Chemical Bonding

A chemical bond is the force that holds together two or more atoms, molecules or ions. The properties of a substance depend on the type of chemical bond between its atoms. The term chemical bond includes ionic, covalent, dative and metallic bonds, as well as intermolecular forces (van der Waals forces) — but van der Waals forces, being weak, are usually not termed pure chemical bonds. NaCl has an ionic bond and is a solid, while water is a covalent compound and a liquid.

Lewis concept of bonding: atoms make bonds to complete their outermost shells and attain a noble-gas-like configuration. This is mostly attained through the formation of an octet in the valence shell.

3.1.1 Ionic bond. An ionic bond is formed by the complete transfer of electrons from an atom with low ionization energy to another atom with high electron affinity. Sodium, ₁₁Na = (2, 8, 1), tends to lose its outermost electron to form Na⁺ (2, 8), which has the electronic configuration of ₁₀Ne, the noble gas nearest to it. Chlorine, Cl (2, 8, 7), gains one electron to form the chloride ion, Cl⁻ (2, 8, 8), also gaining the next noble-gas arrangement. The oppositely charged Na⁺ and Cl⁻ ions are held together by a strong ionic bond in the crystal of NaCl. A similar bond is expected between group 1 and 2 metals and group 16 and 17 elements.

3.1.2 Covalent bond (electron pair bond). A covalent bond is formed by the mutual sharing of electrons between two atoms. While sharing electrons, each atom completes its valence shell and attains the nearest noble-gas configuration. The bond between two Cl atoms is purely covalent and non-polar, because the electronegativity of the two atoms is exactly the same, so the bonded atoms remain electrically neutral and there is no charge on either atom. Other such molecules are H₂, F₂, Br₂ and I₂. Examples of polar covalent bonds are H–Cl, H–Br and H₂O.

3.1.3 Dative bond (coordinate covalent bond). A dative bond is formed between two atoms when the shared pair of electrons is donated by one of the bonding atoms. For example, in the formation of the oxonium (hydronium) ion, H₃O⁺: H₂O has two covalent bonds and two lone pairs of electrons on the oxygen atom, while the proton H⁺ is deficient in electrons. The oxygen atom donates its lone pair to the acceptor H⁺, forming a dative bond.

Carbon monoxide also contains a dative bond between oxygen and carbon. Oxygen shares its two valence-shell electrons with the carbon atom to make a normal double covalent bond, but the valency of carbon is not satisfied with these bonds — it needs one more pair of electrons to complete its octet. Oxygen donates one of its lone pairs for the formation of a covalent bond, which is a dative bond. In the ozone molecule, one oxygen atom donates a pair of electrons to make a coordinate covalent bond with a free radical oxygen atom: the central atom has three bonds in total, including a double covalent bond on one side and a coordinate covalent bond on the other. It carries a positive charge, while the oxygen atom that accepts the lone pair carries a negative charge.

📌 Note (Quick Check 3.1): the book asks students to draw the Lewis structures of N₂ and CS₂, to count the valence-shell electrons of B in BF₃ (B has 6 electrons in its valence shell and can accept a lone pair), and to show the dative bond between NH₃ and BF₃ (N donates its lone pair to B).

3.1.4 Expanded octet in polyatomic ions. Polyatomic ions are ions composed of more than one type of atom. Their formal charge is the net charge on them, calculated on the basis of the number of electrons in their valence shells after the formation of bonds. With the exception of ammonium ion (NH₄⁺), these ions mostly carry a negative charge — for example carbonate (CO₃²⁻), sulphate (SO₄²⁻) and nitrate (NO₃⁻). In some polyatomic ions, the central atom violates the octet rule by expanding its electron density to the higher orbitals. These are said to have expanded octets; prominent examples are SO₄²⁻, ClO₄⁻ and PO₄³⁻.

From the Lewis structure of SO₄²⁻, the number of electrons in the valence shell of the S atom is: 2 × (number of double-bond electrons) + 2 × (number of single-bond electrons) = 2(4) + 2(2) = 12. So S has 12 electrons in its valence shell and exceeds the octet by 4 electrons. The expansion of the octet is caused by the involvement of the d orbital in bonding, which can accommodate the extra electrons. Native S has two unpaired electrons in its p orbitals; the d orbital allows this configuration to extend to 4 unpaired electrons by transferring one electron from 3s and one from the 3p pair. This explains not only the variable oxidation states of S, but also the possibility of accepting extra electrons in its d orbital.

In the same way, the number of valence electrons around the central iodine atom in the tri-iodide ion (I₃⁻) is: 2 × (number of single-bond electrons) + 2 × (number of lone pairs) = 2(2) + 2(3) = 10. The central iodine atom in I₃⁻ has 10 electrons in its valence shell and the octet expands by two electrons.

📌 Note (Quick Check 3.2): period 2 elements cannot have expanded octets, because they have no d orbitals in their valence shell — only period 3 and higher elements can expand their octet.

The concept of electronegativity has been discussed in detail in chapter 1. Here we discuss its effect on the type of bonding. The difference in electronegativity of two bonded atoms provides an approximate measure of the bond polarity and an indication of the type of bond. When this difference is very small or zero, the bond is covalent and non-polar. When it is large, the bond is polar covalent or ionic.

Two atoms having an electronegativity difference less than 0.4 are said to make a pure covalent bond. An electronegativity difference between 0.4 and 1.8 corresponds to a polar covalent bond, whereas above this value the bond between two atoms will be ionic in nature. The electronegativity differences between the atoms in H–H, H–Cl and NaCl are 0 (non-polar), 0.9 (polar covalent) and 2.1 (ionic) respectively. This is why the H–H bond is purely non-polar, H–Cl a polar covalent bond, whereas NaCl is an ionic compound. As the electronegativity difference increases, covalent character decreases and ionic character increases.

📌 Note on the SLOs: this chapter itself does not give a fresh definition of electronegativity, nor its factors (nuclear charge, shielding by inner shells) or its periodic trends — the book states that electronegativity was discussed in detail in chapter 1, and this chapter only applies the electronegativity-difference rule above. No passage on those trends has been invented here.

3.2.1 Dipole moment and polarity of molecules. In compounds such as HF, where the bonded atoms are from different elements, the electronic distribution between the atoms is uneven. One atom carries a partial positive charge and the other a partial negative charge. A molecule with a δ⁺ charge on one part and δ⁻ charge on the other part is called a dipole, and such a molecule is said to have a dipole moment. It is a quantitative measurement of the polarity of a bond or a molecule. The dipole moments of diatomic molecules like HF, HCl, HBr, HI and NO are directed from the positive ends (δ⁺) to the negative ends (δ⁻). Dipole moment is measured in Debye units (D). A higher dipole moment indicates higher polarity in a molecule. In HF the electron density is higher near the F atom and the dipole moment is directed from H to F.

For compounds having more than two atoms, the dipole moment depends on the structure of the molecule. The dipole moment of water is 1.85 D, directed from the end having the two hydrogen atoms to the end with the oxygen atom. A linear H₂O molecule (H–O–H) would have zero dipole moment. The non-zero dipole moment value shows that water is a non-linear molecule. Experiments reveal that the water molecule has a V-shaped structure. In contrast, SO₂ has a dipole moment of 1.61 D and is in the opposite direction to that in water. H₂S is also a non-linear molecule, as the individual bonds are polar, but they do not cancel each other's dipole moment and the overall molecule has some dipole moment.

However, some molecules have net zero dipole moments because symmetry in their structures causes cancellation of the individual bond moments. For example, BeCl₂ is a linear molecule having similar Cl atoms on both sides of the central atom at 180°. The individual Be–Cl bond moments are cancelled out as they are opposite in direction and equal in amount. Similarly, CCl₄ has four C–Cl bonds which are expected to have high polarity due to a large electronegativity difference between C and Cl atoms. The bond moments associated with the four C–Cl bonds are directed in such a way that they cancel each other. The net dipole moment of the CCl₄ molecule is zero, making it a non-polar molecule. The CCl₄ molecule is perfectly tetrahedral. Similarly, BF₃ has a trigonal planar symmetrical structure and its dipole moment is also zero. As a rule, molecules that have the same ligands (atoms or groups of atoms) with the central atom in a regular geometry have individual dipole moments that may not be zero, but the molecule has a net zero dipole moment. Such molecules are said to be non-polar.

📌 Note (Quick Check 3.3): predict with electronegativity values whether HF, KI, CaF₂, ICl and Br₂ are non-polar covalent, polar covalent or ionic — HF is polar covalent, KI and CaF₂ are ionic (large differences), ICl is polar covalent and Br₂ is non-polar (zero difference). (Quick Check 3.4): CO has a dipole moment because it is unsymmetrical (C and O differ in electronegativity and the bond moments cannot cancel), while linear, symmetrical CO₂ has a zero dipole moment; the individual C–Cl bonds in CCl₄ are polar but the molecule overall is non-polar; HF, CH₂Cl₂, O₂ and H₂S are polar, polar, non-polar and polar respectively.

Intermolecular forces are also considered binding forces, just like chemical bonds. However, the attraction between the molecules is much weaker than the chemical bonds. These forces are believed to exist between all kinds of atoms and molecules when they are sufficiently close to each other. Such intermolecular forces are called van der Waals forces. These intermolecular forces bring the molecules close together and give particular physical properties to the substances in gaseous, liquid and solid states.

Three types of such forces are mentioned here:

• i) Instantaneous dipole–induced dipole forces or London dispersion forces — momentary, uneven electron distribution creates a temporary dipole in one particle, which induces a dipole in a neighbour.
• ii) Permanent dipole–permanent dipole forces — the attraction between the permanent partial charges of two polar molecules.
• iii) Hydrogen bonding — the attraction involving a hydrogen atom bonded to a highly electronegative atom and a lone pair on a neighbouring electronegative atom.

📌 Honest book limit: this chapter only names these three types. The book itself says: "The detailed discussion on these forces will be made in the chapter on states and phases of matter (Chapter 5)." So no detailed passage on hydrogen bonding in ammonia and water, and no passage on the anomalous properties of water, exists in this chapter — those SLO wordings are noted here, not invented as book text. What the chapter does give is the strength scale in Table 3.3 (section 3.5): an average hydrogen bond is 20–50 kJ mol⁻¹, against 760 kJ mol⁻¹ for the ionic bond in NaCl and 464 kJ mol⁻¹ for the O–H covalent bond in water — intermolecular forces are far weaker than true chemical bonds.

The bond energy is the average amount of energy required to break all bonds of a particular type in one mole of a substance. It is determined experimentally by measuring the heat involved in a chemical reaction, and its unit is kJ mol⁻¹. Bond energy is a measure of the strength of a bond and its reactivity. The strength of a bond depends on the following factors: electronegativity difference of bonded atoms and size of atoms.

Some average bond energies (Table 3.1, kJ mol⁻¹): H–H 432, H–F 565, H–Cl 427, H–Br 363, H–I 295, C–H 413, C–C 347, C–O 358, N–H 391, O–H 467, C=C 614, C≡C 839, C=O 745, O=O 495, N≡N 941. Consider the role played by electronegativity difference in H–X compounds, where X = F, Cl, Br, I. The data shows that the bond energy of a bond rises with the increasing electronegativity difference between the bonded atoms. As the difference in electronegativity increases, the bond polarity also becomes greater, and this gives rise to additional attractive force for binding the atoms. This is why the bond energy for HF is higher (565 kJ mol⁻¹) than for HI (295 kJ mol⁻¹). It may be noted that the energies of multiple bonds are greater than those of single bonds: C≡C > C=C > C–C.

Bond length is the distance between the nuclei of two atoms forming a covalent bond. Bond lengths are experimentally determined by physical techniques such as electron diffraction, X-ray diffraction or spectral studies. The bond length of a bond is governed by many factors, including electronegativity, size and the nature of the covalent bond (single, double or triple). Some selected bond lengths (Table 3.2, pm): H–H 74, H–Br 144, C–C 154, C=C 133, C≡C 120, C=O 122, Si–H 146, Si–F 155, C–F 135, C–Cl 180, C–Br 196, C–I 214, B–F 130, B–Cl 175.

With an increase in the size of the atoms, the covalent bond length also increases. The bond length of the C–Cl bond is about 180 pm, whereas the C–F bond length is 135 pm, because the Cl atom is much larger. With the rise in electronegativity difference between the bonded atoms, the bond becomes shortened. For example, the Si–F bond length in SiF₄ is found to be near 155 pm, whereas the calculation of the Si–F bond from the covalent radii of Si and F (Si = 117 pm and F = 64 pm) is 181 pm. The electronegativity difference causes an ionic character in the covalent bond. The ionic character results in shortening of the bond length due to the additional attraction between the bonded atoms.

📌 Note (Quick Check 3.5): HI is a stronger acid and a robust reducing agent, whereas HF is a weaker acid — because the H–I bond is much weaker (295 kJ mol⁻¹) than the H–F bond (565 kJ mol⁻¹), so HI gives up its proton and its iodide ion is more easily oxidised; and acetylene (HC≡CH) is more stable than ethene (H₂C=CH₂) in the sense of bond strength per linkage — the triple bond (839 kJ mol⁻¹) is stronger than the double bond (614 kJ mol⁻¹), though it is more reactive toward addition because of its exposed π bonds.

Chemical bonds — ionic, covalent and metallic bonds — are usually termed as true chemical bonds, as they affect the chemical properties of a substance. This is because of certain reasons. Firstly, chemical bonds result in the formation of new species through transfer and sharing of electrons, whereas intermolecular forces act to bring molecules closer and influence the physical properties. However, such a clear distinction between the chemical bonds and intermolecular forces is not possible.

The distinctive feature of the chemical bonds and intermolecular forces is their bond strength. The strength of a force is measured by the bond energy. Table 3.3 provides a comparison among different chemical bonds and intermolecular forces (bond energy, kJ mol⁻¹): ionic bond in NaCl 760; O–H bond in water 464; hydrogen bonding 20–50; permanent dipole–permanent dipole force 5–20; van der Waals forces 1–20.

The bond energy of the ionic bond (sodium chloride, 760 kJ mol⁻¹) is highest, followed by the covalent bond (O–H = 464 kJ mol⁻¹), and the average hydrogen bond energy (20–25 kJ mol⁻¹). It shows that the ionic bond is the strongest form of chemical bonding. It also reveals that chemical bonds are generally much stronger than intermolecular forces. The permanent dipole–dipole forces (5–20 kJ mol⁻¹) and London dispersion forces (1–20 kJ mol⁻¹) are even weaker, as indicated by their low bond energies.

The metallic bond is mostly elaborated in terms of electrostatic forces, although some theories suggest that it may be of covalent nature. In any case, the metallic bond is weaker than both the ionic and covalent bonds. The average bond energy of the metallic bond is 100–150 kJ mol⁻¹. A satisfactory argument for the low strength of the metallic bond is extensive delocalization of electrons within the metallic crystal.

📌 Book limit: this chapter gives no separate passage describing the metallic bond's structure (sea of electrons) beyond this comparison paragraph — the 100–150 kJ mol⁻¹ value and the delocalization argument above are all the book states here.

The VSEPR model predicts and explains the shapes of molecules but does not give reasons for the formation of bonds. VBT is concerned with both the formation of bonds and the shapes of molecules. This method of describing a covalent bond considers a molecule as a combination of atoms. The postulates of VBT are:

• A covalent bond is formed when half-filled orbitals in the valence shells of two atoms with similar energy overlap.
• A greater overlap of the orbitals results in a stronger bond.
• Covalent bonds are directional. The direction of the bond is determined by the shape and mode of the overlapping orbitals.

3.6.1 Formation of sigma bond. A sigma bond is formed by the linear overlap of two half-filled atomic orbitals on adjacent atoms. The orbitals approach each other on the nuclear axis. Both s and p orbitals can overlap head-on to form sigma bonds.

s–s overlap: the s orbital of one atom overlaps with the s orbital of the other to give a bond orbital. This type of overlap occurs during the formation of the H₂ molecule, where each hydrogen atom has a half-filled s orbital. After bond formation, the electrons are paired up and the electron density in this molecule is symmetrical around the two nuclei.

s–p overlap: the s orbital of one atom can overlap with the p orbital of the other to form a covalent bond (σ). For example, in the HCl molecule, a half-filled s orbital of hydrogen overlaps with a half-filled p orbital of chlorine. The electron density is higher close to the Cl atom due to its higher electronegativity value. This is why HCl is a polar molecule.

p–p overlap: an example is the formation of the Cl₂ molecule, where p orbitals of two chlorine atoms overlap on the nuclear axis. The electron density is symmetrically around the nuclei of the two Cl atoms because both have the same value of electronegativity.

📌 Interesting Information: the bond angle in H₂O is 104.5°, whereas in H₂S it is 92°. This is because the orbitals of S are larger and the lone pair exerts a stronger repulsion.

The H₂S molecule is a non-linear molecule formed by the combination of one sulfur and two hydrogen atoms. The two 3p (say 3p_x and 3p_y) orbitals of sulfur, each containing one electron, can overlap with the 1s orbitals of two hydrogen atoms. A V-shaped molecule is thus formed, having a bond angle of 92°.

Formation of π bond. Consider the formation of a double covalent bond between oxygen atoms (O=O). There are two unpaired electrons on each atom in perpendicular p orbitals (say p_x and p_y). The p_x orbitals on the two oxygen atoms are oriented in such a way that they overlap end-to-end linearly. The linear overlap of the p_x orbitals gives a σ bond. However, the p_y orbitals on both atoms are aligned parallel to each other. They overlap in a parallel way so that the two p lobes overlap above the plane of the nuclei and the other two lobes below the plane. This results in the formation of a π bond. The oxygen atoms are doubly bonded through σ and π bonds.

📌 Note (Quick Check 3.6): draw the orbital structures of H₂O and N₂ molecules, and draw the orbital overlap to show the formation of F₂ and HF molecules — F₂ forms by p–p σ overlap (like Cl₂), and HF by s–p σ overlap (like HCl).

A process in which atomic orbitals of slightly different energies and shapes are mixed together to form a new set of equivalent orbitals of same energy and same shape is called hybridization.

📌 Keep in Mind: hybridization is a process of mixing of orbitals in a single atom (or ion); only orbitals of comparable (relatively close) energies can be mixed to form hybrid orbitals; the number of mixing orbitals is always equal to the number of the resulting hybrid orbitals.

3.7.1 Types of hybridization — sp hybridization. In sp hybridization, one s (low energy and spherical) and one p orbital (high energy and dumb-bell shaped) intermix to give a new set of two orbitals of same energy and same shape called sp hybrid orbitals. These sp hybrid orbitals are arranged in linear geometry and oriented at 180°. The electronic configuration of the outermost shell of Be is: ground ₄Be = 2s² (2p empty); excited Be = 2s¹ 2p_x¹; hybridized Be = two sp orbitals, each with one electron. The two sp hybrid orbitals lie linearly. This hybridization explains the geometry of linear molecules such as beryllium chloride, BeCl₂. It is formed when two sp hybrid orbitals of the Be atom overlap with the half-filled p orbitals of chlorine atoms.

sp² hybridization. In sp² hybridization, one s and two p atomic orbitals of an atom intermix to form three orbitals called sp² hybrid orbitals. The three half-filled sp² hybrid orbitals are arranged in a trigonal planar geometry with bond angles of 120°. This explains the geometry of planar molecules such as BF₃. Electronic configuration of ₅B: ground 2s² 2p_x¹; excited 2s¹ 2p_x¹ 2p_y¹; hybridized = three sp² orbitals, each with one electron. The three outermost orbitals of B mix together to give three sp² hybrid orbitals. On the other hand, one of the p orbitals of fluorine is half filled (e.g. 2p_y). BF₃ is formed by the overlap of three half-filled sp² hybrid orbitals of boron with 2p_y orbitals of three fluorine atoms. The structure is trigonal planar with bond angles equal to 120° each.

sp³ hybridization. In sp³ hybridization, one s orbital (low energy and spherical) and three p orbitals (high energy and dumb-bell shaped) intermix to give a new set of four orbitals of same energy and same shape. Each of these hybrid orbitals is a sp³ hybrid orbital. These hybrid orbitals are arranged in the tetrahedral geometry, as shown in the example of CH₄. The electronic configurations of the valence shell of ₆C in its excited and hybridized states are: excited C = 2s¹ 2p_x¹ 2p_y¹ 2p_z¹; hybridized C = four sp³ orbitals, each with one electron. The energies of hybrid orbitals are lower than unhybrid orbitals.

📌 Did you Know? Each sp³ hybrid orbital consists of two lobes, one larger and the other smaller. For the sake of simplicity, the smaller lobe is usually not shown while representing sp³ hybrid orbitals together.

The four new hybrid orbitals of equal energy have a tetrahedral geometry with the carbon nucleus at the center. The methane molecule is formed by the overlap of sp³ hybrid orbitals of carbon with 1s orbitals of four hydrogen atoms separately to form four sigma bonds. The four C–H bonds, which result from sp³–s overlaps, are directed towards the corners of a regular tetrahedron.

The VSEPR model (Valence Shell Electron Pair Repulsion) describes the shapes of molecules based on the electron pairs that surround the central atom. This model was presented by Sidgwick and Powell in 1940. It is based on the assumption that a molecule will take a shape such that the electronic repulsions among the valence electron pairs of that atom are minimum. In order to have the minimum repulsions, the electron pairs arrange themselves at farthest possible distances. This arrangement of the electron pairs determines the geometry of the resulting molecule.

Postulates:

• i. Both the lone pairs (non-bonded) as well as the bond pairs participate in determining the geometries of molecules.
• ii. The electron pairs are arranged around the central atom so as to remain at maximum distance apart to avoid repulsions.
• iii. The electrons of lone pairs occupy more space than the bond pairs. As a result, the non-bonding electron pairs exert greater repulsive forces on bonding electron pairs and thus tend to compress the bond pairs. The magnitude of repulsions between the electron pairs in a given molecule decreases in the following order: lone pair–lone pair (lp–lp) > lone pair–bond pair (lp–bp) > bond pair–bond pair (bp–bp). An electron pair shared by two nuclei occupies less space than a lone pair bound by a single nucleus.
• iv. The two electron pairs of a double bond and three electron pairs of a triple bond contain a higher electronic charge density, but they are regarded as single pairs.
• v. The presence of highly electronegative atoms with the central atom results in decreased electronic repulsions between the bond pairs, but stronger repulsion by the lone pair.

3.8.1 Predicting the shapes of molecules. To illustrate this model, the central atom is named 'A'. The electron pairs around 'A' are designated as 'B'. There may be different numbers of electron pairs around the central atom depending on its valency. It gives rise to various types of molecules, such as AB₂, AB₃, AB₄, etc. The electron pair geometry of a molecule is determined by the total number of electron pairs around 'A', whereas the actual shape of the molecule is determined by the atoms excluding the lone pairs.

Table 3.4 — geometries and shapes: 2 pairs, 0 lone pairs: electron pair geometry linear, shape linear, angle 180°, examples CO₂, BeCl₂. 3 pairs, 0 lone: trigonal, trigonal, 120°, BCl₃, SO₃. 3 pairs, 1 lone: trigonal, angular/V-shaped, less than 120°, SO₂, SnCl₂. 4 pairs, 0 lone: tetrahedral, tetrahedral, 109.5°, CH₄, CCl₄. 4 pairs, 1 lone: tetrahedral, pyramidal, less than 109.5°, NH₃, H₃O⁺. 4 pairs, 2 lone: tetrahedral, angular/V-shaped, less than 109.5°, H₂O, OF₂. 5 pairs, 0 lone: trigonal bipyramidal, trigonal bipyramidal, 120°, 90°, PCl₅, I₃⁻. 6 pairs, 0 lone: octahedral, octahedral, 90°, SF₆, XeF₄.

Steps to determine the shapes of molecules: (1) The least electronegative atom, or the element with the least number of atoms, is mostly selected as the central atom — for example, in CCl₄, the carbon atom is the central atom. (2) The total number of electron pairs around the central atom are counted (including bond pairs and lone pairs) — for example, in CCl₄, the total number of bond pairs around the C atom are 4 and it has no lone pair. (3) The total number of electron pairs determines the electron pair geometry (as in the table above). (4) Finally, the actual shape of the molecule is determined excluding the lone pairs (if any).

📌 Keep in Mind — counting pairs in NH₃: valence electrons in N = 5; electrons shared by 3H = 3 × 1 = 3; total number of electrons = 5 + 3 = 8; total number of electron pairs = 8/2 = 4. Number of lone pairs on N = total number of pairs − number of bond pairs = 4 − 3 = 1. Thus, N has 1 lone pair in NH₃.

AB₂ type molecules (linear geometry). Two electron pairs around the central atom are arranged at an angle of 180° to minimize repulsions, forming a linear geometry. BeCl₂ is of AB₂ type, with Be as the central atom and two bond pairs around it, but no lone pair.

AB₃ type (trigonal planar geometry). The central atom is surrounded by three electron pairs, arranged at maximum distance apart at an angle of 120°, giving a trigonal geometry. For example, BF₃ has a trigonal planar shape with each F–B–F bond angle of 120°. Similar geometries are expected in the hydrides of group 3, i.e. AlH₃, GaH₃, BH₃, etc. In SnCl₂, the Sn atom has 4 electrons in its outermost shell. It makes two bonds with Cl atoms and the remaining two electrons exist as a lone pair. One of the corners of the triangle is occupied by this lone pair, giving rise to a distorted trigonal electron pair geometry (in vapour phase). The actual shape of SnCl₂ is V-shaped and the bond angle is less than 120° due to the lone pair on the Sn atom.

AB₃-type with multiple bonds. SO₃ has all three regions occupied by S=O bonds. Its structure is perfectly trigonal, with each angle equal to 120°. On the other hand, in SO₂, one corner of the triangle is occupied by a lone pair and the other two corners each by a double bond (S=O). Thus, it makes an angular or V-shaped structure, just as SnCl₂ does.

AB₄ type (tetrahedral geometry). The electron pair geometry is a regular tetrahedron, each bond angle 109.5°. For instance, in methane, four bonded electron pairs are directed from the center towards the corners of a regular tetrahedron. On the same grounds, SiH₄, GeH₄ and CCl₄ possess similar shapes. In ammonia (NH₃), there are three H atoms attached to the nitrogen atom, having one lone pair. Due to a lone pair, the ideal angle 109.5° is reduced to 107°. Ammonia has a triangular pyramidal shape. Substitution of hydrogen in NH₃ with electronegative atoms like F or Cl further reduces the bond angles. In NF₃, three highly electronegative F atoms are bonded to the N atom: the strong polarity of the N–F bond pulls the lone pair closer to the nucleus (stronger lone-pair repulsion), and the bond pairs (N–F bonds) are closer to F atoms than to N, so their repulsions weaken and the bonds come closer — the bond angles are further compressed to 102.5°.

Experiments reveal that the water molecule (H₂O) is angular or V-shaped, although it has four electron pairs around the central atom. Two corners of the tetrahedron are occupied by two lone pairs and the remaining two by bond pairs. But, due to the greater repulsions of the lone pairs, the bond angle is reduced to 104.5°. The [H₃O]⁺ ion is formed by the capture of a proton by a water molecule and it has a tetrahedral (trigonal pyramidal) shape. On the other hand, the amide ion, [NH₂]⁻, has a V-shaped structure.

AB₅ type molecules (trigonal bipyramidal geometry). PCl₅ has trigonal bipyramidal geometry: the angles within the plane are 120° and between an axial atom and a planar atom are 90°. Tri-iodide ion [I₃]⁻ is an AB₅ system: the central atom is iodine, with five electron pairs around it — two bond pairs and three lone pairs. The lone pairs occupy the corners of the trigonal region and the iodine atoms occur vertically, one above and one below the plane. The actual shape of the tri-iodide ion is linear and the iodine atoms are farthest apart at an angle of 180°.

AB₆ type molecules (octahedral geometry). AB₆ molecules have 6 electron pairs around the central atom and octahedral geometry. All the bond angles in this type of geometry are 90°. SF₆ is an AB₆ type molecule. XeF₄ is an AB₆ type molecule with four bond pairs and two lone pairs: the two lone pairs remain at farthest distance at an angle of 180°. Excluding the lone pairs, the actual shape of XeF₄ is square planar, with all F–Xe–F angles equal to 90°.

📌 Note (Quick Check 3.7): lone pairs on the central atoms of H₂O (2), ICl₃ (2 on I) and I₃⁻ (3 on central I); bond pairs and lone pairs in SiH₄ (4 bond, 0 lone), H₂Se (2 bond, 2 lone) and PH₃ (3 bond, 1 lone) — giving tetrahedral, V-shaped and pyramidal shapes respectively; and the bond angle in H₂S is smaller than in H₂O because S is larger and its lone pairs repel more strongly (book: H₂O 104.5°, H₂S 92° by VBT). (Quick Check 3.8): draw the Lewis structures for IF₃ and IF₅ and predict their geometry with VSEPR — IF₃ (3 bond + 2 lone pairs) is T-shaped, IF₅ (5 bond + 1 lone pair) is square pyramidal.

3.8.2 Applications of VSEPR model in drug designing. Drugs are chemical substances that prevent, diagnose or treat a disease. Drugs interact with human body at specific points, or with specific processes called targets or substrates, through their bioactive molecules called ligands. A receptor is mostly a protein that receives and responds to a ligand through binding. Examples of targets in the body are receptors, such as enzymes, proteins, nucleic acids and cellular pathways. Each drug interacts with a specific target in the body to a different degree; this feature is called specificity of a drug or a ligand.

Molecular shape is an important feature that determines how a drug interacts with a biological target. Only the ligands with suitable shape can fit in the active sites of a biological target, as a specific key fits in a specific lock. The VSEPR model is successfully applied in determining the shapes of various biological systems, such as substrate recognition, ligand specificity and antibody recognition. For example, aspirin is an analgesic drug (painkiller) used for relief from pain as a primary medicine. It interacts with an enzyme COX (cyclooxygenase) by binding to its active site through its acetyl group (–OCCH₃). The shape of the COX active site and that of the acetyl group on aspirin are compatible with each other. Therefore, the binding is successful to block COX, which is a cause of the pain in the body.

The molecular orbital approach explains the results of quantum mechanical calculations for covalent bonding. The postulates of this theory are:

• During the formation of a molecule, the atomic orbitals of the combining atoms overlap to form new orbitals called molecular orbitals, which are characteristic of the whole molecule.
• The atomic orbitals overlap with the lobe having suitable sign of the wave function of the orbital. For example, one lobe of a p orbital is given the '+' sign and the other is marked with '−' sign.
• Two atomic orbitals overlap to form two molecular orbitals. When same-sign orbitals overlap, the bonding molecular orbital (σ or π) is formed, which has lower energy than the parent atomic orbital, while with opposite signs, high energy anti-bonding molecular orbital (σ* or π*) is formed, which has higher energy than the parent atomic orbitals.
• The number of bonds formed between two atoms is called the bond order and is taken as half of the difference between the number of bonding electrons (say a) and anti-bonding electrons (say b): Bond order = (a − b) / 2.

s–s overlap. In the formation of the H₂ molecule, two s orbitals of H atoms combine to give two molecular orbitals. The bonding molecular orbital is symmetrical about the axis joining the nuclei of the bonded atoms, while the anti-bonding molecular orbital has the electron density away from the nuclei of the overlapping atoms.

p orbitals combining to give σ bonds — a) Head-on overlap: the p orbitals of the two atoms approach along the same axis (say x-axis). This combination of atomic orbitals gives rise to σ (2p_x) bonding and σ* (2p_x) anti-bonding molecular orbitals. b) Sideways overlap: when the axes of two p orbitals (i.e. p_y or p_z orbitals) are parallel to each other, they interact to form π molecular orbitals. The bonding molecular orbitals π (2p_y) or π (2p_z) have zero electron density on the nuclear axis (called nodal plane). On the other hand, anti-bonding molecular orbitals π* (2p_y) and π* (2p_z) have the least electron density in the inter-nuclear region.

3.9.1 Molecular orbital diagrams of some diatomic molecules.

i) Helium. The electronic configuration of He is 1s². For a successful formation of He₂ molecule, 1s orbitals of two He atoms must combine to form bonding (σ 1s) and anti-bonding (σ* 1s) orbitals. Out of four electrons, two enter the bonding molecular orbital σ (1s) and the remaining two occupy the anti-bonding σ* (1s) molecular orbital. But on calculation we discover that the bond order for He₂ is zero: (2 − 2) / 2 = 0. Hence, the He₂ molecule is not formed.

ii) Nitrogen (N₂). Electronic configuration of N is: ₇N: 1s², 2s², 2p_x¹, 2p_y¹, 2p_z¹. The valence shell 2s on both N atoms give σ2s and σ*2s orbitals, whereas 2p orbitals give six molecular orbitals, arranged in increasing order of energy as: σ2s < σ*2s < π2p_y = π2p_z < σ2p_x < π*2p_y = π*2p_z < σ*2p_x. The bond order for N₂ is calculated from its orbital diagram as: (6 − 0) / 2 = 3 — considering valence electrons only (bonding valence electrons 6 in π2p and σ2p, anti-bonding valence electrons 0, after σ2s/σ*2s cancel). Therefore, there are three covalent bonds between the nitrogen atoms in this molecule. One of these is a σ bond while the other two are π bonds.

iii) Oxygen (O₂). The bond energy of the molecular orbitals can be arranged as: σ2s < σ*2s < σ2p_x < π2p_y = π2p_z < π*2p_y = π*2p_z < σ*2p_x. The bond order of oxygen is (6 − 2) / 2 = 2, which shows the presence of one σ and one π bond between the oxygen atoms, i.e. they are linked by a double bond (O=O). Oxygen molecule is paramagnetic in nature, which means it is attracted by a magnetic field. Paramagnetic substances have one or more unpaired electrons in them. A substance with a large number of unpaired electrons is strongly paramagnetic. MOT successfully explains the paramagnetic behaviour of the oxygen molecule: the MO diagram of oxygen shows the presence of two unpaired electrons, one in π* (2p_y) and one in π* (2p_z). Due to the presence of these unpaired electrons, the oxygen molecule has a net magnetic field, which interacts with the external magnetic field. Liquid oxygen is attracted and gets suspended between the poles of a strong magnet.

📌 SLO note — F₂: the book's MOT section diagrams He₂, N₂ and O₂ only; no F₂ MO diagram is printed in this chapter. By the same MOT filling, F₂ has bond order (8 − 6) / 2 = 1 (a single σ bond) and is diamagnetic, since all its π* electrons are paired — this is derived from the chapter's MOT rules, not quoted from a book diagram, and is flagged as such.