbols of the When combining atoms share three combining atoms and having knowledge electron pairs as in the case of two nitrogen of the skeletal structure of the compound atoms in the N2 molecule and the two (known or guessed intelligently), it is easy carbon atoms in the ethyne molecule, a to distribute the total number of electrons triple bond is formed. 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 molecule/ion. For example in the NF3 and N2 molecule CO32–, 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 C2H2 molecule electron pairs are either utilized for multiple bonding or remain as the lone pairs. The basic requirement being4.1.3 Lewis Representation of Simple that each bonded atom gets an octet of Molecules (the Lewis Structures) electrons. The Lewis dot structures provide a picture Lewis representations of a few molecules/of bonding in molecules and ions in terms of ions are given in Table 4.1.the shared pairs of electrons and the octet rule. While such a picture may not explain the bonding and behaviour of a molecule Table 4.1 The Lewis Representation of completely, it does help in understanding the Some Molecules formation and properties of a molecule to a large extent. Writing of Lewis dot structures of molecules is, therefore, very useful. The Lewis dot structures can be written by adopting the following steps: • The total number of electrons required for writing the structures are obtained by adding the valence electrons of the combining atoms. For example, in the CH4 molecule there are eight valence electrons available for bonding (4 from carbon and 4 from the four hydrogen atoms). • For anions, each negative charge would mean addition of one electron. For cations, each positive charge would result in * Each H atom attains the configuration of helium subtraction of one electron from the total (a duplet of electrons) Reprint 2025-26 104 chemistry Problem 4.1 each of the oxygen atoms completing the octets on oxygen atoms. This, however, Write the Lewis dot structure of CO does not complete the octet on nitrogen molecule. if the remaining two electrons constitute Solution lone pair on it. 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: 2s2 2p2 Hence we have to resort to multiple and 2s2 2p4, respectively. The valence bonding between nitrogen and one of electrons available are 4 + 6 =10. the oxygen atoms (in this case a double bond). This leads to the following Lewis Step 2. The skeletal structure of CO is dot structures. 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 4.1.4 Formal Charge bond) between C and O atoms. This Lewis dot structures, in general, do not satisfies the octet rule condition for both represent the actual shapes of the molecules. atoms. In case of polyatomic ions, the net charge is possessed by the ion as a whole and not by a particular atom. It is, however, feasible to assign a formal charge on each atom. The formal charge of an atom in a polyatomic molecule or ion may be defined as the Problem 4.2 difference between the number of valence Write the Lewis structure of the nitrite electrons of that atom in an isolated or free ion, NO2– . state and the number of electrons assigned to that atom in the Lewis structure. It is Solution expressed as : Step 1. Count the total number of valence electrons of the nitrogen atom, Formal charge (F.C.) the oxygen atoms and the additional one on an atom in a Lewis = negative charge (equal to one electron). structure N(2s2 2p3), O (2s2 2p4) 5 + (2 × 6) +1 = 18 electrons total number of valence total number of non electrons in the free — bonding (lone pair) Step 2. The skeletal structure of NO2– is atom electrons written as : O N O total number of Step 3. Draw a single bond (one shared — (1/2) bonding (shared) electrons electron pair) between the nitrogen and Reprint 2025-26 Chemical Bonding And Molecular Structure 105 The counting is based on the assumption 4.1.5 Limitations of the Octet Rule that the atom in the molecule owns one The octet rule, though useful, is not universal. electron of each shared pair and both the It is quite useful for understanding the electrons of a lone pair. structures of most of the organic compounds Let us consider the ozone molecule (O3). and it applies mainly to the second period elements of the periodic table. There are threeThe Lewis structure of O3 may be drawn as: types of exceptions to the octet rule. 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. The atoms have been numbered as 1, 2 and 3. The formal charge on: • The central O atom marked 1 1 Li, Be and B have 1, 2 and 3 valence electrons = 6 – 2 – (6) = +1 only. Some other such compounds are AlCl3 2 and BF3.• The end O atom marked 2 Odd-electron molecules 1 = 6 – 4 – (4) = 0 In molecules with an odd number of electrons 2 like nitric oxide, NO and nitrogen dioxide, • The end O atom marked 3 NO2, the octet rule is not satisfied for all the 1 atoms = 6 – 6 – (2) = –1 2 Hence, we represent O3 along with the formal charges as follows: The expanded octet Elements in and beyond the third period of the periodic table have, apart from 3s and 3p orbitals, 3d orbitals also available for bonding. In a number of compounds of these elements there are more than eight valence electrons We must understand that formal charges around the central atom. This is termed as do not indicate real charge separation within the expanded octet. Obviously the octet rule the molecule. Indicating the charges on the does not apply in such cases. atoms in the Lewis structure only helps in Some of the examples of such compoundskeeping track of the valence electrons in are: PF5, SF6, H2SO4 and a number ofthe molecule. Formal charges help in the coordination compounds. 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. Reprint 2025-26 106 chemistry Interestingly, sulphur also forms many affinity, is the negative of the energy change compounds in which the octet rule is obeyed. accompanying electron gain. In sulphur dichloride, the S atom has an octet Obviously ionic bonds will be formed of electrons around it. more easily between elements with comparatively low ionization enthalpies and elements with comparatively high negative value of electron gain enthalpy.Other drawbacks of the octet theory Most ionic compounds have cations• It is clear that octet rule is based upon derived from metallic elements and anions the chemical inertness of noble gases. from non-metallic elements. The ammonium However, some noble gases (for example + ion, NH4 (made up of two non-metallic xenon and krypton) also combine with elements) is an exception. It forms the cation oxygen and fluorine to form a number of of a number of ionic compounds. compounds like XeF2, KrF2, XeOF2 etc. Ionic compounds in the crystalline • This theory does not account for the shape state consist of orderly three-dimensional of molecules. arrangements of cations and anions held • It does not explain the relative stability of together by coulombic interaction energies. the molecules being totally silent about These compounds crystallise in different crystal structures determined by the size of the energy of a molecule. the ions, their packing arrangements and

4.5 Valence Bond Theory of the valence bond theory is based on the knowledge of atomic orbitals, electronicAs we know that Lewis approach helps in configurations of elements (Units 2), thewriting the structure of molecules but it overlap criteria of atomic orbitals, thefails to explain the formation of chemical hybridization of atomic orbitals and thebond. It also does not give any reason for the principles of variation and superposition. Adifference in bond dissociation enthalpies and rigorous treatment of the VB theory in termsbond lengths in molecules like H2 (435.8 kJ of these aspects is beyond the scope of this mol-1, 74 pm) and F2 (155 kJ mol-1, 144 pm), book. Therefore, for the sake of convenience,although in both the cases a single covalent valence bond theory has been discussed in bond is formed by the sharing of an electron terms of qualitative and non-mathematical pair between the respective atoms. It also treatment only. To start with, let us consider gives no idea about the shapes of polyatomic the formation of hydrogen molecule which is molecules. the simplest of all molecules. Similarly the VSEPR theory gives the Consider two hydrogen atoms A and B geometry of simple molecules but theoretically, approaching each other having nuclei NA it does not explain them and also it has limited and NB and electrons present in them are applications. To overcome these limitations represented by eA and eB. When the two atoms the two important theories based on quantum are at large distance from each other, there mechanical principles are introduced. These is no interaction between them. As these two are valence bond (VB) theory and molecular atoms approach each other, new attractive orbital (MO) theory. and repulsive forces begin to operate. Valence bond theory was introduced Attractive forces arise between: by Heitler and London (1927) and developed (i) nucleus of one atom and its own electron further by Pauling and others. A discussion that is NA – eA and NB– eB. Reprint 2025-26 118 chemistry (ii) nucleus of one atom and electron of together to form a stable molecule having the other atom i.e., NA– eB, NB– eA. bond length of 74 pm. Similarly repulsive forces arise between Since the energy gets released when the bond is formed between two hydrogen atoms,(i) electrons of two atoms like eA – eB, the hydrogen molecule is more stable than (ii) nuclei of two atoms NA – NB. that of isolated hydrogen atoms. The energy Attractive forces tend to bring the two so released is called as bond enthalpy, which atoms close to each other whereas repulsive is corresponding to minimum in the curve forces tend to push them apart (Fig. 4.7). depicted in Fig. 4.8. 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) Fig. 4.8 The potential energy curve for the formation of H2 molecule as a function of internuclear distance of the H atoms. The minimum in the curve corresponds to the most stable state of H2. 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. ThisFig. 4.7 Forces of attraction and repulsion partial merging of atomic orbitals is called during the formation of H2 molecule overlapping of atomic orbitals which results in Experimentally it has been found that the pairing of electrons. The extent of overlap the magnitude of new attractive force is decides the strength of a covalent bond. Inmore than the new repulsive forces. As a general, greater the overlap the stronger is theresult, two atoms approach each other and bond formed between two atoms. Therefore,potential energy decreases. Ultimately a stage is reached where the net force of attraction according to orbital overlap concept, the balances the force of repulsion and system formation of a covalent bond between two acquires minimum energy. At this stage atoms results by pairing of electrons present two hydrogen atoms are said to be bonded in the valence shell having opposite spins. Reprint 2025-26 Chemical Bonding And Molecular Structure 119 4.5.2 Directional Properties of Bonds As we have already seen, the covalent bond is formed by overlapping of atomic orbitals. The molecule of hydrogen is formed due to the overlap of 1s-orbitals of two H atoms. 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 why is it so that CH4 molecule has tetrahedral shape and HCH bond angles are 109.5°? Why is the shape of NH3 molecule pyramidal ? The valence bond theory explains the shape, the formation and directional properties of bonds in polyatomic molecules like CH4, NH3 and H2O, etc. in terms of overlap and hybridisation of atomic orbitals. 4.5.3 Overlapping of Atomic Orbitals When orbitals of two atoms come close to form 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 (Fig. 4.9). Positive and negative sign on boundary surface diagrams in the Fig. 4.9 show the sign (phase) of orbital wave function and are not related to charge. Fig.4.9 Positive, negative and zero overlaps ofOrbitals forming bond should have same sign s and p atomic orbitals(phase) and orientation in space. This is called positive overlap. Various overlaps of s and p hydrogen. The four atomic orbitals of carbon, orbitals are depicted in Fig. 4.9. each with an unpaired electron can overlap with the 1s orbitals of the four H atoms which The criterion of overlap, as the main factor are also singly occupied. This will result in the for the formation of covalent bonds applies formation of four C-H bonds. It will, however, uniformly to the homonuclear/heteronuclear be observed that while the three p orbitals of diatomic molecules and polyatomic molecules. carbon are at 90° to one another, the HCH We know that the shapes of CH4, NH3, and angle for these will also be 90°. That is three H2O molecules are tetrahedral, pyramidal C-H bonds will be oriented at 90° to one and bent respectively. It would be therefore another. The 2s orbital of carbon and the 1s interesting to use VB theory to find out if these orbital of H are spherically symmetrical and geometrical shapes can be explained in terms they can overlap in any direction. Therefore of the orbital overlaps. the direction of the fourth C-H bond cannot Let us first consider the CH4 (methane) be ascertained. This description does not fit molecule. The electronic configuration of in with the tetrahedral HCH angles of 109.5°. carbon in its ground state is [He]2s2 2p2 which Clearly, it follows that simple atomic orbital in the excited state becomes [He] 2s1 2px1 2py1 overlap does not account for the directional 2pz1. The energy required for this excitation is characteristics of bonds in CH4. Using similar compensated by the release of energy due to procedure and arguments, it can be seen that in overlap between the orbitals of carbon and the the case of NH3 and H2O molecules, the HNH Reprint 2025-26 120 chemistry and HOH angles should be 90°. This is in above and below the plane of the disagreement with the actual bond angles of participating atoms. 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 types of overlapping: (i) Sigma(σ) bond, and (ii) pi(π) bond (i) Sigma(σ) bond : This type of covalent 4.5.5 Strength of Sigma and pi Bonds bond is formed by the end to end (head- Basically the strength of a bond depends on) overlap of bonding orbitals along the upon the extent of overlapping. In case of internuclear axis. This is called as head sigma bond, the overlapping of orbitals takes on overlap or axial overlap. This can be place to a larger extent. Hence, it is stronger formed by any one of the following types as compared to the pi bond where the extent of combinations of atomic orbitals. of overlapping occurs to a smaller extent. • s-s overlapping : In this case, there is Further, it is important to note that in the overlap of two half filled s-orbitals along formation of multiple bonds between two the internuclear axis as shown below : atoms of a molecule, pi bond(s) is formed in addition to a sigma bond. 4.6 Hybridisation In order to explain the characteristic geometrical shapes of polyatomic molecules • s-p overlapping: This type of overlap like CH4, NH3 and H2O etc., Pauling introduced occurs between half filled s-orbitals of one the concept of hybridisation. According to him atom and half filled p-orbitals of another the atomic orbitals combine to form new set of atom. equivalent orbitals known as hybrid orbitals. Unlike pure orbitals, the hybrid orbitals are used in bond formation. The phenomenon is known as hybridisation which can be defined as the process of intermixing of the orbitals of • p–p overlapping : This type of overlap slightly different energies so as to redistribute takes place between half filled p-orbitals their energies, resulting in the formation of of the two approaching atoms. new set of orbitals of equivalent energies and shape. For example when one 2s and three 2p-orbitals of carbon hybridise, there is the formation of four new sp3 hybrid orbitals. Salient features of hybridisation: The main (ii) pi( ) bond : In the formation of π bond features of hybridisation are as under : the atomic orbitals overlap in such a 1. The number of hybrid orbitals is equal to way that their axes remain parallel to the number of the atomic orbitals that get each other and perpendicular to the internuclear axis. The orbitals formed hybridised. due to sidewise overlapping consists 2. The hybridised orbitals are always of two saucer type charged clouds equivalent in energy and shape. Reprint 2025-26 Chemical Bonding And Molecular Structure 121 3. The hybrid orbitals are more effective in vacant 2p orbital to account for its bivalency. forming stable bonds than the pure atomic One 2s and one 2p-orbital gets hybridised to orbitals. form two sp hybridised orbitals. These two sp hybrid orbitals are oriented in opposite4. These hybrid orbitals are directed in direction forming an angle of 180°. Each of space in some preferred direction to have the sp hybridised orbital overlaps with the minimum repulsion between electron 2p-orbital of chlorine axially and form two Be- pairs and thus a stable arrangement. Cl sigma bonds. This is shown in Fig. 4.10. 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 are hybridised. (ii) The orbitals undergoing hybridisation Be 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. Fig.4.10 (a) Formation of sp hybrids from s and 4.6.1 Types of Hybridisation p orbitals; (b) Formation of the linear There are various types of hybridisation BeCl2 molecule involving s, p and d orbitals. The different (II) sp2 hybridisation : In this hybridisationtypes of hybridisation are as under: there is involvement of one s and two (I) sp hybridisation: This type of hybridisation p-orbitals in order to form three equivalent involves the mixing of one s and one p orbital sp2 hybridised orbitals. For example, in resulting in the formation of two equivalent BCl3 molecule, the ground state electronicsp hybrid orbitals. The suitable orbitals for configuration of central boron atom is sp hybridisation are s and pz, if the hybrid 1s22s22p1. In the excited state, one of the 2s orbitals are to lie along the z-axis. Each sp electrons is promoted to vacant 2p orbital as hybrid orbitals has 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. This type of hybridisation is also known as diagonal hybridisation. The two sp hybrids point in the opposite direction along the z-axis with projecting positive lobes and very small negative lobes, which 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 1s22s2. In the exited Fig.4.11 Formation of sp2 hybrids and the BCl3 state one of the 2s-electrons is promoted to molecule Reprint 2025-26 122 chemistry a result boron has three unpaired electrons. ground state is 2S 2 2 p 1x 2 p 1y 2 p 1z having threeThese three orbitals (one 2s and two 2p) unpaired electrons in the sp3 hybrid orbitalshybridise to form three sp2 hybrid orbitals. and a lone pair of electrons is present in theThe three hybrid orbitals so formed are fourth one. These three hybrid orbitals overlaporiented in a trigonal planar arrangement with 1s orbitals of hydrogen atoms to formand overlap with 2p orbitals of chlorine to three N–H sigma bonds. We know that the form three B-Cl bonds. Therefore, in BCl3 force of repulsion between a lone pair and a(Fig. 4.11), the geometry is trigonal planar bond pair is more than the force of repulsionwith ClBCl bond angle of 120°. between two bond pairs of electrons. The (III) sp 3 hybridisation: This type of molecule thus gets distorted and the bond hybridisation can be explained by taking the angle is reduced to 107° from 109.5°. The example of CH4 molecule in which there is geometry of such a molecule will be pyramidal mixing of one s-orbital and three p-orbitals as shown in Fig. 4.13. of the valence shell to form four sp3 hybrid orbital of equivalent energies and shape. There is 25% s-character and 75% p-character in each sp3 hybrid orbital. The four sp3 hybrid orbitals so formed are directed towards the four corners of the tetrahedron. The angle between sp3 hybrid orbital is 109.5° as shown in Fig. 4.12. Fig.4.13 Formation of NH3 molecule In case of H2O molecule, the four oxygen orbitals (one 2s and three 2p) undergo sp3 hybridisation forming four sp3 hybrid orbitals out of which two contain one electron each and the other two contain a pair of electrons. These σ four sp3 hybrid orbitals acquire a tetrahedral geometry, with two corners occupied by σ σ 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. 4.14) σ and the molecule thus acquires a V-shape or angular geometry. Fig.4.12 Formation of sp3 hybrids by the combination of s, px , py and pz atomic orbitals of carbon and the formation of CH4 molecule The structure of NH3 and H2O molecules can also be explained with the help of sp3 hybridisation. In NH3, the valence shell (outer) electronic configuration of nitrogen in the Fig.4.14 Formation of H2O molecule Reprint 2025-26 Chemical Bonding And Molecular Structure 123 4.6.2 Other Examples of sp3, sp2 and sp used for making sp2–s sigma bond with two Hybridisation hydrogen atoms. The unhybridised orbital (2px sp3 Hybridisation in C2H6 molecule: In or 2py) of one carbon atom overlaps sidewise ethane molecule both the carbon atoms with the similar orbital of the other carbon assume sp3 hybrid state. One of the four atom to form weak π bond, which consists of sp3 hybrid orbitals of carbon atom overlaps two equal electron clouds distributed above axially with similar orbitals of other atom to and below the plane of carbon and hydrogen form sp3-sp3 sigma bond while the other three atoms. hybrid orbitals of each carbon atom are used Thus, in ethene molecule, the carbon-in forming sp3–s sigma bonds with hydrogen carbon bond consists of one sp2–sp2 sigmaatoms as discussed in section 4.6.1(iii). bond and one pi (π ) bond between p orbitalsTherefore in ethane C–C bond length is 154 which are not used in the hybridisation andpm and each C–H bond length is 109 pm. are perpendicular to the plane of molecule; thesp2 Hybridisation in C2H4: In the formation bond length 134 pm. The C–H bond is sp2–sof ethene molecule, one of the sp2 hybrid sigma with bond length 108 pm. The H–C–Horbitals of carbon atom overlaps axially with bond angle is 117.6° while the H–C–C anglesp2 hybridised orbital of another carbon atom is 121°. The formation of sigma and pi bondsto form C–C sigma bond. While the other two sp2 hybrid orbitals of each carbon atom are in ethene is shown in Fig. 4.15. Fig. 4.15 Formation of sigma and pi bonds in ethene Reprint 2025-26 124 chemistry sp Hybridisation in C2H2 : In the formation 4.6.3 Hybridisation of Elements of ethyne molecule, both the carbon atoms involving d Orbitals undergo sp-hybridisation having two The elements present in the third period unhybridised orbital i.e., 2py and 2px. contain d orbitals in addition to s and p orbitals. The energy of the 3d orbitals are One sp hybrid orbital of one carbon atom comparable to the energy of the 3s and 3poverlaps axially with sp hybrid orbital of the orbitals. The energy of 3d orbitals are also other carbon atom to form C–C sigma bond, comparable to those of 4s and 4p orbitals. while the other hybridised orbital of each As a consequence the hybridisation involving carbon atom overlaps axially with the half either 3s, 3p and 3d or 3d, 4s and 4p is filled s orbital of hydrogen atoms forming possible. However, since the difference in σ bonds. Each of the two unhybridised p energies of 3p and 4s orbitals is significant, no orbitals of both the carbon atoms overlaps hybridisation involving 3p, 3d and 4s orbitals sidewise to form two π bonds between the is possible. carbon atoms. So the triple bond between the The important hybridisation schemes two carbon atoms is made up of one sigma involving s, p and d orbitals are summarised and two pi bonds as shown in Fig. 4.16. below: Shape of Hybridisation Atomic molecules/ Examples type orbitals ions Square dsp2 d+s+p(2) [Ni(CN)4]2–, planar [Pt(Cl)4]2– Trigonal sp3d s+p(3)+d PF5, PCl5 bipyramidal Square sp3d2 s+p(3)+d(2) BrF5 pyramidal Octahedral sp3d2 s+p(3)+d(2) SF6, [CrF6]3– d2sp3 d(2)+s+p(3) [Co(NH3)6]3+ (i) Formation of PCl5 (sp3d hybridisation): The ground state and the excited state outer electronic configurations of phosphorus (Z=15) are represented below. Fig.4.16 Formation of sigma and pi bonds in sp3d hybrid orbitals filled by electron pairs ethyne donated by five Cl atoms. Reprint 2025-26 Chemical Bonding And Molecular Structure 125 Now the five orbitals (i.e., one s, three six sp3d2 hybrid orbitals overlap with singly p and one d orbitals) are available for occupied orbitals of fluorine atoms to form hybridisation to yield a set of five sp3d hybrid six S–F sigma bonds. Thus SF6 molecule has orbitals which are directed towards the five a regular octahedral geometry as shown in corners of a trigonal bipyramidal as depicted Fig. 4.18. in the Fig. 4.17. sp3d2 hybridisation Fig. 4.17 Trigonal bipyramidal geometry of PCl5 molecule It should be noted that all the bond angles in trigonal bipyramidal geometry are not equivalent. In PCl5 the 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 plane and make an angle of 120° with each other; these bonds are termed as equatorial Fig. 4.18 Octahedral geometry of SF6 moleculebonds. The remaining two P–Cl bonds–one lying above and the other lying below the equatorial plane, make an angle of 90° with 4.7 Molecular Orbital Theory the plane. These bonds are called axial bonds. Molecular orbital (MO) theory was developed As the axial bond pairs suffer more repulsive by F. Hund and R.S. Mulliken in 1932. The interaction from the equatorial bond pairs, salient features of this theory are : therefore axial bonds have been found to (i) The electrons in a molecule are present be slightly longer and hence slightly weaker in the various molecular orbitals as the than the equatorial bonds; which makes PCl5 electrons of atoms are present in the molecule more reactive. various atomic orbitals. (ii) Formation of SF6 (sp3d2 hybridisation): (ii) The atomic orbitals of comparableIn SF6 the central sulphur atom has the energies and proper symmetry combineground state outer electronic configuration to form molecular orbitals.3s23p4. In the exited state the available six orbitals i.e., one s, three p and two d are (iii) While an electron in an atomic orbital singly occupied by electrons. These orbitals is influenced by one nucleus, in a hybridise to form six new sp3d2 hybrid molecular orbital it is influenced by orbitals, which are projected towards the six two or more nuclei depending upon the corners of a regular octahedron in SF6. These number of atoms in the molecule. Thus, Reprint 2025-26 126 chemistry an atomic orbital is monocentric while ψA and ψB. Mathematically, the formation of a molecular orbital is polycentric. molecular orbitals may be described by the linear combination of atomic orbitals that can(iv) The number of molecular orbital formed take place by addition and by subtraction of is equal to the number of combining wave functions of individual atomic orbitals atomic orbitals. When two atomic as shown below : orbitals combine, two molecular orbitals are formed. One is known as bonding ψMO = ψA + ψB molecular orbital while the other is Therefore, the two molecular orbitals called antibonding molecular orbital. σ and σ* are formed as : (v) The bonding molecular orbital has σ = ψA + ψB lower energy and hence greater stability σ* = ψA – ψB than the corresponding antibonding The molecular orbital σ formed by the molecular orbital. addition of atomic orbitals is called the bonding (vi) Just as the electron probability molecular orbital while the molecular orbital distribution around a nucleus in an σ* formed by the subtraction of atomic orbital atom is given by an atomic orbital, the is called antibonding molecular orbital as electron probability distribution around depicted in Fig. 4.19. 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. 4.7.1 Formation of Molecular Orbitals Linear Combination of Atomic σ* = ψA – ψB Orbitals (LCAO) According to wave mechanics, the atomic ψA ψBorbitals can be expressed by wave functions (ψ ’s) which represent the amplitude of the σ = ψA + ψBelectron 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 Fig.4.19 Formation of bonding (σ) and antibonding (σ*) molecular orbitals by the linearto obtain directly from the solution of combination of atomic orbitals ψA andSchrödinger wave equation. To overcome this problem, an approximate method known ψB centered on two atoms A and B respectively.as linear combination of atomic orbitals (LCAO) has been adopted. Qualitatively, the formation of molecular Let us apply this method to the orbitals can be understood in terms of the homonuclear diatomic hydrogen molecule. constructive or destructive interference of the Consider the hydrogen molecule consisting electron waves of the combining atoms. In the of two atoms A and B. Each hydrogen atom formation of bonding molecular orbital, the in the ground state has one electron in 1s two electron waves of the bonding atoms orbital. The atomic orbitals of these atoms reinforce each other due to constructive may be represented by the wave functions interference while in the formation of Reprint 2025-26 Chemical Bonding And Molecular Structure 127 antibonding molecular orbital, the electron as the molecular axis. It is important to note waves cancel each other due to destructive that atomic orbitals having same or nearly interference. As a result, the electron density in the same energy will not combine if they do a bonding molecular orbital is located between not have the same symmetry. For example, the nuclei of the bonded atoms because of 2pz orbital of one atom can combine with 2pz which the repulsion between the nuclei is very orbital of the other atom but not with the less while in case of an antibonding molecular 2px or 2py orbitals because of their different orbital, most of the electron density is located symmetries. away from the space between the nuclei. 3. The combining atomic orbitals must Infact, there is a nodal plane (on which the overlap to the maximum extent. Greater electron density is zero) between the nuclei the extent of overlap, the greater will be the and hence the repulsion between the nuclei is electron-density between the nuclei of a high. Electrons placed in a bonding molecular molecular orbital. orbital tend to hold the nuclei together and 4.7.3 Types of Molecular Orbitalsstabilise a molecule. Therefore, a bonding molecular orbital always possesses lower Molecular orbitals of diatomic molecules are energy than either of the atomic orbitals that designated as σ (sigma), π (pi), δ(delta), etc. have combined to form it. In contrast, the In this nomenclature, the sigma ( ) electrons placed in the antibonding molecular molecular orbitals are symmetrical around orbital destabilise the molecule. This is the bond-axis while pi ( ) molecular orbitals because the mutual repulsion of the electrons are not symmetrical. For example, the linear in this orbital is more than the attraction combination of 1s orbitals centered on two between the electrons and the nuclei, which nuclei produces two molecular orbitals which causes a net increase in energy. are symmetrical around the bond-axis. Such It may be noted that the energy of the molecular orbitals are of the σ type and are antibonding orbital is raised above the designated as σ1s and σ*1s [Fig. 4.20(a), page energy of the parent atomic orbitals that 124]. If internuclear axis is taken to be in have combined and the energy of the bonding the z-direction, it can be seen that a linear orbital has been lowered than the parent combination of 2pz- orbitals of two atoms orbitals. The total energy of two molecular also produces two sigma molecular orbitals orbitals, however, remains the same as that designated as 2pz and *2pz. [Fig. 4.20(b)] of two original atomic orbitals. Molecular orbitals obtained from 2px and 4.7.2 Conditions for the Combination of 2py orbitals are not symmetrical around the Atomic Orbitals bond axis because of the presence of positive lobes above and negative lobes below theThe linear combination of atomic orbitals to molecular plane. Such molecular orbitals,form molecular orbitals takes place only if the are labelled as π and =π* [Fig. 4.20(c)]. Afollowing conditions are satisfied: π bonding MO has larger electron density1. The combining atomic orbitals must above and below the inter-nuclear axis. Thehave the same or nearly the same energy. π* antibonding MO has a node between theThis means that 1s orbital can combine with nuclei.another 1s orbital but not with 2s orbital because the energy of 2s orbital is appreciably 4.7.4 Energy Level Diagram for Molecular higher than that of 1s orbital. This is not true Orbitals if the atoms are very different. We have seen that 1s atomic orbitals on two 2. The combining atomic orbitals must atoms form two molecular orbitals designated have the same symmetry about the as σ1s and σ*1s. In the same manner, the 2s molecular axis. By convention z-axis is taken and 2p atomic orbitals (eight atomic orbitals Reprint 2025-26 128 chemistry Fig. 4.20 Contours and energies of bonding and antibonding molecular orbitals formed through combinations of (a) 1s atomic orbitals; (b) 2pz atomic orbitals and (c) 2px atomic orbitals. on two atoms) give rise to the following eight The energy levels of these molecular molecular orbitals: orbitals have been determined experimentally from spectroscopic data for homonuclearAntibonding MOs σ∗2s σ∗2pz π∗2px π∗2py diatomic molecules of second row elements Bonding MOs σ2s σ2pz π2px π2py of the periodic table. The increasing order of Reprint 2025-26 Chemical Bonding And Molecular Structure 129 energies of various molecular orbitals for O2 The rules discussed above regarding the and F2 is given below: stability of the molecule can be restated in terms of bond order as follows: A positive bond1s <  ∗1s <  2s <  ∗2s < 2pz < (π 2px=π 2py) order (i.e., Nb > Na) means a stable molecule < (π ∗2px= π∗ 2py) <  ∗2pz while a negative (i.e., Nb<Na) or zero (i.e., However, this sequence of energy levels Nb = Na) bond order means an unstable of molecular orbitals is not correct for the molecule. remaining molecules Li2, Be2, B2, C2, N2. For Nature of the bond instance, it has been observed experimentally Integral bond order values of 1, 2 or 3 that for molecules such as B2, C2, N2, etc. correspond to single, double or triple bonds the increasing order of energies of various respectively as studied in the classical molecular orbitals is concept. 1s <  ∗1s < 2s <  ∗2s < (π 2 px = π 2 py) Bond-length < 2pz < (π ∗2px =π∗2py) <  ∗2pz The bond order between two atoms in a The important characteristic feature molecule may be taken as an approximate of this order is that the energy of 2pz measure of the bond length. The bond length molecular orbital is higher than that decreases as bond order increases. of 2px and 2py molecular orbitals. Magnetic nature 4.7.5 Electronic Configuration and If all the molecular orbitals in a molecule are Molecular Behaviour doubly occupied, the substance is diamagnetic (repelled by magnetic field). However if one orThe distribution of electrons among various more molecular orbitals are singly occupied itmolecular orbitals is called the electronic is paramagnetic (attracted by magnetic field),configuration of the molecule. From the e.g., O2 molecule.electronic configuration of the molecule, it is possible to get important information about 4.8 BONDING IN SOME HOMONUCLEAR the molecule as discussed below. DIATOMIC MOLECULES Stability of Molecules: If Nb is the number In this section we shall discuss bonding in of electrons occupying bonding orbitals and some homonuclear diatomic molecules. Na the number occupying the antibonding 1. Hydrogen molecule (H2 ): It is formed byorbitals, then the combination of two hydrogen atoms. Each (i) the molecule is stable if Nb is greater hydrogen atom has one electron in 1s orbital. than Na, and Therefore, in all there are two electrons in (ii) the molecule is unstable if Nb is less hydrogen molecule which are present in σ1s than Na. molecular orbital. So electronic configuration of hydrogen molecule is In (i) more bonding orbitals are occupied and so the bonding influence is stronger and a H2 : (σ1s)2 stable molecule results. In (ii) the antibonding The bond order of H2 molecule can be influence is stronger and therefore the calculated as given below: molecule is unstable. N b  N a 2  0 Bond order Bond order =   1 2 2 Bond order (b.o.) is defined as one half the This means that the two hydrogen atoms difference between the number of electrons are bonded together by a single covalent bond. present in the bonding and the antibonding The bond dissociation energy of hydrogen orbitals i.e., molecule has been found to be 438 kJ mol–1 and bond length equal to 74 pm. Since no Bond order (b.o.) = ½ (Nb–Na) Reprint 2025-26 130 chemistry unpaired electron is present in hydrogen vapour phase. It is important to note that molecule, therefore, it is diamagnetic. double bond in C2 consists of both pi bonds 2. Helium molecule (He2 ): The electronic because of the presence of four electrons in configuration of helium atom is 1s2. Each two pi molecular orbitals. In most of the other helium atom contains 2 electrons, therefore, molecules a double bond is made up of a in He2 molecule there would be 4 electrons. sigma bond and a pi bond. In a similar fashion the bonding in N2 molecule can be discussed.These electrons will be accommodated in σ1s and σ*1s molecular orbitals leading to 5. Oxygen molecule (O2 ): The electronic electronic configuration: configuration of oxygen atom is 1s2 2s2 2p4. Each oxygen atom has 8 electrons, hence, He2 : (σ1s)2 (σ*1s)2 in O2 molecule there are 16 electrons. The electronic configuration of O2 molecule, Bond order of He2 is ½(2 – 2) = 0 therefore, is He2 molecule is therefore unstable and does not exist. O2 : (1s)2 ( ∗1s)2 ( 2s)2 ( ∗ 2s)2 (2pz)2 Similarly, it can be shown that Be2 molecule (π2px2 ≡ π2py2) (π∗2p1x ≡ π ∗2py1) (σ1s)2 (σ*1s)2 (σ2s)2 (σ*2s)2 also does not exist. 3. Lithium molecule (Li2 ): The electronic O2 :configuration of lithium is 1s2, 2s1. There are six electrons in Li2. The electronic configuration of Li2 molecule, therefore, is From the electronic configuration of O2 molecule it is clear that ten electrons are Li2 : (σ1s)2 (σ*1s)2 (σ2s)2 present in bonding molecular orbitals and six The above configuration is also written electrons are present in antibonding molecular as KK(σ2s)2 where KK represents the closed orbitals. Its bond order, therefore, is K shell structure (σ1s)2 (σ*1s)2. From the electronic configuration of Li2 Bond order = [Nb – Na] = [10 – 6] =2 molecule it is clear that there are four electrons So in oxygen molecule, atoms are heldpresent in bonding molecular orbitals and two by a double bond. Moreover, it may be notedelectrons present in antibonding molecular that it contains two unpaired electrons inorbitals. Its bond order, therefore, is ½ (4 – π∗2px and π∗2py molecular orbitals, therefore,2) = 1. It means that Li2 molecule is stable and since it has no unpaired electrons it O2 molecule should be paramagnetic, a prediction that corresponds toshould be diamagnetic. Indeed diamagnetic experimental observation. In this way, theLi2 molecules are known to exist in the theory successfully explains the paramagneticvapour phase. nature of oxygen. 4. Carbon molecule (C2 ): The electronic Similarly, the electronic configurationsconfiguration of carbon is 1s2 2s2 2p2. There of other homonuclear diatomic molecules of [ ]are twelve electrons in C2. The electronic the second row of the periodic table can be configuration of C2 molecule, therefore, is written. In Fig. 4.21 are given the molecular C2 : (1s)2 ( ∗1s)2 ( ∗ 2s)2 (π2p2x = π2p2y) orbital occupancy and molecular properties for B2 through Ne2. The sequence of MOs and or KK (2s)2 ( ∗ 2s)2 (π2p2x = π2p2y) their electron population are shown. The bond energy, bond length, bond order, magnetic The bond order of C2 is ½ (8 – 4) = 2 properties and valence electron configurationand C2 should be diamagnetic. Diamagnetic appear below the orbital diagrams.C2 molecules have indeed been detected in Reprint 2025-26 Chemical Bonding And Molecular Structure 131 Fig. 4.21 MO occupancy and molecular properties for B2 through Ne2.